UNIVERSITY OF CALIFORNIA 
 
 LIBRARY 
 
 OF THE 
 
 DEPARTMENT OF 
 
 Received .../.+..&.-.--- 
 
 Accessions No . ..... ^....0..... Booh No . .../.-. 
 
 vts&* 
 
SCHOOL PHYSICS 
 
 A NEW TEXT-BOOK 
 FOR HIGH SCHOOLS AND ACADEMIES 
 
 BY 
 
 ELROY M. A VERY, PH.D., LL.D. 
 | 
 
 AUTHOR OF A SERIES OF PHYSICAL SCIENCE TEXT-BOOKS 
 
 UNIVERSITY OF CALIFORNIA 
 
 DEPARTMENT OF PHYSIOS 
 
 SHELDON AND COMPANY 
 
 NEW YORK AND CHICAGO 
 

 *DK. WERY 1 3' PHYSICAL SCIENCE SERIES. 
 
 FIRST PRINCIPLES OF NATURAL PHILOSOPHY. 
 ELEMENTS OF NATURAL PHILOSOPHY. 
 
 SCHOOL PHYSICS. 
 
 ELEMENTS OF CHEMISTRY. 
 
 COMPLETE CHEMISTRY. 
 
 This contains " The Elements of Chemistry," with an additional 
 chapter on Hydrocarbons in Series, or Organic Chemistry. It can be 
 used in the same class with " The Elements of Chemistry." 
 
 COPYRIGHT, 1895, BY 
 SHELDON AND COMPANY. 
 
 TYPOGRAPHY BY J. 8. GUSHING & Co., NORWOOD, MASS. 
 
PREFACE. 
 
 IN this book will be found an unusual number of prob- 
 lems. It is not intended that each member of each class 
 shall work all of the problems. It is hoped that they -are 
 sufficiently numerous and varied to enable you to select 
 what you need for your particular class. Xo author can 
 make a comfortable Procrustean bedstead. 
 
 For several years there has been a growing tendency in 
 the high schools of the country to indulge in laboratory 
 methods. An effort has been made to adapt this book to 
 such needs. The author has no sympathy with the idea 
 that the pupil should have set before him the impossible 
 task of rediscovering all the physical truths known to 
 modern science. Even were there no other obstacle, indi- 
 vidual life is too short, and but a small part of that short 
 period can be given to a high-school course in natural 
 philosophy. Nor has he any more sympathy with the 
 notion that the high-school laboratory should attempt the 
 full work of the technological school. High-school lab- 
 oratory work has its limitations in the capacities of the 
 pupils, in the time at their disposal, in laboratory equip- 
 ment, etc. Still it affords a needed variation from the 
 old method in which the author stated facts ex cathedra, 
 
 673158 
 
4 SCHOOL PHYSICS. 
 
 to be accepted and memorized by the pupils, and from 
 the less objectionable plan in which the teacher performed 
 all the experiments and the pupil simply observed and 
 admired. Pedagogic practice, having swung from one 
 end of the arc to the other, is now settling down to the 
 golden mean. May it prove that in its excursions it held 
 fast to all the good it found and left the rest behind. 
 
 If, at the beginning of an experiment, John Tyndall 
 could ask, " For what shall I look ? " we may be permitted 
 to suggest that the pupil, ignorant of scientific truths and 
 experimental methods, and without manipulatory skill, 
 needs a text-book something like this to save even his 
 laboratory practice from degenerating into chaotic waste. 
 An effort has been made by the author of this book to 
 introduce the pupil into what is a new world to him, to 
 give him a few elementary lessons in the ways of that 
 world, trusting that, in later years, other hands will guide 
 him over more rugged paths and into higher realms. 
 But, no matter how well an author's work may have 
 been done, it can never take the place of the living and 
 live teacher; it may be a help, but it certainly cannot be 
 a substitute. 
 
 Each pupil is expected to perform as many of the labo- 
 ratory exercises as possible. The classroom work must 
 be kept ahead of the laboratory work; i.e., the pupil 
 must come to the laboratory with some knowledge of 
 the principles involved in the work that he is required to 
 perform. Even then, there will be a grievous waste of 
 time and effort unless the teacher is judicious, vigilant 
 and firm. For instance, it will not be easy, at the begin- 
 ning, to lead pupils to appreciate the importance of mak- 
 
PREFACE. 5 
 
 ing all measurements as accurately as possible with the 
 given instruments, and to realize that there is value in 
 repeated measurements of the same quantity. Much of 
 the benefit to be derived from laboratory practice hangs 
 upon the cultivation of habits of accuracy of observation, 
 the formation of habitually systematic methods, and the 
 development of an ability to reason from observed partic- 
 ulars to general laws. The ability to generalize from 
 observed phenomena should not be expected of many, and 
 must not be demanded. 
 
 The divisions of the class for laboratory practice should 
 be so small that the teacher may get to each pupil at short 
 intervals to check gross errors at the beginning, and thus 
 prevent much waste of time. Ten or twelve is perhaps a 
 fair limit for the size of such divisions. Pupils should be 
 taught neatness and dexterity of manipulation, held to a 
 rigid accountability for the care and condition of all appa- 
 ratus used by them whether it belongs to them or to the 
 school, required to make accurate notes of their work as 
 it proceeds, and encouraged to' write them up neatly and 
 fully in note-books of prescribed form. They should be 
 taught to put their records into tabular form when the 
 nature of the work will permit such a form of record. 
 Additional to all of this is the work of enforcement; 
 questions, discussions, supplementary experiments, and 
 problems. All of this demands so much of time and 
 enthusiasm from the teacher, that the school authorities 
 ought not to forget that " to give good instruction in the 
 sciences requires of the teacher more work than to give 
 good instruction in mathematics and the languages," and 
 that " the teacher should be absolutely at liberty, not only 
 
6 SCHOOL PHYSICS. 
 
 during the physics hours, but also during several other 
 hours of the week, to arrange for and to direct the experi- 
 ments, unvexed by any care of schoolrooms or of pupils 
 save those actually engaged in laboratory work." If the 
 school has not a regularly equipped physical laboratory, 
 as is desirable, a room should be set aside for the exclu- 
 sive use of classes in experimental physics, and fitted for 
 such use as well as the circumstances of the case will 
 allowc 
 
 The author has taken special pains to select experiments 
 and exercises that may be performed with simple and in- 
 expensive apparatus, and many of them have been devised 
 expressly for this work. The author has not disdained any 
 aid that he could draw from any source, but he cheerfully 
 acknowledges his especial obligation to Professor Barker's 
 " Physics," the Harvard College pamphlet, and its ampli- 
 fication in the admirable work of Messrs. Hall and Bergen. 
 Special acknowledgments are also due to Professor Dayton 
 C. Miller of the Case School of Applied Science, who has 
 read the work in manuscript and in proof-sheets ; to Mr. 
 George T. Hanchett of Pawtucket, R. I., for valuable 
 assistance in the chapter on Electricity and Magnetism; 
 and to Mr. Henry C. Muckley, assistant superintendent of 
 the public schools of Cleveland, for his many valuable sug- 
 gestions, and for his aid in correcting proof. To the many 
 others who have given assistance in many ways, the 
 author tenders assurances of grateful appreciation. 
 
 The author would be glad to receive any suggestions 
 from any who may use this book, or to answer any inquiries 
 concerning the study or apparatus. He may be addressed 
 at Cleveland, O. 
 
CONTENTS. 
 
 CHAPTER I. MATTER. 
 
 PAGE 
 
 I. DOMAIN OF PHYSICS ; DIVISIONS OF MATTER ... 9 
 
 II. PROPERTIES OF MATTER ....... 16 
 
 III. CONDITIONS OF MATTER 38 
 
 CHAPTER II. MECHANICS., 
 
 I. MOTION AND FORCE ........ 57 
 
 II. WORK AND ENERGY 83 
 
 III. GRAVITATION 95 
 
 IV. FALLING BODIES 106 
 
 V. PENDULUM 118 
 
 VI. SIMPLE MACHINES 127 
 
 VII. MECHANICS OF LIQUIDS 150 
 
 VIII. MECHANICS OF GASES 179 
 
 CHAPTER * in. ACOUSTICS. 
 
 I. NATURE OF SOUND, ETC. ....... 201 
 
 II. VELOCITY, REFLECTION AND REFRACTION .... 218 
 
 III. CHARACTERISTICS OF TONES ....... 226 
 
 IV. CO-VIBRATION 244 
 
 V. LAWS OF VIBRATION 258 
 
 7 
 
g CONTENTS. 
 
 CHAPTER IV. HEAT. 
 
 PAGE 
 
 I. NATURE OF HEAT, TEMPERATURE, ETC 270 
 
 II. PRODUCTION AND TRANSFERENCE OF HEAT .... 276 
 
 III. EFFECTS OF HEAT 283 
 
 IV. MEASUREMENT OF HEAT 299 
 
 V. RELATION BETWEEN HEAT AND WORK .... 306 
 
 CHAPTER V. RADIANT ENERGY. 
 
 I. NATURE OF RADIATION 312 
 
 II. LIGHT : VELOCITY AND INTENSITY ..... 314 
 
 III. REFLECTION OF RADIANT ENERGY ..... 326 
 
 IV. REFRACTION OF RADIANT ENERGY ..... 347 
 V. SPECTRA, CHROMATICS, ETC. ...... 368 
 
 VI. INTERFERENCE, DIFFRACTION, POLARIZATION, ETC. . . 393 
 
 VII. A FEW OPTICAL INSTRUMENTS 400 
 
 CHAPTER VI. ELECTRICITY AND MAGNETISM. 
 
 I. GENERAL VIEW : 
 
 A. STATIC ELECTRICITY . . . . , .412 
 
 B. CURRENT ELECTRICITY ...... 433 
 
 C. MAGNETISM . . . . . . . 454 
 
 II. ELECTRIC GENERATORS, ELECTROMAGNETIC INDUCTION, ETC. 478 
 
 III. ELECTRICAL MEASUREMENTS 523 
 
 IV. SOME APPLICATIONS OF ELECTRICITY 543 
 
 V. ELECTROMAGNETIC CHARACTER OF RADIATION . . . 579 
 
 APPENDIX 591 
 
 INDEX ,597 
 
CHAPTER I. 
 
 MATTER. 
 
 I. DIVISIONS OF MATTEK. THE DOMAIN OF 
 PHYSICS. 
 
 
 "Read Nature in the language of experiment." 
 
 1. Science is classified knoivledge. General information 
 is valuable, but it is only when facts are classified that 
 the knowledge becomes scientific knowledge. 
 
 2. Matter is anything that occupies space or '-''takes up 
 room." Its existence is made known to us through the 
 senses. Substances are the different kinds of matter, as 
 water, wood, silver, etc. A body is any separate portion 
 of matter, as a book, a table, or a star. 
 
 Structure of Matter. 
 
 Experiment i. Heat the mercury in the bulb of a common ther- 
 mometer. The bulb remains full, but the liquid rises in the tube. 
 There seems to be more mercury than there was before. How can 
 this be ? There must be a greater number of molecules, the molecules 
 must be larger, or they must be further apart. 
 
 Experiment 2. Make a common goose-quill pop-gun. Notice that 
 when you use it the air confined between the two wads is compressed, 
 or made to occupy about half its original space. The air particles 
 were reduced in size or in number, or were crowded together more 
 closely. Perhaps the matter of which a body is made does not actually Jill 
 all the space which the body seems to occupy. 
 
 9 
 
10 SCHOOL PHYSICS. 
 
 Experiment 3. Rub the smooth handle of a fine awl over a piece 
 of fine wire gauze, and the gauze seems to present a continuous sur- 
 face. Perhaps it is the fault of the instrument in your hand, and not 
 the fault of the gauze. Rub the point of the awl over the gauze, and 
 you soon find openings between the metal threads. But the openings 
 are there, whether you can feel them or not. 
 
 Experiment 4. Rub the point of a fine sewing needle over the 
 surface of a window pane. The glass seems to be continuous in its 
 structure, and the needle cannot get through. Perhaps it is the fault 
 of the instrument you are using. Try one more delicate. Let a ray 
 of light fall upon the glass, and it easily finds a passageway between 
 the solid molecules. Rays of light are often used by scientific men as 
 
 instruments for their work. 
 
 
 
 3. Structure of Matter. Many facts, some of which 
 will be considered later, indicate that matter is not con- 
 tinuous ; that any sensible portion of it is a group of very 
 small particles ; that no two of these are in actual con- 
 tact; and that the minute particles of each group are 
 held together by certain attractive forces, to which we 
 must give careful consideration and earnest study. 
 
 (a) When you look at a brick wall from a considerable distance, 
 it has an apparent uniformity of structure. You cannot see that it is 
 made of many bricks, separated by mortar-filled spaces. This is the 
 fault of your sense of vision. As you come nearer, you see what you 
 did not see before, the individual and separated bricks. But such 
 is the structure of the tvall, ivhether you can see it or not. 
 
 4. Divisions of Matter. Matter exists in atoms, mole- 
 cules, and masses. It is very important that we clearly 
 understand what these words mean, or we shall have 
 trouble in trying to understand much that is to follow. 
 
 5. An Atom is the smallest quantity of matter that can 
 enter into combination and thus form molecules and masses. 
 It is the chemical unit of matter, and is considered iixdi- 
 
DIVISIONS OF MATTER. 11 
 
 visible. In nearly every case, an atom is a part of a 
 
 molecule. 
 
 (a) We may say that atoms are the smallest particles of matter 
 that can exist. They seldom exist alone, but quickly unite with 
 others like themselves to form elementary molecules, or with others 
 unlike themselves to form compound molecules. For example, one 
 atom of oxygen combines with another like itself to form an elemen- 
 tary molecule of oxygen, while one atom of oxygen combines with two 
 of hydrogen to form a compound molecule of water. There are more 
 than seventy kinds of atoms now known. 
 
 6. A Molecule is a quantity of matter so small that it 
 cannot be divided without changing its nature. It is the 
 physical unit of matter, and can be divided only by a 
 chemical process. Atoms make molecules ; molecules 
 make masses. 
 
 (a) A molecule is so very small that the smallest particle of matter 
 visible in the best of modern microscopes contains millions of mole- 
 cules. If a drop of water could be magnified until it appeared to be 
 as large as the earth on which we live, each molecule in the drop thus 
 magnified would still look smaller than a base-ball. Even in dense 
 solids, molecules are separated by spaces that are large as compared to 
 their own size. Tait assumes it as probable that the molecule itself 
 does not occupy so much as five per cent, of its share of the whole 
 space. This signifies that the distances between molecules is about 
 three times the diameter of a molecule. 
 
 (fe) Some compound molecules are very complex. The common 
 sugar molecule contains forty-five atoms of three kinds. Elementary 
 molecules make elementary masses or substances. Compound mole- 
 cules make compound masses or substances. The nature of the mole- 
 cule determines the nature of the substance. 
 
 (c) Molecules are believed to be in ceaseless motion, but ever sub- 
 ject to the constraining action of certain molecular forces. Many of 
 the phenomena observed in matter are due to these molecular motions, 
 as will more clearly appear further on. 
 
 7. A Mass is any quantity of matter that is composed of 
 molecules. Masses are elementary or compound. An 
 
12 SCHOOL PHYSICS. 
 
 elementary substance is called an element. There are as 
 many elements as there are kinds of atoms. Compound 
 substances are innumerable. 
 
 (a) We may take a lump of salt, which is a mass, and break it into 
 many pieces ; each piece will be a mass. We may take one of these 
 pieces and crush it to finest powder ; each grain will still be a mass. 
 We may imagine one of these grains of powdered salt to be divided 
 into so many parts that any further division will change them from 
 salt to something else ; these particles of salt, so small that further 
 division would change their nature, are molecules. If one of these 
 molecules is divided, it ceases to be salt ; we have instead an atom of 
 sodium and an atom of chlorine. 
 
 (6) The quantity of matter constituting a mass is not necessarily 
 great. A drop of water may contain a million animalcules. Each 
 animalcule is a mass as truly as the greatest monster of the land or 
 sea. The dewdrop and the ocean, clusters of grapes and clusters of 
 stars, are equally masses of matter. 
 
 (c) The term " mass " also has reference to the quantity of matter 
 in a body. This double use of the word is unfortunate. 
 
 8. Forms of Motion. It is probable that each of these 
 three divisions of matter has its own form or mode of 
 motion. The motion of a mass is often called molar or 
 mechanical motion. The motion of a bullet is an example. 
 The motion of the molecules in a mass constitutes heat. 
 If a bullet strikes a target, the shock that destroys the 
 molar motion of the bullet increases the vibration of the 
 molecules of which the bullet is composed. These molec- 
 ular vibrations constitute heat. When a bullet is thus 
 stopped, it is heated, and the production of heat is ex- 
 plained only in this way. These molar and molecular 
 motions give to matter the power of doing work, the 
 scientific name of which power is energy. 
 
 The motion of atoms within the molecule has not been 
 proved. 
 
DIVISIONS OF MATTER. 13 
 
 (a) Fancy a million flies surrounded by an imaginary shell. If 
 each fly represents a molecule, the contents of the shell represent a 
 mass. Imagine this shell to be thrown through the air. The motion 
 of the shell represents molar motion- As the shell is moving through 
 the air, the flies are moving slowly among themselves within the shell. 
 This motion of the flies represents molecular motion, and is a very dif- 
 ferent thing from the motion of the shell. When the shell strikes the 
 ground, the molar motion is destroyed, but the molecular motions 
 are increased, for the flies are set in much more rapid motion by the 
 shock. This is just about what happens when the bullet is fired 
 against a target. 
 
 Changes in Matter. 
 
 Experiment 5. Hold a piece of platinum wire in the flame of an 
 alcohol or of a Bunsen lamp. It becomes hot, glows, emits light. 
 There has been a change in the platinum. Remove the wire and 
 allow it to cool. Can you see that the wire was permanently changed 
 in any way by the experiment ? 
 
 Experiment 6. AVith forceps, hold a piece of magnesium wire in 
 the flame of an alcohol or of a Bunsen lamp. It becomes hot, glows, 
 emits light. At the end of the experiment do you notice any perma- 
 nent change in the magnesium wire? 
 
 9. Physical and Chemical Changes. Any change that 
 alters the constitution of the molecule, and thus affects 
 the identity of the substance, is a chemical change. 
 Other changes in matter are physical changes. 
 
 10. Phenomena, etc. Any directly observed change in 
 matter is a phenomenon. A supposition (or scientific 
 guess) advanced in explanation of phenomena is an 
 hypothesis. The value of an hypothesis increases with 
 the variety of the phenomena for which it can offer an 
 exclusive explanation. As this variety increases, the 
 hypothesis rises to the rank of a theory. When the theory 
 has acquired so high a degree of probability that it is 
 
14 SCHOOL PHYSICS. 
 
 accepted by the judicious as an established truth, i.e., 
 when it is easier for men to believe it than to doubt it, 
 it becomes a law, e.g., the law of gravitation. In the 
 words of Mr. Huxley, " Law means a rule which we have 
 always found to hold good, and which we expect always 
 will hold good." 
 
 Force. 
 
 Experiment 7. Mount each of two 4x8 inch boards on the trucks 
 of a pair of roller skates (preferably with ball or roller bearings), 
 adjusting the parts so that the two carriages will run in straight lines 
 when set in motion on a level surface. See that the bearings are well 
 oiled. Provide two smooth, straight boards, 6 ft. x 6 in. Cut two 
 wooden blocks with thickness equal to the elevation of the body of the 
 carriage; i.e., so that they may just Slip under the mounted boards 
 when the carriages rest on smooth surfaces. Nail one of these blocks 
 across the face of each of the smooth boards at its end. Raise the 
 
 MG. 1. 
 
 other end of one of the boards a little, until by trial you find that 
 one of the carriages will roll down the incline with a velocity as 
 nearly uniform as is attainable, thus eliminating largely the resist- 
 ance due to friction. Fasten the board in this position. Similarly 
 adjust the other board to the other carriage, and place it side by side 
 with the first board. If the second carriage runs less freely than the 
 first, the second board will require a greater incline than the first 
 board. Provide two pieces of elastic tape or of black-rubber tubing, 
 each | of a yard long. Stitch or clarnp together one end of each. 
 Stretch the joined pieces, and fasten their free ends at points 3 yards 
 apart. Tf the pieces stretch unequally, trim the edges of the stiffer 
 piece until the seam that joins the two pieces shall be midway between 
 the fixed ends. Loosen the fastenings at the ends of the tape, and rip 
 the seam at the middle ; the tensions of the two pieces, when equally 
 
DIVISIONS OF MATTER. 15 
 
 stretched, will pull with equal forces. Tack bne end of each elastic to 
 the top of one of the blocks at the lower end of the smooth board, and 
 the other end of the elastic to the under side of the board that consti- 
 tutes the body of the carriage that was adjusted for that board ; the 
 elastic, when stretched, will be parallel to the long board. Similarly 
 fasten the other elastic to the other block and carriage. Load one 
 carriage with a chalk box filled with iron nails, scraps of lead, or other 
 heavy material ; load the other with a box of chalk. Draw the car- 
 riages toward the upper ends of their respective boards so as to stretch 
 the elastics considerably and equally ; release them at the same time, 
 and notice the speeds at which they are drawn by the equal forces. 
 Try to find some relation between the two velocities and the weights 
 of the two loaded carriages. Transfer part of one load to the other 
 carriage until they will be moved with equal velocities, and determine 
 the approximate relation between the weights of the two loaded 
 carriages. 
 
 11. Force. Every phenomenon necessarily implies a 
 change ; every change necessarily implies a cause. The 
 causes that produce phenomena, or changes in matter, are 
 called forces. The word " force " is difficult of satisfactory 
 definition. As generally used in physical discussions, 
 force signifies the immediate cause that produces, or tends to 
 produce, a change in the velocity or direction of motion of a 
 body ; i.e., a push or a pull. Pushes are often called pres- 
 sures ; and pulls, tensions. Forces act on matter. Equal 
 forces produce equal velocities when applied for the same 
 length of time to equal masses. Matter may now be 
 defined as that which can exert force or be acted on by a 
 force. 
 
 (a) If the intensity of a force varies in successive intervals of time, 
 it is said to be variable ; if its intensity does not change, it is said to 
 be constant. Forces acting between masses of matter separated by 
 sensible distances are called molar forces; e.g., gravitation. Forces 
 acting between molecules separated by insensible distances are called 
 molecular forces ; e.g., cohesion. Forces acting between the atoms of 
 molecules are called atomic forces ; e.g., chemism. 
 
16 SCHOOL PHYSICS. 
 
 12. Experiments. A physical experiment is the produc- 
 tion of physical phenomena under conditions that are con- 
 trolled by a scientific student. It is a question addressed 
 to Nature in the only language that she understands. 
 The value attached to her replies involves a firm belief 
 in the " constancy of nature;" i.e., that under the same 
 physical conditions the same physical results will always 
 be produced. Its purpose is to discover or to illustrate 
 some physical truth. 
 
 (a) If the experiment simply shows how something acts, it is 
 qualitative ; if it shows how much something acts, it is quantitative. 
 
 13. Physics is the branch of science that treats of the laws 
 and physical properties of matter and of those phenomena that 
 depend upon physical changes. It is essentially an experi- 
 mental science. With the explanation that energy signifies 
 the power of doing work, physics, in its most general sense, 
 may be defined as the science that treats of matter and 
 energy. 
 
 II. THE PROPERTIES OF MATTER. 
 
 14. Properties of Matter. Any quality that belongs to 
 matter, or is characteristic of it, is called a property of mat- 
 ter. Any property that can be shown without a chemical 
 change is a physical property. 
 
 15. Extension is that property of matter by virtue of 
 which it occupies space. It has reference to the qualities 
 of length, breadth, and thickness. It is an essential prop- 
 erty of matter, involved in its very definition. 
 
 (a) All matter must have these three dimensions. We say that a 
 line has length, a surface has length and breadth ; but lines and sur- 
 faces are mere conceptions of the mind, and have no material exist 
 
THE PROPERTIES OF MATTER. 17 
 
 ence. The third dimension, which affords the idea of solidity or 
 volume, is necessary to every form of every kind of matter. 
 
 16. Measurement of Extension. There are two linear 
 units in use in this country, the English yard and the 
 international meter. From these are derived units of 
 area and of volume. 
 
 17. The Yard is the distance between two certain marks 
 on gold plugs set in a certain bronze bar, when the bar is 
 at a temperature of 62 F. This bar is kept in the Tower 
 of London. 
 
 (a) The divisions of the yard, as feet and inches, together with its 
 multiples, as rods and miles, are in familiar use. The units of sur- 
 face are squares whose sides are some one of the units of length, as 
 the square yard or the square mile. The units of volume are cubes 
 whose edges are some one of the units of length, as the cubic yard 
 or the cubic inch. 
 
 (6) The standard gallon contains 231 cubic inches. 
 
 18. The Meter. The international meter is the dis- 
 tance between two certain lines on a certain platiniridium 
 bar, when the bar is at the temperature of C. It is 
 equal, as nearly as can be ascertained, to 39.37 inches, or 
 "three feet, three inches and three eighths." This bar is 
 kept at Sevres, near Paris. Like the Arabic system of 
 notation and the table of United States money, the divi- 
 sions and multiples of the meter vary in a tenfold ratio, 
 hence some of the great advantages of the system based 
 upon it. This system is in familiar use by the people 
 of most of the civilized countries of the world and by 
 scientists of all nations. The scientific unit of length is 
 the centimeter, the one-hundredth part of the meter. 
 
 (a) The United States government very carefully preserves, at the 
 office of standard weights and measures in Washington, three accu- 
 rate copies of the international meter. These are authorized by 
 
18 
 
 SCHOOL PHYSICS. 
 
 congress as the standards of length for this country. The length of 
 the yard is determined by the relation above stated. 
 
 .001 m. = 0.03937 inch. 
 .01 m. = 0.3937 " 
 .1 m. = 3.937 inches. 
 
 m. = 39.37 
 
 m. = 393.7 " 
 
 m. = 328 feet 1 inch. 
 
 m. = 0.62137 mile. 
 
 m. = 6.2137 miles. 
 
 19. Metric Measures of Length. Ratio = i : 10. 
 
 f Millimeter (mm.) = 
 DIVISIONS. \ Centimeter (cm.) = 
 { Decimeter (dm.) = 
 UNIT. Meter (m.) = 1. 
 
 Dekameter (D?n.) = 10. 
 MULTIPLES. Hekt meter (Hm.) = 100. 
 Kilometer (Km.) = 1000. 
 Myriameter (Mm.) = 10000. 
 
 The table may be read, " 10 millimeters make 
 1 centimeter, 10 centimeters make 1 decimeter," 
 etc. The denominations most used in practice are 
 printed in Italics. The system of nomenclature is 
 very simple. The Latin prefixes milli-, centi-, and 
 deci-j signifying respectively .001, .01, and .1, and 
 ' already familiar in the mill, cent, and dime of 
 United States money, are used for the divisions ; 
 while the Greek prefixes deka-, hekto-, kilo-, and 
 myria-, signifying respectively 10, 100, 1,000, and 
 10,000, are used for the multiples of the unit. 
 Each name is accented on the first syllable. 
 
 20. Metric Measures of Surface and of 
 5 Volume. As with English measures, the 
 metric units of surface and volume are 
 surfaces or cubes whose sides or edges 
 respectively are some one of the units of 
 length, as the square meter or the cubic 
 centimeter. For square measures, the ra- 
 tio is 1 : 10 2 = 1 : 100 ; thus, one hundred 
 square millimeters make one square centi- 
 meter, etc. For cubic measures, the ratio 
 is 1 : 10 3 = 1 : 1000 ; thus, one thousand 
 cubic centimeters make one cubic deci- 
 FIQ. 2. meter, etc. 
 
THE PROPERTIES OF MATTER. 19 
 
 21. Metric Measures of Capacity. Ratio = i : 10. For 
 
 many purposes, such as the measurement of articles usually 
 sold by dry or liquid measure, a smaller unit than the 
 cubic meter is desirable. For such purposes, the cubic 
 decimeter has been selected -as the standard, and when thus 
 used is called a liter (pronounced leeter). 
 
 In value it is intermediate between the liquid and the 
 dry quarts. 
 
 CMilliliter (ml.) = 1 cu. cm. = 0.061022 cu. in. 
 
 DIVISIONS, -j Centiliter (d.) = 10 " = 0.338 fluid oz. 
 
 [ Deciliter (.) = 100 " = 0.845 gill. 
 
 UNIT. Liter (f.) = 1000 " = 1.0567 liquid qta. 
 
 f Dekaliter (Z>/.) = 10 cu. dm. = 9.08 dry qts. 
 
 MULTIPLES. \ Hektoliter (HI.) = 100 " =2 bu. 3.35 pks. 
 
 [ Kiloliter (JO.) = 1 cu. m. = 264.17 gals. 
 
 LABORATORY EXERCISES. 
 
 Apparatus, etc., Needed. A notebook made of good paper, and 
 having some of its pages ruled in little squares ; paper; pencil ; a school 
 rule ; a yardstick graduated to eighths of an inch ; a meter stick grad- 
 uated to millimeters ; a quart measure ; a liter measure ; a glass vessel 
 graduated to cubic centimeters, i.e., a graduate (see Fig. 3). 
 
 1. With a yardstick, measure the length of your laboratory. 
 
 2. From the table given in 19, compute the equivalent of that 
 length in meters and decimals thereof. 
 
 3. With a meter stick, measure the length of your laboratory, and 
 compare the result with that obtained by computation. 
 
 4. With a meter stick, measure the door of your laboratory, and 
 make an outline sketch thereof, using the scale of 1 : 20. 
 
 5. With a yardstick, measure the width of your laboratory. Draw 
 a ground plan of the room, using the scale of one inch to the yard. 
 
 6. Make the necessary measurements and compute the capacity 
 of the room (a) in cubic feet, (b) in cubic meters, (c) in gallons, 
 (d) in liters. 
 
 7. With the meter stick, measure the length of this leaf of your 
 book. Place the stick on its edge so as to bring the graduation as 
 close as possible to the object to be measured. Bring, not the end of / 
 
20 SCHOOL PHYSICS. 
 
 the rod, but one of the centimeter marks, even with one end of the 
 leaf, and from the stick read the length of the page accurately to 
 0.1 mm. You can divide the smallest division on the scale into tenths 
 by the eye. 
 
 8. As an exercise in subdividing distances by the eye, let the 
 teacher draw a tine line, curved or straight, on cross-section paper, 
 designate certain lines as axes of coordinates, and require each pupil 
 in succession to record in tabular form the locus of each point where 
 the given line crosses one of the lines ruled on the paper. 
 
 9. Make two fine marks with a sharp knife on a table-top or other 
 board, as far apart as is convenient, the distance being more than a 
 meter. Measure as accurately as possible the distance between the 
 marks, estimating fractions of millimeters to tenths, and expressing 
 the results in meters. Do this ten times. Measure the same distance 
 in inches, estimating fractions of the smallest division on the scale to 
 tenths. Express these results in inches and decimals of an inch. Do 
 this ten times. Divide the average number of inches by the average 
 number of meters ; the quotient will be the number of inches in a 
 meter. Express in millimeters the measures that you took in meters, 
 
 and divide the average number of millimeters by the 
 average number of inches; the quotient will be the 
 number of millimeters in an inch. Compare your re- 
 sults with the table given in 19. 
 
 10. With the graduate, measure 250 cu. crn. of water, 
 and pour it into the liter measure. See how often you 
 can repeat the work without overflowing the measure. 
 It will require careful attention to tell just when the 
 water level reaches the required mark. The liquid 
 climbs up the sides of the glass, so that it is difficult 
 to tell where the water-level really is. The eye of the 
 observer should be placed on the level of the required 
 mark 011 the graduate. 
 11. Compute the number of cubic centimeters in a quart. Test 
 your result by the actual measurement of water or of dry sand. 
 
 Impenetrability. 
 
 Experiment 8. Pass a funnel (or a funnel-tube) and a bent 
 tube, as shown in Fig. 4, through the cork of a bottle. Be sure that 
 all joints are air-tight. The delivery-tube is best made of glass, which 
 
THE PROPERTIES OF MATTER. 21 
 
 may be bent when heated to redness in an alcohol or gas flame. 
 
 Place the end of the delivery-tube in a tumbler of water. Pour 
 
 water through the funnel. As it runs into 
 
 the bottle, air will be forced out, and may 
 
 be seen bubbling through the water in the 
 
 tumbler. Directions for glass working may 
 
 be found in Avery's Chemistry, Appendix 4. 
 
 Experiment 9. Thrust a lamp chimney 
 into water. The water will rise inside the 
 chimney, entering at the lower end, and, 
 pushing the air out at the top. Repeat the 
 experiment, closing the upper end of the FIG. 
 
 chimney with the hand (or use an inverted 
 
 tumbler). The water cannot rise as before, because the vessel is filled 
 with air that cannot escape. 
 
 22. Impenetrability is that property of matter by virtue 
 of which two bodies cannot occupy the same space at the 
 same time. 
 
 (a) Illustrations of this property are very simple and abundant. 
 Thrust a finger into a tumbler of water ; it is evident that the water 
 and the finger are not in the same place at the same time. Drive a 
 nail into a piece of wood; the particles of wood are either crowded 
 more closely together to give room for the nail, or some of them are 
 driven out before it. Clearly, the iron and the wood are not in the 
 same place at the same time. The familiar method of measuring the 
 volume of an irregular solid by immersing it in a liquid and then 
 measuring the volume of the liquid displaced by it, implies the impen- 
 etrability of matter. 
 
 23. Mass and Weight. The mass of a body is its 
 quantity of matter. The weight of a body is, in general 
 terms, the measure of the earth's attraction for it. The 
 weight of a body varies as its mass, and with the posi- 
 tion of the body relative to the earth's surface. The 
 mass of a given body is constant ; its weight is not. 
 The word " mass " signifies matter ; the word " weight " 
 signifies force. 
 
22 SCHOOL PHYSICS. 
 
 (a) If the given body could be carried to the moon, its weight there 
 would be the measure of the attraction existing between the body arid 
 the moon ; but as the mass of the moon is less than that of the earth, 
 the attraction between the body and the moou would be less than 
 that between that body and the earth. The mass of the given body 
 would be the same as it was on the earth, but its weight would 
 be less. 
 
 24. Measurement of Mass and Weight. Unfortunately 
 we still have two systems of measurement, one practically 
 limited in use to the United States and the British Em- 
 pire ; the other, international. The English unit of mass 
 is the quantity of matter contained in the avoirdupois 
 pound. The international unit of mass is the kilogram, 
 a certain piece of platiniridium deposited at Sevres, near 
 Paris. For many scientific uses, this unit is too large ; 
 and the gram, which is the one-thousandth part of the 
 kilogram, is generally used. 
 
 (a) The mass of a gram was intended to be, and is very nearly, 
 equal to the quantity of matter in one cubic centimeter of distilled 
 
 water at the temperature 
 of 4 C. As with the 
 meter, the United States 
 
 _WEIGHS e. : |H9il,mL government carefully pre- 
 serves a standard kilo- 
 
 gram. 
 
 (6) The units of weight 
 
 measure the attractions 
 
 of the earth for these 
 FIG. 5. units of mass, and receive 
 
 the same names. Under 
 
 like conditions, a comparison of weights may be substituted for a com- 
 parison of masses, since at any one place the weight varies as the 
 mass. Unfortunately we have in common use pounds Troy, avoir- 
 dupois, and apothecaries', the use varying with the nature of the 
 transaction. On the other hand, the kilogram is definite, having but 
 a single value. 
 
THE PROPERTIES OF MATTER. 
 
 23 
 
 25. Metric Measures of Weight. 
 
 [ Milligram (?ng.) = 
 j Centigram (eg.) = 
 v. Decigram 
 
 Gram 
 
 f Dekagram 
 I Hektogram (Hg.) = 
 ] Kilogram (Kg-) 
 I Myriagram 
 
 (a) A five-cent nickel coin weighs five grams, 
 of water weighs one gram. 
 
 DIVISIONS. 
 UNITS. 
 
 MULTIPLES. 
 
 Ratio=i: 10. 
 
 0.0154 grain. 
 0.1543 
 1.5432 grains. 
 15.432 
 
 0.3527 oz. avoirdupois. 
 3.5274 
 2.2046 Ibs. 
 (Mg.} = 22.046 
 
 A cubic centimeter 
 
 CLASSROOM EXERCISES. 
 
 1. How much water by weight will a liter flask contain? 
 
 2. If sulphuric acid is 1.8 times as heavy as water, what weight of 
 the acid will a liter flask contain ? 
 
 3. If alcohol is 0.8 times as heavy as water, how much will 1,250 
 cu. cm. of alcohol weigh ? 
 
 4. What part of a liter of water is 250 g. of water? 
 
 5. What is the weight of a cubic decimeter of water? 
 
 6. What is the weight of a deciliter of water? 
 
 7. How many gallons of water may be held by a vessel 18 x 19 x 20 
 inches in dimensions ? 
 
 8. How 7 many liters of water may be held by a vessel measuring 
 25 x 35 x 75 cm.? 
 
 LABORATORY EXERCISES. 
 
 -Additional Apparatus, 
 etc. A fairly delicate 
 balance (see Fig. 6) ; 
 English and metric 
 weights ; two rectan- 
 gular wooden blocks, 
 2x3x4 inches ; an 
 iron ball an inch or two 
 in diameter ; a base- 
 ball ; a croquet ball ; a 
 pair of compasses with 
 pencil point ; a pen- 
 knife ; a teacupful of 
 lead bullets; a bottle; 
 wire. 
 
 1. Measure the mass FlG - 6 - 
 
 of each of the three balls in English weight units. 
 
24 SCHOOL PHYSICS. 
 
 2. Compute the metric equivalents of these three weights. 
 
 3. Weigh the three balls, using metric standards, and compare 
 results with those found by computation. 
 
 4. Place a meter stick on the table, and by its edge place two rectan- 
 gular blocks (chalk boxes will answer for rough work). Place a cro- 
 quet ball between the blocks. Move the blocks as near each other as 
 possible with the ball between them, keeping one face of each block 
 in contact with the straight edge of the meter stick, (a) What is the 
 diameter of the ball? (6) What is the^area of its surface? 
 
 5. (a) In similar manner, measure the diameter of a base-ball, 
 (ft) On paper, draw a circle of that diameter, (c) Compute the area 
 of that circle, (rf) With a sharp penknife, cut out the circle, and 
 pass the base-ball through the hole. 
 
 6. (a) In similar manner, measure the diameter of the iron ball. 
 (&) Compute its volume, (c) Compute the weight of the same volume 
 of water, (d) Measure out and weigh that volume of water, and com- 
 pare its weight with the computed result, (e) Iron is how many 
 times as heavy as water? (y) Place the iron ball in a tumbler or 
 beaker filled with water ; catch and measure the water that runs over. 
 (</) How does this measure compare with the computed volume of 
 the ball? 
 
 CAUTION. The pupil must clearly understand that all measure- 
 ments made by him in this course are extremely rude, and scarcely 
 comparable with the measurements of precision made by scientists. 
 Measurements to the hundred-thousandth of an inch and the twenty- 
 thousandth of a second are frequently made, and no painstaking is 
 deemed too great if it will increase the degree of accuracy attained. 
 
 7. From a coil of moderately fine wire (say, No. 30) of unknown 
 length, cut off a piece exactly a meter long, and weigh it carefully. 
 Weigh the rest of the coil, and from the two weights compute the 
 length of the wire. Verify your result by actual measurement. If 
 the error of your result exceeds 1 per cent., repeat the work. 
 
 8. Weigh a dry, clean bottle. Fill the bottle with cold water, wipe 
 its outside surface dry, and weigh the filled bottle in metric units. 
 From the weight of the water, determine the capacity of the bottle. 
 Test the result by measurement with the graduate. 
 
 9. Weigh each of five bullets at least three times. For each 
 bullet take the average of the several weighings as the true weight. 
 Combine these several averages to find the weight of the average 
 bullet. Count the bullets on hand. Multiply the weight of the aver- 
 
THE PROPERTIES OF MATTER. 
 
 25 
 
 age bullet by the number of bullets, and compare the result with the 
 mass of all the bullets as determined by weighing them together. 
 
 Indestructibility. 
 
 Experiment 10. Into a glass tube 2 cm. in diameter, and 15 or 
 20 cm. in length, having one end closed and rounded like a test-tube, 
 place 20 mg. of freshly burnt charcoal. Draw the upper part of the 
 tube out to a narrow neck. Fill the tube with dry oxygen, and seal 
 the tube by fusing the neck. Weigh the tube and its contents very 
 carefully. By gradually heating the rounded end of the tube, the 
 charcoal may be ignited, and, with 
 sufficient care, entirely burned without 
 breaking the tube. When the char- 
 coal has disappeared, weigh the tube 
 and its contents again. The chemical 
 changes that led to the disappearance of 
 the charcoal have caused no change in 
 the weight of the materials used. 
 
 FIG. 7. 
 
 26. Indestructibility is that 
 property of matter by virtue of 
 which it cannot be destroyed. 
 The science of chemistry is based on this fact, the " con- 
 servation of matter." 
 
 Inertia. 
 
 Experiment n. Upon the tip of the forefinger of the left hand 
 place a common calling card. Upon this card, and directly over the 
 
 finger, place a cent. With the nail 
 of the middle finger of the right 
 hand let a sudden blow or "snap" 
 be given to the card. A few trials 
 will enable you to perform the 
 experiment so as to drive the card 
 away, and leave the coin resting upon 
 the finger. Repeat the experiment 
 with the variation of a bullet for 
 the cent and the open top of a bot- 
 tle for the finger tip. 
 
 FIG. 8. 
 
26 SCHOOL PHYSICS: 
 
 Experiment 12. Suspend a heavy weight by a string not much 
 stronger than is necessary to carry the load. Attach a similar string 
 to the under side of the weight. Pull steadily downward on the lower 
 string; in a majority of cases the upper string will break, for it has 
 to support the weight and resist the pull, while the lower string has 
 only to resist the pull. 
 
 Support the weight as before. Pull suddenly downward on the 
 lower string : in a majority of cases the lower string will break, as if 
 there was not time enough for the pull to pass through the weight and reach 
 the upper string. 
 
 Experiment 13. Suspend an iron ball weighing at least 10 pounds 
 by a long, stout string from a firm support. Safety-valve weights 
 may be bought for a few cents a pound, and answer admirably for 
 many such purposes. Tie a string strong enough to carry a weight of 
 several pounds to the ball, and with sudden motion pull the ball 
 horizontally. If the pull is sudden enough, the string will break with- 
 out giving much motion to the ball. This "hanging back" of the 
 ball is very important, and must at least be given a name. Replace 
 the stout string by a thread, and by a series of gentle, well-timed 
 pulls, set the ball swinging. When it is in rapid motion, try to stop 
 that motion by a single pull on the thread. It will be seen that the 
 ball can go ahead as well as hang back. 
 
 27. Inertia signifies the tendency of matter at rest to 
 remain at rest, and of matter in motion to move with uni- 
 form velocity in a straight line. 
 
 (a) Illustrations of the inertia of matter are so numerous, that there 
 should be no difficulty in getting a clear idea of this property. The 
 " running jump " and " dodging " of the playground, the frequent 
 falls which result from jumping from cars in motion, the backward 
 motion of the passengers when a car is suddenly started and their for- 
 ward motion when the car is suddenly stopped, the difficulty in start- 
 ing a wagon and the comparative ease of keeping it in motion, 
 illustrate inertia. By virtue of inertia, a cannon ball pierces the 
 hardened steel armor of a battle ship ; and because of the same prop- 
 erty, it is well not to kick the cannon ball, even when it is resting on 
 a smooth and level surface. 
 
THE PROPERTIES OF MATTER. 27 
 
 Porosity. 
 
 Experiment 14. Pour 30 cu. cm. of water into a long test-tube. 
 Carefully add 20 cu. cm. of strong alcohol, holding the tube so that 
 the latter may run down its side and rest upon the water without 
 mixing with it. Gently bring the tube into a vertical position, mark 
 the height of the liquid in the tube, close the mouth of the tube with 
 the thumb, and thoroughly shake the two liquids together. Notice 
 again the height of the liquid contents of the tube. It looks as if some 
 of the water and some of the alcohol had been forced into the same 
 space, in spite of the impenetrability of matter. 
 
 Experiment 15. Fill a glass tumbler with large shot or peas, and 
 then see how much well-dried sand or salt you can add. Perhaps 
 what happens here is analogous to what happened in Experiment 14. 
 
 28. Porosity is that property of matter by virtue of ivhich 
 spaces exist between the molecules. A body does not com- 
 pletely fill the space it seems to occupy. 
 As a result of this, we have the possi- 
 bility of an interpenetration of two 
 bodies, the molecular volumes of one 
 occupying the intermolecular spaces of 
 the other, so that the resultant volume 
 is less than the sum of the constituent 
 
 FIG. 9. 
 
 volumes. 
 
 (a) When iron is heated, the molecules are pushed further apart, 
 the pores are enlarged, and we say that the iron has expanded. When 
 a piece of iron or lead is hammered, it is made smaller, because the 
 molecules are forced nearer together, thus reducing the size of the 
 pores. Cavities or cells, like those of bread or sponge, are not properly 
 called pores. 
 
 29. Strain and Stress. Any change in the shape or 
 size or volume of a solid is called a strain. Thus, if a 
 mass of metal becomes compressed, or bent, or twisted, or 
 
28 
 
 SCHOOL PHYSICS. 
 
 distorted in any way, it is said to experience a strain. The 
 use of the word " strain " to designate a force that pro- 
 duces a deformation is common in literature, but incorrect 
 in mechanics. The force that produces a strain is called 
 a stress. 
 
 Elasticity. 
 
 Experiment 16. Squeeze a rubber ball. Stretch a rubber band. 
 Stretch a spiral spring. Bend a thin strip of steel, wood, or whale- 
 bone. In each case the volume or form is restored to its initial condition 
 when the distorting force ceases to act. 
 
 Experiment 17. Firmly fasten one end of a piece of spring-brass 
 wire, about No. 27 and about 1 m. long (e.g., grip it in a hand vise), 
 so that the wire hangs vertical. To the 
 lower end of the wire fasten a weight of 75 
 or 100 g. To this weight attach a pointer 
 so that it extends horizontally from the 
 direction of the wire. Turn the weight 
 through a considerable angle, thus twisting 
 the wire. Release the weight, and notice the 
 rapid movements of the pointer of the torsional 
 pendulum. 
 
 30. Elasticity is that property of 
 matter by virtue of which bodies re- 
 sume their original form or size when 
 that form or size has been changed 
 by any external force. There is an 
 elasticity of volume and an elasticity 
 of form or figure. The former is 
 peculiarly a property of gases and 
 liquids ; the latter, of solids. 
 
 FIG. 10. 
 
 (a) The elasticity of a body may be de- 
 veloped by pressure, by pulling, by bending, or by twisting. 
 
THE PROPERTIES OF MATTER. 29 
 
 (6) All bodies possess this property in some degree, because all 
 bodies, solid, liquid, or aeriform, when subjected to pressure (within 
 limits varying with the substance), will resume their original size 
 upon the removal of the pressure. Fluids have no elasticity of form ; 
 on the other hand, all fluids have perfect elasticity of size. The ratio 
 of the numerical value of a stress to the numerical value of the strain 
 produced by it is called the coefficient of elasticity. 
 
 (c) Solids that have little or no ability to resume their original 
 shape after the action of a stress are said to be inelastic or plastic. In 
 the case of even highly elastic solids, when the strain exceeds a certain 
 value, called the limit of elasticity, the substance acts like a plastic 
 solid. A body under stress has reached its limit of elasticity when 
 any further stress will cause a permanent alteration of form or size. 
 
 Molecular Attraction. 
 
 Experiment 18. Dip a finger into water. Upon removing it, 
 notice that it is wet, that water adheres to it. Hold the finger point- 
 ing downward, and notice that a drop of water gathers at the finger 
 tip. That drop is composed of many particles that cling together, or 
 cohere. Something makes the water particles cling to each other and to 
 thejinger, in spite of the force of gravity. 
 
 Experiment 19. Hold the end of a stick of sealing wax in a candle 
 flame. Notice that the fused drop increases in size until it becomes so 
 heavy that the molecular forces can no longer counteract its weight. 
 
 Experiment 20. Cut a lead bullet so as to present two flat, clean 
 surfaces. Press the two parts together with a slight twist- 
 ing motion. They will cling together. Lead disks are made 
 for this purpose. When used, their opposing surfaces 
 
 should be flat and bright. 
 
 FIG. 11 
 
 Experiment 21. Take a sheet of gold leaf in your fin- 
 gers, and try to pick the metal off with the fingers of the other hand. 
 Some of the gold will stick to your fingers. 
 
 31. Cohesion and Adhesion. Cohesion is the force that 
 holds together like molecules; adhesion is the force that holds 
 together unlike molecules. The distinction is traditional 
 rather than necessary. 
 
30 SCHOOL PHYSICS. 
 
 (a) Exhibitions of this force are more noticeable in solids than in 
 liquids ; in aeriform bodies it seems to be wanting. 
 
 (6) This is the force that holds bodies together, and gives them 
 form. Were its action suddenly to cease, brick and stone and iron 
 would crumble to finest powder, and all our homes and cities and 
 selves fall to hopeless ruin. This force acts only at insensible (mo- 
 lecular) distances. Let the parts of a body be separated by a sensible 
 distance, and we say that the body is broken. If the molecules of the 
 parts can again be brought within molecular distance of each other, 
 cohesion will again act, and hold them there. This may be done by 
 simple pressure, as in the cases of wax, freshly cut lead, broken ice, 
 and many powders ; it may be done by welding or melting, as in the 
 case of iron. 
 
 32. Hardness is that property of matter by virtue of which 
 some bodies resist any attempt to force a passage between 
 their particles. The relative hardness of two substances 
 is determined by finding out which of them will scratch 
 the other ; e.g., we know that glass is harder than copper 
 because it will scratch copper. 
 
 (a) The hardness of many solid substances is increased by raising- 
 the body to a high temperature and suddenly cooling it. The process 
 of giving a body a suitable degree of hardness is called tempering. 
 Some substances, like copper, are made softer by raising to a high 
 temperature and slowly cooling. This process is called annealing. 
 
 Tenacity. 
 
 Experiment 22. Cut several strips of manilla paper about 5 by 
 25 cm. Turn each end of each strip over, and fasten the edges with 
 glue so as to make a good hem at each end. In the loop at one end 
 of the paper strip insert a stout rod the length of which exceeds the 
 width of the paper strip. Fasten this rod by a stout string or wire 
 bail to a nail in a board or table-top. Similarly fasten the other end 
 of the strip to the hook of a good spring-balance, held as shown in 
 Fig. 12. Pull steadily with the balance and in" a line with its length, 
 so as to avoid, as far as possible, all friction of the sliding bar to 
 which the hook is attached. Watch the index of the balance all the 
 
THE PROPERTIES OF MATTER. 31 
 
 time, looking directly down upon it so as to avoid the error of parallax. 
 Continue to pull until the paper breaks. Be careful that the recoil 
 of the hook does not injure your hands. Repeat the experiment 
 with several similar strips, recording after each test the maximum 
 reading of the index. If the index does not rest over the zero 
 mark when the balance is in a horizontal position, the proper correc- 
 
 FIG. 12. 
 
 tion should be made for each reading taken. The average of these 
 several readings will be a fair expression of the strength of the paper. 
 Make a similar series of tests with similar strips of paper twice as 
 wide. Compare the two average results. From your data, compute 
 the strength of a strip 2.2 cm. wide and experimentally verify the 
 result. 
 
 33. Tenacity is that property of matter by virtue of ivhich 
 some bodies resist a force tending to pull their particles 
 asunder. Its measure is the ratio between the breaking 
 weight and the area of the cross-section of the body 
 broken. It varies with different substances, with the form 
 of the body, with the temperature, and with the dura- 
 tion of the pull. 
 
 (a) Like hardness and other characteristic properties of matter, 
 tenacity is a variety of cohesion. For any given material, it has been 
 found that tenacity is proportional to area of cross-section; e.g., a rod 
 
32 SCHOOL PHYSICS. 
 
 with a sectional area of a square inch will carry twice as great a load 
 as a rod of the same material with a sectional area of a half square 
 inch ; a rod 10 cm. in diameter will carry four times as great a load 
 as a similar rod 5 cm. in diameter. The explanation of this is simple. 
 Imagine these rods to be cut across, and it will be evident that on 
 each side of the cut the first rod will expose twice as many molecules 
 as will the second, and that the third will expose four times as many 
 as the fourth. But, for the same material, each molecule has the 
 same attractive force. Doubling the number of these attractive mole- 
 cules, which is done by doubling the sectional area, doubles the total 
 attractive force, which, in this case, is called tenacity ; quadrupling 
 the sectional area quadruples the tenacity ; etc. Hence the law. 
 
 34. Malleability is that property of matter by virtue of 
 which some bodies may be rolled or hammered into sheets. 
 
 (a) Steel has been rolled into sheets thinner than the paper upon 
 which these words are printed. Gold is the most malleable metal, 
 and, in the form of gold leaf, has been beaten so thin that 300,000 
 sheets, placed one upon" the other, measured but an inch in height. 
 
 Ductility. 
 
 Experiment 23. Heat the middle of a piece of glass tubing about 
 6 inches long in an alcohol flame until red-hot. Roll the ends of 
 the glass slowly between the fingers, and, when the heated part is soft, 
 quickly draw the ends asunder. That the fine glass wire thus produced 
 is still a tube, may be shown by blowing through it into a glass of 
 water, and noticing the bubbles that will rise to the surface. 
 
 35. Ductility is that property of matter by virtue of which 
 some bodies may be drawn into wire. 
 
 (a) Platinum wire has been made j^-^ of an inch in diameter. 
 Glass, when heated to redness, is very ductile. 
 
 (6) Malleability and ductility are closely related, so that most 
 substances that have great malleability also have high ductility. But 
 this rule is not universal ; lead and tin are very malleable, but only 
 slightly ductile. 
 
 (c) Ductility involves tenacity ; i.e., although a substance may be 
 
THE PROPERTIES OF MATTER. 33 
 
 tenacious without being ductile, it cannot be ductile without being 
 tenacious. The tenacity of most metals is increased by the process of 
 wiredrawing. Cables made of twisted iron or steel wires are stronger 
 than iron chains or rods of equal weight and length. Steel wire with 
 a tenacity of more than 92 tons per square inch of cross-section has 
 been made, and wire with a tensile strength of 70 or 80 tons per 
 square inch is readily procurable. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. A decimeter rule divided to 0.2 mm. ; 
 a diagonal scale ; dividers (see Fig. 13) ; wire ; wire gauge (see Fig. 14) ; 
 calipers (see Figs. 15 and 16) ; a solid cylinder ; a metal 
 tube; a tumbler; tin can; a glass vessel graduated to 
 0.1 cu. cm.; wooden blocks, rods, and bars; clevis; a tin- 
 can cover for scale-pan ; two pieces of |-inch gas-pipe each 
 4 inches long ; a straightedge ; a wheat straw ; two small 
 vises ; sand-bag weights ; soldering tools and materials ; 
 cutting pliers. 
 
 1. What is the length of a full line as printed in this 
 book? Place the graduated edge (not the side) of the 
 decimeter rule on the paper, with some plainly visible 
 mark, as 0.5 or 1 cm. (not the end of the rule), at one end 
 
 of the printed line. Always use a rule in this way for ' ' 
 accurate measurements. 
 
 2. Draw on paper three straight lines with lengths of 2.57 inches, 
 3.34 inches, and 6.4 centimeters respectively. 
 
 3. Tightly pinch the leaves of this book (inside the covers) between 
 two small blocks that come flush with them at the top. Remove some 
 of the leaves so that those that remain make a layer just 1 cm. thick. 
 Count the leaves, and compute in decimals of a millimeter the thick- 
 ness of an average leaf of this book. 
 
 4. Determine the gauge numbers of four pieces of wire. Use the 
 notches around the edge of the steel plate, and not the larger circular 
 openings at the inner end of the notches. If you have a micrometer 
 caliper, determine the diameter of each piece. The best wire gauge 
 to use is that known as the Brown and Sharpe, " B & S." Introduce 
 the wire into the slit which admits it with a very slight pressure, and 
 note the number corresponding to that slit. Be sure that the wire is 
 not rusty, dirty, or bruised at the point where it is gauged. It is 
 convenient to buy such wire wound on spools. . 
 
 3 
 
34 
 
 SCHOOL PHYSICS. 
 
 FIG. 14. 
 
 5. Wind 25 turns of No. 30 annealed wire around a cylinder an inch 
 or more in diameter, being careful that the successive turns are as 
 
 close as possible to each 
 other. Measure the 
 total width of the wire 
 band on the cylinder, 
 and compute the di- 
 ameter of No. 30 wire. 
 Compare your result 
 with the table given in 
 the appendix. 
 
 6. With the outside 
 calipers, measure the 
 diameter of the iron 
 ball used in Exercise 6 
 on p. 24. Compare the 
 result then obtained 
 and recorded in your 
 notebook with that now 
 found. 
 
 7. Measure the di- 
 ameter and length of a small cylinder. If, by measuring the rod at 
 short intervals with the calipers, you find that its diameter is not 
 uniform, use the average of your several 
 
 measurements, (a) Compute the surface area 
 of the cylinder. (&) Compute the volume of 
 the cylinder. 
 
 8. Measure the length and the inside and 
 outside diameters of a metal tube. If you 
 have no inside calipers, bend a piece of an- 
 nealed wire into a V-shape, and use that, 
 (a) Compute the total surface area of the tube. 
 
 volume of metal in the tube, (c) Test 
 your result by the displacement of water. 
 9. (a) With the inside calipers, meas- 
 ure the diameter of the tumbler on the 
 inside, at the bottom and at the top. 
 From these measurements determine the 
 average diameter of the tumbler. Place a straightedge across the top 
 of the tumbler in the line of a diameter. Measure the perpendicular 
 
 FIG. 15. 
 
 Compute the 
 
 FIG. 16. 
 
THE PROPERTIES OF MATTER. 35 
 
 distance from the bottom of the tumbler to the under side of the 
 straightedge. Compute the capacity of the tumbler in cubic centi- 
 meters. (6) Fill the tumbler with water and pour the water into 
 the graduate, and thus test the accuracy of your previous measure- 
 ments and computation. 
 
 10. Using the wire gauge, select coils of No. 30 wire, brass, copper, 
 iron, and steel. From each coil cut oif two pieces each about 1 m. 
 long. Wrap one end of a wire twice about the middle of a piece of 
 gas-pipe, and fasten by twisting the end around the body of the wire, 
 being careful not to make any kink in the body of the wire. Similarly 
 fasten the other end of the wire to the other piece of gas-pipe. Through 
 each piece of gas-pipe pass a 60 cm. piece of wire much stouter than 
 the No. 30 iron or steel, bend these wires sharply at the ends of the 
 gas-pipe, and twist the ends together so as to make a bail in the shape 
 of an isosceles triangle of which .the pipe shall be the shorter side. 
 From one of these bails suspend a tin can or basin (the weight of 
 which, with its bail and gas-pipe, has been ascertained) ; support the 
 other bail so that the can shall be only a few inches above the floor or 
 table. Place a weight of 200 or 300 g. in the pan, and add weights 
 of 10 or 5 g. each until the load breaks the wire. In like manner 
 determine the breaking strength of the other piece of the same kind 
 of wire. Make like tests with the other kinds of wire. Tabulate 
 your results in some such way as the following: 
 
 BREAKING STRENGTH OF Xo. 30 WIRE. 
 
 Copper. Brass. Iron. Steel. 
 
 First test . 
 Second test 
 Averages . 
 
 11. Provide two pieces of hard wood, A and B, and place them on 
 the table as shown in Fig. 17, with their ridges parallel, and a meter 
 apart. Upon these blocks place a w r ooden bar, W, 1.2 cm. ( in.) square 
 and about 104 cm. long. Midway between the supporting ridges 
 place a small clevis, C, made of sheet metal and carrying a scale-pan. 
 In some cases it may be convenient to pass the string through a hole 
 in the table, so that the scale-pan will hang below the table-top. Pro- 
 vide a straightedge a meter long, and faced on the edge at each end 
 with metal of the same thickness as the clevis. Place the straight- 
 
36 SCHOOL PHYSICS. 
 
 edge on W, with its ends over the ridges of A and B. If there is no 
 deflection or " sag " in W, the straightedge will just touch the upper 
 
 surface of C ; otherwise 
 the distance between C 
 and the straightedge 
 will measure the deflec- 
 tion. Place a known 
 weight- (say, 100 g.) in 
 the scale-pan, and to 
 this weight add the 
 weight of the clevis and 
 F IG . 17. the scale-pan, and call 
 
 the sum the load. Meas- 
 ure the deflection of W caused by the load. Double the load, and 
 measure the deflection thus caused. Record these data. 
 
 For quick work, each end of a cord or annealed wire may be 
 fastened to the knob of a known weight, and the cord, thus loaded, 
 placed across the middle of the bar. 
 
 Instead of measuring the deflection thus directly, using a straight- 
 edge, the deflection may be magnified and more easily read in this 
 way : Solder a pin to the further end of the clevis so that it shall 
 project horizontally and at right angles to the length of the wooden 
 bar. Select a straight straw 30 cm. or more in length. Trim the 
 smaller end of the straw so that it may act as a pointer or index. 
 Thrust a needle through the straw a little less than five-sixths of its 
 length from the pointed end. Measure, from the needle toward the 
 nearer end of the straw, a distance just one fifth the length of the part 
 on the other side of the needle, and mark the point thus located by a 
 pen mark on the straw. Thrust the end of the needle carrying the 
 straw into the cork of a bottle so that the needle shall be horizontal 
 when the bottle is upright. Place the bottle so that the height of the 
 needle shall be a little less than that of the pin carried by the clevis, 
 while the straw is parallel with the wooden bar. Adjust the bottle so 
 that the ink mark shall come under the pin on the clevis. Tie or tack 
 any convenient graduated scale so that it shall stand on end against 
 the vertical face of a block, and set it so that the index end of the 
 straw shall stand opposite one of the marks near the bottom of the 
 scale. This mark is to be considered the zero mark. A deflection of 
 1 cm. at the middle of the bar will move the index over 5 cm. of the 
 scale. Read deflections from the edge of the scale. After each weigh- 
 ing, see whether the index returns to the zero of the scale or not. 
 
THE PROPERTIES Otf MATTER. 37 
 
 Replace W by another bar made of the same kind of wood, with 
 the same length and thickness, but 2.4 cm. wide. Load it to produce 
 the same deflections as before, and record the data. In similar man- 
 ner try the narrow bar with the supports 0.5 m. apart, and the broad 
 bar on edge with the supports 1 m. apart. From all the data thus 
 obtained and recorded, concerning the stiffness of beams carrying 
 loads midway between their supports, answer the following questions: 
 What is the relation between the load and the deflection? Between 
 the length of the beam and the deflection? Between the breadth of 
 the beam and the deflection? Between the thickness of the beam 
 and the deflection ? 
 
 12. Experimenting with wooden rods of different lengths, widths, 
 and thicknesses, supported at their ends and loaded in the middle, 
 show that the breaking strength varies directly as the width and as 
 the square of the thickness, and inversely as the length, or that it does 
 not ; i.e., verify or disprove the formula : 
 
 Breaking strength oo . 
 
 (The sign co is read "varies as " or "is proportional to.") 
 
 13. Grip one end of a small straight wire, a yard or so in length, 
 in a small vise. Support the vise firmly, so that the wire may hang 
 vertically. Grip the free end of the wire in another small vise of 
 known weight. Near the lower end of the wire, fix a horizontal 
 pointer (a stiff bristle stuck on with shoemaker's wax will answer), 
 and mark its level on a card fixed upright. Call this level the zero of 
 the card scale. Add a sand bag of the same weight as the vise, and 
 mark the level of the pointer on the card. Remove the sand bag and 
 see if the pointer comes back to zero. Add sand bags or equal 
 weights in succession, marking the successive levels of the pointer 
 on the scale, removing the weights after each trial, and giving the 
 pointer a chance to return to the zero mark. When you find that 
 the wire has been permanently stretched, stop the test. Record 
 the elongation after each weight. Repeat with a similar wire, 
 twice as long. Can you discover any law for the stretching of wire ? 
 If so, record it. Verify that law by similar experiments with other 
 wires. 
 
 14. Using a rod of clear ash, 36 inches long and half an inch 
 square, determine the relation between the force used to twist the 
 rod and the amount of torsion produced; i.e., if a certain force 
 produces a torsion of 5, how much torsion will twice that force 
 produce ? 
 
38 SCHOOL PHYSICS. 
 
 15. Using the same rod or a similar one, determine the relation 
 between the length of the rod and the amount of the torsion. 
 
 16. Using the same rod and one of the same kind of wood and the 
 same length, but | of an inch square, verify the statement that torsion 
 varies as ^j, d representing the diameter of the rod. How does the 
 formula as given agree with the statement that the torsion varies 
 inversely as the square of the cross-section. 
 
 III. THE THREE CONDITIONS OF MATTER, ETC. 
 
 36. Conditions of Matter. Matter exists in three con- 
 ditions or forms, the solid, the liquid, and the aeriform. 
 Liquid and aeriform bodies are fluids. 
 
 37. A Solid is a body whose molecules change their rela- 
 tive positions with difficulty. Such bodies have a strong 
 tendency to retain any form that may be given to them, 
 and can sustain pressure without being supported laterally. 
 A movement of one part of such a body produces motion 
 in all of its parts. 
 
 38. A Fluid is a body whose molecules easily change 
 their relative positions. Fluids cannot sustain pressure 
 without being supported laterally. The term compre- 
 hends liquids, gases, and vapors. 
 
 i 
 
 Cohesion of Liquids. 
 
 Experiment 24. Suspend a clean glass plate of about four inches 
 area from one end of a scale-beam, and accurately balance the same 
 with weights in the opposite scale-pan. The supporting cords may 
 be fastened to the plate with wax. Beneath the plate place a saucer 
 so that when the saucer is filled with water the plate may rest upon 
 the liquid surface, the scale-beam remaining horizontal. Be sure that 
 there are no air-bubbles under the plate. Carefully add small weights 
 to those in the scale-pan. Notice that the water beneath the plate is 
 
THE THREE CONDITIONS OF MATTER. 39 
 
 raised above its level. Add more weights until the plate is lifted 
 from the water. ^Notice that the under surface of the plate is wet. 
 These molecules on the plate have 
 been torn from their companions in 
 the saucer, the adhesion between the 
 water and the plate being greater 
 than the cohesion of the water. 
 The weights added to the original 
 counterpoise were needed to over- 
 come the cohesion of the water 
 molecules. 
 
 39. A Liquid is a body ivhose FlG 18 
 molecules easily change their 
 
 relative positions, yet tend to cling together. Such bodies 
 adapt themselves to the form of the vessel containing 
 them, but do not retain that form when the restraining 
 force is removed. Their free surfaces are always hori- 
 zontal. Water is the best type of liquids. 
 
 40. An Aeriform Body is one whose molecules easily 
 change their relative positions, and tend to separate from 
 each other almost indefinitely. Such bodies are of two 
 kinds, gases and vapors. Gases remain aeriform (i.e., 
 retain the form of air) under ordinary conditions, while 
 vapors resume the solid or liquid form at ordinary tem- 
 peratures. Atmospheric air is the most familiar type of 
 aeriform bodies. 
 
 41. Changes of Condition. Many substances, like iron 
 and gold and water, may be made to exist in all of these 
 three forms by suitable adjustments of temperature and 
 pressure. The identity of ice, water, and steam, is fa- 
 miliar to all. 
 
 (a) Experiments with electric discharges in high vacuums have 
 
40 SCHOOL PHYSICS. 
 
 given results which, in the minds of many, prove the existence of a 
 fourth condition of matter. For matter in this extremely thin or 
 attenuated form, the name " radiant matter " has been proposed. 
 
 Solution. 
 
 Experiment 25. Into a beaker half full of water, drop a few lumps 
 of sugar. Stir the contents of the glass until the solid disappears. 
 
 Experiment 26. Mix 50 g. of pulverized ammonium nitrate arid 
 25 g. of pulverized ammonium chloride (sal-ammoniac). Put the 
 mixture into 75 cu. cm. of cold water in a beaker, and stir the sub- 
 stances together with a small test-tube containing a little cold water. 
 Notice that the solids disappear. Carefully observe the condition of 
 the water in the test-tube. 
 
 42. Solution is the transformation of matter from the solid 
 or gaseous form to the liquid form by means of a liquid called 
 the solvent or menstruum. The process is essentially a 
 change of molecular condition. When the change is 
 from the solid to the liquid form, there is an absorption 
 of heat with a consequent fall of temperature, as is strik- 
 ingly seen in freezing mixtures. The solution of a gas 
 in a liquid is accompanied by a release of heat and a con- 
 sequent rise of temperature. When the solvent has dis-' 
 solved as much of a given substance as it can, the solution 
 is said to be saturated. 
 
 (a) The solubility of any solid in any liquid is constant at a given 
 temperature, and may be determined by experiment. The solubility 
 of any gas is also constant under the same conditions ; it varies with 
 temperature, pressure, and the nature of the solvent. With a mix- 
 ture of gases, each is dissolved in the same quantity as if it were 
 present alone, and under the same pressure as in the mixture. 
 
 Crystallization. 
 
 Experiment 27. Dissolve about a quarter of a pound of alum in 
 a pint of hot water. Hang several strings in the solution, and set 
 
THE THKEE CONDITIONS OF MATTER. 41 
 
 the vessel containing it aside for the night. In the morning notice 
 the regularity and similarity of the crystals that have formed on the 
 strings. 
 
 43. Crystallization. Many solids forming slowly from 
 the liquid or aeriform condition, and thus haying great 
 freedom of molecular motion, assume regular forms, with a 
 certain number of plane surfaces symmetric- 
 ally arranged, and with a definite internal struc- 
 ture. Such bodies are called crystals. Thus 
 quartz crystallizes in hexagonal prisms termi- 
 nated by hexagonal pyramids. 
 
 (a) The internal structure is exhibited in the cleavage, 
 and in the appearance of sections cut from the crystal 
 and viewed by polarized light. The planes of cleavage 
 are certain definite planes along which separation is most 
 easily effected. 
 
 (>) The form and structure of crystals are of great importance to 
 the chemist and the mineralogist, as the nature of many substances 
 may be ascertained thereby. (See definition of " crystallography " in 
 " The Century Dictionary.") 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Bottles containing concentrated solu- 
 tions of potassium nitrate (saltpeter) and of ammonium chloride 
 (sal ammoniac) ; several pieces of window glass 4 or 5 inches square ; 
 a magnifying lens, preferably mounted (the glasses used in botanical 
 study will answer admirably); a Bunsen or an alcohol lamp; test- 
 tube ; iodine ; Hessian crucible ; brimstone ; saucer ; bottle ; round or 
 ' rat-tail " file ; Florence flask ; corks and cork-borers ; glass tubing ; 
 retort-stand ; two plain tumblers of thin glass and of the same size ; 
 waste- jar. 
 
 1. (a) Slowly warm a piece of thoroughly cleaned glass over the 
 lamp ; hold the glass horizontal, and pour a little of the solution of 
 saltpeter upon it. Move the glass quickly so as to spread the liquid 
 over its surface, and then, hold it over the waste-jar so as to drain off 
 the surplus* solution. When a cloudy patch appears on the glass, 
 examine it carefully through the lens, make a drawing of what you 
 see, and label it " KNO 3 Crystals." 
 
42 SCHOOL PHYSICS. 
 
 (&) Take a similar course with the other solution, and label the 
 drawing NH 4 C1 Crystals." 
 
 2. Drop a single crystal of iodine into the bottom of a test-tube 
 (Fig. 20), and heat it gently. After the tube has been well filled 
 with the beautiful iodine vapor, allow it to cool. With a 
 p| magnifying lens, examine the iodine crystals that form on the 
 walls of the test-tube. 
 
 3. Melt about 200 g. of sulphur (brimstone) in a Hessian 
 crucible (Fig. 21), and allow it to cool until a crust forms over 
 it. Through a hole pierced in this crust, pour out the still 
 liquid sulphur. When the crucible is cool, break it, and with 
 a magnifying glass examine the needle-shaped sulphur crystals 
 with which it is lined. The crucible may be saved by pouring 
 all of the melted sulphur into a pasteboard box, and allowing 
 ' the crystals to form there. 
 
 4. Fill a clear glass tumbler with fresh hydrant or well water. Fill 
 a similar vessel with water that has recently been w T ell boiled. Set 
 both in a moderately warm, quiet place, and let them 
 
 stand over night. Examine the walls of the two 
 tumblers, and account for the difference in their 
 appearance. 
 
 5. With a round file, work a notch in the edge of 
 a saucer, and a hole about a centimeter in diameter 
 in the middle of the bottom. Invert the saucer in 
 
 an earthenware or tin pan, and cover it with water. FlG 2 i. 
 
 Fill a bottle with water, and stand it upside down 
 
 with its mouth around the hole 
 in the saucer. Fill a Florence 
 flask with water, and, holding 
 it under water, close its mouth 
 with a cork carrying a bent 
 glass delivery-tube. Keeping 
 the flask and tube full of 
 water, thrust the free end of 
 the tube through the notch in 
 the edge of the saucer, and 
 FlG 22 place the flask on the retort- 
 
 stand. Be sure that flask, tube, 
 
 and bottle are full of water. Heat the flask carefully until the water 
 
 has boiled for several minutes. The collection bottle will be found to 
 
THE THREE CONDITIONS OF MATTER. 
 
 43 
 
 contain something besides water ; it is air. Can you imagine whence 
 it came ? Repeat the experiment with water that has been recently 
 boiled in an open vessel. Do you collect any air now ? Perhaps the 
 boiling of water expels air that it holds in solution. Think about it. 
 Has your work given you any information as to the solubility of air 
 in water ? As to the porosity of water ? 
 
 Superficial Molecules. 
 
 Experiment 28. Fill a tumbler brimming full of water. With 
 a pipette (Fig. 23), add more water, drop by drop and patiently, until 
 the water in the tumbler is actually heaped up higher 
 than the edges of the glass. Try to imagine an invisi- 
 ble skin stretched over the liquid surface to keep it 
 from overflowing the edge of the tumbler. 
 
 Experiment 29. Carefully place a fine sewing 
 needle upon the surface of water. With care, and 
 perhaps repetition, the needle 
 may be made to float. If you 
 have serious trouble in mak- 
 FIG. 24. i n g ik float, draw it between 
 
 the fingers or wipe it with an 
 
 oily cloth. A hair-pin bent slightly near the tips may 
 be used to lower the needle so that neither end shall F IG< 23. 
 touch the water before the other. Closely examine 
 the surface of the water. Notice that the needle rests in a little 
 depression or bed, just as it would if the surface of the water was 
 a thin skin or membrane. 
 
 Experiment 30. Blow a soap-bubble without detaching it from the 
 pipe or tube. Leave the tube open, and notice that the film contracts, 
 diminishing the size of the bubble, and expelling some of the air from 
 it. The current of air from the interior of the bubble may be made 
 to deflect the flame of a candle. 
 
 Experiment 31. Float two sewing needles on the. surf ace of water 
 about a quarter of an inch apart, and let a drop of alcohol fall upon 
 the water between them. Notice that the needles separate as if they 
 had been supported on a stretched membrane, and the membrane had 
 been cut so that its parts might separate, each carrying its needle 
 with it. 
 
44 SCHOOL PHYSICS. 
 
 Experiment 32. Drop a few small pieces of camphor upon the 
 surface of clean, warm water. Notice their peculiar gyratory motions. 
 
 Experiment 33. Moisten a small bit of paper, and stick it to the 
 concave side of a watch crystal near the edge, as an indicator. Dip 
 the part of the convex surface on the side indicated by the paper into 
 alcohol, so that not more than a sixth of the rim shall be wet. Hold- 
 ing the crystal so that the adhering drop of alcohol shall be under the 
 paper bit, float it on the surface of a shallow dish of water a foot or 
 more in diameter. The glass will skim across the surface of the water 
 with the segment that was wet with alcohol astern. 
 
 44. Superficial Films. The molecular forces of a liquid 
 are strikingly manifested at its surface, so that every liquid 
 may be regarded as bounded by a superficial film. This 
 film is physically different from the interior of the liquid 
 mass, and is a seat of energy. Two of the properties of 
 these films are called surface viscosity and surface tension. 
 
 45. Surface Viscosity. The superficial film of a liquid 
 is, as a rule, exceedingly viscous as compared with the inte- 
 rior mass. It is comparatively hard to move or break. To 
 this toughness of the superficial film, the floating of a 
 needle or the walking of an insect on water must in part 
 be ascribed, for the depth of the dimple is not sufficient to 
 account for the support afforded to so heavy a body. A 
 solution of soap in water has greater surface viscosity than 
 has pure water, hence its adaptability to the formation of 
 bubbles. 
 
 (a) The surface viscosity of a solution of gum arabic. is sufficient 
 to enable frothiug when the solution is shaken, but not enough for 
 the formation of bubbles ; that of water is so little that pure water 
 will not froth; and that of alcohol is so* eminently feeble that alcohol 
 is often used in pharmacy to mix with superficially viscous liquids for 
 the purpose of checking or preventing frothing. To the same prop- 
 erty is attributed the smoothing of a rough sea by pouring oil upon 
 
THE THREE CONDITIONS OF MATTER. 
 
 45 
 
 it. The new surface is comparatively rigid, and is not so easily broken 
 into surf. 
 
 46. Surface Tension. Experiments show that a liquid 
 surface (as the surface that separates waterfront air, or oil 
 from water) is in a state of tension similar to that of a mem- 
 brane stretched equally in all directions. This tension is 
 practically independent of the form of the surface. It 
 depends on the nature and temperature of the liquid, 
 diminishing as the temperature rises. Pure water has 
 a surface tension higher than that of any other substance 
 that is liquid at ordinary temperatures, except mercury ; 
 hence the mixture of any other liquid with water lessens 
 the surface tension of the water, as was shown in Experi- 
 ments 31 and 33. 
 
 (a) In a liquid film, such as a soap-bubble, " it is possible that no 
 part of the liquid may be so far from the surface as to have the poten- 
 tial and density corresponding to the interior of a liquid mass;" i.e., the 
 film may be mostly surface. The exterior and the interior surfaces of 
 
 the bubble act like two 
 
 sheets of india-rubber 
 
 stretched equally in 
 
 length and breadth. 
 
 Their tendency to con- 
 tract forces air from 
 
 the interior of the bub- 
 ble, and repays the 
 
 work performed, or 
 
 energy expended, in 
 
 increasing the surfaces 
 
 when the bubble was 
 
 blown. 
 
 Surface tension may 
 
 be studied under very 
 favorable conditions by using soap or collodion films. If a rough- 
 ened ring is dipped into a strong solution of Castile soap, to which 
 
 FIG. 25. 
 
 FIG. 26. 
 
46 SCHOOL PHYSICS. 
 
 glycerin has been added, a plane film will be found stretched across 
 it. To such a ring, tie a loop of thread and secure another film, as 
 shown in Fig. 25. With a hot wire, puncture the film inside the 
 thread loop, and the tension of the film will pull the thread outward 
 in all directions, as shown in Fig. 26. Such films may be made to 
 stretch themselves in singularly beautiful forms on wire skeletons of 
 cubes, pyramids, cylinders, etc. 
 
 (6) The tension of the superficial film tends to reduce the contained 
 liquid to the form that gives the greatest volume with the least area 
 of surface ; hence the spherical form of soap-bubbles, air-bubbles 
 in water, raindrops, shot, etc. The various forms assumed by liquid 
 masses under the influence of surface tension are conveniently studied 
 by relieving them of the influence of gravity by floating them in 
 liquids of their own density, and with which they will not mix. 
 Thus, one may make a mixture of alcohol and water of the same 
 density as olive oil. Masses of olive oil placed in such a mixture will 
 neither rise nor sink. If left free, they will assume the globular form. 
 When limiting conditions are imposed upon them, they assume geo- 
 metrical forms of great interest, all having the smallest superficial 
 area possible under the conditions imposed. 
 
 (c) When camphor floats on water, solution is likely to take place 
 more rapidly on one side of each piece than on the other. The sur- 
 face tension becomes weaker where the camphor solution is the 
 stronger; and the lump, being pulled in different directions by unequal 
 surface tensions, moves in the direction of the strongest tension, i.e., 
 toward the side on which the least camphor is dissolved. If a drop 
 of ether (a very volatile liquid) is held near the surface of water, its 
 vapor will condense on the surface of the water, weakening the 
 surface tension there. Surface currents may be noticed flowing in 
 every direction from under the drop of ether. 
 
 Capillarity. 
 
 Experiment 34. Partly fill a' thin, clean beaker with water, and a 
 similar beaker with clean mercury. Notice that the upper surfaces of 
 the two liquids are level except at the edges near the glass. Notice, fur- 
 ther, that the water is lifted at the edge by the glass, and that the 
 mercury is depressed. 
 
 Experiment 35. Support a clean glass rod vertically in the water, 
 and notice that the liquid is lifted by the rod, as shown at a in 
 
THE THREE CONDITIONS OF MATTER. 
 
 47 
 
 Fig. 27. Remove the rod. Notice that it is wet. Wipe the rod dry, 
 and place it similarly in the mercury. Notice that this liquid is de- 
 pressed by the rod. Remove the rod, and notice that it was not wetted 
 by the mercury. 
 
 Smear the glass rod with oil, and place it in the water, as before. 
 Notice that the water is depressed thereby. Remove the rod, and 
 notice that it is not wetted by the water. Place a clean strip of tin, 
 
 FIG. 27. 
 
 lead, or zinc, in the mercury. Notice that the mercury is lifted. 
 Remove the strip, and notice that the strip was wetted by the 
 mercury. - 
 
 47. Capillary Attraction. The excess of the attraction 
 of one of two fluids, one of which is generally air, for the 
 wall of a vessel with which they have a common line of 
 contact, is called capillary attraction; it is proximately 
 accounted for by surface tension. The common surface 
 of the wall and of the more attracted fluid makes the 
 acuter angle with the common surface of the fluids. The 
 truth suggested by our experiments is general : all liquids 
 that wet the sides of solids placed in them will be lifted^ 
 while those that do not will be pushed down. 
 
 Experiment 36. So place two small, clean glass plates in a shallow 
 dish of clean water, that the angle included between the plates shall 
 
48 SCHOOL PHYSICS. 
 
 be very acute, and that the edges in contact shall be vertical. The 
 vertical edges not in contact may be held apart by a thin strip of 
 wood placed between them, the whole being held together by a rubber 
 band placed horizontally around the plates. Notice the rise of the 
 liquid between the plates, and the outline of the hyperbola traced 
 upon them by the surface of the lifted liquid. 
 
 Experiment 37. Wet the inner surfaces of several clean glass 
 tubes of small and different diameters (1 mm. and less) to remove 
 the adhering air-film. Support the tubes vertically in pure water. 
 Notice that the water rises in the tubes, as shown at b in Fig. 27 ; that, 
 the less the diameter of the tube, the greater the elevation of the 
 water ; and that the free surface of the water in the tube is concave. 
 
 Remove the tubes, and similarly support them in clean mercury. 
 Notice that the mercury is depressed in the tubes, as shown at c in 
 Fig. 27 ; that, the less the diameter of ths tube, the greater the depres- 
 sion ; and that the free surface of the mercury in the tubes is convex. 
 
 Experiment 38. Make a tapering capillary tube by drawing out 
 a glass tube that has been heated to redness. Clean the tube thor- 
 oughly, and into its larger end 
 introduce a drop of water. 
 - + Jiliiiii Notice the concave form of the 
 
 two free liquid surfaces, and the 
 motion of the water toward 
 the smaller end of the tube. 
 
 Empty the tube, and intro- 
 F IG . 28. duce a drop of mercury into the 
 
 smaller end. Notice the convex 
 
 form of the two free liquid surfaces, and the motion of the mercury 
 toward the larger end of the tube. 
 
 48. Capillary Tubes. The rise of liquids in capillary 
 tubes is explained by the action of cohesion as a force act- 
 ing at insensible distances, and producing a tension of the 
 superficial film of the liquid. This tension produces an 
 upward pull where the liquid surface is concave, and a 
 downward pressure where the liquid surface is convex. 
 The effect of this tendency is, in the case of water, partly 
 
THE THKEE CONDITIONS OF MATTER. 
 
 49 
 
 to neutralize the downward pull of gravity. The follow- 
 ing facts have been experimentally established: 
 
 (1) Liquids ascend in tubes ivhen they wet them, i.e., when 
 the liquid surface is concave; and they are depressed when 
 they do not wet them, i.e., when the liquid surface is convex. 
 
 (2) The elevation or the depression varies inversely as the 
 diameter of the tube. 
 
 (3) The elevation or the depression decreases as the tem- 
 perature rises. 
 
 (a) The extreme range of the forces that produce capillary action 
 seems to lie between a thousandth and a twenty-thousandth part of a 
 millimeter. Familiar illustrations of capillary action are numerous, 
 such as the action of blotting-paper, sponges, lamp-wicks, etc. 
 
 Absorption. 
 
 Experiment 39. Fill a large test-tube with dried ammonia (see 
 Chemistry, 67) by displacement over mercury. Heat a piece of 
 
 FIG. 29. 
 
 charcoal to redness, and plunge it into the mercury. When it is cool, 
 slip it under the mouth of the test-tube, and let it rise into the ammonia 
 
50 
 
 SCHOOL PHYSICS. 
 
 atmosphere. Notice that the mercury rises in the tube as if the gas 
 was absorbed by the charcoal. 
 
 49. Absorption. Some solids have the power of taking 
 up or absorbing gases. Thus, a porous body like charcoal 
 has the ability to condense on its surface a large quantity 
 of some gases through the molecular attraction exerted 
 between its surface and the molecules of the gas. Box- 
 wood charcoal is able thus to absorb ninety times its 
 volume of ammonia gas. This absorption is increased 
 by pressure, and decreased by a rise of temperature. 
 
 Diffusion. 
 
 Experiment 40. Half fill a jar with water. Through a long- 
 stemmed funnel (Fig. 30) reaching to the bottom of the jar, pour a 
 strong aqueous solution of copper sulphate 
 (blue vitriol). The plane of separation be- 
 tween the colored and the colorless liquids is 
 clearly visible. Allow the jar to stand undis- 
 turbed for several weeks, observing it from 
 day to day. The plane of demarcation be- 
 tween the strata becomes blurred, the liquids 
 mix, the solution becomes uniform. 
 
 Experiment 41. Partly fill a test-tube or 
 other tall glass vessel with water tinted with 
 blue litmus. Through a funnel-tube reach- 
 ing to the bottom of the vessel, drop a little 
 strong sulphuric acid. Notice the reddish 
 color (caused by the action of the acid on 
 ::: JP IG 3Q the litmus) moving slowly upward. 
 
 Experiment 42. Wet the inner surface of a clear tumbler or 
 beaker with strong ammonia water, leaving a few drops of the 
 liquid in the bottom. Cover it with a sheet of writing paper. 
 Moisten the inner surface of a like vessel with strong hydrochloric 
 (muriatic) acid. Invert the second vessel over the first, mouth to 
 
THE THREE CONDITIONS OF MATTER. 
 
 51 
 
 mouth, so that the contents of the two vessels shall be separated only 
 
 by the paper. Each vessel is filled with an invisible gas. Remove 
 
 the paper, and notice 
 
 that the invisible gases 
 
 quickly diffuse into each 
 
 other and form a dense 
 
 cloud. 
 
 If two bottles are filled 
 with different gases, as 
 oxygen and hydrogen, 
 and the bottles con- 
 nected 'by a glass tube 
 two or three feet long, 
 with the bottle con- 
 taining the lighter gas FlG 31 
 (hydrogen) above the 
 other, the gases still mix by diffusion through the tube, but the 
 
 process, of course, requires more 
 
 time. 
 
 Experiment 43. Cement a small 
 porous battery-cup to a large funnel- 
 tube, mouth to mouth. Pass the end 
 of the funnel-tube snugly through the 
 cork of a bottle, B, partly filled with 
 water, and provided with a delivery- 
 tube, d, drawn out to a jet, as shown in 
 Fig. 32. When a bell-glass, C, contain- 
 ing hydrogen is placed over the porous 
 cup, that gas diffuses inward so much 
 more rapidly than the air can diffuse 
 outward, that an increased pressure is 
 exerted on the surface of the water. 
 If all the joints are tight, water will be 
 thrown from the jet. The experiment 
 may be simplified by allowing the tube 
 to dip into .water in an open vessel. 
 Bubbles will then rise through the 
 water. 
 
52 SCHOOL PHYSICS. 
 
 50. Diffusion. The gradual and spontaneous mixing of 
 two fluids that are placed in contact is called diffusion. 
 It takes place without application of external force, and 
 even in opposition to the force of gravity. It is explained 
 only by the motions and attractions of the molecules of 
 the two fluids. 
 
 (a) Some liquids, such as mercury and water, do not mix at all 
 when placed in contact. Other liquids, such as chloroform and water, 
 mix only in certain proportions. The chloroform takes up a little 
 water, and the water takes up a little chloroform, but even the two 
 mixed liquids will not mix. Still other liquids, and all gases, mix in 
 all proportions. When two such fluids are placed in contact, diffu- 
 sion begins of itself, and goes on continuously until the fluids are in 
 a state of uniform mixture. 
 
 (5) Even with our most powerful microscopes, we cannot follow 
 these motions or detect any currents. The motions are molecular, 
 not molar. 
 
 51. Kinetic Theory of Gases. A perfect gas consists 
 of free, elastic molecules in constant and rapid motion. 
 Each molecule moves in a straight line and with a uni- 
 form velocity, until it strikes another molecule or the 
 vessel in which the gas is contained. When these mole- 
 cules encounter each other, they behave much as billiard 
 balls would do if no energy were lost in their collisions. 
 Each molecule travels a very small distance between one 
 encounter and another, so that it is every now and then 
 changing its velocity both in magnitude and direction. 
 The magnitude of the velocity may be computed, and one 
 direction is just as likely as any other. 
 
 (a) One result of this motion of free molecules is, that, if in any 
 part of the containing vessel the molecules are more numerous than 
 in a neighboring region, more molecules will pass from the first region 
 into the second than will pass in the opposite direction ; i.e., the gas 
 
THE THREE CONDITIONS OF MATTER. 53 
 
 will diffuse itself equally through the vessel. Even when two gases 
 are placed in the same vessel, each gas diffuses itself in the same way 
 that it would if the other gas was not present ; but the molecules of 
 the two gases will encounter each other, and every collision will check 
 the process. Thus the interdiffusion of two gases is slower than the 
 equalization of the density of a single gas. It is said that in a given 
 vessel a given stage in the diffusion of liquids requires as many days 
 as a like stage in the diffusion of gases requires seconds. 
 
 (6) A second result is, that the blows that the molecules thus strike 
 upon the walls of the containing vessel are so numerous, that their 
 total effect is a continuous, constant force or pressure. 
 
 Osmose. 
 
 Experiment 44. Tie a piece of wet parchment-paper over the 
 mouth of a large funnel-tube, and pour a saturated solution of copper 
 sulphate into the stem of the tube until the liquid a little more than 
 fills the bulb. Support the funnel-tube in a clear glass vessel of water, 
 adjusting the height of the tube so that the two liquids shall stand at 
 the same level. Watch the apparatus, and soon you may notice that 
 the bluish tint appears in the water in the outer vessel, and that the 
 liquid is rising in the stem of the funnel-tube. Evidently both liquids 
 are passing through the parchment membrane, the greater flow being 
 inward. 
 
 52. Osmose. The tendency of fluids to pass through 
 porous partitions and to mix is called osmose. 
 
 (a) "When two solutions differing in strength and composition are 
 separated by a porous diaphragm, they pass with unequal rapidities. 
 The action of the fluid that passes with the greater rapidity is called 
 endosmosis ; that of the other fluid is called exosmosis. 
 
 (ft) Soluble substances have a wide range of diffusibility. Bodies 
 of rapid diffusibility through porous membranes, like common salt 
 and sugar, generally have a crystalline form, and are called crystalloids. 
 Bodies of slow diffusibility through porous membranes generally have 
 the amorphous, glue-like character that gives them the name of 
 colloids. Colloids are often separated from crystalloids by placing 
 the mixture in a vessel having a parchment-paper bottom, and sus- 
 pending it in another vessel containing water. This process is called 
 dialysis. 
 
54 SCHOOL PHYSICS. 
 
 CLASSROOM EXERCISES. 
 
 1. What is science ? 
 
 2. What is matter? 
 
 3. Define the several divisions of matter. 
 
 4. What is the difference between a hypothesis and a theory? 
 
 5. (a) What is a gram? (6) A liter? 
 
 6. On what property of matter does compressibility depend? 
 
 7. If you thrust a knitting-needle into a mass of dough, is the 
 hole thus made a pore ? What is a pore ? 
 
 8. What is the difference between a fluid and a liquid? 
 
 9. Are molecules of water larger or smaller than those of steam ? 
 Give a reason for your answer. 
 
 10. Are intermolecular spaces greater in water or in steam ? Give 
 a reason for your answer. 
 
 11. Considered with reference to the three conditions of matter, 
 are cohesion and heat cooperative, or antagonistic ? 
 
 12. Why can you not blow a soap-bubble with pure water ? 
 
 13. Tell how, with two pieces of glass and a plate of water, you 
 can produce a hyperbolic curve. 
 
 14. Upon what property do most of the characteristic properties of 
 matter depend? Name five universal and three characteristic prop- 
 erties of matter. Define inertia. 
 
 15. State definitely how you could separate a solution of loaf-sugar 
 from a solution of gum-arabic with which it was mixed. What is the 
 name of the process employed? After such separation, how could you 
 separate the sugar from its water of solution ? 
 
 16. Find out how many pounds you weigh. Express that weight 
 in kilograms. 
 
 17. State the kinetic theory of gases. 
 
 18. Does the number of steps that a man takes in traveling a 
 mile vary directly or inversely with the length of the steps ; i.e., does 
 
 nccl or ncc- ? 
 
 19. If No. 27 spring-brass wire breaks under a load of 15 pounds, 
 calculate the breaking strength of No. 25 brass wire. (See table of 
 wire-gauge numbers in the appendix.) 
 
 20. If No. 27 spring-brass wire has a breaking strength of 15 pounds, 
 and No. 30 annealed iron wire one of 5 pounds, compute the ratio be- 
 tween the tenacities of spring-brass and of annealed iron. 
 
THE THREE CONDITIONS OF MATTER. 55 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Draughtsman's triangle; proportional 
 dividers ; cardboard ; Castile soap ; glycerin ; glass funnel ; rubber 
 tubing ; clay pipe ; a good balance that weighs to centigrams, and has 
 a centigram u rider ; " a silver coin ; nitric acid ; salt ; ammonia water. 
 
 1 . Press one side of the triangle firmly against the edge of a ruler 
 resting on a sheet of paper. Trace a pencil line along one of the 
 other sides of the triangle. Without allowing the ruler to move, 
 slide the triangle along its edge, and trace another line along the other 
 edge, as before. In like manner draw several more lines, all of which 
 will be parallel. 
 
 2. Draw AB, a line 7.3 cm. long. Divide it into 5 equal parts. 
 From A draw an indefinite straight line, AX, making an angle of 30 
 or 40 degrees with AB. Set the dividers to any convenient length, 
 say 2 cm., and, measuring from A, lay off on AX as many equal 
 distances as the number of parts into which AB is to be divided ; i.e., 
 5 such equal distances. Mark these equidistant points on AX, in 
 succession, a, b, c, d, and e. Draw the straight line Be. Using the 
 triangle and rule as in Exercise 1, draw lines through d, c, b, and a, 
 parallel to Be. These parallel lines will divide AB into 5 equal 
 parts, as required. With the dividers, test the equality of the several 
 parts of AB. 
 
 3. Divide a line 7 cm. long into 3 equal parts. Set the index of the 
 proportional dividers at the division on the scale for thirds. Open 
 the dividers until the points of the longer legs rest upon the ends of 
 the given line. The distance between the points of the shorter legs 
 may be laid off in succession from one end of the given line, which 
 will thus be divided into thirds, as required. 
 
 4. Carefully heat a tumbler, and half fill it with boiling water. 
 Cover it with cardboard. Invert a second 
 
 tumbler over the first. Watch the apparatus 
 for a few minutes. If you notice any change 
 in the appearance of the upper tumbler, find 
 out whether it is due to a change in the inner 
 or the outer surface of the glass. What prop- 
 erty of the cardboard is thus illustrated ? 
 
 5. Make of No. 24 iron wire a skeleton of a 
 square pyramid with edges 5 cm. long, and 
 
 attach a handle, as shown in Fig. 33. Also make two wire rings 
 
56 SCHOOL PHYSICS. 
 
 6 cm. in diameter and with wire handles. Make a soap-bubble solu- 
 tion as follows : Dissolve 10 g. of Castile soap, in fine shavings, in 
 400 cu. cm. of warm water, recently boiled, shaking the mixture from 
 time to time. When the soap is dissolved, allow the solution to 
 stand for several hours. Pour off the clear liquid, and to it add 
 250 cu. cm. of good glycerin, shaking the two thoroughly together. 
 
 (a) Slip a piece of rubber tubing over the shank of a glass funnel 
 about 10 cm. across the top. Dip the edges of the funnel into the 
 solution, catch a film, and blow as large a bubble as you can. 
 
 (&) Blow a bubble with a common clay pipe. Detach it from the 
 pipe, and catch it on one of the iron rings. Bring the other ring into 
 contact with the bubble on the other side, and draw the bubble into 
 cylindrical form. 
 
 (c) Immerse the pyramidal frame into the solution, and try to 
 secure a film on each side, thus forming a hollow, regular penta- 
 hedron. 
 
 6. Weigh accurately a clean United States silver coin, which is an 
 alloy containing ten per cent, of copper. Place two or three drops of 
 strong nitric acid on the coin, and allow it to stand until the action of 
 the acid on the coin seems to cease. Wash the coin thoroughly in a 
 tumbler of pure water. Measure the water in the graduate (cubic 
 centimeters), and determine the number of drops in a cubic centi- 
 meter. Divide this water into two equal parts. To one part, add a few 
 drops of a strong solution of common salt (brine) ; the milky appear- 
 ance indicates the presence of a silver compound. To the other part 
 of the water, add a few cubic centimeters of ammonia water ; the blue 
 tint indicates the presence of a copper compound. Weigh the coin 
 again, and ascertain how much of it was eaten off. Compute the 
 weight of silver and of copper in each drop of the measured liquid. 
 
CHAPTER II. 
 
 MECHANICS: MASS PHYSICS. 
 I. MOTION AND FORCE. 
 
 53. Mechanics is the branch of physics that treats of 
 forces and their effects. 
 
 (a) Mechanics is commonly divided into kinematics and dynamics, 
 and the latter into statics and kinetics. Some of these distinctions 
 seem "artificial, unscientific, and confused," and they will not be 
 rigidly observed in the present book. 
 
 54. Motion, Velocity, and Acceleration. Motion is 
 change of position. A body lias a motion of translation 
 when any point in it moves along a straight line, and a 
 motion of rotation when any point in it describes a circular 
 arc about some other point in it as a center. Velocity is 
 rate of motion, and its magnitude is expressed by say- 
 ing that it is such a distance in such a time, as ten miles 
 an hour, or one meter a second. Velocity may be uniform 
 or variable. The velocity of a body at any instant is 
 the distance it would pass over in the next unit of time 
 if left wholly free from any outside influence. Thus, 
 the velocity of a falling body at the end of the third 
 second of its fall is the distance it would pass over in the 
 
 fourth second if it could be freed from the attraction of 
 
 57 
 
58 SCHOOL PHYSICS. 
 
 the earth and the resistance of the air. A variable velocity 
 is accelerated or retarded. The change of velocity per unit 
 of time (i.e., the rate of change of velocity) is called acceler- 
 ation. Acceleration is positive or negative (+or ) 
 respectively as the velocity is accelerated or retarded. If 
 the acceleration remains constant, the velocity is uniformly 
 accelerated or retarded according to the algebraic sign of 
 the acceleration. 
 
 (a) A body passing over unit of space in unit of time has unit 
 velocity. The velocity per second multiplied by the number of 
 seconds measures the distance traversed in any given time by a body 
 moving with a uniform velocity. Representing these functions by 
 I for distance, v for velocity per second, and t for time counted in 
 seconds, we have 
 
 I = vt. (1) 
 
 From this fundamental formula we derive algebraically the fol- 
 lowing : 
 
 v = -, and t = -. 
 
 t v 
 
 If two of these values are known, they may be substituted in one of 
 these formulas, and the third value obtained thence. If a body moves 
 at the rate of 50 feet per second for 12 seconds, and the distance 
 traversed is desired, formula (1) is applicable : 
 
 l = vt; I = 50 x 12 ; 1 = 600, the number of feet. 
 
 (6) Represent constant acceleration by a. In t seconds, a body 
 starting from rest will have acquired a velocity represented by at. 
 
 v = at. ^ (2) 
 
 This is the formula for a body starting from a state of rest, and hav- 
 ing a uniformly accelerated velocity. Half the sum of the initial and 
 the final velocities is the average velocity. In the case now under 
 consideration, the initial velocity was zero, and the final velocity was 
 at ; therefore, the average velocity of a body starting from rest, and 
 
 gaining a velocity uniformly accelerated for t seconds, is - or \ at. 
 
MOTION AND FORCE. 59 
 
 The average velocity multiplied by the number of time-units equals 
 the distance traversed ; therefore, / = \ at x t, or 
 
 / = *<<. 4^v ( 3 > 
 
 From this formula we derive algebraically the following: 
 a = *l, and i =JH 
 
 Equating the values of t in equations (2) and (3), we may deduce 
 
 
 the following : 
 
 2a 
 
 (c) To find the distance passed over in any particular unit of time, 
 it may be necessary to subtract the distance traversed in t 1 units, 
 from the distance traversed in t units, the whole time. Representing 
 this distance traversed in a single time-unit by I', we have 
 
 therefore, /' = * a(2 1 - 1). ^^^U^^Jf 5 ) 
 
 (c?) Suppose that a body moving with a uniformly accelerated 
 velocity starts from rest and passes over 7 meters in the first second. 
 How far does it move in the next 3 seconds? If the body moves 
 7 meters in the first second under the conditions stated, its average 
 velocity for that second is 7 meters, and its velocity at the end of 
 that time is 14 meters. All of this velocity is gained in this single 
 second ; hence, a = 14. Starting from rest, it moves 4 seconds-, 
 hence, t = 4. Substituting these values in formula (3), 
 
 'l = %at*rl = % x 14 x 16 = 112, 
 
 the distance passed over in 4 seconds. From this, subtract the dis- 
 tance passed over in the first second, and we have 105, the number of 
 meters passed over in the second, third, and fourth units of time, as 
 called for. This solution illustrates the method of applying physical 
 formulas to the solution of physical problems. 
 
 (e) For want of a fixed point for reference, it is impossible to 
 determine absolute motion. All the members of our solar system have 
 very complicated motions, and the most distant stars seem to have a 
 general drift through space. We are therefore obliged to deal exclu- 
 sively with relative motion. Unless otherwise specified, the motions 
 
60 SCHOOL PHYSICS. 
 
 spoken of in this book are relative to some point on the earth. 
 The point from which motion or its measurement starts is called 
 the origin. 
 
 55. Laws for Accelerated Motion. From the foregoing 
 we derive the following laws for the motion of bodies 
 starting from rest, and having a uniformly accelerated 
 velocity : 
 
 (1) The velocity at the end of any unit of time equals 
 acceleration multiplied by the number of time-units. (For- 
 mula 2.) 
 
 (2) Acceleration equals twice the distance traversed in 
 the first unit of time ; when t = 1, formula (3) becomes 
 
 1 = a. 
 
 (3) The distance traversed in any single unit of time 
 equals half the acceleration multiplied by one less than 
 twice the number of time-units. (Formula 5.) 
 
 (4) The total distance traversed in any given time equals 
 half the acceleration multiplied by the square of the number 
 of time-units. (Formula 3.) 
 
 56. Graphic Representation of Motions. A straight line 
 may definitely represent uniform motion in a straight line, 
 the direction of the line indicating the direction of the 
 motion, and the length of the line representing the mag- 
 nitude of the motion. 
 
 (a) Any convenient unit of length may be chosen to represent any 
 unit of velocity, but, when the scale has been determined, it should 
 not be changed in any given discussion. For example, two motions, 
 one having an easterly direction and a magnitude of 10 yards per 
 second, and the other having a southerly direction and a magnitude 
 of 15 yards per second, may be fully represented by a horizontal line 
 
 2 inches long and a vertical line 3 inches long, the chosen scale of 
 
MOTION AND FORCE. 61 
 
 magnitudes being 5:1; i.e., each inch of the length of either line 
 representing a velocity of 5 yards per second. 
 
 (6) In indicating a line by the letters at its extremities, the order 
 of the letters is that in which the line is to be drawn. 
 
 57.- The Composition of Motions. A motion may be 
 the resultant of two or more component motions, as 
 the motion of a person who is walking on the deck of a 
 moving ship. Under such conditions, several distinct 
 cases may arise. 
 
 (a) When two motions have the same direction, the magnitude of 
 the resultant motion is the sum of the magnitudes of the components, 
 and the direction will be unchanged ; e.g., when the brakeman on a 
 railway freight train that is running from Cleveland to Buffalo, at 
 the rate of 20 miles per hour, runs at the rate of 4 miles per hour 
 along the car-tops toward the locomotive, he is really approaching 
 Buffalo at the rate of 24 miles per hour. 
 
 (ft) When two motions have opposite directions, the magnitude of 
 the resultant motion will be the arithmetical difference of the magni- 
 tudes of the components, and the direction will be that of the greater 
 component ; e.g., when the brakeman above mentioned runs toward 
 the rear of the train, he is approaching Buffalo at the rate of 16 miles 
 per hour. 
 
 (c) When two component motions have different directions, the 
 finding of the resultant involves the application of a principle known 
 as the parallelogram of motions. 
 The lines that properly represent 
 the components are made adja- 
 cent sides of a parallelogram. 
 The diagonal drawn from the 
 angle included between these 
 sides represents the resultant in 
 both magnitude and direction. 
 Thus, let AB and AC represent 
 
 the two component motions. Draw BD and CD to complete the 
 parallelogram. From A, the included angle, draw the diagonal AD. 
 This diagonal will be a complete graphic representation of the re- 
 sultant. The resultant will be greater than the difference between 
 
62 SCHOOL PHYSICS. 
 
 the components, and less than their sum. If each component had a 
 velocity of 25 meters per second, which was represented by lines 
 25 millimeters in length, and AD has a length of 45 millimeters, then 
 the result of compounding the two as indicated will be motion with a 
 velocity of 45 meters per second, and in the direction of A D. 
 
 (rf) When the included angle, as BAC, is a right angle, the re- 
 sultant line is the hypotenuse of a right-angled triangle, and its 
 magnitude will be the square root of the sum of the squares of the 
 components. When the components are equal, and include an angle 
 of 120 degrees, the resultant divides the parallelogram into two equi- 
 lateral triangles, and is equal to either of the components. In other 
 cases the magnitude of the resultant may be determined by a careful 
 construction of the parallelogram and a careful measurement of the 
 diagonal, or, more accurately, by the processes of plane trigonometry. 
 
 (e) When there are three or more components, the resultant of any 
 two may be compounded with a. third ; the resultant thus obtained 
 may be compounded with a fourth component ; etc. The diagonal of 
 the last parallelogram thus constructed will represent the resultant of 
 all the components. 
 
 58. The Resolution of Motions. The converse of the 
 process described in the last paragraph, i.e.. the finding 
 of two or more motions that may be substituted as an 
 equivalent for a given motion, is called the resolution of 
 motions. It most frequently consists in finding the sides 
 of a parallelogram the diagonal of which represents the 
 given motion. 
 
 (a) It is evident that, for a given diagonal, an infinite number of 
 parallelograms may be constructed. 
 
 (6) When the direction of the two components or the magnitude 
 of the two components is prescribed, or the direction and the magni- 
 tude of one of the components are prescribed, the problem becomes 
 determinate. 
 
 59. Momentum. So far, motion has been considered, 
 with reference to its speed and direction. But the result 
 of the action of a force upon a body depends upon the 
 
MOTION AND FORCE. 63 
 
 mass of the body as well as upon its velocity. If m 
 represents the mass of the body, and v its velocity, the 
 product, mv, will represent its quantity of motion. This 
 product is called momentum. 
 
 (a) The momentum of a body having a mass of 20 pounds and a 
 velocity of 15 feet is twice as great as that of a body having a mass of 
 5 pounds and a velocity of 30 feet. 
 
 NOTE. The expression "mass into velocity," or "mass multiplied 
 by velocity," need not disturb the pupil's ideas. The multiplier must 
 be abstract, and the product must be of the same kind as the multipli- 
 cand. Still, by a sort of ellipsis, the abbreviated phrase means the 
 same as the longer one, and is more commonly used. 
 
 CLASSROOM EXERCISES. 
 
 1. Find the momentum of a 500-pound ball moving 500 feet a 
 second. 
 
 2. By falling a certain time, a 200-pound ball has acquired a 
 velocity of 321.6 feet. What is its momentum? 
 
 3. A boat that is moving at the rate of 5 miles an hour weighs 4 
 tons ; another that is moving at the rate of 10 miles an hour weighs 
 2 tons. How do their momenta compare? 
 
 4. What kind of motion is caused by a single, constant force? 
 Illustrate your answer. 
 
 5. A stone weighing 12 ounces is thrown with a velocity of 1,320 
 feet per minute. An ounce ball is shot with a velocity of 15 miles 
 per minute. Find the ratio between their momenta. 
 
 6. An iceberg of 50,000 tons moves with a velocity of 2 miles an 
 hour. An avalanche of 10,000 tons of snow descends with a velocity 
 of 10 miles an hour. Which has the greater momentum? 
 
 7. Two bodies weighing respectively 25 and 40 pounds have equal 
 momenta. The first has a velocity of 60 feet a second. What is the 
 velocity of the other ? 
 
 8. Two balls have equal momenta. The first weighs 100 Kg., and 
 moves with a velocity of 20 m. a second. The other moves with a 
 velocity of 500 m. a second. What is its weight? 
 
 9. Three men start from Cleveland: the first goes 10 miles east- 
 ward; the second goes 15 miles southward; the third goes 18 miles 
 
64 SCHOOL PHYSICS, 
 
 southwesterly. Represent these journeys by lines, using a scale of 
 1 inch to 3 miles, and indicating directions by arrowheads. 
 
 10. A railway train moves at the rate of 40 miles an hour. Express 
 its velocity per second in feet. 
 
 11. If the mean distance of the earth from the sun is 92,390,000 
 miles, and it requires 16 minutes 36 seconds for a ray of light to pass 
 over the diameter of the earth's orbit, what is the velocity of light, 
 expressed in miles per second? 
 
 12. A body at rest receives a constant acceleration of 20 feet per 
 second. How far will it move in 6 seconds, and what will be its 
 velocity at the end of that time ? 
 
 13. Draw a circle and ascertain its area. (See appendix.) 
 
 14. Find the volume of a sphere that will just pass through the 
 circle that you draw. 
 
 15. If the breaking weight of Xo. 27 spring-brass wire is 15 Ibs., 
 determine the diameter of a wire of the same material and quality 
 that can just carry a load of 50 Kg. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. A. protractor; a metric rule; three 
 balls ; an elastic cord. 
 
 1. Draw a circle 3 inches in diameter, and divide its circumference 
 into arcs of 10 degrees each. 
 
 2. Draw a triangle with a base line 7.27 inches long, and with 
 angles at the extremities of this line measuring 23 and 32 degrees 
 respectively. Measure the altitude and compute the area of the 
 triangle. 
 
 3. Two forces, capable of giving a certain body velocities of 35 m. 
 and of 56 m. respectively, act on that body at an angle of 25 degrees 
 with each other. Determine the magnitude of the resultant velocity, 
 and its direction relative to that of the smaller component. (In your 
 drawings represent the direction of each velocity by an arrowhead.) 
 
 4. Resolve a velocity of 50 m. into two components that make with 
 its direction angles of 20 and 45 degrees respectively. Use a scale 
 of 1 : 500. Determine the magnitude of each component. 
 
 5. Resolve a velocity of 20 m. into two components with magni- 
 tudes of 13 and 17 m. respectively. Use a scale of 1 : 200. Determine 
 the angle that each component makes with the given velocity. 
 
 6. Resolve a velocity of 35 m. into two components, one of which 
 
MOTION AND FORCE. 65 
 
 shall have a magnitude of 24.5 m., and make an angle of 63 degrees 
 with the given velocity. Use a scale of 1 : 350. Determine the mag- 
 nitude of the other component and the angle included between the 
 two components. 
 
 7. Draw two lines bisecting each other at right angles, and mark 
 the ends of the lines to represent the cardinal points of the compass, 
 as in a map. From the intersection of the two lines draw another 
 line to represent the velocity of a United States cruiser steaming 
 south of southeast at the rate of 19 miles an hour. Determine the 
 rate of the southerly and the easterly motions of the ship. Record 
 on your diagram the scale used. 
 
 8. Carefully weigh a meter of Xo. 30 copper wire, such as was used 
 in Exercise 10, p. 35, and from the data ascertained in that exer- 
 cise calculate the length of a piece of such wire that would just break 
 under its own weight when suspended by one end. 
 
 9. From the table given in the appendix, ascertain the diameter 
 of Xo. 30 wire. Calculate the breaking strength of a copper rod 
 1 sq. cm. in cross-section, the quality of the copper being the same as 
 that of the wire used in Exercise 8. 
 
 10. On a level table, connect two balls of equal mass by an elastic 
 cord or band. Separate the balls until the cord has been stretched to 
 about double its ordinary length, and mark the positions of the balls. 
 Release the balls simultaneously, and mark the place where they 
 meet. If they meet midway between their positions as first marked, 
 show that the given force has produced equal momenta in the two 
 baUs. 
 
 11. Repeat Exercise 10, using balls one of which weighs twice as 
 much as the other. If one ball moves twice as far as the other, show 
 that 1 = 21'; v = 2v' ; mv = 2mv' = mV. 
 
 60. Laws of Motion. The following propositions, 
 known as Newton's Laws of Motion, are so important, 
 and so famous in the history of physical science, that they 
 ought to be remembered by every student : 
 
 (1) Every body continues in its state of rest or of uniform 
 motion in a straight line unless compelled to change that 
 
 state by an external force. 
 5 
 
66 SCHOOL PHYSICS. 
 
 (2) Every change of motion (momentum) is in the direc- 
 tion of the force impressed, and is proportionate to it. 
 
 (3) Action and reaction are equal and opposite in direc- 
 tion. 
 
 61. First Law of Motion. The first law of motion 
 results directly from inertia, and suggests the following 
 definition : Force is that which changes or tends to change 
 a body's state of rest or motion. 
 
 (a) It is impossible to furnish perfect examples of this law, because 
 all things within our reach or observation are acted upon by some 
 external force. 
 
 62. Second Law of Motion. The second law of motion 
 is sometimes given as follows : A given force will produce 
 the same effect, whether the body on which it acts is in motion 
 or at rest ; whether it is acted on by that force alone or by 
 others at the same time. In the law as given by Newton 
 ( 60), the word " motion " is doubtless used in the sense 
 of "momentum." 
 
 (a) The law as given by Newton points out that forces may be 
 compared by comparing the momenta that they produce in equal 
 times. Representing force by /, mass by m, and acceleration by a, 
 we have/= ma. 
 
 If the forces act on equal masses, the changes of momenta will vary 
 with the changes of velocity, i.e., as the acceleration ; hence, the 
 acceleration that a force generates may be used to measure that force 
 (see 106). 
 
 63. Elements of a Force. In treating of forces, we 
 have to consider three things : 
 
 (1) The point of application, or the point at which the 
 force acts. 
 
MOTION AND FORCE. 67 
 
 (2) The direction, or the right line along which it 
 tends to move the point of application. 
 
 (3) The magnitude, or value when compared with a 
 given standard, or the relative rate at winch it is able 
 to produce motion in a body free to move. 
 
 64. Measurement of Forces. It frequently is desirable 
 to compare the magnitudes of two or more forces. That 
 they may be compared, they must be measured; that 
 they may be measured, a standard of measure or unit of 
 force is necessary. Units of force are of two kinds. 
 
 65. The Gravity Unit. A force may be measured by 
 comparing it with the weight of some known quantity or 
 mass of matter. Although the force of gravity varies at 
 different placee, this is a very simple and convenient way, 
 and often answers every purpose. The gravity unit of 
 force is the weight of any standard unit of mass, as the 
 kilogram or pound. 
 
 (a) As the force of gravity exerted upon a given mass is variable, 
 it will not suffice, when scientific accuracy is required, to speak of a 
 force of 10 pounds, but we may speak of a force of 10 pounds at the 
 sea-level at New York City. 
 
 66. The Absolute Unit The absolute unit of force is the 
 force that, acting for unit of time upon unit of mass, will 
 produce unit of acceleration (i.e., change of velocity}. 
 
 The foot-pound-second (F.P.S.) unit of force is the 
 force that, applied to one pound of matter for one second, 
 will produce an acceleration of one foot per second. It is 
 called a poundal. 
 
 The centimeter-gram-second (C.G.S.) unit of force is 
 the force that, acting for one second upon a mass of one 
 
SCHOOL PHYSICS. 
 
 gram, produces an acceleration of one centimeter per 
 second. It is called a dyne. 
 
 (a) Absolute units are invariable in value. Gravity units may 
 easily be changed to absolute units. At New York the force of 
 gravity acting upon one pound of matter left free to fall 
 will produce an acceleration of 32.16 feet per second for 
 every second that it acts; consequently, at New York a 
 force of one pound equals 32.16 poundals. Since the same 
 force produces an acceleration of 980 centimeters per 
 second, it appears that the weight of a gram at New York 
 corresponds to a force of 980 dynes. 
 
 (6) A force is measured in poundals or dynes by mul- 
 tiplying the number of units of mass moved by the number 
 representing the acceleration produced, only such units 
 being used as are indicated by the initials F.P.S. or C.G.S. 
 respectively. The acceleration may be determined by di- 
 viding the total velocity that the force has produced by 
 the number of seconds that the force has acted. 
 
 (c) The simplest way of measuring a force is to use a 
 dynamometer, of which the spring-balance (Fig. 35) is a 
 familiar example. The dynamometer may be graduated 
 in pounds, grains, poundals, or dynes. 
 
 CLASSROOM EXERCISES. 
 
 1. A railway train 120 yards long moves at the rate of 30 miles 
 an hour. How long will it take to pass completely over a bridge 
 120 feet long? 
 
 2. At the sea-level at New York a force of 25 pounds equals how 
 many poundals? 
 
 3. Under the same conditions, a force of 5 Kg. equals how many dynes? 
 
 4. A poundal equals how many dynes? 
 
 5. Compare the momentum of a 64-pound cannon ball moving 
 with a velocity of 1,300 feet per second, with that of an ounce bullet 
 moving with a velocity of 400 yards per second. 
 
 6. If a beam 3 m. long, 10 cm. wide, and 5 cm. thick, is bent 0.5 cm. 
 by a certain load, how much would a similar beam 4 in. long be 
 depressed by the same load? 
 
 7. What property of matter is illustrated in the removal of dust 
 from a carpet by beating? 
 
 FIG. 36. 
 
MOTION AND FORCE. 69 
 
 67. Graphic Representation of Forces. Forces may be 
 represented by lines, the point of application determining 
 one end of the line, the direction of the force determining 
 the direction of the line, and the magnitude of the force 
 determining the length of the line. 
 
 (a) It will be noticed that these three elements of a force ( 63) 
 are the ones that define a line. By drawing the line as above 
 indicated, the units of force being numerically equal to the units 
 of length, we have a complete graphic representation of the given 
 force. The unit of length adopted in any such representation may 
 be determined by convenience; but, 
 the scale once determined, it must 
 be adhered to throughout the prob- 
 lem. Thus, the diagram represents 
 two forces applied at the point B. 
 These forces act at right angles to 
 each other. The arrowheads indi- 
 
 cate that the forces represented act FIG. 36. 
 
 from B toward A and C respec- 
 tively. The force that acts in the direction, BA, being 20 Ibs., and 
 the force acting in the direction, SC, being 40 Ibs., the line, BA, must 
 be one-half as long as BC. The scale adopted being 1 mm. to the 
 pound, the smaller force will be represented by a line 2 cm. long, 
 and the greater force by a line 4 cm. long. 
 
 68. Resultant Motion. Motion produced by the joint 
 action of two or more forces is called resultant motion. 
 
 The single force that will produce an effect like that of 
 the component forces acting together is called the result- 
 ant. The single force that, acting with the component 
 forces, will keep the body at rest is called the equilibrant. 
 The resultant and the equilibrant of any set of component 
 forces are equal in magnitude, and opposite in direction. 
 
 The point of application, direction, and magnitude of 
 each of the component forces being given, the direction 
 
70 SCHOOL PHYSICS. 
 
 and magnitude of the resultant force are found by a 
 method known as the composition of forces. 
 
 Experiment 45. Suspend two similar spring-balances, A and B, 
 from any convenient support, as shown in Fig. 37. From the wooden 
 
 rod carried by their hooks, suspend 
 a known weight. Be sure that the 
 dynamometers hang vertical, and 
 therefore parallel. Record the 
 readings of the dynamometers. 
 Carefully measure the distances, 
 CD and DE, and record them. 
 E If the dynamometers are accurate, 
 
 the work has been carefully done, 
 and the weight of the rod is incon- 
 siderable, the results should show 
 that 
 
 W = A + B, and that - = 
 B CD 
 
 If the weight of the rod is considerable, place the rod in the hooks, 
 and notice the readings of the dynamometers. Then hang the weight 
 from the rod, and represent the increase in the readings by A and B. 
 The result should be as given above. 
 
 69. Composition of Forces. Under composition of 
 forces there are several cases, of which the more im- 
 portant are the following : 
 
 (1) When the component forces act in the same direction 
 and along the same line. The magnitude of the resultant 
 is then the sum of the given forces. Example : Rowing a 
 boat down-stream. 
 
 (2) When the component forces act in opposite directions 
 and along the same line. The magnitude of the resultant is 
 then the difference between the given forces. Motion will 
 be produced in the direction of the greater force. Ex- 
 ample : Rowing a boat up-stream. 
 
MOTION AND FORCE. 71 
 
 (3) The resultant of two forces that act in the same direc- 
 tion along parallel lines has a magnitude equal to the sum of 
 the magnitudes of the components, and its point of applica- 
 tion divides the line joining the points of application of the 
 components inversely as the magnitudes of said components. 
 This principle is illustrated by Experiment 45. 
 
 (4) When two equal parallel forces act at different points 
 on a body and in opposite directions, the arrangement consti- 
 tutes what is called a couple. It produces rotary motion, and 
 the components can have no resultant. 
 
 (a) If a magnetic needle is placed in an east and west position, 
 the attraction of the north magnetic pole of the earth attracts one 
 end of the needle and repels the other with equal parallel forces, the 
 effect of which is to turn the needle upon its pivot until it is in a 
 north and south position. The attraction and the repulsion constitute 
 a couple. 
 
 (5) When the component forces have a given point of 
 application (i.e., when they are " concurring forces"} and 
 act at an angle with each other, as when a boat is rowed 
 across a stream, the resultant may be ascertained by the 
 "parallelogram of forces." 
 
 70. Parallelogram of Forces. In the diagram, let AB 
 and AC represent two forces 
 acting upon the point, A. 
 Draw the two dotted lines to 
 complete the parallelogram. 
 
 From A, the point of applica- \ ^\\ 
 
 tion, draw the diagonal, AD. c FJQ 
 
 This diagonal will be a com- 
 plete graphic representation of the resultant. If two forces, 
 such as those represented in the diagram, act simultane- 
 
72 
 
 SCHOOL PHYSICS. 
 
 ously upon a body at A, that body will move over the 
 path represented by AD, and come to rest at D. The 
 process is very similar to the composition of motions 
 mentioned in 57. 
 
 (a) When the two component forces act at right angles to each 
 other, the determination of the numerical value of the resultant is 
 like that of finding the length of the hypotenuse of a right-angled 
 triangle ; it is the square root of the sum of the squares of the two 
 components. (See 57, d.) 
 
 Experiment 46. The principle of the parallelogram of forces may 
 be verified as follows : H and K represent two pulleys that work with 
 very little friction. Fix them to the frame of the blackboard. Knot 
 together three silk cords ; pass two of them over 
 the pulleys ; suspend three weights, P, Q, and 
 R, as shown in the figure. R must be less than 
 the sum of P and Q. When the apparatus has 
 come to rest, take the points, A and B, so that 
 AO : BO : : P : Q. Complete the parallelogram, 
 A OBD, by drawing lines upon the board. Draw 
 the diagonal, OD. It will be found by meas- 
 urement that AO : OD : : P : R ; or that 
 BO : OD : : Q : R. Either equality of ratios 
 affords the verification sought. 
 
 FIG. 3<). 
 
 Experiment 47. Modify the experiment by supporting two spring- 
 balances, A and B, from P and S, two nails in the frame of the black- 
 board. Hook them with a third dynamometer, C, into a small ring, 
 Z, as shown in Fig. 40. Pull steadily on / in some downward direc- 
 tion. Mark on the board the centers of the rings, Z and /, and record 
 the readings of the three dynamometers. Remove the apparatus, and 
 through the points indicated draw on the board the lines, ZP, ZS, 
 and ZI. Using any convenient scale, lay off the lines, ZE, ZA, and 
 ZI, proportional to the readings of the respective dynamometers. 
 Complete the parallelogram, ZETA. Draw the diagonal, ZT, meas- 
 ure its length, and determine the magnitude that it represents accord- 
 ing to the scale adopted. If the work has been accurately done, 
 ZI and ZT will be equal in value, and form a straight line. ZT 
 
MOTION AND FORCE. 
 
 73 
 
 is the resultant, and Zl is the equilibrant, of the components, ZE 
 and ZA. Place the apparatus horizontal and repeat the work. 
 
 FIG. 40. 
 
 71. Composition of More than Two Forces. If more 
 than two forces concur, the re- 
 sultant of any two may be com- 
 bined with a third, their resultant 
 with a fourth, and so on. The 
 last diagonal will represent the 
 resultant of the given forces. 
 As is indicated by Fig. 41, it is 
 not necessary that all of the forces act in the same 
 plane. 
 
 FIG. 41. 
 
74 SCHOOL PHYSICS. 
 
 72. Resolution of Forces. The operation of finding the 
 components to which a given force is equivalent is called the 
 resolution of forces. It is the converse of the composition 
 of forces. Represent the given force by a line. On this 
 line as a diagonal, construct a parallelogram. An infinite 
 number of such parallelograms may be constructed with 
 a given diagonal. Other conditions must be added to 
 make the problem definite. (See 58, 5.) 
 
 (a) By way of illustration, let it be required to resolve a force of 
 20 pounds into two components that act at right angles to each other, 
 one of them to be a force of 12 pounds. The problem is to construct 
 a rectangle one side of which shall measure 12 units, and the diagonal 
 of which shall measure 20 units. Draw a vertical and a horizontal 
 line intersecting at A. From A, measure off 12 units on the vertical 
 line, thus securing the point, B. From B, draw a line, BX, parallel 
 to the horizontal line that passes through A. From A as a center, 
 and with a radius equal to 20 units, describe an arc cutting BX at 
 a point, which mark C. From C, draw a line parallel to AB, and 
 intersecting the horizontal line drawn through A at a point, which 
 mark D. AB and AD will be the components sought. 
 
 73. Third Law of Motion. Examples of the third law 
 of motion are very common. When we strike an egg 
 upon the table, the reaction of the table breaks the egg. 
 The action of the egg may make a dent in the table. The 
 reaction of the air, when struck by the wings of a bird, 
 supports the bird if the action is greater than the weight. 
 The oarsman urges the water backward with the same 
 force that he urges his boat forward. In springing from a 
 boat to the shore, muscular action tends to drive the boat 
 adrift ; the reaction, to put the passenger ashore. These 
 illustrations suggest the idea that every action of a force 
 develops another force opposite in direction, so that two 
 forces, instead of one, are apparently in action. 
 
MOTION AND FORCE. 
 
 75 
 
 Reaction. 
 
 Experiment 48. Make a railway of two wooden strips 1^ inches 
 by i inch, and about 6 feet long, fastened together by three or five 
 crosspieces, as shown in Fig. 42. The distance between the rails 
 should be about an inch. Place the railway on a board, and fasten 
 down the middle crosspiece with a screw. Spring up the ends, and 
 support them by books or wooden blocks. At the toy shop, get 
 several large glass marbles, or other elastic balls, and place them 
 on the middle of the railway. Bring one ball to the highest point of 
 the track, and let it roll down against the others. Ball No. 1 gives its 
 motion to No. 2, and comes to rest ; No. 2 gives it to No. 3, and in 
 
 FIG. 42. 
 
 turn comes to rest. The energy is thus passed through the line to 
 No. 7, which is driven some distance on the up grade, as to the posi- 
 tion shown by the dotted line at 8. From 8, this ball rolls down 
 grade, and passes its energy along the line, forcing No. 1 up the grade 
 to a lesser distance than before. The balls will repeat their motions 
 several times, until they are finally 
 brought to rest by friction, etc. 
 
 Experiment 49. Repeat Experi- 
 ment 48 after replacing the middle 
 ball by a lead ball of the same size. 
 
 Experiment 50. This action of 
 ivory or glass balls is due to the fact 
 that they are elastic, and are flattened 
 by the blow. To show that this is so, 
 smear a flat stone or iron plate with 
 paint. Before the paint becomes dry, 
 place one of the glass balls on the 
 smeared surface, and notice the size FlG ^ 
 
 of the round spot thus made. Then 
 
 drop the ball from a height of several inches, and notice that the 
 spot is larger* than before. 
 
76 
 
 SCHOOL PHYSICS. 
 
 74. Elasticity and Reaction. The effects of action and 
 reaction are modified largely by elasticity, but never so as 
 to destroy their equality. 
 
 (a) From any convenient support, as the door-frame, hang, by 
 strings of equal length, two clay balls of equal mass, or two such bags 
 
 of shot or of sand, so that they 
 will just touch each other. If 
 one is drawn aside and let fall 
 against the other, both will move 
 forward, but only half as far as 
 the first would had it met no 
 resistance. The gain of momen- 
 tum by the second is due to the 
 action of the first. It is equal to 
 the loss of momentum by the 
 first, which loss is due to the re- 
 action of the second. 
 
 (6) If two glass or ivory balls, 
 which are elastic, are similarly 
 placed, and the experiment re- 
 peated, it will be found that the 
 first ball will give the whole of 
 its motion to the second, and re- 
 main still after striking, while 
 the second will swing as far as 
 the first would have done if it 
 had met no resistance. In this 
 case, as in the former, it will be 
 seen that the first ball loses just as much momentum as the second 
 gains. These balls may be suspended by gluing a narrow strip of 
 leather to each, leaving a little loop at the middle of the strip for the 
 fastening of the string. 
 
 75. Reflected Motion is the motion produced in a body by 
 the reaction between it and another body against which it 
 strikes. A ball rebounding from the wall of a house or 
 from the cushion of a billiard table is an example of 
 reflected motion. 
 
 FIG. 44. 
 
MOTION AND FORCE. 77 
 
 76. Law of Reflected Motion. The angle, ABD, in- 
 cluded between the direction of the moving body before it 
 strikes the reflecting surface, and a perpendicular to that 
 surface drawn from the point of contact, is called the angle 
 of incidence. The angle between the perpendicular and 
 the direction of the moving body after striking is called 
 the angle of reflection. When the bodies are perfectly elastic, 
 the angle of incidence is equal to the angle of reflection, and 
 lies in the same plane. When the elasticity of the bodies is 
 imperfect, the angle of reflection is greater than the angle of 
 
 incidence. If a glass or ivory ball is shot from A against 
 an elastic surface at B, the center of the semicircle, it will 
 be reflected back to O, making the angles, ABD and CBD, 
 equal. If the ball or the body at B is not perfectly elastic 
 (e.g., if a lead ball is used), the path of the ball after reflec- 
 tion will make with the normal line, BD, an angle greater 
 than ABD. 
 
 77. Curvilinear Motion. When a ball at the end of a 
 string is whirled around the hand, there is a consciousness 
 of a pull on the string. A moment's observation and 
 reflection impress one with the fact that the ball is de- 
 flected by the tension of the string from the rectilinear 
 path which it tends to follow in accordance with the first 
 
78 SCHOOL PHYSICS. 
 
 law of motion, and is thus constrained to move in a curved 
 line. There are evidently two forces involved in the pro- 
 duction of such a motion, a tangential component, which 
 sets the ball in motion ; and a centripetal component, as 
 exhibited in the tension of the string. 
 
 The resistance offered by the body to its deflection from 
 a rectilinear path is due to its inertia, and is commonly 
 called by the ill-chosen name " centrifugal force." From 
 this point of view, centrifugal force may be defined as the 
 reaction of a moving body against the force that makes it 
 move in a curved path. 
 
 (a) Examples and effects of this so-called centrifugal force maybe 
 suggested as follows: the sling, wagon turning a corner, railway 
 curves, water flying from a revolving grindstone, broken fly-\vlieels, 
 erosion of river-beds, a pail of water whirled in a vertical circle, the 
 inward leaning of the circus horse and rider, the centrifugal drying 
 apparatus of the laundry or the sugar refinery, difference between 
 polar and equatorial weights of a given mass, elongation of the 
 equatorial diameter of the earth, etc. 
 
 (ft) " The student cannot be too early warned of the dangerous 
 error into which so many have fallen who have supposed that a mass 
 has a tendency to fly outwards from a center about which it is revolv- 
 ing, and therefore exerts a centrifugal force which requires to be 
 balanced by a centripetal force." Tail. 
 
 78. Measurement of Centrifugal Forces. The laws of 
 centrifugal force may be studied or illustrated by means 
 of the whirling table and accompanying apparatus, some 
 of which is represented in Fig. 46. It may be shown that 
 
 Centrifugal Force = 
 
 in which m represents the mass of a body moving in a cir- 
 cular path ; v, its velocity ; and r, the radius. Of course, 
 the numerical result will represent absolute units of force. 
 
MOTION AND FORCE. 
 
 79 
 
 Tliis formula justifies the following laws of centrifugal 
 force : 
 
 (1) The force varies directly as the mass. 
 
 (2) The force varies directly as the square of the velocity 
 (radius being constant). 
 
 (3) The force varies inversely as the radius (velocity 
 being constant). 
 
 FIG. 46. 
 
 CLASSROOM EXERCISES. 
 
 1. Represent graphically the resultant of two forces, 100 and 150 
 pounds respectively, exerted by two men pulling a weight in the same 
 direction. Determine its value. 
 
 2. In similar manner, represent the resultant of the same forces 
 when the men pull in opposite directions. Determine its value. 
 
 3. Suppose an attempt is made to row a boat at the rate of 4 miles 
 an hour directly across a stream flowing at the rate of 3 miles an 
 hour. Determine the direction and velocity of the boat. 
 
 4. A flag is drawn steadily downward 64 feet from the masthead of 
 a moving ship. During the same time, the ship moves forward 24: feet. 
 Represent the direction and length of the actual path of the flag. 
 
 5. A sailor climbs a mast at the rate of 3 feet a second. The ship is 
 sailing at the rate of 12 feet a second. Over what space does he 
 actually move during 20 seconds? 
 
 6. A foot-ball simultaneously receives three horizontal blows, one 
 from the north, having a force of 10 pounds ; one from the east, having 
 
80 SCHOOL PHYSICS. 
 
 a force of 15 pounds ; and one from the southeast, having a force of 
 25 pounds. Determine the direction of its motion. 
 
 7. Why does a cannon recoil or a shot-gun "kick" when fired? 
 Why does not the velocity of the gun equal the velocity of the 
 ball? 
 
 8. If the river mentioned in Exercise 3 is a mile wide, how far 
 did the boat move, and how much longer did it take to cross than if 
 the water had been still ? 
 
 9. A plank 12 feet long has one end on the floor, and the other end 
 raised 6 feet. A 50-pound cask is being rolled up the plank. Resolve 
 the gravity of the cask into two components, one perpendicular to 
 the plank, to indicate the plank's upward pressure ; and one parallel 
 to the plank, to indicate the muscular force needed to hold the cask in 
 place. Find the magnitude of this needed muscular force. 
 
 10. To how many poundals is a force of 60 pounds equal ? 
 
 11. To how many dynes is a force of 60 kilograms equal? 
 
 12. What is meant by a force of 10 pounds? To how many 
 poundals is it equal ? 
 
 13. A force of 1,000 dynes acts on a certain mass for one second, and 
 gives it a velocity of 20 cm. per second. What is the mass in grams ? 
 
 Ans. 50. 
 
 14. A constant force, acting on a mass of 12 g. for one second, gives 
 it a velocity of 6 cm. per second. Find the force in dynes. 
 
 15. -A force of 490 dynes acts on a mass of 70 g. for one second. 
 What velocity will be produced? Ans. 7 cm. per second. 
 
 16. Show how the principle of resolution of forces and the prin- 
 ciple of the 'couple may be applied to explain the action of a 
 windmill. 
 
 17. Determine, in absolute units, the centrifugal force of a 10- 
 pound body moving with a velocity of 20 feet per second, in a circle 
 of 5 feet radius. Ans. 800 poundals. 
 
 18. Without drawing a diagram, find the numerical value of the 
 resultant of two concurrent forces of 5 Kg. and 12 Kg. respectively, 
 acting at right angles to each other. 
 
 19. Resolve a force of 30 pounds into two component forces acting 
 at a right angle, one of them being a force of 18 pounds. 
 
 20. Determine the point of application of the resultant of two 
 forces of 8 and 11 pounds respectively, acting in the same direction 
 along parallel lines 57 inches apart. 
 
 21. A railway train is moving southeastward at the rate of 30 miles 
 
MOTION AND FORCE. 81 
 
 an hour, (a) How fast is it moving eastward? (&) How fast is it 
 moving southward? 
 
 22. A mass of 10 Kg. moves with a velocity of 20 m. a second in a 
 circular path with a radius of 10 m. What is its centrifugal force? 
 
 23. (a) What will be the effect upon the motion of a boat if air 
 is blown directly against the sail from a huge bellows placed astern ? 
 (6) What will be the effect if the air is drawn in by a valve under 
 the bellows, and forced out directly backward ? 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Two small pulleys that work with very 
 little friction; two good spring-balances; a fish-line or other stout, 
 flexible cord ; a sheet of paper ; four thumb-tacks ; boards ; hammer 
 and nails ; brace and bits ; hand-saw. 
 
 1. Bore a small hole through a meter stick at the middle of its 
 length and near one edge. Through this hole, pass a wire nail of 
 such size that it may carry a good load and yet allow the stick to 
 turn freely upon it as an axis. Make a stout wire clevis that shall 
 come down on each side of the stick and support each end of the nail 
 without rubbing the sides of the stick. Through the upper part of 
 the clevis, pass the hook of a spring-balance, and support the dyna- 
 mometer so that the stick may hang at an elevation convenient for ob- 
 servation. As the stick hangs in the clevis with the hole near its upper 
 edge, load one end of it with putty until the stick hangs horizontal. 
 Note the reading of the dynamometer. Over each end of the stick, 
 slip a loose single loop of silk thread, the weight of which may be 
 ignored; from them hang unequal but known weights. Shift the 
 position of the weights until the loaded apparatus hangs in equilib- 
 rium. Note the distance of each loop from the middle of the stick, 
 and the reading of the dynamometer. Determine the ratio between 
 the sum of the two suspended weights and the difference between the 
 two observed readings of the dynamometer. Using the scale of 1 to 
 10, draw a horizontal line to represent the meter stick, and mark its 
 middle point F. On this line, represent the points of application of 
 the two suspended weights, and mark them P and W. Using any 
 convenient scale, draw lines from P and W, and place arrowheads to 
 represent the forces acting at those points. In similar manner, draw 
 and mark a line to represent the equilibrant of those forces. Add a 
 reference to the paragraph of this book that treats of the subject 
 chiefly illustrated by this exercise. 
 6 
 
82 SCHOOL PHYSICS. 
 
 2. Two forces pulling toward the east act on two points of a rigid 
 body 5 feet asunder. Represent this body by a vertical line, on 
 which locate the two points of application, using the scale of an inch 
 to the foot. One of these forces has a magnitude of 7 pounds, and the 
 other has one of 11 pounds. Using the scale of a half-inch to the 
 pound, draw graphic representations of these forces, their resultant 
 and their equilibrant. 
 
 3. Arrange apparatus as shown in Fig. 39. Make P equal 5 pounds, 
 and Q equal 7 pounds. Add unknown weights at li until the cords, 
 OH and OK, include an angle that is acute or not very obtuse. Back 
 of the cords around 0, support a board of such thickness that the 
 face of the board shall j ust touch the cords. With thumb-tacks, fasten 
 a sheet of paper to this board ; and on the paper, with rule and pencil, 
 draw lines from in the direction of H, K, and R. Using the scale 
 of a half-inch to the pound, represent forces acting from along the 
 lines, OH and OK, with magnitudes of 5 and 7 pounds respectively. 
 Complete the parallelogram, and draw the diagonal, OD. Lay off from 
 0, and on the line, OR, a distance equal to OD. Which line on your 
 paper represents the gravity of the unknown weight? From the 
 length of this line compute the mass of R. Place R on the balance 
 or hang it from the spring-balance, and thus determine its mass by 
 weighing. Compare these two results. Does OD form a continua- 
 tion of the straight line, ROf If it does not, your work has been ill 
 done. If ROD is a straight line, what does OD represent? 
 
 4. Provide two strings, each about a foot long. Tie one end of 
 one string to the ring of a spring-balance. Tie one end of the other 
 string to the ring of another spring-balance. By these strings, sup- 
 port the dynamometers from nails driven at points about one corner 
 of the blackboard, and corresponding more or less closely to H and K 
 in Fig. 39. Cut off two pieces of cord, each about 2 feet long. 
 Tie a small loop that will not slip at each end of each cord. Pass the 
 first cord through the loop at one end of the second cord. Pass the 
 loops at the ends of the first cord over the hooks of the two dyna- 
 mometers. To the free end of the second cord, attach a weight of 
 10 pounds. The loop at the upper end of the cord that carries the 
 weight will slip along the length of the cord that joins the dyna- 
 mometers until the apparatus is in equilibrium. Place the board carry- 
 ing a fresh sheet of paper as was done in the last exercise. On the 
 paper, mark three intersecting lines as indicated by the strings between 
 the dynamometers and the load, and mark their common point of 
 
WORK AND ENERGY. 83 
 
 intersection 2T, as in Fig. 40. Prolong the vertical line upward 5 
 inches to a point, which mark T. Construct the parallelogram of 
 which ZT is a diagonal, and the two sides of which, meeting at Z, 
 coincide with the lines already drawn upon the paper. Mark the 
 left-hand corner of the parallelogram E, and the opposite corner 
 A . What does Z T represent ? What is the scale adopted ? On that 
 scale determine the magnitudes represented by the lengths of ZE 
 and ZA. Compare these magnitudes with the readings of the 
 dynamometers, and determine the magnitude of the error of your 
 work. Record a reference to the paragraph in the text-book illus- 
 trated and approximately verified by this exercise. 
 
 5. Change the point of support of one of the dynamometers so as 
 to increase the angle included between the component forces. Repeat 
 the experiment. 
 
 6. Change the point of support of one of the dynamometers so as 
 to make the angle between the components very acute. Repeat the 
 experiment. Compare the diagram made with those made in Exer- 
 cises 4 and 5. 
 
 7. Without using a protractor, lay off an angle of 60. 
 
 8. Two forces, of 7 and 16 units respectively, have a resultant of 
 21 units. By construction and measurement, determine the angle 
 between the two components. 
 
 II. WORK AND ENERGY. 
 
 79. Work. In physical science, the word "work" 
 signifies the overcoming of resistance of any kind. Work 
 implies a change of position, and is independent of the 
 time taken to do it. When a force causes motion through 
 space, i.e., when it moves a body, it is said to do work on 
 that body. When the expansive force of steam presses 
 against the piston of an engine and overcomes the resist- 
 ance, i.e., when it moves the piston, it does work. 
 
 (a) A man who is supporting (not lifting) a heavy weight may be 
 putting forth great effort, but he is not doing work in the scientific 
 sense of that expression. 
 
84 SCHOOL PHYSICS. 
 
 80. Units of Work. It is often necessary to represent 
 work numerically ; hence the necessity for a unit of meas- 
 urement. Four work-units are in use ; viz., the foot-pound 
 and the kilogrammeter (which are gravitation units), and 
 the foot-poundal and the erg (which are absolute units). 
 
 (1) The foot-pound is the amount of work required to 
 raise one pound one foot high against the force of gravity. 
 It is the unit in common use among English-speaking 
 engineers. See Appendix 1. 
 
 (2) The kilogrammeter is the amount of work required to 
 raise one kilogram one meter high against the force of gravity. 
 
 (3) The foot-poundal is the amount of work done by a 
 force of one poundal in producing a displacement of one foot. 
 It is numerically equal to the foot-pound multiplied by 
 the acceleration of gravity expressed in feet per second ; 
 thus, at New York, a foot-pound is equivalent to 32.16 
 foot-poundals. 
 
 (4) The erg is the amount of work done by a force of one 
 dyne producing a displacement of one centimeter. It is the 
 unit in common use among scientists. Since there are 
 980,000 dynes in the weight of one kilogram of matter at 
 New York, a kilogrammeter there equals 98,000,000 ergs. 
 A foot-poundal is equivalent to 421,402 ergs ; a foot-pound 
 is equivalent to 32.16 times that many ergs. 
 
 (a) To get a numerical estimate of work done, we multiply the 
 number of units of force by the number of units of displacement : 
 
 Work done =fi. 
 
 Since the resistance overcome is numerically equal to the force acting, 
 the work done may be computed by multiplying, in a similar manner, 
 the resistance by the space : 
 
 Work done wl. 
 
WORK AND ENERGY. 85 
 
 In this formula, w represents the resistance ; and Z, the length or dis- 
 tance. When the body is simply lifted against the force of gravity, 
 w represents weight. A weight of 25 pounds raised 3 feet, or one 
 of 3 pounds raised 25 feet, represents 75 foot-pounds. A weight of 
 15 kilograms raised 10 meters represents 150 kilogram meters. 
 
 81. Activity and Horse-Power. In measuring work 
 done, no consideration is given to the time taken. In 
 considering an engine or other agent that is to do the 
 work, the time required is a very important thing. The 
 activity of an agent is the rate at which it can do work, and 
 is measured by the work it can do in unit time. The unit in 
 most common use for the measurement of activity is the horse- 
 power. It represents the ability to do 550 foot-pounds per 
 second. 
 
 TT p _ pounds x feet 
 ~~ 550 x seconds' 
 
 (a) The practical unit of electrical activity is the watt, which is^ 
 equal to 10 7 ergs per second. One horse-power equals 746 watts, or 
 746 x 10 7 ergs per second. 
 
 82. Energy is the power of doing work, and is possessed 
 by bodies by virtue of work having been done upon them. 
 If a falling cannon ball can overcome a greater resistance 
 than a flying base-ball, it has more energy ; more work 
 was done upon it. 
 
 The two fundamental ideas with which physics concerns 
 itself are matter and energy. 
 
 (a) " We are acquainted with matter only as that which may have 
 energy communicated to it from other matter. Energy, on the other 
 hand, we know only as that which, in all natural phenomena, is con- 
 tinually passing from one portion of matter to another. It cannot 
 exist, except in connection with matter." Maxwell. 
 
86 SCHOOL PHYSICS. 
 
 83. Types of Energy. It is a general and familiar fact 
 that bodies in motion can do work on other bodies. A 
 camion ball falling toward the earth has energy, because 
 of its mass and its velocity. Even before it began to fall, 
 it had a power of doing work, because work had been done 
 in lifting it into its elevated position. Thus there are 
 two types of energy, which may be designated as energy 
 of motion and energy of position. Energy of motion is 
 called kinetic energy ; energy of position is called potential 
 energy. Energy that is not kinetic is potential. 
 
 (a) A falling weight or running stream possesses energy of motion ; 
 it is able to overcome resistance by reason of its mass and velocity. 
 On the other hand, before the weight began to fall, it had the power 
 of doing work by reason of its elevated position with reference to the 
 earth. When the water of the running stream was at rest in the lake 
 among the hills, it had a power of doing work, an energy that was 
 not possessed by the waters of the pond in the valley below. In 
 either case, work had to be done to lift the body into its elevated 
 position, and thus to endow it with potential energy. In bending a 
 bow, or in elongating the spring of a dynamometer, or in winding up 
 a watch, work is performed in distorting the bow or the spring, and, 
 by virtue of this distortion, the instruments possess potential energy. 
 
 (6) Kinetic and potential energies are interconvertible. Imagine 
 a ball thrown upward with a velocity that will keep it in motion for 
 two seconds. At the end of one second it has lost some of its initial 
 velocity, and hence some of its kinetic energy ; but it has gained an 
 elevated position, and has therefore acquired some potential energy. 
 This -potential energy just equals the loss of kinetic energy, and exists 
 by virtue of that loss. At the end of another second it has no ve- 
 locity, and, therefore, no kinetic energy. But the energy with which 
 the ball began its upward flight has not been annihilated ; it has been 
 wholly converted into potential energy. If at this moment the ball 
 is caught, all of the original kinetic energy may be kept in store as 
 potential energy. 
 
 (c) If we ignore the disappearance (not loss) of the energy 
 expended in overcoming the resistance of the air, the ball would, 
 when permitted to fall, reach the level from which it started with its 
 
WORK AND ENERGY. 
 
 87 
 
 original velocity and kinetic energy. At the start, at the finish, or at 
 any intermediate point of either its ascent or descent, the sum of the 
 two types of energy is the same. It may be all kinetic, all potential, 
 or partly both, but the sum of the two is constant. 
 
 (rf) The pendulum affords a good and simple illustration of kinetic 
 and potential energy, their equivalence and convertibility. When the 
 pendulum hangs at rest in a vertical position, as Pa, it has no energy 
 at all. Considered as a mass of mat- 
 ter separated from the earth, it cer- 
 tainly has potential energy; but 
 considered as a pendulum, it has not. 
 If we draw the pendulum aside to b, 
 we raise it through the space, ah; 
 that is, we do work upon it. The 
 energy thus expended is now stored 
 up as potential energy, ready to be 
 reconverted into energy of the kinetic 
 type, whenever we let it drop. As it 
 falls the distance, Aa, in passing from 
 b to a, this reconversion is gradually 
 going on. When the pendulum 
 reaches a, its energy is all kinetic, and just equal to that spent in 
 raising it from a to b. This kinetic energy now carries it on to c, 
 lifting it again through- the space, ah. Its energy is again all poten- 
 tial, just as it was at b. If we could free the pendulum from the 
 resistances of the air and friction, the energy originally imparted to 
 it would swing to and fro between the extremes of all potential and 
 all kinetic; but, at every instant, and at every point of the arc 
 traversed, the total energy would be an unvarying quantity, always 
 equal to the energy originally exerted in swinging it from a to b. 
 
 Velocity and Energy. 
 
 Experiment 51. Into a pail full of moist clay or stiff mortar, drop 
 a bullet from the height of one yard. Xotice the depth to which the 
 bullet penetrates. Drop the bullet from a height of four yards. It 
 will strike fche clay with twice the velocity ( 107) and penetrate 
 four times as far as it did before. This suggests that perhaps an 
 increase in the velocity of a given body increases the energy of that 
 body more rapidly than it increases the momentum; that the mass 
 being the same, the energy varies as the. square of the velocity ; E cc v 2 . 
 
88 SCHOOL PHYSICS. 
 
 84. Relation of Velocity to Energy. Any moving 
 body can overcome resistance, or perform work ; it has 
 energy. We must acquire the ability to measure this 
 energy. In the first place, we may notice that its defi- 
 nition indicates that it may be measured by the units used 
 in measuring work; i.e., in units of force and displacement. 
 In the next place, we may notice that the direction of the 
 motion is unimportant. A body of given weight and 
 velocity can at any instant do as much work when going 
 in one direction as when going in another. This energy 
 may be expended in penetrating an earth-bank, knocking 
 down a wall, or lifting itself against the force of gravity. 
 Whatever the work actually done, the manner of expend- 
 iture does not change the amount of energy expended. 
 We may therefore find to what vertical height the given 
 velocity would lift the body ( 110), and thus determine 
 its energy in foot-pounds or kilogr ammeters. 
 
 85. Kinetic Energy Measured in Gravitation Units. 
 Representing the weight of a body by w, and the vertical 
 height to which its velocity can carry it by Z, it is evident 
 that the kinetic energy can do wxl units of work. 
 When we come to study the laws of falling bodies, we 
 shall find that 
 
 l =W 
 
 in which g represents the acceleration due to gravity, i.e., 
 32.16 feet or 980 cm. (see 107, c?). Substituting this 
 value of I in the equation given above, we have 
 
 2 
 
 Kinetic Energy = . 
 
WORK AND ENERGY. 89 
 
 If w is measured in pounds and v in feet, this measures 
 the energy in foot-pounds ; if w is measured in kilograms 
 and v in meters, it measures the energy in kilogram- 
 meters. 
 
 (a) In measuring work, we consider resistance and the distance 
 through which it is overcome ; in measuring energy, we consider the 
 force and the distance through which it acts. A foot-pound of energy 
 is the amount of energy that must be expended in doing, or that is 
 capable of doing, a foot-pound of work. Similarly, a kilogrammeter 
 of energy is the amount of energy that must be expended in doing, or 
 that is capable of doing, a kilogrammeter of work. 
 
 86. Kinetic Energy Measured in Absolute Units. We 
 have already seen ( 62, a) that a force may be measured 
 by the momentum it produces. 
 
 /= ma- 
 
 But the measurement of work ( 80, a) introduces the 
 additional factor, ?, representing the number of units of 
 displacement. Introducing this factor into the equation 
 above, we have, for work or kinetic energy, 
 
 K.E. =fl = mal 
 In 54 (6) we have 
 
 '*=#' 
 
 2a 
 
 Substituting this value of I in the second member of the 
 equation above, we have 
 
 (a) If m is measured in pounds and v in feet, this formula gives 
 a numerical expression for foot-poundals ; if m is measured in grams 
 and v in centimeters, it gives that expression in ergs. Foot-poundals 
 may be reduced to foot-pounds by dividing by 32.16, the value of g; 
 ergs may be reduced to kilogrammeters by dividing by 98,000,000. 
 
90 SCHOOL PHYSICS. 
 
 87. Potential Energy Measured. In the case of a body 
 raised above the surface of the earth, its potential energy 
 may be measured, 
 
 (1) In gravitation units, by the product w x h. 
 
 (2) In absolute units, by the product m x h x g. 
 
 88. Conservation of Energy. In 83 (d) it was stated 
 that, were it not for friction and the resistance of the 
 air, the pendulum would vibrate forever ; that the energy 
 would be indestructible. Energy is withdrawn from the 
 pendulum to overcome these impediments, but the energy 
 thus withdrawn is not destroyed. What becomes of it 
 will be seen when we study heat. The truth is that en- 
 ergy is as indestructible as matter; this is what is meant by 
 the conservation of energy. 
 
 (a} Energy cannot be created ; it cannot be destroyed. Taking 
 the universe as a whole, its quantity is unchangeable. For the present 
 we must admit that a given amount of energy may disappear, and 
 escape our search, but it is only for the present. We shall soon learn 
 to recognize the fugitive even in disguise. 
 
 (/;) Transformations of energy are constantly recurring, and it is 
 the prime duty of every student of physical science to watch for them 
 and to try to recognize them in every phenomenon. 
 
 CLASSROOM EXERCISES. 
 
 1. What is the horse-power of an engine that will raise 8,250 pounds 
 176 feet in 4 minutes ? 
 
 2. A ball weighing 192.96 pounds is rolled with a velocity of 100 
 feet a second. How much energy has it ? A ns. 30,000 foot-pounds. 
 
 3. A projectile weighing 50 Kg. is thrown obliquely upward with 
 a velocity of 19.6 m. How much kinetic energy has it? 
 
 4. Two bodies weigh 50 pounds and 75 pounds respectively, and 
 have equal momenta. The first has a velocity of 750 feet per second. 
 What is the velocity of the second ? 
 
 5. A body weighing 40 Kg. moves at the rate of 30 Km. per hour, 
 Find its kinetic energy. 
 
WORK AND ENERGY. 91 
 
 6. What is the horse-power of an engine that can raise 1,500 
 pounds 2,376 feet in 3 minutes? Ans. 36 H.P. 
 
 7. A cubic foot of water weighs about 62 \ pounds. What is the 
 horse-power of an engine that can raise 300 cubic feet of water every 
 minute from a mine 132 feet deep. 
 
 8. A body weighing 100 pounds moves with a velocity of 20 miles 
 per hour. Find its kinetic energy. 
 
 9. A weight of 3 tons is lifted 50 feet, (a) How much work was 
 done by the agent ? (6) If the work was done in a half minute, what 
 was the necessary horse-power of the agent ? 
 
 10. How long will it take a 2-horse-power engine to raise 5 tons 
 100 feet? 
 
 11. How far can a 2-horse-power engine raise 5 tons in 30 seconds? 
 
 12. What is the horse-power of an engine that can do 1,650,000 
 foot-pounds of work in a minute ? 
 
 13. What is the horse-power of an engine that can raise 2,376 
 pounds 1,000 feet in 2 minutes? 
 
 14. If a perfect sphere rests on a perfect horizontal plane in a 
 vacuum, there will be no resistance, other than its own inertia, to 
 a force tending to move it. How much work is necessary to give 
 to such a sphere, under such circumstances, a velocity of 20 feet a 
 second, if the sphere weighs 201 pounds? Ans. 1,250 foot-pounds. 
 
 15. A railway car weighs 10 tons. From a state of rest it is moved 
 50 feet, when it is moving at the rate of 3 miles an hour.. If the 
 resistances from friction, etc., are 8 pounds per ton, how many foot- 
 pounds of work have been expended upon the car ? (First find the 
 work done in overcoming friction, etc., through 50 feet, which is 50 
 foot-pounds x 10 x 8. To this,, add the work done in giving the car 
 kinetic energy.) 
 
 16. Determine, by the composition of forces, whether three con- 
 curring forces with magnitudes of 5, 6, and 12 pounds, respectively, 
 can be in equilibrium. 
 
 17. Explain why a soap-bubble blown at one end of a tube con- 
 tracts, and forces a current of air out of the other end of the 
 tube. 
 
 18. A railway train moves past a station at the rate of 20 miles an 
 hour. A mail agent throws out a parcel, in a direction perpen- 
 dicular to the track and with a horizontal velocity of 20 feet per 
 second. Determine the velocity of the parcel at the beginning of its 
 flight. 
 
92 SCHOOL PHYSICS. 
 
 19. A constant force acting on a mass of 15 grams for 4 seconds 
 gives it a velocity of 20 cm. per second. Find the magnitude of the 
 force in dynes. 
 
 20. A 250-pound projectile is fired from a 12-ton gun with an 
 initial velocity of 1,420 feet per second. Determine the velocity of 
 the gun's recoil. 
 
 21. What is the centrifugal force of a 20-pound mass moving uni- 
 formly once in 5 seconds around a circle 6 feet in diameter? 
 
 22. A man pushes at the rear of a street car and in the line of its 
 motion with a force of 50 pounds. How much work does he per- 
 form while the car moves 10 feet? 
 
 23. A man pushes at one corner of the rear platform of a street car 
 with a force of 50 pounds, and in a direction that makes an angle of 
 45 with the car's line of motion. How much work does he perform 
 while the car moves 10 feet ? 
 
 24. A man pushes directly against the side of a street car with a 
 force of 50 pounds. How much work does he perform while the 
 car moves 10 feet along the track? 
 
 25. A man pushes against the corner of the front platform of a 
 street car with a force of 50 pounds, and in a direction that makes 
 an angle of 135 with the track. How much work does he perform 
 while the car moves forward 10 feet? 
 
 26. Determine the magnitude of the kinetic energy of a body 
 having a mass of 50 pounds, and a velocity of 30 feet per second, 
 (a) in gravitation units ; (6) in absolute units. 
 
 27. If a man does 1,056,000 foot-pounds in a working day of 8 
 hours, what horse-power represents his working power? 
 
 Ans. & H.P. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Whirling table (Fig. 46) and attach- 
 ments ; wooden blocks ; rubber cord ; speed counter. 
 
 1. Determine the ratio between the circumferences of the driver 
 wheel and the follower (i.e., the two wheels that carry the belt) of 
 the whirling table by counting the revolutions made by the spindle, c, 
 while the large wheel revolves once. 
 
 2. To the whirling table, attach a disk on which rests a ball. 
 Rotate the apparatus and make a record of the consequent phenome- 
 non. Connect the ball by a stiff elastic cord to the center of the 
 
WORK AND ENERGY. 
 
 93 
 
 disk. Rotate the apparatus with increasing speed, and make a note 
 of what takes place. (See Fig. 48.) 
 
 3. To the whirling table, attach a frame carrying two tubes contain- 
 ing mercury and water, and supported at an 
 
 angle, as shown in Fig. 49. Rotate the ap- 
 paratus rapidly, and make a record of any- 
 thing peculiar that attracts your notice. FlG 48 
 
 4. To the whirling table, attach the appa- 
 
 ratus consisting of flexible hoops, as 
 shown in Fig. 50. The hoops are 
 firmly fixed at the bottom, but the 
 central spindle passes freely through 
 FIG. 49. the holes where the hoops cross each 
 
 other at the top. Rotate the appa- 
 ratus rapidly, and record any result noticed that has any bearing 
 on the shape of the earth. 
 
 5. Replace the flexible hoops by an inflexible iron ring about a 
 foot in diameter. From the upper point of this 
 
 ring, suspend successively a skein of thread, a 
 looped chain, and a globular glass vessel contain- 
 ing some mercury and some ink-colored water. 
 In each case, rotate the apparatus, and record 
 your observations, as you are supposed to do in 
 all such cases. 
 
 6. From the extremities of different axes, suc- 
 cessively suspend wooden solids of various geo- 
 metrical forms ; e.g., sphere, oblate spheroid, prolate spheroid, cylin- 
 der, etc. Rotate and record as, before. 
 
 7. To the whirling table, attach the frame carrying two balls of 
 equal mass (see Fig. 46) free to slide on a wire, and connected by a 
 thread. By trial, find a position for the balls such that the joined 
 balls will be on opposite sides of the center of rotation, and yet not 
 slide toward either end of the wire when the spindle is put in rapid 
 rotation. Measure the distance of each ball from the center of rota- 
 tion. What is the tendency of each ball ? What case under com- 
 position of forces is thus illustrated? 
 
 8. Change the balls for two joined balls of unequal but known 
 masses. Place them one on each side of the center of rotation, and 
 so that they will retain their positions when the spindle is rapidly 
 rotated. When these positions have been determined, measure the 
 
 FIG. 50. 
 
94 
 
 SCHOOL PHYSICS. 
 
 distances from the center of rotation to the centers of the two balls, 
 arid see how the ratio between the distances compares with the ratio 
 between the masses of the balls. What do you suppose to be the 
 purpose ol this exercise? 
 
 9. Fig. 51 represents a very valuable attachment for the whirling 
 table. A ball of known mass slides on a horizontal wire. To this 
 ball is attached a flexible cord that turns around a pulley at the bot- 
 tom, divides into two, passes over the pulleys at the top, and carries 
 adjustable and slotted disk weights. The middle cord passes through 
 the slots of the weights. The cord and the center of the disks must 
 lie in the center of rotation. Rotate the apparatus with gradually 
 increasing speed until the outward pull of the ball just begins to lift 
 
 the load. Keeping this speed con- 
 stant, count the number of revolu- 
 tions that the driving wheel makes 
 in 10 seconds. Find the average of 
 several such trials. Measure the 
 horizontal distance between the cen- 
 ter of the ball and the axis of rota- 
 tion, and thence compute the velocity 
 of the ball in the recent trials. 
 Compare the result with the formula 
 given in 78. Repeat the experi- 
 ment, using a " speed counter " to 
 determine the number of revolutions 
 made by the spindle in 10 seconds, and computing anew the velocity 
 of the ball. 
 
 Replace the ball by one twice as heavy and at the same distance 
 from the center of rotation. Double the load carried by the vertical 
 cords. Counting as before, determine the rate of rotation necessary 
 to lift the load. Compare the result with the first law given in 78. 
 
 Determine the load that may be lifted by the ball when the driver 
 makes twice as many revolutions as before; when it makes three 
 times as many revolutions. Compare results with the second law 
 given in 78. 
 
 Taking any of these trials as a standard for comparison, move the 
 ball to a point twice as far from the center of rotation, and turn the 
 driving wheel half as fast. How will the two velocities of the ball 
 compare? At this slower rate of rotation, determine the load that 
 may be lifted. Compare the result with the third law given in 78. 
 
 FIG. 51. 
 
GRAVITATION. 
 
 95 
 
 Tabulate all of your results as usual. 
 
 10. Float upon water two blocks of wood, one of which is twice as 
 heavy as the other. Connect them by a stretched rubber cord. 
 Release the blocks, and they will move toward each other, but with 
 unequal velocities. Determine how much faster one moves than the 
 other, and compare their momenta. 
 
 11. On a page of cross-section paper (i.e., paper ruled in squares 
 1 mm. or 0.1 inch on a side, which can be purchased at nearly any 
 optician's) select arbitrarily some corner of a square ; mark it 0, and 
 call it "the origin of coordinates." Mark the right-hand end of 
 the horizontal line passing through the origin, X, and the left-hand 
 end of the same line, X'. Call the line, X'X, " the axis of abscissas." 
 Mark the upper end of the vertical line passing through the origin, Y, 
 and the lower end of the line, Y' . Call the line, Y' Y, " the axis of 
 ordinates." From 0, count off, on the axis of abscissas, three vspaces 
 to a point, which mark M. On the vertical line, measure two spaces 
 upward to a point, which mark P The distance OM is called "the 
 abscissa " of the point, P. The distance MP is called " the ordinate " 
 of the point, P. Negative abscissas would be measured from O toward 
 X', and negative ordinates would be drawn downward from the axis 
 of abscissas. 
 
 Using the same axes of coordinates, locate points having co- 
 ordinates with the following values: 
 
 Points, 
 a 
 b 
 c 
 d 
 
 Abscissas. 
 -3 
 -2 
 
 
 
 2 
 
 Ordinates. 
 
 12 
 
 4 
 
 
 
 -1.3 
 
 Points. A bscissas. Ordinates. 
 
 e 4 -2 
 
 / 6 -2.4 
 
 g 8 -2.67 
 
 h 10 2.86 
 
 Through the points thus located, draw a line with as nearly uniform 
 a curve as 
 
 III. GEAVITATION, ETC. 
 
 89. Gravitation. Every particle of matter in the uni- 
 verse has an attraction for every other particle. This 
 attractive force is called gravitation. 
 
96 
 
 SCHOOL PHYSICS. 
 
 (a) Gravitation is unaffected by the interposition of any substance. 
 During an eclipse of the sun, the moon is between the sun and the 
 earth. But at such a time, the sun and earth attract each other with 
 the same force that they do at other times. 
 
 (6) Gravitation is independent of the kind of matter, but depends 
 upon the quantity or mass, and the distance. Mass does not mean 
 size. The planet Jupiter is about 1,300 times as large as the earth, 
 but it has only about 300 times as much matter, because it is only 
 0.23 times as dense. 
 
 90. Law of Gravitation. The mutual attraction between 
 two bodies varies directly as the product of their masses, and 
 inversely as the square of the distance between their centers 
 of mass. For example, doubling this product doubles the 
 attraction ; doubling the distance, quarters the attraction ; 
 doubling both the product and the distance halves the 
 attraction. 
 
 (a) Represent the attraction between two units of mass at unit 
 distance by a. Then, in the case of two bodies containing respectively 
 m and n units of mass, the attraction of either for the other at unit 
 distance will be mna. If the distance be increased to d units, the 
 
 attraction will be ^ 
 
 (&) Notice that this attraction is mutual. 
 The earth draws the falling apple with a 
 force that gives it a certain momentum; 
 the apple draws the earth with an equal 
 force, that gives to it an equal momentum. 
 
 91. Gravity. The most familiar 
 illustration of gravitation is the 
 attraction between the earth and 
 bodies upon or near its surface. 
 This particular form of gravitation 
 is commonly called gravity. Its 
 measure is weight. Its direction is 
 that of the plumb line, i.e., vertical. 
 
 FIG. 52. 
 
UNIVERS; 
 
 DEPARTMENT OF 
 GRAVITATION. 97 
 
 92. Weight. As the mass of the earth remains con- 
 stant, doubling the mass of the body weighed doubles the 
 product of the masses, and consequently doubles the 
 weight. When we ascend from the surface of the earth, 
 there is nothing to interfere with the working of the law 
 of universal gravitation ; but when we descend below the 
 surface, we leave behind us particles of matter the attrac- 
 tion of which partly counterbalances that of the rest of the 
 earth. The weight of a body at one place on the surface 
 of the earth differs from its weight at another place, 
 because the earth is not a perfect sphere and its density 
 is not uniform. 
 
 93. Law of Weight. Bodies weigh most at the surface 
 of the earth. For bodies in the earth's crust, the weight varies 
 approximately as the distance from the center. For bodies 
 above the earths surface, the weight varies inversely as the 
 square of the distance from the center. 
 
 (a) Let the heavy black line of Fig. 53 represent a spherical shell 
 of uniform thickness and density with bodies at c and e within the 
 shell, and at i and n, without the shell. 
 For such conditions, these propositions 
 have been established : 
 
 (1) The attraction of the matter com- 
 posing the shell draws bodies within the 
 shell, as at c and e, equally in all direc- 
 tions. 
 
 (2) The attraction of the matter com- 
 posing the shell pulls bodies outside the 
 
 shell, as at t'-or n, just as it would if the FIG. 53. 
 
 entire mass of the shell were concentrated 
 at its center, c. 
 
 In assuming that such a shell with a radius of 4,000 miles repre- 
 sents the earth, we ignore the variation between polar and equatorial 
 7 
 
98 SCHOOL PHYSICS. 
 
 diameters, the variation in the density of the earth's crust, and the 
 possible variation of its thickness. Still, make the assumption. 
 Then, at a depth of 15 miles, a body weighing 100 pounds at the 
 surface would weigh about 100 pounds x f j$$. At an elevation of 
 4,000 miles above the surface (8,000 miles from the center), it would 
 
 4000 2 
 
 weigh 100 pounds x - = 25 pounds. 
 
 oUOU 
 
 CLASSROOM EXERCISES. 
 
 1. Suppose the earth to be solid. How far below the surface 
 would a 10-pound ball weigh only 4 pounds ? 
 
 Solution. As the weight is to be reduced six tenths, it must be 
 carried 0.6 of the way to the center. 
 
 Ans. 4,000 miles x 0.6 = 2,400 miles. 
 
 2. On the same supposition, what would a body weighing 550 
 pounds on the surface of the earth weigh 3,000 miles below the sur- 
 face? A ns. 137^ pounds. 
 
 3. Two bodies attract each other with a certain force when they 
 are 75 m. apart. How many times will the attraction be increased 
 when they are 50 m. apart? Ans. 2. 
 
 4. Given three balls. The first weighs 6 pounds, and is 25 feet 
 distant from the third. The second weighs 9 pounds, and is 50 feet 
 distant from the third, (a) Which exerts the greater force upon 
 the third? (&) How many times as great? Ans. f. 
 
 5. A body at the earth's surface weighs 900 pounds. What would 
 it weigh 8,000 miles above the surface ? 
 
 6. How far above the surface of the earth will a pound avoirdu- 
 pois weigh only an ounce ? Ans. 12,000 miles. 
 
 7. At a height of 3,000 miles above the surface of the earth, what 
 would be the difference in the weights of a man weighing 200 pounds 
 and of a boy weighing 100 pounds? Ans. 32.65 pounds. 
 
 8. Find the weight of a 180-pound ball 2,000 miles above the 
 earth's surface. 
 
 9. (a) If the earth was solid, would a 50-pound cannon ball weigh 
 more 1,000 miles above the earth's surface, or 1,000 miles below it? 
 (&) How much ? 
 
 10. If the moon was moved to three times its present distance 
 from the earth, what would be the effect (a) on its attraction for the 
 earth ? (6) On the earth's attraction for it ? 
 
 11. A team pulling northeast with a force of 800 pounds, moves a 
 
GRAVITATION. 99 
 
 railway car 12 feet along a track running north. How much work is 
 done by the team ? 
 
 12. How far above the surface ot the earth must 2,700 pounds be 
 placed to weigh 1,200 pounds? Ans. 2,000 miles. 
 
 13. What effect would it have on the weight of a body to double 
 the mass of the body and also to double the mass of the earth? , 
 
 14. A 50-pound ball moving with a velocity of 75 feet per second 
 strikes a 200-pound ball squarely, and rebounds with a velocity of 25 
 feet. What velocity was given to the 200-*pound ball by the collision ? 
 
 94. Center of Mass. A body's center of mass is the 
 point about which all the matter composing the body may 
 be balanced. It is also called the center of inertia. In 
 some cases it is also the center of gravity. 
 
 (a) The force of gravity tends to draw every particle of matter 
 toward the center of the earth, or downward in a vertical, line. We 
 may, therefore, consider the effect of this force upon any body as the 
 sum of an almost infinite number of parallel forces, each, of which is 
 acting upon one of the particles of which that body is composed. 
 We may also consider this sum of 
 forces, or total gravity, as a result- 
 ant force, GP, acting upon a single 
 point, just as the force exerted by two 
 horses harnessed to a whiffletree is 
 equivalent to another force equal to 
 the sum of the forces exerted, by the 
 horses, and applied at a single point at 
 or near the middle of the whiffletree. 
 This single point, G, which may be re- 
 garded as the point of application of 
 the force of gravity acting upon a body, 
 is called the center of mass of that FlG 54 
 
 body ; in other words, the weight of a 
 body and its mass may be considered as concentrated at a single point. 
 
 (&) When a body is acted on by any force, there is, owing to the 
 inertia of each particle, a series of reactions in the opposite direction, 
 the resultant of which has its application at a point called the center 
 of inertia. 
 
100 
 
 SCHOOL PHYSICS. 
 
 (c) Any force acting on a body at its center of mass tends to pro- 
 duce a motion of translation in the direction of that force ; but, if the 
 force acts on the body at any other point, it and the reaction at the 
 center of mass form a couple that tends to produce rotary motion ot 
 the body. 
 
 (d) In a freely falling body, no matter how irregular its form or 
 how indescribable the curves made by any ot its projecting parts, 
 the line of direction in which the center of mass moves is a vertical 
 line. 
 
 95. To find the Center of Mass. In a body suspended 
 from a point, the center of mass will be brought as low as 
 possible, and will, therefore, lie in a vertical line drawn 
 through the point of support. This fact affords a ready 
 means of determining this point experimentally. 
 
 (a) Let any irregularly shaped body, as a stone or chair, be sus- 
 pended so as to move freely. Drop a plumb line from the point of 
 
 suspension, and make it fast or mark 
 its direction. The center of mass 
 will lie in this line. From a second 
 point, not in the line already deter- 
 mined, suspend the body; let fall a 
 plumb line as before. The center of 
 mass will lie in this line also. But to 
 lie in both lines, it must lie at their 
 intersection. 
 
 (&) If a flat piece of cardboard can 
 be balanced on the point of a pin, its 
 center of mass lies vertically above the 
 point of support, midway between the 
 two sides of the cardboard. When a 
 body is of uniform density and regular 
 shape, its center of mass and its center 
 of figure will coincide $ e.g., the center 
 of mass of a sphere of uniform density is at its center of volume. 
 
 FIG. 55. 
 
 96. May be Outside the Body. In some bodies, as a 
 ring or box or hollow sphere or cask, the center of mass 
 
GRAVITATION. ', 
 
 does not lie in the matter of which the body is com- 
 posed. 
 
 (a) This fact may be illustrated by the " balancer," represented in 
 Fig. 56. The center of mass lies a little above the line joining the 
 two heavy balls, and thus under the foot of 
 the waltzing figure. But the point, wherever 
 found, will have the same properties as if it 
 lay in the mass of the body. 
 
 97. The Base. The side on which 
 a body rests is called its base. If the 
 body is supported on legs, as a chair, 
 the base is the polygon formed by 
 joining the points of support. 
 
 98. Equilibrium. A body sup- 
 ported at a single point will rest in 
 equilibrium when a vertical line pass 
 
 ,, , n, . FIG. 56. 
 
 ing through its center 01 mass, i.e., 
 the line of direction, also passes through the point of 
 support. A body supported on a surface will rest in 
 equilibrium when the line of direction ( 94, d) falls 
 within its base. In general terms, a body is in equilib- 
 rium when the resultant of all the forces acting on it is 
 zero. The center of mass will be supported when it coin- 
 cides with the point of support, or is in the same vertical 
 line with it. When the center of mass is supported, 
 the whole body is supported and rests in a state of 
 equilibrium. 
 
 (a) When the line of direction falls without the base, weight and 
 reaction of support become forces that form a couple and overturn 
 the body. 
 
SCHOOL PHYSICS. 
 
 Experiment 52. With the point of a penknife blade, make a hole 
 of 2 or 3 mm. diameter in the large end of an egg. In the small end, 
 prick a pinhole. Blow the- contents of the shell out through the 
 larger hole. Rinse and dry the shell. Drop a little pulverized rosin 
 or melted sealing wax through the larger hole into the smaller end of 
 the egg. Support the egg in a small tin can (that may be obtained 
 from any kitchen) or in any other convenient way, and pour a few 
 grams of melted lead through the larger hole and into the smaller end. 
 The lead will not run out through the pinhole even if the rosin or 
 sealing wax is not used. The larger hole may be neatly concealed 
 with a piece of thin paper put on with flour paste. Try to make your 
 " magical egg " lie on its side. 
 
 99. Kinds of Equilibrium. There are three kinds of 
 equilibrium : 
 
 (1) A body supported in such a way that, when slightly 
 displaced from its position of equilibrium, it tends to return 
 to that position, is said to be in stable equilibrium. Such a 
 displacement raises the center of mass. 
 
 (2) A body supported in such a way that, when slightly 
 displaced from its position of equilibrium, it tends to fall 
 further away from that position, is said to be in unstable 
 equilibrium. Such a displacement lowers the center of 
 mass. 
 
 (3) A body supported in such a way that, when displaced 
 from its position of equilibrium, it tends neither to return to 
 its former position nor to fall further from it, is said to be 
 in neutral or indifferent equilibrium. Such a displacement 
 neither raises nor lowers the center of mass. 
 
 100. Stability. When the line of direction falls within 
 the base, the body stands ; when without the base, the body 
 falls over. The stability of a body is measured by the 
 amount of work that must be done to overturn it. This 
 
GRAVITATION. 103 
 
 amount may be increased by enlarging the base, 01 by 
 lowering the center of mass, or both. 
 
 (a) Let Fig. 57 represent the vertical section of a brick placed 
 upon its side, its position of greatest stability. In order to stand 
 the brick upon its end, g, the center 
 of mass, must pass over the edge, c ; 
 that is to say, the center of mass 
 
 must be raised a distance equal to a 
 
 the difference between ga and gc, FlG - 57 - 
 
 or the distance, nc. But to lift g this distance is the same as to lift 
 the whole brick vertically a distance equal to nc. Draw similar 
 figures for the brick when placed upon its edge and upon its end. In 
 each case, make gn equal to ga, and see that the value of nc decreases. 
 But nc represents the distance that the brick, or its center of mass, 
 must be raised, before the line of direction can fall without the base 
 and the body be overturned. To lift the brick, or its center of mass, 
 a small distance involves less work than to lift it a greater distance. 
 Therefore, the greater the value of nc, the more work required to 
 overturn the body, or the greater its stability. But this greater value 
 of nc evidently depends upon a larger base, a lower position for the 
 center of mass, or both. 
 
 (6) When the body rests upon a point, as does the sphere, or upon 
 a line, as does the cylinder, a very slight force is sufficient to move it, 
 no elevation of the center of mass being necessary. 
 
 CLASSROOM EXERCISES. 
 
 1. Why does a person stand less firmly when his feet are parallel 
 and close together than when they are more gracefully placed ? 
 
 2. Why can a child walk more easily with a cane than without ? 
 
 3. Why will a book placed on a desk-lid stay there, while a marble 
 will roll off? 
 
 4. Why is a ton of stone on a wagon less likely to upset than a ton 
 of hay similarly placed ? 
 
 5. If a falling body near the surface of the earth gains an accelera- 
 tion of 32.16 feet, what would be its acceleration 240,000 miles from 
 the center of the earth ? 
 
 6. A body is simultaneously acted upon by two forces, one of which 
 would give it a velocity of 100 feet per second northward, while the 
 
104 SCHOOL PHYSICS. 
 
 other would give it a northeasterly velocity of 75 feet per second. 
 Determine the magnitude and direction of the resultant velocity. 
 
 7. A given force, acting for ten minutes upon a body weighing 100 
 pounds, produces a velocity of a mile a minute. Determine the mag- 
 nitude of the force in poundals. 
 
 8. How many gallons of water, each weighing 8 pounds, can a 100- 
 
 horse-power engine raise to a height of 200 feet 
 in 10 hours ? 
 
 9. Why have the Egyptian pyramids great 
 stability ? 
 
 10. Why is it easier for a baby elephant than 
 for a baby boy to learn to walk ? 
 
 11. Where is the axis of rotation of a carriage 
 wheel? Where should the center of mass of a 
 carriage wheel be ? 
 
 12. A boy placed a step-ladder as shown in 
 Fig. 58, and it stood. Why? He then climbed 
 
 to its top, and it fell. Why? 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Plumb bob; chalk; cardboard; box 
 as described below ; screw-eye ; mortar. 
 
 1. Drive small tacks into the frame of a slate at adjacent corners. 
 Tie the middle of a stout thread to one of the tacks. Fasten a small 
 weight to one end of the thread, and support the apparatus from the 
 other end. Mark on the slate the direction in which the thread 
 crosses it. Similarly support the slate by the other tack, and mark 
 the direction of the thread by another line. Place the intersection of 
 the two lines over the end of the finger, and see if the slate is bal- 
 anced. The point thus located approximately represents what? 
 
 2. Cut a rectangle from cardboard. Draw its two diagonals. 
 Balance the cardboard to see how near the center of mass coincides 
 with the center of area. Can the center of mass lie on the surface 
 of such a body ? 
 
 3. Drive a wire nail into a vertical support, and cut off the head of 
 the nail. Bore several holes through an irregularly shaped board 
 near its edges. Using one of these holes, hang the board on the nail. 
 From the nail^hang a chalked plumb line. When the plumb line has 
 come to rest, " snap " it so as to make a vertical line on the board. 
 Change the position of the board, the nail passing through another 
 
GRAVITATION. 105 
 
 of the holes. Chalk the line, suspend and "snap" as before. Place 
 the intersection of the two chalk lines over the end of the finger, and 
 see if the board then balances. Using another hole, similarly chalk 
 another line, and see if the three lines have a common point of inter- 
 section. 
 
 4. Fill a box, about 2x4x8 inches (a shallow cigar box will do), 
 with stiff mortar, and nail down the cover. Stand it on end, so that 
 the 8" edges will be vertical. (It is common for architects and 
 mechanics to indicate "feet" by one tick, and "inches " by two ticks, 
 as in the preceding sentence.) Insert a small screw-eye or hook at the 
 middle of one of the 4" x 8" surfaces ; it will be approximately on a 
 level with the center of mass. Tack a small wooden strip to the 
 table, at the foot of this side, to keep the box from slipping when 
 pulled. Tie one end of a cord to this screw-eye, and the other end to 
 the hook of a spring-balance. Hold the dynamometer so that its axis 
 and the string lie in a straight line that is perpendicular to the side 
 of the box. Carefully observing the scale of the dynamometer, pull 
 steadily until the box falls over. Record the maximum reading of 
 the scale. On one of the 2" x 8" faces, draw and bisect a diagonal. 
 What is the difference between half the length of the diagonal and 
 half the height of the box as it was standing? Record that differ- 
 ence. What does it represent? 
 
 Instead of using the spring-balance, one may pass the cord over a 
 pulley adjusted at the level of the screw-eye, attach a scale-pan of 
 known weight to the free end of the cord, and add weights until the 
 box begins to overturn. 
 
 If the screw-eye pulls out, pass a cord or wire around the box at 
 the proper level, and attach the other cord to it at the proper place. 
 A wire with a loop at one end may be passed through the box from 
 one face to the opposite side, and there made fast before filling the 
 box. The loop will then take the place of the screw-eye. It is 
 especially desirable thus to connect the opposing 2" x 4" and the 
 2" x 8" faces. 
 
 Place the box so that its 4" edges shall be vertical. Ascertain and 
 record the force necessary to overturn the box by a horizontal pull, as 
 before. On one of the 2" x 4" faces, draw and bisect a diagonal. 
 Find how much the semi-diagonal exceeds 2", the semi-altitude of the 
 box. Record this difference. 
 
 Transfer the screw-eye to the middle of one of the 2" x 8" sides, 
 and place the box with its 8" edges vertical. Ascertain and record 
 
106 SCHOOL PHYSICS. 
 
 the force necessary to overturn the box, as before. On one of the 
 4" x 8" faces, draw and bisect a diagonal. Find how much the semi- 
 diagonal exceeds 4", the semi-altitude. Record this difference. 
 
 Place the box so that its 2" edges shall be vertical. Ascertain and 
 record the force necessary to overturn the box, as before. Find how 
 much the semi-diagonal of the 2" x 4" face exceeds 1", the semi- 
 altitude. Record this difference. 
 
 Transfer the screw-eye to the middle of one of the 2" x 4" sides, 
 and place the box with its 4" edges vertical. Ascertain and record 
 the force necessary to overturn the box, as before. Find how much 
 the semi-diagonal of a 4" x 8" face exceeds 2", the semi-altitude, and 
 record that difference. 
 
 Place the box so that its 2" edges shall be vertical. Ascertain and 
 record the force necessary to overturn the box, as before. Find how 
 much the semi-diagonal of the 2" x 8" surface exceeds 1", the semi- 
 altitude, and record that difference. 
 
 Weigh the box. Multiply its weight by the excess of the semi- 
 diagonal over the semi-altitude in each case. What do these products 
 represent? What do they measure? If weight is measured in 
 pounds and decimals thereof, and diagonals and altitudes in feet and 
 decimals thereof, these products will represent what kind of units ? 
 Compare these several products with the corresponding forces used 
 in overturning the box. Do you discover any relation between them ? 
 
 5. Cut a piece of board 20" long, 3" wide at one end, and 7" 
 wide at the other end. Find a point on the surface of the board 
 as near as possible to the center of mass, and over it paste a patch of 
 black paper an inch in diameter. On the same side of the board, 
 and a foot or so from the other paper, paste a patch of red paper 
 about 2" in diameter. Toss the board up edgewise in the open air, 
 so that it will turn end over end, carefully observing the motion of 
 the two paper patches relative to each other. Record and explain 
 what you see. 
 
 IV. FALLING BODIES. 
 
 101. Freely Falling Bodies. When a body is left un- 
 supported and free to move under the influence of the 
 force of gravity and without any resistance, it is a freely 
 falling body. 
 
FALLING BODIES. 
 
 107 
 
 (a) Unless the body falls from a very great ^height, the change in 
 the intensity of the attraction due to the change of distance from the 
 center of the earth is so small that it may, without sensible error, be 
 disregarded. It is, therefore, common to consider gravity a constant 
 force ; hence, if we ignore the resistance of the air, the laws for fall- 
 ing bodies will be the same as for uniformly accelerated motion. 
 
 Experiment 53. From the upper window, drop simultaneously 
 an iron and a wooden ball of the same size. Be careful that your 
 fingers do not " stick " to one ball longer than to the other. Notice 
 that the two balls of different weight strike the ground at practically 
 the same time. 
 
 102. Velocities of Falling Bodies. When a feather and 
 a cent are dropped from the same 
 height, the cent reaches the ground 
 first. This is not because the cent 
 is heavier, but because the feather 
 meets with more resistance from 
 the air in proportion to its mass. 
 If this resistance can be removed 
 or equalized, the two bodies will 
 fall equal distances in equal times, 
 or with the same velocity. The 
 resistance may be avoided by drop- 
 ping them in a glass tube from which 
 the air has been removed. The re- 
 sistances may be nearly equalized by 
 making the two falling bodies of 
 the same size and shape but of dif- 
 ferent weights, as in the preceding 
 experiment. 
 
 FIG. 59. 
 Experiment 54. Tack a strip of wood 
 
 half an inch square to the straight edge of a plank 16 feet long. 
 
108 SCHOOL PHYSICS. 
 
 Fasten metal strips an inch wide to the sides of the wooden strip 
 so as to make a double-track way which should be straight and 
 smooth. Divide the edge of the plank on one side of the track into 
 16 foot-spaces, plainly marked. Raise one end of the plank a foot 
 higher than the other. Place a glass or an iron ball at the top of 
 the inclined track. Notice how often the classroom clock ticks in a 
 second. Place a finger on top of the ball, thus holding it ready for a 
 start. Repeat the word " tick " in unison with the clock until you 
 " feel " the rhythm of its swing, and, just at the moment of a " tick," 
 lift the finger from the ball, which will begin to roll down the track. 
 Notice and record the position of the ball at the end of successive 
 seconds. To locate the ball at the end of the allotted period, place 
 on the upper side of the half-inch strip a wooden block just wide 
 enough to hold its position, and just thick enough to produce an 
 easily audible click when struck by the ball. By trial, place this 
 block so that the tick and the click shall coincide. Repeat your ob- 
 servations, and average the results of similar trials. The greater 
 the number of carefully conducted trials, the more valuable will be 
 your averages. 
 
 The ball will roll down the inclined plane, about 1 foot in the 
 first second, 4 feet in 2 seconds, 9 feet in 3 seconds, 16 feet in 4 
 seconds, etc. The average results may be tabulated as follows : 
 
 Number of Spaces fallen Velocities at the End Total Number of 
 Seconds. each Second. of each Second. Spaces fallen. 
 
 112 1 
 
 234 4 
 
 35 6 9 
 
 47 8 16 
 
 / 2<-l 2t t* 
 
 Representing the velocity gained each second (acceleration) by a, 
 and, consequently, the value of each of our spaces by a, we have, 
 from the above, the already familiar formulas, V = \a (2z 1); v = at; 
 (see 54). 
 
 103. Unimpeded Fall. By giving a greater inclination 
 to the plane used in Experiment 54, the ball will roll 
 more rapidly, and our unit of space will increase from one 
 foot, as supposed thus far, to two, three, four, or five feet, 
 
FALLING BODIES. 109 
 
 and so on ; but the number of such spaces will remain as 
 indicated in the table above. By disregarding the resist- 
 ance of the air, we may say that when the plane becomes 
 vertical, the body becomes a freely falling body. Our 
 unit of space has now become 16.08 feet, or 490 centi- 
 meters. It will fall this distance during the first second, 
 three times this distance during the next second, five 
 times this distance during the third second, and so on. 
 
 104. Galileo's Device. The laws of accelerated motion, 
 as given in 55, were first experimentally verified by 
 Galileo. To avoid the difficulty of accurate observation of 
 the very rapid motion of a freely falling body, he used an 
 inclined plane, down the groqved edge of which a heavy 
 ball was made to roll. 
 
 (a) Let AB represent a plane so inclined that the velocity of a 
 body rolling from B toward A will be readily observable. Let C be 
 a heavy ball. The gravity of the ball may be represented by the ver- 
 tical line, CD. But CD may be resolved into CF, which represents a 
 force acting perpendicular to the plane and producing pressure upon 
 it but no motion at all, and CE, 
 which represents a force acting par- 
 allel to the plane, the only force of 
 any effect in producing motion. , It 
 may be shown geometrically that 
 
 EC:CD::BG:BA. 
 By reducing, therefore, the inclina- 
 tion of the plane, we may reduce the 
 magnitude of the motion-producing 
 
 component of the force of gravity, and thus reduce the velocity. This 
 will not affect the laws of the motion, that motion being changed 
 only in amount, not at all in character. 
 
 105. Atwood's Device. The At wood machine consists 
 essentially of a wheel or pulley, R, over the grooved edge 
 
110 SCHOOL PHYSICS. 
 
 of which are balanced two equal weights suspended by a 
 long silk thread which is both light and strong. The axle 
 
 of this wheel is preferably sup- 
 ported upon the circumferences 
 of four friction wheels, r, r, r', r', 
 for greater delicacy of motion. 
 As the thread is so light that 
 its weight may be disregarded, 
 it is evident that the weights 
 will be in equilibrium whatever 
 
 FIG. HI. ,T . ... mi . 
 
 their position. This apparatus 
 
 is supported upon a pillar seven or eight feet high. A 
 weight or rider placed upon one of the weights pro- 
 duces motion with a moderate but uniformly accelerated 
 velocity. 
 
 (a) Suppose that the balanced masses weigh 49.5 grams each, and 
 that the rider weighs 1 gram. The total mass moved is 100 grams, and 
 the force acting is the weight of 1 gram. When this force of 1 gram 
 moves a mass of 1 gram (freely falling body), it produces a velocity 
 too great for easy observation ; when the same force acts on the mass 
 100 times as great, it produces a velocity only T 7 as great as it pro- 
 duced in the other case, when the gram mass fell alone. Thus we may 
 produce variations in acceleration as we desire. 
 
 106. Acceleration Due to Gravity. In the latitude of 
 New York, a freely falling body gains a velocity of 
 32.16 feet, or 980 centimeters, during the first second 
 of its fall. It makes a like gain of velocity during each 
 subsequent second of its fall. This distance is, therefore, 
 called the acceleration due to gravity, and is generally repre- 
 sented ly the letter g. 
 
 107. Formulas for Falling Bodies. Since the motion of 
 a freely falling body is uniformly accelerated motion, the 
 
FALLING BODIES. Ill 
 
 formulas for freely falling bodies may be derived from 
 those for uniformly accelerated motion ( 54) by substitut- 
 ing the definite quantity, </, for the indefinite quantity, a. 
 Hence, we have for bodies starting from rest : 
 
 (1) V=fft. 
 
 (2) J' = j(2*-l). 
 
 (3) l = 
 
 (a) For bodies rolling down an inclined plane, these formulas 
 may be made applicable by multiplying the value of g by the ratio 
 between the height and the length of the plane. 
 
 (&) If t = 1, formula (1) becomes v g; i. e., the velocity of a body 
 falling freely for one second from a state of rest equals the acceleration. 
 
 (c) If t = 1, formula (3) becomes I \g, i.e., the space traversed 
 in a second by a body freely falling from a state of rest equals half of 
 the acceleration. 
 
 (d) From formula (1) we derive the value, t = -. Substituting 
 
 g 
 
 this value in formula (3), we have I = \g x = . Hence, v = V2 gl, 
 
 9 ' 2 9 
 
 showing that the velocity of a falling body varies as the square root 
 of the distance it has fallen. 
 
 {e} Xone of these formulas involve any expression for mass, thus 
 indicating that the velocity of a falling body is not affected by its 
 mass. 
 
 108. Laws of Falling Bodies. For bodies starting 
 from rest, these formulas may be translated as follows : 
 
 (1) The velocity of a freely falling body at the end of 
 any second of its descent is equal to 32.16 feet (980 cm.) 
 multiplied by the number of the second. 
 
 (2) The distance traversed by a freely falling body dur- 
 ing any second of its descent is equal to 16.08 feet (490 cm.) 
 multiplied by one less than twice the number of the second. 
 
 (3) The distance traversed by a freely falling body dur- 
 
112 SCHOOL PHYSICS. 
 
 m 
 
 ing any number of seconds is equal to 16.08 feet (490 cm.) 
 multiplied by the square of the number of seconds. 
 
 109. Initial Velocity of Falling Bodies. A body may 
 be thrown downward as well as dropped. In such a case 
 the effect of the throw must be added to the effect of 
 gravity. 
 
 110. Bodies thrown Upward. When a body is thrown 
 vertically upward, gravity diminishes its velocity every 
 second by g. The time of the ascent may be found by 
 dividing the initial velocity by the acceleration of gravity : 
 
 t= V ~. 
 
 9 
 
 Projectiles. 
 
 Experiment 55. From a strip of wood shaped like a meter stick 
 or common lath, cut a piece about 10 cm. long. Cut equal notches at 
 two corners, a and e, as shown in Fig. 62. Nail the middle of this 
 piece across the end of the rest of the lath, thus making a T-shaped 
 form. Clamp the other end of the long leg firmly in a vise so that 
 the edge, ae, and the corresponding edge of the long piece, shall be 
 horizontal and several feet above a level floor. Place lead bullets at 
 a and e. Strike the long piece a sharp, hori- 
 zontal blow near the cross-piece. One of the 
 bullets will be shot horizontally, and the 
 ; other will be dropped nearly vertically. 
 
 Will the bullets strike the floor at the same 
 
 time ? Repeat the experiment several times, and do not expect more 
 than approximate agreements. 
 
 111. Projectiles. Every projectile is acted upon by an 
 impulsive force and the force of gravity. The path of 
 a projectile is a parabolic curve, the resultant of these 
 forces. 
 
FALLING BODIES. 
 
 113 
 
 (a) Suppose a ball to be thrown horizontally. Its impulsive force 
 will give a uniform velocity, and may be represented by a horizontal 
 line divided into equal parts, the mag- 
 nitude of each part being equal to 
 that of the velocity. The force of 
 gravity may be represented by a ver- 
 tical line divided into unequal parts, 
 representing the spaces 1, 3, 5, 7, etc., 
 over which gravity would move it in 
 successive seconds. Constructing par- 
 allelograms of forces, we find that at 
 the end of the first second the ball 
 will be at A, at the end of the next 
 second at JB, at the end of the third 
 at C, at the end of the fourth at Z>, etc. 
 The resistance of the air modifies the 
 nature of the curve somewhat. The 
 horizontal distance, GE, is called the 
 range of the projectile. 
 
 CLASSROOM EXERCISES. 
 
 1. What will be the velocity of a body after it has fallen 4 seconds? 
 Solution : v=gt = 32.16 x 4 = 128.64. Ans. 128.64 feet. 
 
 2. A body falls for several seconds. During one of these seconds 
 it passes over 530.64 feet. Which one is it ? 
 
 Solution : /' = ^(2 1 - 1) 
 
 530.64 = 16.08 x (2 1 - 1) ; .-. t = 17. 
 
 Ans. 17th second. 
 
 3. A body was projected vertically upward with a velocity of 96.4 
 feet. How high did it rise ? 
 
 v 96.48 
 
 g -32.16 ~ 6 ' 
 
 = 16.08 x 9,= 144.72. Ans. 144.72 feet. 
 
 FIG. 63. 
 
 Salmon:- 
 
 4. How far will a body fall during the third second of its fall ? 
 
 5. How far will a body fall in 10 seconds? Ans. 1,608 feet. 
 
 6. How far in 1 second? Ans. 4.02 feet. 
 
 7. How far will a body fall during the first second and a half of 
 its fall? 
 
 8 
 
114 SCHOOL PHYSICS. 
 
 8. How far in 12| seconds? 
 
 9. A body passed over 787.92 feet during its fall. What was the 
 time required? Ans. 7 seconds. 
 
 10. What velocity did it finally obtain ? 
 
 11. A body fell during 15^ seconds. Give its final velocity. 
 
 12. In an Atwood machine, the weights carried by the thread are 
 7| ounces each. When the "rider," which weighs one ounce, is in 
 position, what is the acceleration ? 
 
 13. A stone is thrown horizontally from the top of a tower 257.28 
 feet high, with a velocity of 60 feet a second. Where will it strike 
 the ground? Ans. 240 feet from the tower. 
 
 14. When a fishing line with a heavy sinker is thrown into a stream 
 with a rapid current, it often is carried down stream to the full 
 length of the line, and held suspended in the water. Draw a diagram 
 showing the forces acting on the sinker, and how equilibrium is se- 
 cured. Neglect the buoyancy of the water. 
 
 15. A body is thrown directly upward with a velocity of 80.4 feet, 
 (a) What will be its velocity at the end of 3 seconds, and (6) in what 
 direction will it be moving ? 
 
 16. In Fig. 63, what is represented by the following lines: Fl? 
 Fa? Aa? Fc? Ddf 
 
 17. A body falls 357.28 feet in 4 seconds. What was its initial 
 velocity? Ans. 25 feet. 
 
 18. A ball thrown downward with a velocity of 35 feet per second 
 reaches the earth in 12| seconds, (a) How far has it moved, and (&) 
 what is its final velocity? 
 
 19. (a) How long will a ball projected upward with a velocity of 
 3,216 feet continue to rise? (6) What will be its velocity at the end 
 of the fourth second ? (c) At the end of the seventh ? 
 
 20. A ball is shot from a gun with a horizontal velocity of 1,000 
 feet, at such an angle that the highest point in its flight is 257.28 feet. 
 What is its range? Ans. 8,000 feet. 
 ^ 21. A body was projected vertically downward with a velocity of 
 10 feet. It was 5 seconds falling. Required the entire space passed 
 over. Ans. 452 feet. 
 
 22. Required the final velocity of the same body. Ans. 170.8 feet. 
 
 23. A body was 5 seconds rolling down an inclined plane, and 
 passed over 7 feet during the first second. Give (a) the entire space 
 passed over, and (6) the final velocity. 
 
 24. A body rolling down an inclined plane has, at the end of the 
 
FALLING BODIES. 115 
 
 first second, a velocity of 20 feet, (a) What space would it pass over 
 hi 10 seconds ? (&) If the height of the plane was 800 feet, what was 
 its length? Ans. (6) 1,286.4 feet. 
 
 25. A body was projected vertically upward, and rose 1,302.48 feet. 
 Give (a) the time required for its ascent, and (ft) the initial velocity. 
 
 26. A body projected vertically downward has, at the end of the 
 seventh second, a velocity of 235.12 feet. How many feet did it 
 traverse in the first 4 seconds? Am. 297.28 feet. 
 
 27. A body falls from a certain height; 3 seconds after it has 
 started, another body falls from the height of 787.92 feet. From what 
 height must the first fall if both are to reach the ground at the same 
 instant? Ans. 1,608 feet. 
 
 28. A body falls freely for 6 seconds. What is the space traversed 
 during the last two seconds of its fall ? 
 
 29. When a body is thrown upward, does its velocity vary directly 
 or inversely with the number of time-units it has been rising ? 
 
 30. See definition of "parabola" in the dictionary. When would 
 the curved line, FCE in Fig. 63, become parallel with the vertical 
 line, FG? 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Inclined track; iron balls; pendu- 
 lum; electromagnets; a voltaic battery; turnbuckle; blade of hack- 
 saw ; screws ; screw-driver ; needles ; thread. 
 
 1. Graduate to centimeters the edge of the plank used in Experi- 
 ment 54, using the part outside the track that was not graduated to 
 feet. Elevate one end of the plank as in that experiment. 
 
 On the vertical face of a movable wooden support, and more than 
 a meter from its foot, tack a horizontal strip of soft wood, the thick- 
 ness of which is not less than the radius of the iron ball mentioned 
 below. Into the vertical face of this strip press a stout needle nearly 
 to its eye. The hole through the needle should be vertical. An inch 
 or so above the needle set a common screw. Fasten one end of a 
 thread that will pass through the eye of the needle, and having a 
 length of about 110 cm., to a small iron ball. Pass the other end of 
 the thread through the eye of the needle, fasten it to the screw, and 
 wrap it around the screw until the center of the ball hangs about a 
 meter below the needle. 
 
 Instead of using the needle as above described, a small, firm cork 
 
116 SCHOOL PHYSICS. 
 
 may be fastened to the vertical face of the strip, and a threaded 
 needle drawn vertically through the middle of the cork. The thread 
 may then be fastened to the screw, although the cork will probably 
 pinch it firmly enough to support the ball. Such cork supports are 
 easily provided, and convenient for quick adjustment. 
 
 Swing the ball as a pendulum, and count the number of times it 
 passes through its arc in 60 seconds. If the number of swings 
 exceeds 60, turn the screw so as to unwind some of the thread, and 
 increase the distance between the ball and the needle, or the under 
 side of the cork. Swing the ball and count as before, continuing the 
 adjustment until the ball makes 60 swings in 60 seconds. Place the 
 pendulum so that as it swings, and as the ball rolls down the inclined 
 track, both may be observed at the same time. 
 
 With the assistance of a friend who understands such things, fix 
 two electromagnets that are on the same circuit so that their attrac- 
 tion will hold an iron ball at the upper end of the inclined track, 
 and the iron pendulum-bob at one end of the arc through which it 
 is to swing. Close the circuit of the battery, and bring the two iron 
 balls into their respective positions, separated from the magnets 
 only by bits of thin paper. The attraction of the magnets will hold 
 the balls, one at the top of the track, and the other at the end of 
 its arc. 
 
 Break the circuit, and the two iron balls will be released simulta- 
 neously. By trial, adjust the inclination of the track so that the ball 
 will roll the whole length in 4 seconds, as measured by the swings of 
 the pendulum. By repeated trials, verify the accuracy of the figures 
 in the second and fourth columns of the table given in Experiment 54. 
 
 2. From the frame of a small pulley running with little friction 
 suspend a weight of about 2 pounds. Place the wheel of the pulley 
 so that it will run on a No. 10 wire tightly stretched between oppo- 
 site sides of the laboratory, one end of the wire being a little higher 
 than the other. The wire may be tightened with a turnbuckle. 
 Just above the wire, and parallel with it, stretch a cord. From the 
 upper end of the wire start the pulley with its load, and note the 
 point where it is at the end of 3 seconds. If the distance traversed 
 in the 3 seconds is not at least 9 feet, increase the inclination of the 
 wire. Mark the point where the pulley is at the end of the third 
 second by a strip of paper hung from the cord so that its lower end 
 will be struck by the top of the pulley as it passes. Mark the point 
 on the cord above the starting point of the pulley by tying a thread 
 
FALLING BODIES. 117 
 
 there. Divide the intervening distance into 9 equal parts. Hang 
 similar paper strips from the cord, at distances of 5 such equal parts 
 and of 8 such equal parts above the strip already hung, and of 7 such 
 equal parts and 16 such equal parts below it. 
 
 Swing the pendulum that vibrates seconds. As its thread passes a 
 vertical line on the wooden support drawn downward f rom the needle, 
 start the pulley, and see if it taps the 'successive strips as the pendu- 
 lum successively passes the vertical line. If the weight carried by 
 the pulley is of iron, the weight and the pendulum-bob may be simul- 
 taneously released as in Exercise 1. 
 
 XOTE. A good Atwood machine is an expensive piece of appa- 
 ratus, and unfortunately many schools and laboratories have none. 
 If any particular school 'is thus equipped, the teacher should provide 
 for its use in the verification of the laws of falling bodies, the approx- 
 imate determination of the acceleration due to gravity, etc. 
 
 3. Modify Experiment 53 by using two iron balls of different mass 
 supported by the attraction of two electromagnets that are in the 
 same circuit. Tie the magnets to a stick, and hold them and the 
 magnetically supported balls from an upper window. When you 
 are sure that the balls are at the same level, break the circuit. A co- 
 worker standing on the ground will report whether the different 
 masses make the journey in the same time. 
 
 4. A ball is thrown horizontally with a velocity of 20 feet a second. 
 Using any convenient scale and the cross-section paper, map the posi- 
 tion of the ball at the end of half seconds for 5 seconds. Bend the 
 thin blade of a hack-saw or other flexible bar so that its edge will 
 pass through as many of these points as possible. Along the side of the 
 blade, trace a pencil mark to represent the path of the ball. See Ex- 
 ercise 11, p. 95, and compare your curve with Fig. 63. If any point 
 thus located lies much out of the curve, reexamine your work for 
 that point. On your diagram, lay off and measure coordinates for the 
 point that represents the position of the ball at the end of 3.25 seconds 
 and 5.5 seconds from the beginning of its fall. Compare the results 
 of your work with corresponding results obtained by computation. In 
 tracing the curve, run the pencil to the lower end of the saw blade. 
 
 5. From a rectangular wooden block about 30 x 23 x 4 cm., cut 
 a semi-cycloid, thus shaping the piece marked B in Fig. 64. Cut 
 a groove in the curved edge, and fasten the block against the black- 
 board so that its long edge shall be vertical. A small ball that 
 has rolled down the cyeloidal path will be projected with a con- 
 
118 SCHOOL. PHYSICS. 
 
 stant horizontal velocity and an accelerated vertical velocity. Let 
 one of two pupils working together adjust, by repeated trials, a ruler 
 so that the projected ball will just touch it, and thence determine 
 and mark the point passed over by the center of the ball. In this 
 way determine the loci of points sufficiently numerous to plot on the 
 
 blackboard the path described by the 
 center of the projected ball. From 
 the center of the ball at the lowest 
 point of its cycloidal path draw a 
 horizontal line, and mark oif a num- 
 ber of equal spaces upon it. These 
 will represent the horizontal motions 
 of the ball in equal intervals of time. 
 From each division on this line, draw 
 a vertical line, /, to the plotted path, 
 and measure the lengths of these 
 lines. They represent the spaces 
 fallen in the several intervals of time. 
 Show that, for each interval of time, 
 jr IG 54. / = kt z , k being some constant. If 
 
 the horizontal intervals are made 
 
 equal to the horizontal speed of the ball per second, k will equal \ g. 
 From the measurements made on the blackboard, plot the curve on 
 cross-section paper. 
 
 V. THE PENDULUM. 
 
 112. A Simple Pendulum is a single material particle 
 supported by a line without weight, and capable of oscil- 
 lating about a 'fixed point. Such a pendulum has 
 a theoretical but not an actual existence. Its prop- 
 erties may be approximately determined by experi- 
 menting with a small lead ball suspended by a fine 
 thread. 
 
 113. Motion of the Pendulum. When the pendulum is 
 drawn from its vertical position, the force of gravity, MGr, 
 
THE PENDULUM. 
 
 119 
 
 FIG. 65. 
 
 is resolved into two components, one of which, MC, pro- 
 duces pressure at the point of support, while the other, 
 MH, acts at right angles to it, producing motion toward N. 
 As the pendulum approaches iV, 
 its kinetic energy increases. This 
 energy carries the weight beyond 
 N toward 0, against the action of 
 the continually increasing compo- 
 nent, OP. By the time the pen- 
 dulum has arrived at 0, its kinetic 
 energy has been wholly trans- 
 formed into potential energy. 
 Then OP pulls the weight toward 
 N again, transforming the poten- 
 tial energy into kinetic, which, 
 in turn, carries the weight once 
 more toward M. Thus the pendulum oscillates for an 
 indefinite time by the alternate action of gravity and its 
 acquired energy of motion. 
 
 114. Definitions. The motion from one extremity of 
 the arc through which a pendulum swings to the other is 
 called an oscillation. The "time occupied in moving over 
 this arc is called the time or period of oscillation. The 
 angle measured by half this arc is called the amplitude of 
 oscillation. The trip from M to is an oscillation. The 
 angle, MAN, is the amplitude of oscillation. 
 
 (a) The motion from M to and back again, one " swing-swang," 
 is sometimes called a " complete vibration." The time occupied by the 
 round trip, or in passing from any point to its next passage in the 
 same direction through the same point, is sometimes called a " com- 
 plete period." 
 
120 
 
 SCHOOL PHYSICS. 
 
 Experiment 56. Suspend three lead bullets and a small iron ball 
 as shown in the accompanying figure. The lengths of the threads, 
 measured between the points of support and the 
 centers of the balls, should be as 1: |-: ^; e.g., 
 1 yard, 9 inches, and 4 inches respectively. 
 Set one of the pendulums swinging through a 
 small arc, and count the oscillations made in 
 10 seconds. Set the same pendulum swinging 
 through a somewhat larger arc, and count the 
 oscillations as before. Record and compare 
 results. Repeat the experiments with each of 
 the pendulums, recording and comparing results 
 in each case. Note the effect of amplitude or 
 of mass on the period of oscillation. 
 
 From your notes, or by fresh experiment, 
 determine the period of each pendulum, and 
 observe the relation between the period of oscil- 
 lation and the length of the pendulum. 
 
 Place a magnet under the iron ball, so that 
 when the latter swings it will just clear the end 
 of the magnet. Swing the iron pendulum, and 
 count the number of oscillations made in 10 
 
 seconds. The attraction of the magnet being added to that of the 
 earth, the acceleration is increased and the period is lessened. 
 
 115. Laws of the Pendulum. When the amplitude of 
 oscillation does not exceed three degrees, the period of 
 oscillation depends mainly upon the length of the pen- 
 dulum and the acceleration due to gravity. Representing 
 period by , and length by I, the relation is expressed 
 by the formula 
 
 FIG. 66. 
 
 The following laws are consistent with this formula and 
 with the results of numberless experiments : 
 
 (1) At any given place, the vibrations of a given pen- 
 dulum are isochronous, i.e., are made in equal periods. 
 
THE PENDULUM. 121 
 
 (2) The period of oscillation is independent of the mate- 
 rial or the mass of the pendulum. 
 
 (3) The period of oscillation varies directly as the square 
 root of the length. 
 
 (4) The period of oscillation varies inversely as the square 
 root of the acceleration. 
 
 116. The Compound Pendulum. Any pendulum other 
 than the simple or ideal pendulum is a compound pendulum. 
 In its most common form, it consists of a slender rod, 
 flexible at the top, and carrying at the bottom a heavy 
 mass of metal known as the bob. 
 
 117. The Seconds Pendulum. At any given place, a 
 seconds pendulum is one that makes a single oscillation in 
 a second. At the sea-level, its length is about 39 inches 
 at the equator and about 39.2 inches near the poles. Its 
 value at the sea-level at New York may be found by 
 making =1, and ^=980.19 cm., in the formula 
 
 and solving the equation for the value of I. 
 
 (a) The length of the seconds pendulum being known, the length 
 of any other pendulum may be found when the period of oscillation 
 is given, or the period of oscillation may be found when the length 
 is given. As the seconds pendulum is inconveniently long, use is 
 often made of one one-fourth as long, which oscillates in half 
 seconds. 
 
 Center of Oscillation. 
 
 Experiment 57. Drive a small wire nail through a flat board of 
 any form, at some point near its edge, as shown in Fig. 67. Hold 
 
122 
 
 SCHOOL PHYSICS. 
 
 the ends of the wire by the finger and thumb, and allow the board to 
 hang in a vertical plane. Fasten a small bullet to the end of a thread, 
 and pass the thread over the wire so that the bullet 
 hangs close to the board. Move the hand that sup- 
 ports the wire horizontally and in the plane of the 
 board. Board and bullet will swing as pendulums. 
 If one swings more rapidly than the other, lengthen 
 or shorten the string until they swing together. 
 With the thread at this length, and board and 
 bullet hanging in equilibrium, mark the point on 
 the board opposite the center of the ball. Holding 
 the board by the wire as before, move it with varied, 
 sudden, and irregular motions in the plane of the 
 board. The bullet will not quit the marked place 
 on the board. 
 
 FIG. 67. 
 
 118. Centers of Suspension and Oscillation. In every 
 pendulum not simple, the parts near the center of suspen- 
 sion tend to move faster than those further away, and 
 force the latter to move more rapidly than they other- 
 wise would. Between these, there is a particle that moves, 
 of its own accord, at the rate forced upon the 
 others. This particle fulfills all the conditions of 
 a simple pendulum that has the period of the 
 compound pendulum. Its position is called the 
 center of oscillation or percussion. 
 
 (a) Fig. 68 represents a wooden bar, suspended so as to 
 have freedom of motion about the point S, which thus be- 
 comes the center of suspension. G indicates the center of 
 mass, and O the center of oscillation. S and are inter- 
 changeable ; i.e., if the pendulum is suspended from its 
 center of oscillation, the period remains the same. 
 
 FIG. 08. 
 
 119. The Real Length of a Pendulum. If we consider 
 the length of the compound pendulum to be the distance 
 
THE PENDULUM. 
 
 128 
 
 between the centers of suspension and oscillation, all the 
 laws of the simple pendulum become applicable to the 
 compound pendulum. 
 
 120. Uses of the Pendulum. -- The continued motion of 
 a clock is due to the force of gravity 
 acting upon the weights, or to the elas- 
 ticity of the spring. But the weights 
 have a tendency toward positively accel- 
 erated motion, and the spring toward 
 negatively accelerated motion. Either 
 defect would be fatal in a timepiece. 
 The properties of the pendulum set forth 
 in the first law -enable us to regulate this 
 motion, and to make it available for the 
 desired end. 
 
 The pendulum is also used to deter- 
 mine the relative and absolute accelera- 
 tion of gravity at different places, and in 
 this way the figure of the earth. Having 
 at any given place a pendulum of known 
 length, its period may be determined and 
 the value of g computed from the formula 
 given in 115. FIQ 69 
 
 (a) A pendulum has a strong tendency to maintain its plane of 
 oscillation, a fact that has been used in the experimental demonstra- 
 tion of the rotation of the earth upon its axis. The chief function of 
 the wheel-work of a clock is to register the number of the vibrations 
 of the pendulum. If the clock gains time, the pendulum is length- 
 ened by lowering the bob ; if it loses time, the pendulum is shortened 
 by raising the bob. 
 
124 
 
 SCHOOL PHYSICS. 
 
 CLASSROOM EXERCISES. 
 
 No. 
 
 INCHES. 
 
 OSCILLATIONS. 
 
 PERIOD. 
 
 No. 
 
 CM. 
 
 OSCILLATIONS. 
 
 PERIOD. 
 
 1 
 
 9 
 
 20 per min. 
 
 9 
 
 11 
 
 99.33 
 
 ? 
 
 ? 
 
 2 
 
 ? 
 
 30 " 
 
 9 
 
 12 
 
 9 
 
 9 
 
 2 sec. 
 
 3 
 
 30 
 
 ? 
 
 ? 
 
 13 
 
 9 
 
 9 
 
 2 min. 
 
 4 
 
 16 
 
 ? 
 
 ? 
 
 14 
 
 24.83 
 
 ? 
 
 9 
 
 5 
 
 ? 
 
 9 
 
 | sec. 
 
 15 
 
 9 
 
 8 per sec. 
 
 ? 
 
 6 
 
 9 
 
 ? 
 
 5- min. 
 
 16 
 
 397.32 
 
 9 
 
 ? 
 
 7 
 
 39.37 
 
 ? per min. 
 
 9 
 
 17 
 
 11.03 
 
 9 
 
 9 
 
 8 
 
 9 
 
 10 
 
 9 
 
 18 
 
 ? 
 
 9 
 
 10 sec. 
 
 9 
 
 10 
 
 V per sec. 
 
 9 
 
 19 
 
 2,483.25 
 
 9 
 
 9 
 
 10 
 
 9 
 
 1 per min. 
 
 9 
 
 20 
 
 9 
 
 9 
 
 4 sec. 
 
 21. How will the periods of oscillation of two pendulums compare, 
 their lengths being 4 feet and 49 feet respectively? Ans. As 2 : 7. 
 
 22. Of two pendulums, one makes 70 oscillations a minute, the 
 other, 80 oscillations a minute. How do their lengths compare? 
 
 Ans. As 64 : 49. 
 
 23. If one pendulum is 4 times as long as another, what are their 
 relative periods of oscillation? 
 
 24. The length of a seconds pendulum being 39.1 inches, what 
 must be the length of a pendulum to oscillate in second ? 
 
 25. How long must a pendulum be to oscillate (a) once in 8 seconds? 
 (b) In i second? 
 
 26. How long must a pendulum be to oscillate once in 3^ seconds? 
 
 27. Find the length of a pendulum that will oscillate 5 times in 4 
 seconds. Ans. 25.02 -f inches. 
 
 28. A pendulum 5 feet long makes 400 oscillations during a certain 
 time. , How many oscillations will it make in the same time after the 
 pendulum rod has expanded 0.1 of an inch? 
 
 29. At Paris, g = 981 cm. Determine the length of the seconds 
 pendulum at that place. 
 
 30. A lead ball is suspended as a pendulum. From the center of 
 the ball it is 83 inches to its center of suspension. The pendulum 
 oscillates 206 times in 5 minutes. From the formula given in 115, 
 determine the acceleration due to gravity at the time and place of the 
 experiment. Ans. 32.188 feet. 
 
THE PENDULUM. 125 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Wooden bars, etc., for pendulums; a 
 pendulum-clock ; a piece of sheet iron ; mercury ; a telegraph sounder 
 or an electric bell. 
 
 1. Set up a pendulum of length as great as you can conveniently. 
 Set up another that oscillates just twice as often in a given time. 
 Determine the ratio between the lengths of the two pendulums. 
 Shorten the shorter pendulum until it oscillates three times as fast 
 as the other. Determine the relative lengths as before. Shorten the 
 shorter pendulum again until it oscillates four times as fast, and find 
 the ratio as before. In your notebook, record the data obtained, using 
 the following form, and placing the ascertained ratios in the places of 
 x, y, and z : 
 
 Relative Numbers Relative 
 
 of Oscillations. Lengths. 
 
 1 .1 
 
 2 x 
 
 3 y 
 
 4 z 
 
 5 ? 
 
 6 * 
 
 Can you see any law or rule governing in such cases? Try, with- 
 out experiment, to put the proper figures in the places of the two 
 interrogation points. 
 
 2. Set up the pendulum used in Exercise 1, p. 115, or a similar 
 one, and adjust its length so that it will oscillate 60 times in 60 
 seconds. The eye of the needle should be not much larger than is 
 necessary for the thread used. Measure the distance from the center 
 of the bob to the needle. From the data thus secured, compute the 
 value of g. 
 
 3. Set up a similar pendulum, but with a shorter thread. Adjust 
 the length of the pendulum by turning the screw until the pendu- 
 lum oscillates 60 times in 30 seconds. Measure the length of the 
 pendulum. Compare its period with that of the one used in Exer- 
 cise 2. Compare its length with that of the one used in Exercise ?. 
 How do these comparisons tally with the statement made in 
 115 (3) ? 
 
126 SCHOOL PHYSICS. 
 
 4. Shorten the thread of the pendulum used in Exercise 3 until 
 the pendulum oscillates 60 times in 20 seconds. Measure the length 
 of the pendulum. Compare its period with that of those used in 
 Exercises 2 and 3. Compare its length with the lengths of those. 
 How do these results conform to the law referred to above ? 
 
 5. Using these pendulums successively, test the accuracy of the 
 law given in 115 (1). 
 
 6. Using either of these pendulums and another prepared by 
 you for that purpose, test the accuracy of the second law given in 
 115. 
 
 7. On a stout thread, fasten 5 or 6 lead bullets at successive inter- 
 vals of 10 cm., and suspend the combination as a pendulum. Swing 
 it as a pendulum. Does the string retain its rectilinear form while 
 the compound pendulum is oscillating? Account for any observed 
 difference in this respect between this pendulum and those previously 
 used. 
 
 8. Through the laboratory meter stick or a similar strip of wood, 
 drill or burn a small hole 3 cm. from one end. Using this as a center 
 of suspension, locate the center of oscillation. Determine the real 
 length of the meter-stick pendulum. Suspend a bullet by a single 
 thread, and adjust its length so that it will swing with the same 
 period as the meter-stick pendulum. Compare the length of this 
 pendulum with the distance between the centers of suspension and 
 oscillation of the other pendulum. 
 
 9. Remove the dial of a clock, and study the movements of the 
 escapement (mn in Fig. 69), and of the escapement wheel, R. What 
 does it enable the lifted weights or the coiled spring of the clock 
 to do to the pendulum ? What does it enable the pendulum to do to 
 the weights or the spring? What would happen to the weights or 
 to the spring if the escapement should be suddenly removed? What 
 would happen to the pendulum if the escapement should be removed? 
 How many times must the pendulum oscillate that the escapement 
 wheel may turn around once ? 
 
 10. Suspend a^heavy metallic ball by two fine wires that are gripped 
 at the lower horizontal edge of a metallic clamp. To the bottom of 
 the ball, solder a short pointed iron or platinum wire. (See Fig. 44.) 
 Make a slight depression in a small plate of sheet iron, and solder 
 a small copper wire to the plate. Fasten the plate beneath the pen- 
 dulum bob so that the wire pointer will just touch a drop of mer- 
 cury placed in the depression in the plate. The mercury globule 
 
SIMPLE MACHINES. 127 
 
 should be so placed that when the pendulum swings, its pointer shall, 
 at each oscillation, touch the mercury, but not the plate. Connect 
 the wire that is soldered to the plate with one pole of a voltaic cell 
 or battery. Connect the other pole of the battery through a tele- 
 graph sounder or single-stroke electric bell with the end of the pendu- 
 lum wire where it protrudes above the supporting clamp. Swing the 
 pendulum. As the pointer passes through the mercury, it will " close 
 the circuit " of the battery, and the sounder will click or the bell 
 will strike. Adjust the length of the pendulum until it gives 60 sig- 
 nals in 60 seconds. Make this pendulum a permanent feature of the 
 laboratory. 
 
 11. From a board, cut two isosceles-triangular pieces with sides of 
 4 and 24 inches. Insert a small screw-eye at the pointed end of one, 
 and another screw-eye at the middle of the 4-inch side of the other. 
 Suspend the wooden pieces by the screw-eyes, and swing them as pen- 
 dulums. Determine the period of each, and thence compute the real 
 lengths of the two pendulums. 
 
 VI. SIMPLE MACHINES. 
 
 121. Machines. In mechanics, the word " machine " 
 signifies an instrument for the 
 
 conversion of motion or the 
 transference of energy. Thus, 
 a machine may be designed 
 to convert rapid motion into 
 slow motion ; e.g., a crowbar. 
 There are six simple ma- FlG - 70 - 
 
 chines, the lever, the wheel and axle, the pulley, the in- 
 clined plane, the wedge, and the screw. 
 
 122. Weight and Power. The action of a machine 
 involves two forces, the weight and the power. The 
 
128 SCHOOL PHYSICS. 
 
 power signifies the magnitude of the force that acts upon one 
 part of the machine ; the weight signifies the magnitude of 
 the force exerted by another part of the machine upon some 
 external resistance. The general problem relating to ma- 
 chines is to find the ratio between power and weight ; 
 i.e., to determine the " mechanical advantage" of the 
 machine. 
 
 (a) It is common in elementary discussions to neglect friction, 
 and to assume that the parts of the machine are perfectly rigid and 
 without weight. 
 
 123. A Machine cannot Create Energy. No machine 
 can create or increase energy. In fact, the use of a machine 
 is accompanied by a waste of the energy that is needed to 
 overcome the resistances of friction, the air, etc. A part 
 of the energy exerted must, therefore, be used upon the 
 machine itself, thus diminishing the amount that can be 
 transmitted or utilized for doing the work in hand. 
 
 124. General Laws of Machines. The operations of a 
 machine are subject to the principles of " the conservation 
 of energy ; " the work done by the power equals the work 
 done on the weight. 
 
 (1) The power multiplied by the distance through which it 
 moves equals the weight multiplied by the distance through 
 which it moves: Pl = Wl'. 
 
 (2) The power multiplied by its velocity equals the weight 
 multiplied by its velocity : Pv= Wv' . 
 
 125. Efficiency of Machines. As was hinted in 123, 
 part of the work done upon a machine is expended in over- 
 coming resistances that correspond to waste, resistances 
 
SIMPLE MACHINES. 129 
 
 other than that which the machine was designed to over- 
 come, .such as friction, etc. The ratio that the useful work 
 done by the machine bears to the total work done on the 
 machine is called the efficiency of the machine. If this ratio 
 could be brought up to unity, we should have a perfect 
 machine, the impossible thing that would supply " per- 
 petual motion." 
 
 (a) Whenever we find that a machine does less work than was 
 done upon it, we should bear in mind that the missing energy has 
 not been destroyed. Mechanical energy has been transformed into 
 a familiar form of molecular energy, and exists somewhere in the form 
 of heat. 
 
 126. Impediments to Motion. The impediments to 
 motion most frequently met in the use of machines result 
 from rigidity or from friction. The first of these is fa- 
 miliarly illustrated in the stiffness of a pulley rope. The 
 second will receive further consideration in the following 
 paragraph, Due allowance must be made for these hin- 
 drances in all close calculations of the useful work of any 
 machine. If the machine is designed merely to support 
 a load, the greater the impediments, the less the power 
 required ; if the machine is designed to move a load, 
 the greater the impediments, the greater the power re- 
 quired. 
 
 127. Friction is the resistance that a moving body 
 meets from the surface on ivhich it moves, and may be 
 rolling or sliding. It is due partly to the adhesion of 
 bodies, but more largely to their roughness. Friction 
 proper is independent of the velocity of the motion and of 
 the area of contact. It depends upon the nature of the two 
 surfaces and upon the pressure upon them, and varies 
 
130 
 
 SCHOOL PHYSICS. 
 
 FIG. 71. 
 
 directly as such pressure. The quotient arising from 
 dividing the force necessary to keep the body in motion 
 
 by the normal pressure 
 that the body exerts on 
 the surface over which it 
 moves, i.e., the ratio be- 
 tween the friction and the 
 pressure, is called the co- 
 efficient of friction. 
 
 (a) Friction is generally lessened by polishing and lubricating the 
 surfaces that move upon each other, and often by making the two 
 bodies of different material. The axles of railway cars are made of 
 steel, the boxes in which they turn are made of brass, the surfaces are 
 made smooth and kept oiled. In spite of all these precautions, the 
 axle often becomes heated by friction to such an extent as to render 
 it necessary to stop the train. 
 
 128. A Lever is an inflexible bar freely movable about a 
 fixed axis called the fulcrum. Every lever is said to have 
 two arms. The power arm is the perpendicular distance 
 from the fulcrum to the line in which the power acts ; the 
 weight arm is the perpendicular distance from the ful- 
 crum to the line in which the weight acts. If the arms 
 are not in the same straight line, the lever is called a 
 bent lever. 
 
 (a) There are three classes of levers, depending upon the relative 
 positions of power, weight, and fulcrum. 
 
 Fia. 72. 
 (1) If the fulcrum is between the power and weight (PFW), the 
 
SIMPLE MACHINES. 
 
 131 
 
 lever is of the first class (Fig. 72) ; e.g., crowbar, balance, steelyard, 
 scissors, pincers. 
 
 (2) If the weight is between the power and the fulcrum (P WF), 
 the lever is of the second class 
 
 (Fig. 73); e.g., cork-squeezer, nut- 
 cracker, wheelbarrow. ^r 
 
 (3) If the power is between the p 
 weight and the fulcrum (WPF), 
 the lever is of the third class 
 (Fig. 74) ; e.g., fire-tongs, sheep- 
 shears. 
 
 FIG. 74. 
 
 FIG. 75. 
 
 (b) In the bent lever, represented in Fig. 75, and acted upon 
 
 by two forces not par- 
 allel, the arms are not 
 FP'and FW,butFP 
 and FW. 
 
 129. Mechanical 
 Advantage of the 
 Lever. The gen- 
 eral laws of machines may be adapted to the lever as 
 follows : A given power will support a weight as many times 
 as great as itself as the power arm is times as long as the 
 weight arm. 
 
 (a) The ratio between the arms of the lever will be the same as the 
 ratio between the velocities of the power and the weight, and the same 
 as the ratio between the distances moved by the power and the weight. 
 If the power arm is twice as long as the weight arm, the power will 
 move twice as fast and twice as far as the weight does. The power 
 and weight are inversely proportional to the corresponding arms of 
 the lever : 
 
 P: W::WF:I>F. 
 
 The power multiplied by the power arm equals the weight multi- 
 plied by the weight arm : 
 
 P x PF = W x WF. 
 
 NOTE. In all experimental work, the lever should be loaded so as 
 to be in equilibrium before the power and weight are applied. It is 
 
132 SCHOOL PHYSICS. 
 
 to be noticed that, when we speak of the power multiplied by the 
 power arm, we refer to the abstract numbers representing the power 
 and power arm. We cannot multiply pounds by feet, but we can 
 multiply the number of pounds by the number of feet. 
 
 130. The Moment of a Force with respect to a given 
 point is its tendency to produce rotation about that point, 
 and is measured by the product of the numbers represent- 
 ing respectively the magnitude of the force and the perpen- 
 dicular distance between the given point and the line of the 
 force. 
 
 (a) In the case of the lever represented in Fig. 72, the weight arm 
 is 8 mm., and the power arm is 30 mm. Suppose that the power is 
 4 grams and represent the weight by x. Then the moment of the 
 force acting on the power arm will be represented by (4 x 30 =) 120, 
 and the moment of the force acting on the weight arm by 8 a:. 
 
 131. Moments Applied to the Lever. Sometimes several 
 forces act upon one or both arms of a lever, in the same 
 
 1V or in opposite direc- 
 
 tions. Under such 
 
 & 
 20 1 Jg r s r 1 30 circumstances, the 
 
 c \ d \ / Zever m7 50 in equi- 
 
 i% s 2^ ifc librium when the sum 
 
 of the moments of the 
 
 forces tending to turn the lever in one direction is equal to 
 the sum of the moments of the forces tending to turn the 
 lever in the other direction. Representing the moments 
 of the several forces acting upon the lever represented 
 in the figure by their respective letters and numerical 
 values, 
 
 b+ c +d=a+e+f 
 
 or c + d a = e-\-f b. 
 
 30 + 30+40 = 30 + 25+45. 
 30 + 40-30 = 25 + 45-30. 
 
SIMPLE MACHINES. 
 
 133 
 
 132. The Balance is essentially a lever of the first class, 
 having equal arms. The beam carries a pan at each end, 
 one for the weights 
 used, the other for the 
 article to be weighed. 
 
 (a) Dishonest dealers some- 
 times use balances with arms 
 of unequal lengths. When 
 buying, they place the goods 
 on the shorter arm ; when 
 selling, on the longer. The 
 cheat may be exposed by 
 changing the goods and 
 weights to the opposite sides 
 
 of the balance. The true weight may be found by weighing the 
 article first on one side and then on the other, and taking the geo- 
 metrical mean of the t\vo false weights ; that is, by finding the square 
 root of the product of the two false weights. 
 
 (6) The true weight of a body may be found with a false balance 
 in another way. Place the article to be weighed in one pan, and 
 counterpoise it, as with shot or sand placed in the other pan. Remove 
 the article, and place known weights in the pan until they balance the 
 shot or sand in the other pan. These known weights will represent 
 the true weight of the article in question. 
 
 133. 
 
 Compound Lever. Sometimes it is not convenient 
 to use a lever sufficiently long to 
 make a given power support a given 
 weight. A combination of levers, 
 called a compound lever, may then 
 be used. Hay scales may be men- 
 tioned as a familiar illustration 
 of the compound lever. In this 
 case we have the following statical 
 
 FIG. 78. law : 
 
134 SCHOOL PHYSICS. 
 
 The continued product of the power and the lengths of the 
 alternate arms, beginning with the power arm, equals the 
 continued product of the weight and the lengths of the alter- 
 nate arms, beginning with the weight arm. 
 
 CLASSROOM EXERCISES. 
 
 1. If a power of 50 pounds acting upon any kind of machine 
 moves 15 feet, () how far can it move a weight of 250 pounds? 
 (b) How great a load can it move 75 feet? 
 
 2. If a power of 100 pounds acting upon a machine moves with 
 a velocity of 10 feet per second, (a) to how great a load can it give a 
 velocity of 125 feet per second? (6) With what velocity can it move 
 a load of 200 pounds ? 
 
 3. A lever is 10 feet long with its fulcrum in the middle. A power 
 of 50 pounds is applied at one end. (a) How great a load at the other 
 end can it support? (6) How great a load can it lift? 
 
 Ans. (b) Anything less than 50 pounds. 
 
 4. The power arm of a lever is 10 feet. The weight arm is 5 feet, 
 (a) How long will the lever be if it is of the first class? (6) If it is 
 of the second class? (c) If it is of the third class? 
 
 5. A bar 12 feet long is to be used as a lever, keeping the weight 
 3 feet from the fulcrum, (a) What class or classes of levers may it 
 represent? (b) What weight can a power of 10 pounds support in 
 each case ? 
 
 6. The length of a lever is 10 feet. Four feet from the fulcrum 
 and at the end of that arm is a weight of 40 pounds ; two feet from 
 the fulcrum, on the same side, is a weight of 1,000 pounds. What 
 force at the other end will counterbalance both weights? 
 
 Ans. 360 pounds. 
 
 7. At the opposite ends of a lever 20 feet long, two forces are act- 
 ing whose sum is 1,200 pounds. The lengths of the lever arms are as 
 2 to 3. What are the two forces when the lever is in equilibrium? 
 
 8. The length of a lever is 8 feet, and its fulcrum is in the center. 
 A force of 10 pounds acts at one end ; 1 foot from it is another of 
 100 pounds ; 3 feet from the other end is a force of 100 pounds. The 
 direction of all the forces is downward. Where must a downward 
 force of 80 pounds be applied to balance the lever ? 
 
 Ans. 3 feet from the fulcrum. 
 
SIMPLE MACHINES. 135 
 
 9. The length of a lever, ab, is 6 feet. The fulcrum is at c. A 
 downward - force of 60 pounds acts at a ; one of 75 pounds, at a 
 point, d, between a and c, 2|- feet from the fulcrum. Required the 
 amount of equilibrating force acting at 6, the distance between b and 
 c being f of a foot. 
 
 10. On a lever, ab, a downward force of 40 pounds acts at a, 10 
 feet from fulcrum, c; on the same side, and 6| feet from c, a 56-pound 
 force, d, acts upward. The distance, 6c, is 3 feet. A downward force 
 of 96 pounds acts at b. (a) Where must a fourth force of 28 
 pounds be applied to balance the lever, and (6) what direction must 
 it have ? 
 
 11. A beam 18 feet long is supported at both ends. A weight of 1 
 ton is suspended 3 feet from one end, and a weight of 14 hundred- 
 weight 8 feet from the other end. Give the pressure on each point of 
 support. Ans. 2,288| pounds at one end. 
 
 12. The length of a lever is 3 feet. Where must the fulcrum be 
 placed so that a weight of 200 pounds at one end shall be balanced 
 by 40 pounds at the other end ? 
 
 13. In one pan of a false balance, a roll of butter weighs 1 pound 
 9 ounces ; in the other, 2 pounds 4 ounces. Find the true weight. 
 
 14. A and B, at opposite ends of a bar 6 feet long, carry a weight 
 of 300 pounds suspended between them. A's strength being twice as 
 great as B's, where should the weight be hung? 
 
 15. A and B carry a quarter of beef weighing 450 pounds on a rod 
 between them. A's strength is 1| times that of B's. The rod is 8 feet 
 long. Where should the beef be suspended? 
 
 16. The length of a lever is 16 feet. At one end is a weight of 100 
 pounds. What power applied at the other end, 3^ feet from the ful- 
 crum, is required to move the weight? 
 
 17. A power of 50 pounds acts upon the long arm of a lever of the 
 first class. The arms of this lever are 5 and 40 inches respectively. 
 The other end acts upon the long arm of a lever of the second class. 
 The arms of this lever are 6 and 33 inches respectively, (n) Figure 
 the machine, (b) Find the weight that may be thus supported, 
 (c) What power will support a weight of 4,400 kilograms? 
 
 18. A uniform bar of metal 10 inches long weighs 4 pounds. A 
 weight of 6 pounds is hung from one end of the bar. Determine the 
 position of the fulcrum upon which the loaded bar will balance. 
 
136 
 
 SCHOOL PHYSICS. 
 
 FIG. 70. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. A handful of wheat; weights made of 
 bags containing sand ; a tin can of known weight to serve as a scale- 
 pan ; wooden bars, blocks; and board as described below ; plumbago 
 powder; a stout coverless dry-goods box to replace the frame shown 
 in Fig. 81, and a wooden cylinder about 8 inches in diameter and 
 long enough to reach across the box from side to side. 
 
 1. Weigh five samples of wheat, each containing 20 grains. Deter- 
 mine the w r eight of the average grain of wheat and the number 
 
 of such grains of 
 wheat in a bushel of 
 60 pounds. 
 
 2. Support a 
 wooden bar, prefera- 
 bly graduated (the 
 yardstick or the meter 
 rod will answer ad- 
 mirably), by a pin and 
 clevis at the middle of 
 its length, as shown in 
 Fig. 79. Put the bar in equilibrium (as in all such experimental 
 cases), and provide stops 2 or 3 inches below each end of the bar 
 to limit its oscillations. Support 
 equal and known weights by thread 
 loops at equal distances from the 
 middle of the lever, and compare 
 the reading of the dynamometer 
 with the sum of the suspended 
 weights. Do they agree ? If not, 
 why not ? Make the necessary cor- 
 rection. 
 
 3. Modify the apparatus used 
 in Exercise 2 by removing the 
 dynamometer and adding a coun- 
 terpoise, as shown in Fig. 80. Re- 
 place the weight at A with one 
 twice as heavy, and shift its position until the bar is in equilibrium. 
 Note the distances of C and B from 0. Using either form of ap- 
 paratus, load the two arms of the lever with weights of varying ratios, 
 
 FIG. 80. 
 
SIMPLE MACHINES. 137 
 
 and note the agreement or disagreement of your results with the sev- 
 eral statements made in 129 and 131. 
 
 4. Provide two additional fixed pulleys and use the apparatus in an 
 experimental verification of the equations given in 131. 
 
 5. Take two points at slightly different distances from 0, the ful- 
 crum of the balance-beam. Suspend an unknown weight from one of 
 these points, and counterpoise it with known weights at the other point 
 so taken. Verify the statements made in 132 (a). 
 
 6. From one of the points taken as directed in Exercise 5, sus- 
 pend a tin can, and put the lever in equilibrium. From the other 
 of those two points, suspend a body of unknown weight, and find 
 its true weight by the process of double weighing, as described in 
 132 (&). 
 
 7. Get a board 4 or 5 feet long and about 1 foot wide ; also a 
 wooden block about 2x4x8 inches. Plane the board on one side, 
 and the block on one of its 2 x 8 inch and on one of its 4 x 8 inch 
 faces. Insert a small screw-eye or screw-hook at the middle of one 
 of its 2x4 inch faces. Weigh the block. Attach a cord to the screw- 
 eye so that the block may be drawn lengthwise on the board, the 
 other end of the cord being attached to a spring-balance or to a scale- 
 pan, as shown in Fig. 71. Place the board horizontal, with its rough 
 surface up. Place the 2x8 inch rough surface of the block on the 
 board, and draw the block, using the spring-balance or sufficient 
 weights, and keeping the cord horizontal. Ascertain what force is 
 necessary to start the load. Determine the force that will just main- 
 tain the sliding motion while you keep tapping on the table. Deter- 
 mine the coefficient of friction for these two surfaces. Find the 
 averages of several tests. 
 
 Place the block upon its 4x8 inch rough surface, and repeat the 
 work. How does the coefficient of friction now compare with that 
 obtained in the first set of tests ? 
 
 Turn the board over, and place the 2x8 inch smooth face of the 
 block upon it. Make a similar set of tests. 
 
 Place the block on its 4x8 inch smooth face, and make another set 
 of tests. How does the coefficient obtained in the last set of tests com- 
 pare with that of the third set ? How do the coefficients of the third 
 and fourth sets compare with those of the first and second sets? 
 
 Repeat the third and fourth sets of tests with weights on the blocks 
 so that the load moved shall be successively 2, 3, and 4 times the 
 weight of the block. 
 
138 SCHOOL PHYSICS. 
 
 Smear the smooth surfaces of the board and the block with pow- 
 dered graphite or plumbago, such as is sold for chains of bicycles, 
 and repeat the tests with the heavier loads previously used. 
 
 Record all of the conclusions that you draw from this series of 
 experiments. 
 
 8. Place the block with its broad and smooth face upon two round 
 lead pencils that lie parallel upon the smooth face of the board. 
 Determine the coefficient of rolling friction, and compare it with the 
 coefficient of sliding friction for the same surfaces. 
 
 9. Wind the draw-cord several times around a cylinder, and arrange 
 apparatus as shown in Fig. 81. Load the cylinder with four equal 
 
 weights carried on cords, so that 
 the weight of the cylinder and 
 its load shall equal the weight 
 of the block and some one of its 
 loads as used in Exercise 7. 
 Determine the coefficient of roll- 
 ing friction, and compare it with 
 
 that obtained for sliding friction 
 FIG. 81. i i 
 
 under an equal pressure. 
 
 10. Prepare a slightly tapering pine rod about 15 inches long and 
 about 1 inch square at the larger end. Balance it upon a knife-edge or 
 other sharp support to determine the distance of the center of mass 
 from the- ends of the rod. The block marked A in Fig. 17 will answer 
 as a fulcrum for this and the other purposes of this exercise. Indicate 
 the line of support by a pencil mark across the rod. Weigh the rod 
 accurately. Half an inch from the heavy end of the rod, suspend by a 
 thread loop a weight of 20 grams, and so adjust the fulcrum that the 
 lever thus loaded will balance. In all such cases, see that the fulcrum- 
 edge is exactly crosswise the length of the lever. Measure the dis- 
 tances between the fulcrum and the weight, and the fulcrum and the 
 center of mass. Determine the moment of the 20 grams and of the 
 weight of the lever, and see how the two compare. Shift the position 
 of the 20 grains weight, and repeat the work. Increase the suspended 
 weight to 25 or 30 grams, and repeat the previous tests. Record your 
 conclusions. 
 
 11. Suspend a weight of 100 grams 5 centimeters from one end of 
 a meter bar, and a weight of 500 grams 5 centimeters from the other 
 end. Find the point from which the bar thus loaded must be sus- 
 pended in order that the " system " may just balance. From the 
 
SIMPLE MACHINES. 
 
 139 
 
 principles of 94 and 131, calculate the weight of the meter bar. 
 Verify the result by actual weighing. 
 
 134. The Wheel and Axle consists of a wheel united to 
 a cylinder in such a way that they may turn together on a 
 common axis. It 
 is a modified lever 
 of the first or 
 second class. 
 
 (a) Considered as a 
 lever, the fulcrum is 
 FlG 82 at the common axis, 
 
 while the arms of the 
 
 lever are the radii of the wheel and of the 
 axle. The usual arrangement is to take ac, 
 the radius of the wheel, as the power arm, and 
 axle, as the weight arm. 
 
 FIG. 83. 
 
 , the radius of the 
 
 135. Mechanical Advantage of the Wheel and Axle. 
 Evidently, what was said concerning the advantage of 
 the lever is equally ap- 
 plicable here : 
 
 or 
 
 P : W:: W F : PF, 
 P: W'.'.r-.R, 
 
 the radii of the wheel 
 and of the axle respec- 
 tively being represented 
 by R and r. But 
 
 r : R : : d : D, and r : R : : c : C. 
 
 In other words, the mechanical advantage of this machine 
 equals the ratio between the radii, diameters, or circumfer- 
 ences of the wheel and of the axle. 
 
 FIG. 84. 
 
140 
 
 SCHOOL PHYSICS. 
 
 FIG. 85. 
 
 136. Modifications of the Wheel and Axle. It is not 
 necessary that an entire wheel be present, a single spoke 
 
 or radius being sufficient 
 for the application of the 
 power, as in the case of 
 the windlass (Fig. 84) 
 or the capstan (Fig. 85). 
 
 (a) In the differential or 
 Chinese windlass, different 
 parts of the cylinder have 
 different diameters, the rope 
 winding upon the larger and 
 unwinding from the smaller 
 parts. By one revolution, the load is lifted a distance equal to the 
 difference between the circumferences of the two parts of the axle. 
 
 (6) The advantage of the wheel and axle may be increased by 
 combining several, so that the axle of the first may act on the wheel 
 of the second, and so on. The arrange- 
 ment is closely analogous to the compound 
 lever. The transmission of motion may 
 be effected in three or more ways : 
 
 (1) By the friction of their circum- 
 ferences, as in some sewing machines. 
 
 (2) By bands or belts, as in a turning 
 lathe, bicycle, or sewing machine. 
 
 (3) By teeth or cogs, as in Fig. 86. In 
 any case, the advantage may be computed 
 by applying the general laws of machines 
 ( 124). 
 
 CLASSROOM EXERCISES. 
 
 1. The pilot wheel of a boat is 3 feet in diameter; the axle, 6 
 inches. The resistance of the rudder is 180 pounds. What power 
 applied to the wheel will move the rudder ? 
 
 2. Four men are hoisting an anchor of 1 ton weight. The barrel 
 of the capstan is 8 inches in diameter. The circle described by the 
 handspikes is 6 feet 8 inches in diameter. How great a pressure 
 must each of the men exert ? 
 
 FIG. 80. 
 
SIMPLE MACHINES. 
 
 141 
 
 3. With a capstan, four men are raising a 1,000-pound anchor. 
 The barrel of the capstan is a foot in diameter. The handspikes used 
 are 5 feet long. Friction equals 10 per cent of the weight. How much 
 force must each man exert to raise the anchor ? 
 
 4. The circumference of a wheel is 8 feet; that of its axle, 16 
 inches. The weight, including friction, is 85 pounds. How great 
 a power will be'required to raise it ? 
 
 5. A power of 70 pounds, on a wheel whose diameter is 10 feet, 
 balances 300 pounds on the axle. Give the diameter of the axle. 
 
 6. An axle 10 inches in diameter, fitted with a winch 18 inches 
 long, is used to draw water from a well, (a) How great a power 
 will it require to raise a cubic foot of water which weighs 62 pounds ? 
 (6) How much to raise 20 liters of water ? 
 
 7. A capstan whose barrel has a diameter of 14 inches is worked 
 by two handspikes, each 7 feet long. At the end of each handspike 
 a man pushes with a force of 30 pounds ; 2 feet from the end of each 
 handspike a man pushes with a force of 40 pounds. Required the 
 effect produced by the four men. 
 
 8. How long will it take a horse, working at the end of a bar 7 
 feet long, the other end being in a capstan which has a barrel of 14 
 inches' diameter, to pull a house through 5 miles of streets, if the 
 horse walks at the rate of 2| miles an hour? 
 
 9. Give a good definition and illustration of "inductive reasoning." 
 (Get your information from any available source, but get it.) 
 
 137. A 
 
 i_ 
 
 FIG. 
 
 Pulley is a wheel having a grooved rim for carry- 
 ing a rope or other 
 ^yj\ line, and turning on 
 
 an axis carried in a 
 ; frame, called a pulley 
 
 block. The pulley is 
 
 fixed if the block is 
 
 stationary (Fig. 87) ; 
 
 the pulley is movable 
 
 if the block moves 
 
 during the action of 
 
 the power (Fig. 88). 
 
 FIG. 88. 
 
142 
 
 SCHOOL PHYSICS. 
 
 (a) The pulley is a lever with equal arms of the first or second class, 
 but, when it moves, the attachments of the forces are moved. The 
 underlying fact that enables 
 the pulley to afford any me- 
 chanical advantage is the 
 uniformity of the tension of 
 the cord in all of its parts, 
 the pulley itself serving only 
 to diminish the friction. 
 
 FIG. 89. 
 
 138. Systems of Pul- 
 leys. Combinations 
 of pulleys are made in 
 great variety. In the 
 forms most commonly 
 used, one continuous cord passes 
 around all the pulleys. Fre- 
 quently two or more sheaves are 
 mounted in the same block and 
 turn on the same axis, as in the 
 common block and tackle, shown in Fig. 90. 
 
 FIG. 90. 
 
 FIG. 91. 
 
 (a) Another arrangement, sometimes 
 seen on board merchant ships, requires a 
 separate cord for each pulley. (See Fig. 102.) 
 
 (&) In the differential pulley, an endless 
 chain is reeved upon a solid wheel that has 
 two grooved rims and is carried in a fixed 
 block above, and upon a pulley below, as is 
 shown in Fig. 91. The two rims of the 
 single wheel in the upper block have dif- 
 ferent diameters, and carry projections to 
 keep the chain from slipping on them. 
 When the chain is pulled down until the 
 upper wheel turns once upon its axis, the 
 chain between the two pulleys is shortened 
 by the difference between the circumferences 
 
SIMPLE MACHINES. 143 
 
 of the two rims of the upper wheel, and the load is lifted half that 
 distance. This device avoids the use of inconveniently long ropes or 
 chains. In Fig. 91, the hoisting apparatus is hooked into the triangu- 
 lar frame of a traveler which is supported by rollers on the rail- 
 way overhead. 
 
 139. Mechanical Advantage of the Pulley. With the 
 ordinary arrangement of pulleys, like the block and 
 tackle, the part of the cord to which the power is applied 
 carries but a part of the load, the magnitude of that part 
 varying inversely as the number of sections into which 
 the movable pulley divides the load. With pulleys thus 
 arranged, a given power will support a weight as many 
 times as great as itself as there are parts of the cord sup- 
 porting the movable block. 
 
 W=Pxn. 
 
 (a) In the case of the differential pulley, the mechanical advan- 
 tage may be determined by the laws given in 124. 
 
 (6) In all experiments to determine the mechanical advantage 
 of a system of pulleys, as in all similar experiments, see that the 
 apparatus is in equilibrium before applying P and W. 
 
 140. An Inclined Plane is a smooth, hard, inflexible surface, 
 inclined so as to make an 
 
 oblique angle with the horizon. 
 
 (a) When a body is placed on 
 an inclined plane, the gravity pull 
 is resolved into two component 
 forces. One of these acts perpen- 
 dicularly to the plane, producing 
 pressure on it, the other compo- FIG. 92. 
 
 nent tending to produce motion 
 
 down the plane. To resist this last-mentioned tendency, and thus 
 to hold the body in its position," a force may be applied in three 
 ways : 
 
144 
 
 SCHOOL PHYSICS. 
 
 (1) In a direction parallel to the length of the plane. 
 
 (2) In a direction parallel to the base of the plane; i.e., hori- 
 zontal. 
 
 (3) In a direction parallel to neither the length nor the base. 
 
 141. Mechanical Advantage of the Inclined Plane. The 
 mechanical advantage to be derived from the use of an 
 inclined plane varies with the three 
 conditions above given. 
 
 20 Kg. 
 
 10 "Kg. 
 
 FIG. 93. 
 
 (1) When a given power acts par- 
 allel to an inclined plane, it will sup- 
 port a weight as many times as great 
 as itself as the length of the plane is 
 times as great as its vertical height. 
 
 (2) When a given power acts horizontally, it will sup- 
 port a weight as many times as great as itself as the 
 horizontal base of the plane is times as great as its vertical 
 height. 
 
 (3) When the power acts in a direction parallel to 
 neither the length nor the base, no law can be given. 
 The ratio of the power to the weight may be determined 
 trigonometrically, or, with 
 
 approximate accuracy, by 
 resolving the force of grav- 
 ity, the construction and 
 measurement being care- 
 fully done. 
 
 (a) In Fig. 9, LM repre- 
 sents an inclined plane on which 
 a ball is to be supported by a 
 force acting parallel to the 
 plane. Represent the gravity of W by the vertical line, WC, and 
 
SIMPLE MACHINES. 145 
 
 resolve it into two components. WD produces pressure on the plane, 
 and WB draws the body down the plane. A force represented by 
 WB', the equilibrant of WB, will just balance the downward pull of 
 WB, and hold the ball in position. From the similarity of the tri- 
 angles, CWB and LMN, it may be proved that 
 
 WB : WC : : MN : ML. 
 
 Careful construction and measurement will give the same result. 
 But WB, or its equal, WB' } represents the power, and WC represents 
 the weight of the body. MN represents the height of the plane, and 
 ML its length. Therefore 
 
 P : W : : h : I. 
 
 By similarly resolving the force of gravity into two components, 
 one perpendicular to the plane and the other horizontal, the second 
 law as given above may be established. 
 
 CLASSROOM EXERCISES. 
 
 1 . With a fixed pulley, what power will support a weight of 50 
 pounds? 
 
 2. With a movable pulley, what power will support a weight of 
 50 pounds? 
 
 3. With block and tackle, the fixed block having four sheaves and 
 the movable block having three, what weight may be supported by a 
 power of 75 pounds ? If an allowance of | is made for friction and 
 rigidity of ropes, what is the maximum weight that may be thus 
 supported ? 
 
 4. With a system of five movable pulleys, one end of the rope being 
 attached to the fixed block, what power w T ill raise a ton ? 
 
 5. If, in the system mentioned in Exercise 4, the rope is attached 
 to the movable block, what power will raise a ton? If an allowance 
 of 25 per cent is made for friction and rigidity of ropes, what power 
 will be required ? 
 
 6. With a pulley of six sheaves in each block, what is the 
 least power that will support a weight of 1,800 pounds, allow- 
 ing for friction? What will be the relative velocities of P 
 and W? 
 
 10 
 
146 SCHOOL PHYSICS. 
 
 7. Figure a set of pulleys by which a power of 50 pounds will 
 support a weight of 250 pounds. 
 
 8. A boy who can lift only 100 pounds wishes to put a barrel of 
 flour (196 pounds) into a wagon-box 5 feet above the ground. He 
 backs the wagon to one end of a plank 20 feet long and weighing 
 125 pounds. Show that he can, without help, use the plank as an 
 inclined plane for his purpose, and state how much force he exerts 
 (a) in getting the plank into position, and (6) how much in lifting 
 the flour? (c) How much work does he perform in lifting the flour ? 
 
 Am. (a) 62| pounds; (b) 49 + pounds. 
 
 9. How much energy must be expended to pull a 100-pound 
 weight up an inclined plane 10 feet, the vertical ascent accomplished 
 being 6 feet, and the coefficient of friction being 0.2? 
 
 10. The base of an inclined plane is 10 feet ; the height is 3 feet. 
 What force, acting parallel to the base, will balance a weight of 
 2 tons? 
 
 11. An incline has its base 10 feet ; its height, 4 feet. How heavy 
 a ball will 50 pounds power roll up ? 
 
 12. How great a power will be required to support a ball weigh- 
 ing 40 pounds on an inclined plane whose length is 8 times its 
 height? 
 
 13. A weight of 800 pounds rests upon an inclined plane 8 feet 
 high, being held in equilibrium by a force of 25 pounds acting parallel 
 to the base. Find the length of the plane. 
 
 14. A load of 2 tons is to be lifted along an incline. The power is 
 75 pounds. Give the ratio of the incline that may be used. 
 
 15. A 1,500-pound safe is to be raised 5 feet. The greatest power 
 that can be applied is 250 pound's. Give the dimensions of the shortest 
 inclined plane that can be used for that purpose. 
 
 16. A weight of 400 pounds is being raised by a block and tackle. 
 One end of the rope is fastened to the upper block. Each block has 
 two sheaves and weighs 10 pounds. What is the pressure on the 
 support of the upper block ? Disregard the weight of the rope. 
 
 Ans. 522 pounds. 
 
 142. A Wedge is a triangular prism of hard material, 
 fitted to be driven between objects that are to be sepa- 
 rated, or into anything that is to be split. It is simply a 
 movable inclined plane, or two such planes united at their 
 
SIMPLE MACHINES. 
 
 147 
 
 bases. The power is generally applied in repeated blows 
 on the thick end or "head." For a wedge thus used, no 
 definite law of any prac- 
 tical value can be given, 
 further than that, with a 
 given thickness, the longer 
 the wedge, the greater the 
 mechanical advantage. 
 
 FIG. 95. 
 
 143. A Screw is a cylinder, generally of wood 
 or metal, with a spiral ridge (the thread) wind- 
 ing about its circumference. 
 The thread works in a nut, 
 within which there is a cor- 
 responding spiral groove to 
 receive the thread. That the 
 screw is a modified inclined 
 plane, may be shown by 
 winding a triangular piece 
 of paper around a cylinder, 
 FIG. 97. as shown in Fig. 98. 
 
 (a) The power is generally applied by a 
 
 wheel or a lever, and moves 
 
 through the circumference 
 
 of a circle. The distance 
 
 between two consecutive 
 
 turns of any one continuous 
 
 thread, measured in the di- 
 rection of the axis of the 
 
 screw, is called the pitch of 
 
 the screw. 
 
 (6) The screw is largely used where great FIG. 99. 
 
 resistances are to be overcome, as in raising buildings, compressing 
 hay or cotton, propelling ships, etc. It is also used in accurate 
 
 FIG. 98. 
 
148 SCHOOL PHYSICS. 
 
 measurements of small distances, of which application the sphe- 
 rometer, and the micrometer calipers, afford good illustrations. 
 
 144. Mechanical Advantage of the Screw. With the 
 screw, a given power will support a weight as many times as 
 great as itself as the circumference described by the power is 
 times as great as the pitch of the screw. 
 
 145. Compound Machines. We have now considered 
 each of the six traditional simple machines. When any 
 two or more of these machines are combined, the me- 
 chanical advantage may be found by computing the 
 effect of each separately, and then compounding them ; 
 or by finding the weight that the given power will 
 support, using the first machine alone, considering the 
 result as a new power acting upon the second machine, 
 and so on. 
 
 CLASSROOM EXERCISES. 
 
 1. A bookbinder has a press, the screw of which has a pitch of i of 
 an inch. The nut is worked by a lever that describes a circumference 
 of 8 feet. How great a pressure will a power of 15 pounds applied at 
 the end of the lever produce, the loss by friction being equivalent to 
 240 pounds ? 
 
 2. A screw has 11 threads for every inch in length. If the lever 
 is 8 inches long, the power 50 pounds, and friction absorbs ^ of the 
 energy used, what resistance may be overcome by it? 
 
 3. A screw with threads lj inches apart is driven by a lever 4| feet 
 long. What is the mechanical advantage of the apparatus? 
 
 4. How great a pressure will be exerted by a power of 15 pounds 
 applied to a screw whose head is 1 inch in circumference, and whose 
 threads are $ of an inch apart ? 
 
 5. At the top of an inclined plane that rises 1 foot in 20 is a 
 wheel and axle. The radius of the wheel is 2| feet; radius of axle, 
 4| inches. What load may be lifted by a boy who turns the wheel 
 with a force of 25 pounds ? 
 
SIMPLE MACHINES. 
 
 149 
 
 6. In moving a building, the horse is harnessed to the end of 
 a lever 7 feet long, acting on a capstan barrel 11 inches in diameter. 
 On the barrel winds a rope belonging to a system of 2 fixed and 
 3 movable pulleys. What force will be exerted by 500 pounds power, 
 allowing for loss by friction ? 
 
 7. In raising a building, why do the men who work the jackscrews 
 pull upon the levers by a series of jerks instead of steady pulls? 
 
 W 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus. Pulleys and cords that are strong enough 
 to support at least 100 pounds.* 
 
 1. Experimentally determine the ratio of power to weight with 
 pulleys arranged as shown 
 in Fig. 100. 
 
 2. Determine the loss due 
 to friction and to the rigidity 
 of the ropes used in Exer- 
 cise 1. 
 
 3. Experimentally deter- p IG JQQ 
 mine the ratio of power to 
 
 weight with pulleys arranged as shown in Fig. 101. 
 
 4. Show how the work done at P, in Exercise 3, compares with 
 
 the work done at W, and account 
 
 for any difference if you find 
 any to exist. 
 
 5. Experimentally Determine 
 the ratio between P and W with 
 pulleys arranged as shown in 
 Fig. 102. Determine the static 
 law of such a combination. 
 
 6. The height of an inclined 
 
 plane is its horizontal base. 
 
 A globe weighing 250 Kg. is sup- 
 ported in place by a force acting 
 
 at an angle of 45 with the base. 
 
 The pressure of the globe upon 
 
 the plane is less than 250 Kg. 
 
 By construction and measure- 
 ment, determine the magnitude of the support- 
 ing force. 
 
 Fm. 102. 
 
150 SCHOOL PHYSICS. 
 
 7. With the conditions as given in Exercise 6, except that the 
 pressure of the globe upon the plane is more than 250 Kg., determine 
 the magnitude of the supporting force. 
 
 8. Place the board used in Experiment 7 so that it may be used 
 again as an inclined plane. Tie one end of a cord to the carriage 
 used in the same experiment, and the other end to a spring-balance. 
 The dynamometer and the cord are to be used in pulling the carriage 
 up the incline. Varying the load and the inclination of the plane in 
 each case, verify the statements made in 141. Be sure that the 
 board does not bend or sag under the load. Watch for error in the 
 zero point of the balance when held in^ different positions, and, if any 
 is detected, make correction for it. To determine the correction to 
 be made for friction, find first the pull necessary to move the carriage 
 up the incline at a uniform speed, and then the pull which will allow 
 it to move down the incline at a uniform speed. The difference be- 
 tween these two pulls will be twice the force required to overcome the 
 friction, and the average of the two pulls will be the force that would 
 be required if friction could be eliminated. 
 
 9. Arrange an inclined plane so that its base shall be 1| times its 
 height. Draw a diagram for the resolution of the force of gravity 
 and determine the tendency of a ball that weighs 7^ pounds to roll 
 down the plane, and the pressure of the ball on the plane. Suspend 
 the ball by two spring-balances, so that one of them is drawn par- 
 allel to the plane and the other perpendicular to it when the ball is 
 just lifted off the plane. Note the reading of the dynamometers and 
 compare them with the computed results. 
 
 VII. THE MECHANICS OE LIQUIDS. 
 
 146. Compressibility and Elasticity of Liquids. Liquids 
 are nearly incompressible. When the pressure is removed, 
 the liquids regain their former volume, showing thus 
 their perfect elasticity. The practical incompressibility 
 of liquids is of great mechanical importance. 
 
THE MECHANICS OF LIQUIDS. 151 
 
 Liquid Pressure. 
 
 Experiment 58. Fill a small bottle with water, hold a Prince 
 Rupert drop in its mouth, and break off the tapering end of the 
 " drop." The whole " drop " will- be instantly shattered, and the force 
 of the concussion transmitted in every direction to the bottle, which 
 will be thus broken. These " drops " are not expensive. 
 
 Experiment 59. Tie a piece of thin sheet rubber (such as you can 
 get from the druggist or dentist, or from a broken toy balloon) over 
 the large end of a lamp-chimney. Reinforce the other end by wind- 
 ing upon it a dozen turns of wrapping twine, and fit it with a fine- 
 grained cork or rubber stopper through which passes snugly a bit of 
 glass tubing. (See Chemis- 
 try, Appendices 4 [6] and 9.) 
 Connect the glass tubing and 
 a supported funnel by two 
 or three feet of rubber tub- 
 ing. Fill the apparatus with 
 water, loosening the cork for F IGi N)3. 
 
 a moment to allow the escape 
 
 of air. See that the funnel is still half full of water and elevated 
 above the chimney. Notice the effect of the water pressure on the 
 sheet rubber. Hold the chimney in various positions, keeping the 
 center of the sheet rubber at a uniform distance below the level of 
 the funnel, and notice whether the elastic sheet is stretched more or 
 less when the liquid pressure upon it is horizontal, upward, or down- 
 ward. Then try it at varying distances below the level of the water 
 in the funnel, and determine whether such vertical distance or "head" 
 has any relation to the pressure. 
 
 Experiment 60. To the cork of Experiment 59, fit a bit of glass 
 tubing that has been drawn to a jet at the outer end. Hold the 
 chimney in different positions and at different depths, adding water 
 as may be necessary to keep a constant level in the funnel. 
 
 147. Transmission of Pressure. Fluids transmit pres- 
 sures in every direction. 
 
 (a) Fig. 104 represents a number of balls placed in a vessel. 
 Imagine these balls to have perfect freedom of motion and perfect 
 
152 
 
 SCHOOL PHYSICS. 
 
 FIG. 104. 
 
 elasticity. It is evident that if a downward pressure, say of 10 grams, 
 is applied to 2, it will force 5 and 4 toward the left, and 6, 7, and 
 8 toward the right, thus forming lateral pressure. This motion of 
 5 will force 1 upward, and 9 downward, etc. 
 Owing to the perfect elasticity and freedom of 
 motion, there will be no loss, and the several 
 balls will be moved just as if the original pres- 
 sure had been applied directly to each one. The 
 pressure will be thus transmitted to all of the 
 balls without loss, and the total pressure exerted 
 on the sides of the vessel will equal 10 grams 
 multiplied by the number of balls that touch the sides. It makes no 
 difference with the result whether the pressure exerted by 2 was the 
 result of its own weight only, this weight together with the weight 
 of overlying balls, or both of these with still additional pressure. 
 
 (6) Disregarding viscosity, we may consider a fluid to be made 
 up of molecules having the perfect elasticity and freedom of motion 
 assumed for the balls just discussed. Hence, when pressure is applied 
 to one or more of the molecules of a fluid, the pressure will be trans- 
 mitted as now explained. 
 
 148. Pascal's Law. Pressure exerted anyivhere upon a 
 liquid inclosed in a vessel is transmitted undiminished in all 
 directions, and acts with the 
 same force upon all equal sur- 
 faces, and in a direction at 
 right angles to those surfaces. 
 
 (a) Provide two communicating 
 tubes of unequal sectional area. 
 When water is poured into these, 
 it will stand at the same height in 
 both tubes, a fact which of itself 
 partly confirms the law above given. 
 If, by means of a piston, the water 
 in the smaller tube is subjected to 
 pressure, the pressure will force the 
 water back into the larger tube, 
 and raise its level there. To prevent this result, a piston must be 
 
 FIG. 105. 
 
THE MECHANICS OF LIQUIDS. 
 
 158 
 
 fitted to the larger tube, and held there with a greater force. If, for 
 example, the smaller piston has an area of 1 sq. cm., and the larger 
 piston an area of 16 sq. cm., a weight 
 of 1 Kg. may be made to support a 
 weight of 16 Kg. 
 
 149. The Hydraulic Press. - 
 
 Pascal's law finds an important 
 application in the hydraulic 
 press, in the more common 
 forms of which the pressure of 
 a piston operated by a lever is 
 transmitted through a pipe to 
 a piston of larger area. The 
 press is represented in section by Fig. 107, and in per- 
 spective by Fig. 108. 
 
 (a) If the power arm of the lever is ten times as long as the weight 
 arm, a power of 50 Kg. will exert a pressure of 500 Kg. upon the 
 
 FIG. 10G. 
 
 FIG. 107. 
 
 water beneath the piston, a. If this piston has a sectional area of 
 1 sq. cm., and the piston in B has an area of 500 sq. cm., then the pres- 
 
154 
 
 SCHOOL PHYSICS. 
 
 sure of 500 Kg. exerted by the small piston will produce a pressure 
 of 500 Kg. x 500 or 250,000 Kg. upon the lower surface of the large 
 piston. 
 
 FIG. 108. 
 
 Pressure due to Gravity. 
 
 Experiment 61. Make a small hole in the bottom of a tin fruit- 
 can or similar vessel. Push the can downward into water until the 
 open mouth of the can is " near the water's edge." The liquid will 
 spurt upward through the hole in a little jet. Why? 
 
 Experiment 62. Get a lamp-chimney, preferably cylindrical. 
 With a diamond or a steel glass-cutter, cut a disk of window glass 
 a little larger than the cross-section of the lamp-chimney. Pour some 
 fine emery powder on the disk, and rub one end of the chimney upon 
 it, thus grinding them until they fit accurately. With wax, fasten a 
 
THE MECHANICS OF LIQUIDS. 
 
 155 
 
 thread to the center of the ground surface of the disk, and draw that 
 surface against the ground end of the chimney. Holding the chimney 
 in the hand, or supporting it in any 
 convenient way, place it in water as 
 shown in Fig. 109. The upward pres- 
 sure of the water will hold the disk in 
 place. Pour water carefully into the 
 tube; the disk will fall as soon as the 
 weight of the water in the chimney, 
 plus the weight of the disk, exceeds the 
 upward pressure of the water. 
 
 FlG 
 
 Experiment 63. Into a U-tube, pour 
 
 enough mercury to fill each arm to the 
 
 depth of 3 or 4 cm. Place the U-tube 
 
 upon a table, and hold it upright by 
 
 any convenient means. Back of it, and 
 
 resting against it, stand a card having 
 
 a horizontal line, a, drawn on it to 
 
 mark the level of the mercury in the 
 
 two arms of the tube. To one arm, attach the neck of a funnel by 
 
 means of a bit of rubber tubing. The funnel may be held by the 
 
 ring of a retort stand. Pour water 
 slowly into the funnel until it is 
 nearly full, and mark the level of 
 the water by a suspended weight 
 or other means. In one arm, the 
 mercury will be depressed below 
 the line marked on the card; in 
 the other arm, it will be raised 
 above it an equal distance. Mark 
 these two mercury levels by dotted 
 horizontal lines on the card. Re- 
 move the funnel and replace it by 
 a funnel- or thistle-tube, making 
 the connection by means of a per- 
 forated cork. Pour water into the 
 funnel-tube until it stands at the 
 level indicated by the suspended 
 FIG. 110. weight, being careful that no air is 
 
156 
 
 SCHOOL PHYSICS. 
 
 confined in the tubes. Although much less water is in the funnel-tube 
 than was in the funnel, it forces the mercury into the position indi- 
 cated by the dotted lines on the card. The downward pressure of the 
 water in each case is measured by a mercury column with a height, ce, 
 equal to the vertical distance between the two dotted lines. 
 
 Experiment 64. Provide several glass vessels, open at each end, 
 and having equal bases, but varying shapes and capacities. In any 
 convenient way, support one of them, as M in Fig. 111. Close the 
 lower end of the vessel with a glass or metal disk, ground to fit it 
 
 FIG. 111. 
 
 water-tight, the disk being supported by a thread carried from one 
 end of a balance-beam. Place known weights in the scale-pan at the 
 other end of the beam, so that the disk shall be held firmly in place. 
 Pour water carefully into the upper or open end of the vessel, until 
 the pressure loosens the disk and allows a little to escape. By an 
 index rod, suspended weight, or other convenient means, mark the 
 upper level of the water at the moment when some of the liquid 
 begins to escape below. Repeat the experiment with the other ves- 
 sels in succession, using the same counterpoise in each case. The 
 disk will be loosened when the water has reached the marked level, 
 
THE MECHANICS OF LIQUIDS. 157 
 
 although the quantity of water used varies. The glass vessels for 
 this experiment may be easily secured by using glass tubing, a glass 
 funnel, corks, lamp chimneys, etc. (See Avery's Chemistry, Appen- 
 dix 4.) 
 
 150. Liquid Pressure due to Gravity. The downward 
 pressure of a liquid is independent of the shape of the 
 containing vessel and of the quantity of the liquid. It is 
 proportional to the depth of the liquid and the area of the 
 base. 
 
 151. Rules for Liquid Pressure. 
 
 (1) To find the downward or the upward pressure on any 
 submerged horizontal surface, find the weight of an imaginary 
 column of the given liquid, the base of which is the same 
 as the given surface, and the altitude of which is the same 
 as the depth of the given surface beloiv the surface of the 
 liquid. 
 
 (2) To find the pressure upon any vertical surface, find 
 the weight of an imaginary column of the liquid, the base of 
 which is the same as the given surface, and the altitude of 
 which, is the same as the depth of the 'center of the given 
 surface below the surface of the liquid. 
 
 (a) A cubic foot of water weighs 62.42 Ibs. or about 1,000 oz. 
 
 Liquid Level. 
 
 Experiment 65. Remove the jet from the cork used in Experi- 
 ment 60, and insert in its place a glass tube about two feet long. 
 Holding the chimney on the table-top with this glass tube upright, 
 fill the apparatus with water. Does the water stand at a higher level 
 in the funnel, or in the tube V Raise and lower the funnel, and for 
 each position notice the relation between the liquid levels in the 
 funnel and the tube. 
 
158 
 
 SCHOOL PHYSICS. 
 
 152. Communicating Vessels. When any liquid is 
 placed in one or more of several vessels communicat- 
 ing with each other, it 
 will not come to rest un- 
 til it stands at the same 
 height in all of the ves- 
 sels. This principle is 
 embodied in the familiar 
 expression, "Water seeks 
 its level." The princi- 
 ple is illustrated, on a 
 large scale, in the sys- 
 tem of pipes by which 
 water is distributed in 
 FIG. 112. cities. 
 
 CLASSROOM EXERCISES. 
 
 1. What will be the pressure on a dam in 20 feet of water, the dam 
 being 30 feet long? 
 
 2. What will be the pressure on a dam in 6 m. of water, the dam 
 being 10 m. long? 
 
 3. Find the pressure on one side of a cistern 5 feet square and 12 
 feet high, filled with water. 
 
 4. Find the pressure on one side of a cistern 2 m. square and 4 m. 
 high, filled with water. 
 
 5. A cylindrical vessel having a base of a square yard is filled with 
 water to the depth of two yards. What pressure is exerted upon the 
 base ? 
 
 6. A cylindrical vessel having a base of a square meter is filled 
 with water to the depth of 2 meters. What pressure is exerted upon 
 the base ? 
 
 7. What will be the upward pressure upon a horizontal plate a foot 
 square at a depth of 25 feet of water ? 
 
 8. What will be the upward pressure upon a horizontal plate 
 30 cm. square at a depth of 8 m. of water? 
 
THE MECHANICS OF LIQUIDS. 159 
 
 9. A square board with a surface of 9 square feet is pressed against 
 the bottom of the vertical wall of a cistern in which the water is 8 ; ^ 
 feet deep. What pressure does the water exert upon the board ? 
 
 10. A cubical vessel with a capacity of 1,728 cubic inches is two- 
 thirds full of sulphuric acid, which is 1.8 times as heavy as water. 
 Find the liquid pressure on one side of the vessel. 
 
 11. A conical vessel has a base with an area of 237 sq. cm. Its 
 altitude is 38 cm. It is filled with water to the height of 35 cm. 
 Find the pressure on the bottom. A ns. 8,295 g. 
 
 12. In Exercise 11, substitute inches for centimeters, and then find 
 the pressure on the bottom. 
 
 13. What is the total liquid pressure on a prismatic vessel con- 
 taining a cubic yard of water, the bottom of the vessel being 2 by 
 3 feet? 
 
 14. The lever of a hydraulic press is 6 feet long, the piston rod 
 being 1 foot from the fulcrum. The area of the tube is half a 
 square inch ; that of the cylinder is 100 square inches. Find the 
 weight that may be raised by a force of 75 pounds. 
 
 15. What is the pressure on the bottom of a pyramidal vessel filled 
 with water, the base being 2 by 3 feet, and the height 5 feet ? 
 
 16. What is the pressure on the bottom of a conical vessel 4 feet 
 high, filled with water, the base being 20 inches in diameter? 
 
 17. At what depth in water will the liquid pressure be 1 Kg. per 
 square centimeter? 
 
 18. A closed cylindrical vessel 30 cm. high is filled with water. 
 At the middle of its height, a bent tube communicates with the in- 
 terior of the vessel. Water stands in this tube at a height of 50 cm. 
 above the middle of the opening into the cylinder. What is the 
 liquid pressure per square centimeter on the upper end of the cylin- 
 der? On the lower end? 
 
 19. An upright cylindrical jar having a base of 100 sq. cm. and a 
 height of 20 cm. is filled with water. An open tube 1 sq. cm. in 
 cross-section passes through the cover, rises 30 cm. above it, and is 
 filled with water, (a) What is the weight of the water in the jar 
 and tube? (6) What is the liquid pressure on the square centimeter 
 of the base that lies exactly beneath the tube? (c) What square 
 centimeter of the base has a greater pressure ? (c?) A less pres- 
 sure? 
 
 20. (a) In the case of the jar and tube described in Exercise 19, 
 what is the liquid pressure upon that square centimeter of water at 
 
160 SCHOOL PHYSICS. 
 
 the level of the under side of the cover and beneath the tube? (6) Is 
 the liquid pressure against each square centimeter of the cover greater, 
 or less, than this ? (c) What is the total liquid pressure against the 
 cover ? 
 
 21. In the case of the jar and tube considered in Exercise 20, sub- 
 tract the total liquid pressure against the cover from the total liquid 
 pressure against the base, and compare the result with the weight of 
 the water in the jar and tube. 
 
 LABORATORY EXERCISES. 
 
 A dditional Apparatus, etc. Stout glass tubing ; an acid bottle ; a 
 wine bottle; linseed oil; rubber stoppers; mercury; tall hydrometer 
 jar. 
 
 1. Bend a piece of glass tubing into the shape shown in Fig. 113, 
 and support it upright in any convenient way. If you remove the 
 top and bottom from a box, and cut a slot in one of the remain- 
 ing sides, you will have a cheap and convenient support, Remove 
 the funnel from the apparatus used in Experiment 59, and connect 
 the rubber tubing to the glass tube at B. Half fill the 
 5 tube with water colored with red ink, and it becomes 
 a pressure gauge. The two liquid levels will lie in 
 the same horizontal plane. Mark this level on the 
 open arm of the gauge, and make it the zero of a 
 scale extending upward. Remember that an eleva- 
 tion of the liquid level above the zero mark measures 
 half the difference between the two liquid levels of 
 the gauge. Place the chimney in water at such a 
 depth that the liquid pressure exerted upon the rub- 
 ber diaphragm, and transmitted through all the coil- 
 ings of the rubber tubing, shall depress the surface at 
 m and raise that at n, until the difference of their 
 FIG. 113. levels, on, is, say, 1 cm. Note the depth of the dia- 
 phragm below the level of the water. Hold the chim- 
 ney in as many different positions as is convenient, but with the center 
 of the diaphragm at the same depth, and note the reading of the gauge. 
 Sink the chimney to a greater depth until on becomes successively 
 2 cm., 3 cm., etc., up to the limit of the gauge. Compare your results 
 with 147 and 150, and indicate any and all of the statements therein 
 made that your work confirms. 
 
THE MECHANICS OF LIQUIDS. 
 
 161 
 
 2. Cut the bottoms from a large bottle, and from another bottle of 
 about equal height but much less diameter. Close their mouths by 
 corks perforated by bits of glass tubing. Support the bottomless 
 bottles by thrusting their necks downward through two holes bored 
 in the top of a box. With rubber tubing, connect the glass tubes 
 that pass through the corks, making thus two communicating vessels. 
 Half fill the bottles with water, and mark the liquid level on each 
 bottle. Pour a measured quantity of oil into the smaller bottle until 
 it forms a layer several centimeters thick. The water-levels have 
 been changed. Pour measured quantities of the oil into the other 
 bottle until the water is restored to its marked levels. How do the 
 thicknesses of the two oil layers compare ? How do the volumes of 
 the two oil layers compare? How would the ratio between the 
 weights of these oleaginous additions differ from the ratio between 
 their volumes? With the calipers, measure the internal diameters 
 of the two bottles ; compute the cross-section areas of the two oil 
 cylinders. How does the ratio between these areas differ from the 
 previously determined ratios for volume and weight ? How does the 
 downward pressure per square centimeter in one branch correspond 
 to the pressure per square centimeter in the other branch ? 
 
 3. Provide a stout glass tube of the shape shown in 
 Fig. 114. Pour mercury into the upper end until it stands 
 at a depth of 1 or 2 cm. in the bend at a. Provide a 
 hydrometer jar with a depth as great as the length, ce, 
 and nearly fill it with water. Lower the long leg of the 
 tube into the water about ^ of its length. Measure the 
 vertical distance between the levels of the water within 
 and without the tube, and call it w. Measure the ver- 
 tical distance between the two mercury-levels, and call 
 it m. Lower the tube until f of the long arm is in the 
 water. Determine the distance between the two water- 
 levels, and call it w 1 ; determine the difference in the two 
 mercury-levels, and call it m'. Lower the tube until the 
 
 bend at c rests on the edge of the hydrometer jar, and, as FIG. 114. 
 before, determine the differences of the water-levels (to") 
 and of the mercury-levels (m"). What does the difference in the 
 mercury-levels in each case represent ? From the data secured, test 
 
 the equality of these ratios : = = / if you find that the quan- 
 tities are proportional, finish the following incomplete expression 
 11 
 
162 SCHOOL PHYSICS. 
 
 of the relation : In the body of a liquid, the upward pressure varies 
 as ... 
 
 4. Considering m, m', and m" as abscissas, and w, w', and w" as 
 ordinates, give a graphic representation of the data obtained in Ex- 
 ercise 3. Is your line straight, or curved? If it is straight, what does 
 that fact show? If it is curved, what does that fact show? 
 
 Principle of Archimedes. 
 
 Experiment 66. Suspend a stone or brick by a slender cord or 
 fine wire from the hook of a spring-balance, and note the reading of 
 the scale. Transfer the suspended load from air to water, and note 
 the reading. Transfer the load to a strong brine, and note the read- 
 ing. Transfer the load to kerosene, and note again the reading. It 
 seems as if the liquids help to support the stone, with a buoyant 
 force of varying magnitude. 
 
 Experiment 67. From one end of a scale-beam, suspend a cylin- 
 drical metal bucket, b, with a solid cylinder, a, that fits accurately 
 
 FIG. 115. 
 
 into it hanging below. Counterpoise with weights (shot or sand) in 
 the opposite scale-pan. Immerse a in water, and the counterpoise 
 
THE MECHANICS OF LIQUIDS. 163 
 
 will descend, as if a had lost some of its weight. Carefully fill 6 with 
 water. It will hold exactly the quantity displaced by a. Equilibrium 
 will be restored. 
 
 Experiment 68. For rough work, a spring-balance may take the 
 place of the beam-balance ; a tin pail may take the place of b ; a 
 piece of stone suspended beneath the pail by strings tied to the ears 
 of the pail may take the place of o; a larger tin pail filled with water 
 and set in a tin pan may take the place of the vessel of water shown 
 in Fig. 115. Note the weight of the smaller pail, with and without 
 the suspended stone. Lower the apparatus so that the stone shall be 
 immersed in the water, and note the reading of the scale. Determine 
 the loss of weight resulting from the immersion of the stone. The 
 volume of water forced from the pail and caught in the pan is equal 
 to what other volume ? Remove the pan, immerse the stone as before, 
 pour the water from the pan into the upper pail, and note the read- 
 ing of the scale. To what other reading is it equal? To what is the 
 weight of the water displaced by the stone equal ? 
 
 Experiment 69. Modify the experiment again as follows : Instead 
 of the suspended bucket, b, place a tumbler upon the scale-pan. In- 
 stead of the cylinder, a, suspend any convenient solid heavier than 
 water, as a potato. Counterpoise the tumbler and the potato with 
 weights in the other scale-pan. Provide an overflow-can by inserting 
 a spout about 6 cm. long and 7 or 8 mm. in diameter in the side of a 
 vessel (as a tin fruit-can) about an inch below the top of the can. 
 This spout should slope slightly downward. Fill the can with water 
 and catch the overflow from the spout in a cup. Throw away the water 
 thus caught. Wait a minute for the spout to stop dripping and then 
 carefully immerse the potato in the water of the can, catching in the 
 cup every drop of water that overflows. Wait a minute for the spout 
 to stop dripping. The equilibrium of the balance is destroyed, but it 
 may be restored by pouring into the tumbler the water that was dis- 
 placed by the potato and caught in the cup. 
 
 -Experiment 70. Provide a wooden cube just 5 cm. on an edge. 
 Coat it with shellac varnish, or dip it into hot paraffins. - Weigh it; 
 also weigh a saucer. Place a beaker or tumbler in the saucer, and fill 
 it with water. Stick two pins or needles into one face of the cube, 
 and, using them as handles, immerse the cube in the water of the 
 beaker. Remove the beaker, and weigh accurately the saucer and its 
 liquid contents. Pour the water from the saucer into a graduate, and 
 
164 
 
 SCHOOL PHYSICS. 
 
 measure it in cubic centimeters. How does its volume compare with 
 the volume of the wooden cube ? What should that quantity of water 
 weigh according to 24 (a) ? Subtract the weight of the saucer empty 
 from the weight of the saucer with the liquid overflow. How do 
 these two weights of the water compare? Has your work been well 
 done? The weight of the wood is what fractional part (expressed 
 decimally, of course) of the weight of the water ? 
 
 153. Archimedes' Principle. -(- It is evident that, when a 
 solid is immersed in a fluid, it will displace exactly its own 
 volume of the fluid.J Immerse a solid cube one centi- 
 meter on each edge in water, s,o that its upper face shall 
 be level and one centimeter below the surface of the liquid, 
 as shown in Fig. 116. The lateral pressures upon any 
 two opposite vertical surfaces of the cube, as a and 5, 
 are clearly equal and opposite. Their resultant is zero. 
 They have no tendency to move the solid. The vertical 
 
 pressures on the other two 
 faces, c and d, are not equal. 
 The upper face sustains a pres- 
 sure equal to the weight of a 
 column of water having a base 
 one centimeter square (i.e., the 
 face, d) and an altitude equal 
 to the distance, dn. This imag- 
 inary column of water has a 
 volume of one cubic centimeter 
 and a weight of one gram. The 
 FIG 11(J downward pressure on d is one 
 
 gram. As the face, c, has the 
 
 same area and is at twice the depth, the upward pressure 
 upon it is two grams. The resultant of the two vertical 
 and opposite forces acting on the cube is an upward pres- 
 
THE MECHANICS OF LIQUIDS. 165 
 
 sure of one gram; i.e., the cube is partly supported by a 
 buoyant force of one gram, which is the weight of the cubic 
 centimeter of water that it displaces. No matter what 
 the depth to which the block is immersed, this net upward 
 pressure, or buoyant effect, is always the same. This 
 truth, discovered by Archimedes, may be stated thus :/A 
 body is buoyed up by a force equal to the weight of the fluid 
 that it displaces. \ Hence the apparent weight of a body in 
 a fluid (e.g., water or air) is less than its true weight. 
 This buoyant effect is often spoken of as a "loss of 
 weight." 
 
 (a) In the above discussion, the effect of atmospheric pressure is 
 left out of the account. It affects equally the top and bottom of the 
 tjlock. 
 
 Flotation. 
 
 Experiment 71. Place the tin can mentioned in Experiment 69, 
 upon one scale-pan, and fill it with water, some of which will over- 
 flow through the spout. Do not let any of the water fall upon the 
 scale-pan. When the spout has ceased dripping, counterpoise the 
 vessel of water with weights in the other scale-pan. Place a floating 
 body on the water. This will destroy the equilibrium, but water will 
 overflow through the spout until the equilibrium is restored. This 
 shows that the floating body has displaced its own weight of water. 
 
 Experiment 72. Place a fresh egg in a vessel of fresh water ; it is 
 a little heavier than the water, and will sink. Place it in salt water ; 
 it is a little lighter than the brine, and will float. Carefully pour the 
 fresh water on the salt water in a tall, narrow vessel. Place the egg 
 in the water ; it will descend until it reaches a layer of the liquid with 
 a density like its own, and there it will float. 
 
 154. Floating Bodies. When a solid is immersed in a 
 liquid it falls under one of three cases, according as the 
 weight of the solid is less than, equal to, or greater than 
 that of the displaced liquid. In the first case, the buoyant 
 
166 SCHOOL PHYSICS. 
 
 effect of the liquid ( 153) exceeds the weight of the 
 body, and the body rises to the surface and floats. In 
 the second case, buoyancy and weight are equal and op- 
 posite, and their resultant is zero ; the body is in equi- 
 librium in any part of the liquid. In the third case, 
 the weight exceeds the buoyancy, and the body sinks. 
 But in any case, Archimedes' principle is strictly true. 
 A floating body is only partly immersed, and the volume 
 of liquid displaced by it is only a fraction of its own 
 volume. In order that it may float at rest, the forces 
 acting upon it must be in equilibrium ; i.e., the upward 
 and the downward pressures must be equal. Conse- 
 quently, the law of flotation is : fA floating body will sink 
 in a liquid until it displaces a weight of the liquid equal to 
 its own weight.) 
 
 (a) Sometimes a heavy substance is given such a shape that it 
 displaces enough of a lighter fluid to float thereon. Thus, an iron 
 kettle or an iron ship floats on water, although iron is much heavier 
 than water. 
 
 (6) Just as the gravity of a body may be considered as acting upon 
 a single point called the center of mass, so the buoyant effort of a 
 fluid may be considered as acting upon a single point called the 
 center of buoyancy. The center of buoyancy is situated at the center of 
 mass of the displaced fluid. 
 
 CLASSROOM EXERCISES. 
 
 1. How much weight will a cubic decimeter of iron lose when 
 placed in water ? 
 
 2. How much weight will it lose in a liquid 13.6 times as heavy 
 as water? 
 
 3. If the cubic decimeter of iron weighs only 7,780 g., what does 
 your answer to Exercise 2 signify ? 
 
 4. How much weight will a cubic foot of stone lose in water ? 
 
 5. If 100 cu. cm. of lead weighs 1,135 g., what will it weigh in 
 water? 
 
THE MECHANICS OF LIQUIDS. 167 
 
 6. If a brass ball weighs 83.8 g. in air, and 73.8 g. in water, what is its 
 volume ? 
 
 7. A cubical vessel 20 cm. on an edge has fitted into its top a tube 
 2 cm. square and 10 cm. high. Box and tube being filled with water, 
 (a) what is the weight of the water ? (6) What is the liquid pressure 
 on the bottom of the vessel ? (c) If the weight and pressure differ, 
 explain the difference. 
 
 8. In Fig. 117, the line, ABC, represents 
 the surface of water that has been distorted 
 from its level condition. Show what force 
 acts on any water particle in the distorted 
 surface, as the one at B, and moves it so 
 that the surface becomes level. At what 
 
 moment does that force vanish ? FIG. 117. 
 
 155. Density and Specific Gravity. The density of a 
 substance is its mass per unit of volume. The specific 
 gravity of a substance is the ratio betiveen the weight of any 
 volume of the substance and the weight of a like volume of 
 some other substance taken as a standard; i.e., it is the 
 ratio of its density to that of some standard substance. 
 For solids and liquids, the standard is distilled water at 
 its temperature of maximum density (4 C. or 39.2 F.); 
 for gases and vapors, the standard is hydrogen or air 
 under a barometric pressure of 76 centimeters, and at 
 the temperature of C. 
 
 (a) Since the weights of bodies are proportional to their masses, 
 specific gravity is equivalent to relative density. The term " density " 
 has nearly displaced " specific gravity " in scientific works. 
 
 (6) To illustrate, in the simplest way, what is meant by density 
 (i.e., specific gravity), suppose that 1 cu. cm. of marble weighs 2.7 g. 
 Since 1 cu. cm. of water weighs 1 g., the marble is 2.7 times as heavy 
 as water, volume for volume. In shorter phrase, the density of marble 
 is 2.7. To avoid the difficulty of obtaining just a unit volume of the 
 substance, the principle of Archimedes is utilized, as will be illus- 
 trated. 
 
168 
 
 SCHOOL PHYSICS. 
 
 156. To Find the Density of a Solid Heavier than 
 Water. The most common way of determining the 
 
 density of such a body, 
 if it is insoluble in 
 water, is to find its 
 weight in air (w) ; find 
 its weight when im- 
 mersed in water (w')\ 
 divide the weight in air 
 by the loss of weight in 
 water. 
 
 w 
 
 FIG. 118. 
 
 D = 
 
 w w 
 
 (a) This method is illustrated by the following example : 
 
 (1) Weight of the solid in air (w} 113.4 g. 
 
 (2) " " " " " water (w'} 79.14 g. 
 
 (3) " " equal bulk of water (to to') ... 34.26 g. 
 
 (4) Density the solid (l)-(3) . 3.31 
 
 157. The Hydrometer. Instruments called hydrometers 
 are made for the more convenient determination of den- 
 sities. There are hydrometers of constant volume, and 
 hydrometers of constant weight. The Nicholson hydrom- 
 eter of constant volume is a hollow cylinder carrying 
 at its lower end a basket, d, heavy enough to keep the 
 apparatus upright in water. At the top of the cylinder 
 is a vertical rod carrying a pan, a, for holding weights, 
 etc. The whole apparatus must be lighter than water, 
 so that a certain weight ( W) must be put into the pan 
 to sink the apparatus to a fixed point marked on the 
 rod (as <?). The given body, which must weigh less than 
 IF, is placed in the pan, and enough weights (w) added 
 
THE MECHANICS OF LIQUIDS. 
 
 169 
 
 to sink the point, c, to the water line. It is evident that 
 the weight of the given body is W w. The given body 
 
 FIG. 119. 
 
 is now taken from the pan and placed in the basket, when 
 additional weights, a?, must be added to sink the point, <?, 
 to the water line. 
 
 D 
 
 W- 
 
 158. To Find the Density of a Solid Lighter than Water. 
 Fasten to it another body heavy enough to sink it in 
 water. Find the loss of weight for the combined mass 
 when weighed in the water. Do the same for the heavy 
 body. Subtract the loss of the heavy body from the loss 
 of the combined mass. Divide the weight of the given 
 body by this difference. 
 
 159. To Find the Density of a Solid Soluble in Water. 
 
 Determine the density of the given solid with reference to 
 some liquid, the density (<?) of which is known, and in 
 which the solid is not soluble. Multiply the result 
 
1TO 
 
 SCHOOL PHYSICS. 
 
 obtained by any of the processes previously described by 
 the density of the liquid used. 
 
 __ wd 
 w w f * 
 
 160. To Find the Density of a Liquid. There are sev- 
 eral methods of finding the density of a liquid, but the 
 principle in each is that already given. 
 
 (a) Four of these methods are given here ; others will be found in 
 the Laboratory Exercises. 
 
 (1) Weigh a flask first, empty ; next, full of water ; then, full of 
 the given liquid. Subtract the weight of the empty flask from the 
 other two weights ; the results represent the weights of equal volumes 
 of the given substance and of the standard. Divide as before. A flask 
 of known weight, graduated to measure 100 or 1,000 grams or grains of 
 water, is called a specific-gravity flask. Its use avoids the first and 
 second weighings above mentioned, and simplifies the work of division. 
 
 (2) Find the loss of weight of any insoluble solid in water and in 
 the given liquid. Divide the latter loss by the former. A solid thus 
 used is called a specific-gravity bulb. 
 
 (3) The Fahrenheit hydrometer of constant volume is made of glass, 
 
 the bulb at the bottom being loaded 
 with mercury or shot. Its weight (W) 
 being accurately determined, the in- 
 strument is placed in water, and a 
 weight (w) sufficient to sink a marked 
 point on the rod to the water-line is 
 placed in the pan. The weight of water 
 displaced by the instrument = W + w. 
 The hydrometer is then removed, wiped 
 dry, and placed in the given liquid. 
 A weight (ar) sufficient to sink the 
 hydrometer to the marked point is 
 placed in the pan. 
 
 FIG. 120. D - W + X 
 
 W+w 
 
 (4) As generally made, a hydrometer of constant weight con- 
 sists of a glass tube near the bottom of which are two bulbs. 
 
THE MECHANICS OF LIQUIDS. 
 
 171 
 
 The lower and smaller bulb is loaded with mercury or shot. The 
 
 tube and upper bulb contain air. The point to which it sinks 
 
 when placed in water is marked zero. The tube is graduated, 
 
 the scale being arbitrary, and varying with the 
 
 purpose for which the instrument is intended. 
 
 Such hydrometers are used to determine the 
 
 degree of concentration of certain liquids, as 
 
 acids, alcohols, milk, solutions of sugar, etc. 
 
 According to their uses, they are known as 
 
 acidometers, alcoholometers, lactometers, saccharom- 
 
 eters, etc. 
 
 FIG. 121. 
 
 161. To Find the Density of a Gas. 
 
 The density of an aeriform body is found 
 by comparing the weights of equal vol- 
 umes of the standard (air or hydrogen) 
 and of the given substance. The method 
 is strictly analogous to that first given 
 for liquids. The determination of the density of gases 
 presents many practical difficulties which cannot be con- 
 sidered in this place. 
 
 *. 
 
 NOTE. The weight of any solid or liquid, in grams per cubic 
 centimeter, represents its density. 
 
 The weight of a cubic foot of any solid or liquid is equal to 62.421 
 pounds avoirdupois multiplied by its density. 
 
 The weight of a cubic centimeter of any solid or liquid is equal to 
 1 gram multiplied by its density. 
 
 The weight of a liter of any liquid or a cubic decimeter of any solid 
 is equal to 1 kilogram multiplied by its density. 
 
 162. Water Power. An elevated body of water is a 
 storehouse of potential energy. As the water runs to 
 a lower level, it may be made to turn a wheel, and thus 
 to move machinery, etc., a good illustration of the con- 
 version of potential into kinetic energy. 
 
 " (a) Water-wheels are of different kinds, their relative advantages 
 depending upon the nature of the water-supply and of the work to be 
 
172 
 
 SCHOOL PHYSICS. 
 
 done. In the overshot wheel (Fig. 122), the water falls into buckets 
 at the top, and by its weight, aided by the force of the current, turns 
 the wheel. Such wheels have been made nearly 100 feet in diameter. 
 
 FIG. 122. 
 
 The little water that they need must have a considerable fall. In the 
 breast wheel, the water is received at or near the level of the axis ; 
 thus the weight of the water and the force of the current are turned 
 to account. In the undershot wheel, the water acts upon a few float- 
 
 FIQ. 123. 
 
 boards at the bottom, the force of the current turning the wheel. The 
 most efficient form of water-wheel is the turbine, one form of which is 
 shown in Fig. 123. The wheel, B, and the inclosing case, D, are placed 
 
THE MECHANICS OF LIQUIDS. 178 
 
 on the floor of a penstock wholly submerged in water under the 
 pressure of a considerable head. The water enters, as shown by the 
 arrows, through openings in D, which are so constructed that it strikes 
 the buckets of B in the direction of greatest efficiency. After leaving 
 the buckets, the " dead water " escapes from the central part of the 
 wheel, sometimes by a vertical draft-tube. The weight of the water 
 in this tube increases the velocity with which the water strikes the 
 buckets. A central shaft, A, is carried by the wheel, and communi- 
 cates its motion to the machinery above. The wheel itself rests upon 
 a central pivot carried by cross-arms from the bottom of the outer 
 case. The case, Z>, is covered with a top, !T, which protects the wheel 
 from the vertical pressure of the water. 
 
 CLASSROOM EXERCISES. 
 
 NOTE. Be on the alert to recognize Archimedes' Principle in dis- 
 guise. Consider the weight of water 62^ pounds per cubic foot. 
 
 1. What is the density of a body that floats with half of its vol- 
 ume under water ? 
 
 2. Assuming the density of aluminium to be 2.6, determine the 
 weight of an aluminium sphere 25 cm. in diameter. 
 
 3. A piece of metal weighing 52.35 g. in air is placed in a cup filled 
 with water. The overflowing water weighs 5 g. What is the density 
 of the metal ? 
 
 4. A solid weighing 695 g. in air loses 83 g. when weighed in water, 
 (a) What is its density ? (b) How much would it weigh in alcohol 
 that has a density of 0.792 ? 
 
 5. A 1,000-grain bottle holds 708 grains of benzoline. Find the 
 density of the benzoline. 
 
 6. A solid that weighs 2.4554 ounces in air, weighs only 2.0778 
 ounces in water. Find its density. 
 
 7. A specimen of gold that weighs 4.6764 g. In air, loses 0.2447 g. 
 weight when weighed in water. Find its density. 
 
 8. A ball weighing 970 grains, weighs in water 895 grains, in alco- 
 hol 910 grains. Find the density of the alcohol. 
 
 9. A body loses 25 grains in water, 23 grains in oil, and 19 grains 
 in alcohol. Required the density of the oil and of the alcohol. 
 
 10. A body weighing 1,536 g., weighs in water 1,283 g. What is 
 its density? 
 
174 SCHOOL PHYSICS. 
 
 11. Calculate the density of sea water from the following 
 data : 
 
 Weight of bottle empty 3.5305 g. 
 
 " " filled with distilled water . . 7.6722 g. 
 
 " " " sea " . . 7.7849 g. 
 
 12. Determine the density of a piece of wood from the following 
 data : weight of wood in air, 4 g. ; weight of sinker, 10 g. ; weight of 
 wood and sinker under water, 8.5 g. ; density of sinker, 10.5. 
 
 13. A piece of a certain metal weighs 3.7395 g. in air; 1.5780 g. 
 in water; 2.2896 g. in another liquid. Calculate the densities. of the 
 metal and of the unknown liquid. 
 
 14. Find the density of a piece of glass, a fragment of which weighs 
 2,160 grains in air, and 1,51 1 grains in water. 
 
 15. A lump of ice weighing 8 pounds is fastened to 16 pounds of 
 lead. In water, the lead alone weighs 14.6 pounds, while the lead and 
 ice weigh 13.712 pounds. Find the density of the ice. 
 
 16. A piece of lead weighing 600 g. in air weighs 545 g. in water, 
 and 557 g. in alcohol. Find (a) the density of the lead ; (&) the density 
 of the alcohol ; (c) the volume of the lead. 
 
 17. A person can just lift a 300-pound stone in the water. What 
 is his lifting capacity in the air (density of the stone, 2.5) ? 
 
 18. A liter flask holds 870 g. of turpentine. Required the density 
 of the turpentine. 
 
 [In the next two exercises, the weight of the empty flask is not 
 taken into account.] 
 
 19. A liter flask containing 675 g. of water had its remaining space 
 filled with fragments of a mineral, and was found to weigh 1,487.5 g. 
 Required the density of the mineral. 
 
 20. A liter flask was four-fifths filled with water; the remaining 
 space being filled with sand, the weight was found to be 1,350 g. 
 Required the density of the sand. 
 
 21. A weight of 1,000 grains will sink a certain Nicholson hydrom- 
 eter to a mark on the rod carrying the pan. A piece of brass plus 40 
 grains will sink it to the same mark. When the brass is taken from 
 the pan and placed in the basket, it requires 160 grains in the pan to 
 sink the hydrometer to the same mark on the rod. Find the density 
 of the brass. 
 
 22. A Fahrenheit hydrometer, which weighs 2,000 grains, re'quires 
 1,000 grains in the pan to sink it to a certain depth in water. ' It re- 
 
THE MECHANICS OF LIQUIDS. 175 
 
 quires 3,400 grains in the pan to sink it to the same depth in sulphuric 
 acid. Find the density of the acid. 
 
 23. A certain body weighs just 10 g. It is placed in one of the 
 scale-pans of a balance, together with a flask full of pure water. The 
 given body and the filled flask are counterpoised with shot in the 
 other scale-pan. The flask is removed, and the given body placed 
 therein, thus displacing some of the water. The flask, being still 
 quite full, is carefully wiped and returned to the scale-pan, when it is 
 found that there is not equilibrium. To restore the equilibrium, it 
 is necessary to place 2.5 g. with the flask. Find the density of the 
 given body. 
 
 24. What would a cubic foot of coal (density, 2.4) weigh in a solu- 
 tion of potash (density, 1.2) ? 
 
 25. 500 cu. cm. of iron (density, 7.8) floats on mercury. With 
 what force is it buoyed up? 
 
 26. A piece of cork weighing 2.3 g. was attached to a piece of iron 
 weighing 38.9 g. Both were found to weigh in water 26.2 g., the iron 
 alone weighing 33.9 g. in water. Required the density of the cork. 
 
 27. A piece of wood weighing 300 grains has tied to it a piece of 
 lead weighing 600 grains ; together they weigh in water 472.5 grains. 
 The density of lead being 11.35, (a) what does the lead weigh in 
 water? (&) What is the density of the wood? 
 
 28. A Fahrenheit hydrometer weighs 618 grains. It requires 93 
 grains in the pan to sink it to a certain mark on the stem. When 
 wiped dry and placed in olive oil, it requires only 31 grains to sink 
 it to the same mark. Find the density of the oil. 
 
 29. A platinum ball weighs 330 g. in air, 315 g. in water, and 303 g. 
 in sulphuric acid. Find (a) the density of the ball ; (&) the density 
 of the acid ; (c) the volume of the ball. 
 
 30. A hollow ball of iron weighs 1 Kg. What must be its least 
 volume to float on water ? 
 
 31. A body whose density is 2.8 weighs 37 g. Required its weight 
 in water. 
 
176 SCHOOL PHYSICS. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. A piece of rock-salt ; naphtha ; pine rod, 
 loaded and graduated as described below ; rectangular prism of hard 
 wood ; piece of brimstone ; bottle with ground-glass stopper ; kerosene ; 
 wooden cylinder and support ; Y-tube ; pinchcock. 
 
 1. Determine the density of two solids heavier than water, the 
 solids being supplied by the teacher. 
 
 2. Determine the density of a solid lighter than water. 
 
 3. Determine the density of an unknown liquid without using a 
 specific-gravity flask or a hydrometer. 
 
 4. Rock-salt is soluble in water, and insoluble in naphtha. Deter- 
 mine the density of a specimen of rock-salt. 
 
 5. Determine the density of a liquid, using a specific-gravity bulb. 
 
 6. Redetermine the density of one of the solids used in Exercise 1, 
 using a Nicholson hydrometer. 
 
 7. Get a rectangular block of hard wood about 5x6x7 centime- 
 ters. The exact dimensions are not essential. Weigh the block on a 
 spring-balance suspended from some firm support (not held in 
 the hand). Measure the dimensions of the block as accurately as 
 possible, and compute its volume in cubic centimeters and cubic inches. 
 Determine the weight of the block in grams per cubic centimeter, and 
 in ounces per cubic inch. 
 
 8. Provide a water-proofed wooden cylinder about 1 cm. in diam- 
 eter and about 20 cm. long, and a support for holding the cylinder 
 upright in the water in such a way that it may easily move up and 
 down without tipping much from a vertical position. Accurately 
 measure the length of the cylinder. When the cylinder is floating 
 upright in water, joggle it a few times, and see that it comes to rest 
 each time at the same depth. Accurately measure the length of the 
 submerged part of the cylinder, and from the two measurements, com- 
 pute the density of the cylinder. 
 
 9. Make a rod of white pine or other light wood, just 1 cm. square 
 and about 30 cm. long. Graduate one side of the rod to millimeters, 
 with the zero of the scale at the loaded end. In one end, bore a hole, 
 and pound in enough sheet lead to make the rod stand on end when 
 floated in water and with about half of it immersed. Fill the rest of 
 the cavity with putty, and dip the rod into hot paraffme. Place the 
 rod in water, and read from the scale the depth to which it sinks. 
 
THE MECHANICS OF LIQUIDS. 177 
 
 Using it as a hydrometer of constant weight, determine the density 
 of alcohol and of a 20-per-cent solution of common salt. 
 
 10. Paste a strip of writing paper around the upper end of the rod 
 used in Exercise 9, one edge of the paper overlapping the end of the 
 stick so as to make a small cup. Float the rod as before, and place 
 enough shot or sand in the cup to bring one of the graduations ex- 
 actly to the water-level. Add successively weights of 1 g., 2 g., 3 g., 
 etc., and at each addition, note how much the rod sinks. Record the 
 teachings of the experiment. 
 
 11. Fill the tin can used in Experiment 69, until water overflows 
 through the spout. Weigh a small beaker, and place it under, the 
 spout. Weigh a piece of^ roll sulphur (brimstone) about 5 cm. long, 
 suspend it by a fine thread, and lower it into the water in the tin can, 
 catching in the beaker every drop of water that overflows. Weigh 
 the beaker with its liquid contents, and by subtraction find the weight 
 of water it contains. Suspend the sulphur by the thread from the 
 scale-pan, and weigh it in water. Record your data as follows : 
 
 (a) Weight of sulphur in air = ? 
 
 (6) Weight of beaker = ? 
 
 (c) Weight of beaker and water = ? 
 
 (rf) Weight of displaced water (c-Z>) =? 
 
 (e) Weight of sulphur in water = V 
 
 (/) Loss of weight in water (a e) = ? 
 
 Compare (e?) with (/), and record the fact thus indicated. From the 
 recorded data, determine the density of the sulphur. 
 
 12. Provide a bottle that will hold two or three ounces of water, 
 and that has a ground-glass stopper ; a thread with which to suspend 
 the bottle ; a cloth with which to wipe the bottle ; a delicate spring- 
 balance ; water ; kerosene. Without any other apparatus or supplies, 
 determine the density of the kerosene. 
 
 13. Fill a bottle like that used in Exercise 12 with water, and put 
 the stopper firmly into place. Without removing the stopper or add- 
 ing to your material, determine the density of the kerosene. 
 
 14. Get a glass U-tube with an internal diameter of 8 or 10 mm. 
 and having arms that are close together and about 50 cm. long (see 
 Fig. 110) ; a meter stick graduated to millimeters ; a small funnel for 
 pouring liquids into the U-tube ; some support that will hold the 
 U-tube upright; water; kerosene. Without additional material, 
 determine the density of the kerosene. 
 
 12 
 
178 SCHOOL PHYSICS. 
 
 15. Get a lead or glass Y-tube (i.e., a three-way tube), each arm of 
 which has a length of about 5 cm., and an internal diameter of about 
 
 5 mm. ; two pieces of glass tubing each having an ex- 
 ternal diameter about equal to that of the Y - tu.be, and 
 a length of 50 cm. ; two pieces of rubber tubing about 
 5 cm. long, for connecting the two straight tubes to the 
 Y-tube ; a piece of rubber tubing about 10 cm. long to 
 attach to the other arm of the Y-tube, and a pinchcock 
 IG ' ' (see Chemistry, Appendix 20) or other device for clos- 
 ing the free end of the tube; the 
 meter stick used in Exercise 14 ; 
 two tumblers ; water ; kerosene. 
 Without additional material, deter- 
 mine the density of kerosene. Make 
 any necessary corrections for capil- 
 lary action. Remember that you 
 can easily suck air from or through 
 the apparatus. 
 
 16. Using the apparatus shown 
 in Fig. 110, and a meter stick, de- 
 termine the density of mercury. 
 
 17. Wind closely 10 m. of No. 22 
 spring-brass wire upon a rod about 
 3 cm. in diameter, and suspend the 
 spiral thus formed in front of a ver- 
 tical meter stick or other scale, as 
 shown in Fig. 125. To the lower 
 end of the spring, the extremity of 
 the wire having been bent into a 
 horizontal index, attach two small 
 scale-pans arranged so that one 
 shall be about 10 cm. below the 
 other. Place a glass of water upon 
 an adjustable stand or easily mov- 
 able blocks so that the lower pan 
 may be kept immersed while the 
 upper pan is always above the water. 
 In the upper pan, place a small solid 
 
 that will sink in water, and note the elongation of the spring as in- 
 dicated by the movement of the index over the scale, lowering the 
 
THE MECHANICS OF GASES. 
 
 dish of water as may be necessary to keep the lower pan submerged 
 and freely suspended. Then place the solid in the lower pan, and 
 similarly weigh it in water. Determine the density of the solid. 
 
 18. Place a 1-gram weight in the upper pan of the Jolly balance 
 described in Exercise 17, and note the elongation of the spring. 
 Assuming that the spring will stretch proportionally for other loads, 
 obtain in grams the two weights of another small solid that will sink 
 in water, and determine its density. 
 
 19. Place a cork in the upper pan of the Jolly balance, and a sinker 
 in the lower pan, and weigh them. Fasten the sinker to the cork, 
 place both in the lower pan, and weigh them. Determine the density 
 of the cork. 
 
 20. Remove both pans from the Jolly balance, and suspend the 
 glass stopper of a bottle from the lower end of the spring. With 
 this apparatus, determine the density of kerosene. 
 
 VIII. THE MECHANICS OF GASES. 
 
 163. Pneumatics is the branch of physics that treats of 
 the mechanical properties of gases, and describes the ma- 
 chines that depend for their action chiefly on the pressure 
 and elasticity of air. 
 
 (a) As water was taken as the type of liquids, so atmospheric air 
 will be taken as the type of gases. All statements made in Section 
 VII. concerning fluids, apply to gases as well as to liquids. 
 
 NOTE. It is taken for granted that the school has an air-pump, 
 an instrument that will soon be described, and the simpler pieces of 
 apparatus that generally accompany it. 
 
 Weight of Air. 
 
 Experiment 73. On a delicate balance, carefully weigh a thin 
 glass or metal vessel that will hold several liters, and that may be 
 closed by a stopcock. Pump the air from the vessel, close the stop- 
 cock, remove the vessel from the pump and carefully weigh it again. 
 
180 
 
 SCHOOL PHYSICS. 
 
 FIG. 120. 
 
 Its loss of weight measures the weight of the air removed. If more 
 convenient, the following may be substituted for the foregoing: 
 Into a half-liter Florence flask, put about 100 
 cu. cm. of water. Place the flask on a sand-bath 
 and boil the water. The steam will expel the air 
 from the flask. After the boiling has continued 
 for some time, remove the lamp, and, when the 
 boiling has ceased, loosely cork the flask. Cool 
 the upper part of the flask by putting a wet cloth 
 around it ; the water will boil again. Then tightly 
 close the flask with a rubber stopper. When the 
 flask has cooled to the temperature of the room, 
 shake it. The peculiar " water-hammer " sound of 
 the water indicates a good vacuum in the flask. 
 Weigh the flask and its contents. Loosen the 
 cork and weigh again. The increase of weight is the weight of 
 the air admitted to the flask. Subtract the volume of the water from 
 the capacity of the flask to find the volume of the air thus weighed 
 and compute the weight of the air per cubic centimeter. Record the 
 readings of the thermometer and barometer at the time and place 
 of the experiment. 
 
 Experiment 74. Draw out a piece of glass tubing to a jet, and 
 push it through a perforation in a cork that snugly fits a bottle. Slip 
 a short piece of snugly fitting rubber tubing over the 
 outer end of the glass tubing, and insert the cork so 
 that the jet shall project into the bottle. Remove by 
 suction as much air as possi- 
 ble from the bottle, pinch the 
 rubber tubing tightly, place it 
 under water, and remove the 
 pressure. Something will force 
 water into the bottle, forming 
 the " fountain in vacuo," as 
 shown in Fig. 127. 
 
 FIG. 127. 
 
 Experiment 75. Fill a 
 tumbler with water, place a 
 slip of thick paper over its 
 
 FIG. 128. 
 
 mouth and hold it there while the tumbler is inverted ; the water will 
 be supported when the hand is removed from the card. 
 
THE MECHANICS OF GASES. 181 
 
 Experiment 76. Over the upper end of a cylindrical receiver, tie 
 tightly a wet bladder or sheet of writing paper and allow it to dry. 
 Then exhaust the air. The bladder will be 
 forced inward, bursting with a loud noise. 
 Replace the bladder with a thin sheet of 
 india-rubber. Exhaust the air. The rub- 
 ber sheet will be pressed inward, and nearly 
 cover the inner surface of the receiver. 
 
 Experiment 77. The Magdeburg hem- 
 ispheres are accurately fitting, metallic 
 vessels, generally three or four inches in 
 diameter. Their edges are provided with 
 projecting lips, and fit one another air-tight ; FiaTl29. 
 
 the lips prevent sidewise slipping. Grease 
 
 the edges to make more sure of a tight joint, fit the hemispheres 
 to each other, and exhaust the air with a pump. Close the stop- 
 cock, remove the hemispheres from 
 the pump, attach the second handle, 
 and, holding the hemispheres in dif- 
 ferent positions, try to pull them 
 apart. When you are sure that the 
 pressure that holds them together 
 is exerted in all directions, place 
 them under the receiver (i.e., the 
 bell-glass) of the air-pump, and ex- 
 haust the air from around them. 
 The pressure seems to be removed, 
 for the hemispheres fall apart of 
 their own weight. 
 
 Experiment 78. Connect the lamp- 
 chimney apparatus used in Experi- 
 ment 59 by a thick-walled rubber 
 tube, and partly exhaust the air with 
 
 FIG. 130. the air-pump or by suction. Hold 
 
 the chimney in different positions, 
 
 and notice that the pressure that pushes in the rubber diaphragm is 
 exerted equally in all directions. Any change of pressure will be 
 shown by a change in the form of the rubber cup. 
 
182 
 
 SCHOOL PHYSICS. 
 
 164. The Air. These experiments show that air has 
 weight, that it exerts great pressure at the surface of the 
 earth, and that this pressure is transmitted equally in all 
 directions, in accord with Pascal's law. Under ordinary 
 atmospheric conditions, a liter of air weighs about 1.3 
 grams ; a cubic foot weighs about an ounce and a quarter. 
 As the atmospheric pressure is due to the weight of the 
 overlying air, it follows that atmospheric pressure must 
 decrease as we ascend from the sea-level. 
 
 Atmospheric Pressure. 
 
 Experiment 79. Into one end of a piece of stout glass tubing about 
 1 m. long, and with a bore of about 1 cm., closely press a good cork or 
 rubber stopper. Fill the tube with water ; close the open end with 
 the forefinger ; invert the tube over the water-bath, and, when the 
 
 end is under water, remove the 
 finger. Note whether the water 
 falls away from the corked encl 
 of the tube. Loosen or remove 
 the cork, and note the result. 
 
 Experiment 80. Fill with 
 mercury a stout glass tube 
 closed at one end and about 
 50 cm. long ; a long " ignition 
 tube " will answer. Invert it 
 at the mercury-bath as shown 
 in Fig. 131. Note whether the 
 mercury falls away from the 
 closed end of the tube. 
 
 Experiment 81. Select a 
 stout glass tube about 80 cm. 
 
 FlG 131 long, several millimeters in in- 
 
 ternal diameter, and closed at 
 
 one end. Twist a piece of paper into the shape of a hollow cone, and, 
 using it as a funnel, fill the tube with mercury. With an iron wire, 
 
THE MECHANICS OF GASES. 183 
 
 remove any air-bubbles that you see in the tube. Close the open 
 end with the finger, and invert the tube at the mercury-bath, as shown 
 in Fig. 131. When the finger is removed, the mercury falls away 
 from the upper end of the tube, and finally comes to rest at a height 
 of about 30 inches (or 76 cm.) above the level of the mercury in the 
 bath, leaving a vacuum at the upper end of the tube. This historical 
 experiment was first performed in 1643, by Torricelli, Galileo's pupil. 
 If the tube is supported upright, the height of the sustained mer- 
 cury column may be found to vary from day to day. If it is 
 placed under a tall bell-glass and the air exhausted, the column 
 will fall as the atmospheric pressure on the surface of the mercury 
 decreases. 
 
 Experiment 82. Modify the last experiment by selecting a tube 
 open at both ends. Thoroughly soak in water such a membrane as 
 comes tied over the stoppers of perfumery bottles, and tie it tightly 
 over One end of the tube. When the membrane is thoroughly dry, 
 fill the tube with mercury, and invert it at the mercury-bath as before. 
 After measuring the height of the supported liquid column, prick a 
 pinhole through the membrane, and notice what takes place. 
 
 165. Atmospheric Pressure. In spite of the tendency 
 of liquids to seek their level, we see that something sup- 
 ports a liquid column of great weight in the Torricellian 
 tube. The removal of the air from the surface of the 
 mercury in the bath shows that the pressure of the atmos- 
 phere is this supporting force. Since the size of the tube 
 will not affect the height of the column, we may assume 
 that the tube has a cross-section of one square centimeter. 
 Then the supported mercury will measure 76 cu. cm. As 
 the density of mercury is 13.596, this quantity of mercury 
 will weigh 13.596 times 76 grams. The weight thus 
 sustained shows that the atmospheric pressure at the sea- 
 level is approximately 1,033.3 e^raflis per square centimeter, or 
 14.7 pounds per square inch. For rough work or " in round 
 numbers," it is often said that this pressure, which is called 
 
184 
 
 SCHOOL PHYSICS. 
 
 an atmosphere^ is a kilogram per square centimeter, or 
 fifteen pounds per square inch. 
 
 (a) Pascal carried a Torricellian tube to the top of a mountain, and 
 there found that the mercury column was three inches shorter, showing 
 that, as the weight of the atmospheric column diminishes, the counter- 
 balanced column of mercury also diminishes. He then took a tube 
 40 feet long, and closed at one end. Having filled it with water, he 
 inverted it over a water-bath. The water in the tube came to rest at 
 a height of 34 feet. The weights of the two columns were equal. 
 Experiments with still other liquids gave corresponding results, all of 
 which strengthened the theory that the supporting force is atmos- 
 pheric pressure, and left no doubt as to its correctness. 
 
 (6) Since mercury is more than ten thousand times as heavy, bulk 
 for bulk, as air under the ordinary conditions of temperature and 
 atmospheric pressure, a mercury column about 76 cm. (or 30 inches) 
 tall is able to counterbalance an air column of equal cross-section 
 reaching from the bottom to the top of our atmosphere. 
 
 166. The Barometer. A Torricellian tube, firmly fixed 
 to an upright support and properly graduated, 
 constitutes a mercurial barometer. The zero of 
 the scale is at the surface of the mercury in the 
 cistern. 
 
 (a) When scientific accuracy is required, the cistern of 
 the barometer is made with a flexible leather bottom 
 that can be raised or lowered by a screw until the 
 surface of the mercury just touches the point of an in- 
 dex, with which the zero of the scale coincides. For 
 the more accurate reading of the scale, some instruments 
 are provided with verniers. In every case, the extreme 
 height of the convex surface of the mercury should be 
 taken, and, if the scale has no vernier, the divisions of 
 the scale should be subdivided by the eye as accurately 
 as possible. The height of the barometer is, in such 
 cases, corrected for temperature, for variations of graV- 
 ity, for capillarity, for expansion of the scale, for eleva- 
 tion above sea-level, etc. 
 FIG. 132. 
 
UNIVERSITY OF CALIFORNIA 
 
 DEPARTMENT OF PHYSICS 
 
 THE MECHANICS OF GASES. 
 
 185 
 
 (6) The aneroid barometer is an easily portable instrument, and 
 avoids the use of any liquid. It consists of a circular metallic box, 
 exhausted of air, the corrugated dia- 
 phragm of which is held in a state of 
 tension by springs. Varying atmos- 
 pheric pressures cause movements of the 
 diaphragm. These movements, being 
 multiplied by delicate levers and a fine 
 chain wound around a pinion, move the 
 index pointer over a graduated scale. 
 Such barometers are made so delicate 
 that they show a difference in atmos- 
 pheric pressure when transferred from 
 an ordinary table to the floor. Their 
 very delicacy involves the necessity for 
 careful usage or frequent repairs. 
 
 FIG. 133. 
 167. Barometric Variations. 
 
 Observation shows frequent variations in the barometric 
 readings. Some slight changes are found to be periodic, 
 but the greater changes follow no known law. The util- 
 ity of a barometer depends largely upon the fact that these 
 irregular variations correspond to changes in the pressure of 
 the air column that rests on the surface of the mercury in 
 the cistern, and, therefore, signal coming meteorological 
 changes. 
 
 0) The falling of the mercury generally indicates the approach of 
 foul weather; a sudden .fall denotes the coming of a storm. The 
 rising of the mercury indicates the approach of fair weather or the 
 " clearing up " of a storm. 
 
 (6) Sometimes the "barometer falls" and the looked-for storm 
 does not appear. In such a case, it should be remembered that the 
 barometer announced only a diminution of atmospheric pressure, and 
 that we, influenced by experience, inferred the coming of a storm. 
 Barometric declarations are reliable; inferences from those declara- 
 tions are subject to error. 
 
 (c) The barometer is also used for the approximate determination 
 - of altitudes above sea-level. 
 
186 SCHOOL PHYSICS. 
 
 CLASSROOM EXERCISES. 
 
 1. Give the pressure of the air upon a man the surface of whose 
 body is 20 square feet. 
 
 2. A soap-bubble has a diameter of 4 inches. Give the pressure of 
 the air upon it. 
 
 3. What is the weight of the air in a room 30 by 20 by 10 feet? 
 
 4. What will be the total pressure of the atmosphere on a deci- 
 meter cube of wood when the barometer stands at 760 mm.? 
 
 5. How much weight does a cubic foot of wood lose when weighed 
 in air? 
 
 6. (a) What is the pressure on the upper surface of a Saratoga 
 trunk 1\ by 3 feet? (b) How happens it that the owner can open 
 the trunk ? 
 
 7. (a) What effect would it have Upon the height of the barometer 
 column if the barometer tube was enlarged until it had a sectional 
 area of 1 sq. cm. ? (6) Assuming that the density of mercury is 13.6, 
 and that the barometer stands at 760 mm., what is the atmospheric 
 pressure per square centimeter of surface? Ans. 1,033.6 g. 
 
 8. A certain room is 10 m. long, 8 m. wide, and 4 m. high, (a) 
 What weight of air does it contain? (6) What is the pressure upon 
 its floor? (c) Upon its ceiling? (d) Upon each end? (e) Upon 
 each side? (/) What is the total pressure upon the six surfaces? 
 (g) Why is not the room torn to pieces ? 
 
 9. An* empty toy balloon weighs 5 g. When filled with 10 1. of 
 hydrogen, what load can it lift ? A liter of hydrogen weighs 0.0896 g. 
 
 Elastic Force. 
 
 Experiment 83. Tightly close the opening of a toy balloon, foot- 
 ball, or other rubber bag, only partly filled with 
 air. Place it under the receiver of an air-pump, 
 as shown in the accompanying figure, and ex- 
 haust the air from the receiver. The flexible 
 wall of the bag will be pushed back by the in- 
 numerable impacts of the moving molecules 
 against the confining surface. The observed 
 phenomenon is in strict accord with the kinetic 
 theory of gases, 51. 
 
 Experiment 84. For the rubber bag of Ex- 
 periment 83, substitute successively a dish containing soap-bubbles, 
 
THE MECHANICS OF GASES. 187 
 
 and a bottle with its mouth opening under water in a tumbler. Ex- 
 haust the air as before, and notice the effect of the molecular impacts 
 on the liquid walls of the confined air. 
 
 Experiment 85. Half fill a small bottle with water, and close the 
 neck with a cork through which a small tube passes. The lower end 
 of this tube should dip into the liquid ; the upper end should 
 be drawn out to a jet. Apply the lips to the upper end of 
 the tube, and force air into the bottle. 
 
 Experiment 86. Place the bottle, arranged as above 
 described, under the receiver of an air-pump, and exhaust 
 the air from the receiver. Water will be driven in a jet 
 from the tube. 
 
 Experiment 87. Apparatus dealers supply " bursting 
 
 squares " made of thin glass, and sealed F ~ 
 under the ordinary atmospheric pressure. 
 Place one of these " squares " upon the plate of the air- 
 pump, cover it with wire netting as a protection against 
 accident, and over all place a bell-glass. Exhaust the 
 air from the bell-glass, and the elastic force of the air 
 confined in the square will burst the thin glass walls 
 
 FIG. 136. outward. 
 
 168. Elastic Force of Gases. When a glass vessel (see 
 Fig. 126) is open, the atmospheric pressure on the outer 
 surface is exactly balanced by the pressure on the inner 
 surface. Closing the stopcock will not destroy the 
 equality of pressures ; the elastic force of the confined gas 
 will just equal the pressure of the surrounding atmosphere. 
 If the stopcock is closed when the gas is under a pressure 
 of two atmospheres, the equality will still continue, each 
 being about thirty pounds per square inch. In neither 
 case will the vessel be subjected to any stress by the gas 
 within or without. The elastic force of a gas supports and 
 equals the pressure exerted upon it. 
 
188 
 
 SCHOOL PHYSICS. 
 
 Relation of Volume to Pressure. 
 
 Experiment 88. Provide a stout glass tube more than a meter 
 long, bent as shown in Fig. 137, the short arm being closed. Pour a 
 small quantity of mercury into the tube so that its surfaces in the two 
 tubes are in the same horizontal line. By holding "the tube nearly 
 level, bubbles of air may be passed into the short arm or from it until 
 
 the desired result is 
 secured. The air in 
 the short arm will 
 then be under a pres- 
 sure of one atmos- 
 phere. Fasten the 
 tube to an upright 
 support, and place a 
 scale graduated to 
 millimeters by each 
 arm, the zero of each 
 scale being just at the 
 mercury levels. Pour 
 mercury into the long 
 arm of the tube, thus 
 increasing the pres- 
 sure on the air con- 
 fined in the short 
 arm. When the ver- 
 tical distance between 
 the levels of the mer- 
 cury in the two arms 
 is one fourth the 
 height of the baro- 
 metric column at the 
 time and place of the 
 experiment, the pres- 
 sure upon the confined 
 air will be f atmos- 
 pheres, i.e., a pressure of about 95 cm. of mercury ; the elastic force 
 of the confined air just supports this pressure, and must, therefore, 
 be atmospheres ; the volume of the confined air is f what it was 
 under a pressure of one atmosphere. Tf more mercury is added 
 
 FIG. 137. 
 
THE MECHANICS OF GASES. 
 
 189 
 
 until the vertical distance between the two mercurial surfaces is 
 half the height of the barometric column, the pressure and the elastic 
 force will be f atmospheres, or about 114 cm. of mercury; the volume 
 of the confined air will be f what it was under a pressure of one 
 atmosphere. When mercury has been poured into the long arm until 
 the vertical distance, CA, is equal to the height of the barometric 
 column, the pressure will be two atmospheres, or about 152 cm. of 
 mercury, and the volume of the confined air will be half what it was 
 under a pressure of one atmosphere. 
 
 Experiment 89. Nearly fin the barometer tube used in Experi- 
 ment 81, or a similar tube more than half as long and graduated to 
 cubic centimeters, with mercury, and invert it 
 over a mercury-bath as shown in Fig. 138. 
 Lower the tube into the tank until the mercury 
 within the tube and without it is at the same 
 level. The confined air is under the same pres- 
 sure as the external air; e.g., 76 cm. of mer- 
 cury. Note the volume of the confined air. 
 Raise the tube until this volume of the confined 
 air is doubled, and measure the height of the 
 mercury column in the tube. It will be found 
 that the confined air is under a pressure half 
 that of the external air; e.g., 38 cm. of mer- 
 cury. 
 
 Addenda. Suppose the volume of gas con- 
 fined in each of the last two experiments meas- 
 ured 5 cm. under a pressure of one atmosphere. 
 Arrange the data just obtained in the following 
 form, and complete the table : 
 
 Pressures. 
 
 76 
 
 95 
 114 
 152 
 
 38 
 
 Volumes. 
 5 
 4 
 
 10 
 
 Products. 
 380 
 
 FIG. 138. 
 
 169. Boyle's Law. When the temperature remains 
 constant, the volume of a gas varies inversely as the pres- 
 
190 ' SCHOOL PHYSICS. 
 
 sure upon it; i.e., the product of a given volume of gas 
 by its pressure is constant. 
 
 Vcc , or V x P = a constant quantity. 
 
 (a) Later experiments have shown that Boyle's law is only 
 approximately true, and that all gases deviate from it as they near 
 the point of liquefaction. This law is often called Mariotte's. 
 
 CLASSROOM EXERCISES. 
 
 1. Under ordinary conditions, a certain quantity of air measures 
 one liter. Under what conditions can it be made to occupy (a) 500 
 cu. cm.? (b) 2,000 cu. cm.? 
 
 2. Under what circumstances would 1 cubic foot of air, at the 
 freezing temperature, weigh about 2 ounces? 
 
 3. Into what space must we compress (a) a liter of air to double its 
 elastic force? (6) Two liters of hydrogen ? 
 
 4. A barometer standing at 30 inches is placed in a closed vessel. 
 How much of the air in the vessel must be removed that the mercury 
 may fall to 15 inches? 
 
 5. A vertical tube, closed at the lower end, has at its upper end a 
 frictionless piston that has an area of 1 square inch. The weight of 
 this piston is 5 pounds, and it confines 24 cubic inches of dry steam, 
 (a) What is the elastic force of the confined steam ? (6) If the 
 piston is loaded with a weight of 10 pounds, what will be the 
 volume of the confined steam? 
 
 6. Mercury stands at the same level in both arms of a tube like 
 that shown in Fig. 137. The barometer rises, and thereupon is noticed 
 a difference in the heights of the two mercury columns in the J-tube. 
 In which arm does the mercury stand the higher ? Why ? 
 
 Siphon. 
 
 Experiment 90. Place a pail of clean water on the table, and an 
 empty water pail on the floor. Place one end of a piece of thick- 
 walled rubber tubing, about a yard long, in the water. Hold the 
 other end of the tubing below the level of the table-top, and fill the 
 tube with water by suction. Notice the transfer of water from one 
 pail to the other. Be careful that the flexible walls of the tubing do 
 
THE MECHANICS OF GASES. 191 
 
 not close upon each other at the edge of the upper pail, and thus cut 
 off the flow. 
 
 Experiment 91. Change the positions of the pails, placing the 
 one containing water on the table. Gradually lower the rubber tub- 
 ing into the water, allowing air to escape from the upper end as water 
 enters at the lower end. When the tube is filled with water, pinch one 
 end of it tightly, and carry it below the level of the table-top. Raise 
 and lower this end of the tubing to see if the distance of the opening 
 below the edge of the upper pail has anything to do with the rate of 
 flow. 
 
 Experiment 92. Using a bent glass tube of small internal diame- 
 ter and two tumblers or bottles, arrange apparatus to transfer water 
 from a higher to a lower level, essentially as in Experiment 91. Put 
 the apparatus in operation on the plate of the air-pump, cover it with 
 a bell-glass, and quickly exhaust the air. The flow of liquid ceases, 
 but begins anew when air is again admitted. 
 
 170. The Siphon is essentially a tube with unequal arms, 
 used to carry liquids from one level, over an elevation, to 
 a lower level by means of atmospheric pressure. It is 
 generally set in action by filling it with the liquid, closing 
 its ends, placing the end of the shorter arm in the liquid 
 to be moved, bringing the end of the longer arm to a 
 lower level, and then opening the ends. The flow will 
 continue until the liquids stand at the same level, or until 
 air enters the tube at the end of the shorter arm. 
 
 171. Explanation of the Siphon. The vertical distance 
 from the level of the upper liquid to the highest point of 
 the tube (ab) is the length of one arm (see Fig. 189) ; 
 the vertical distance from the highest point of the tube 
 to the lower end of the tube, or to the level of the liquid 
 into which it dips (cd), is the length of the other arm. 
 The second of these must exceed the first. 
 
 Consider the horizontal layer of molecules in the tube 
 
192 
 
 SCHOOL PHYSICS. 
 
 d; 
 
 J 
 
 at the levels, a and d. The atmospheric pressures, whether 
 direct or transmitted by the liquids in accordance with 
 Pascal's law, will be upward and equal ; represent them 
 by p. The weight of the water in the short arm produces 
 a downward pressure at a; represent this by w. The 
 
 resultant of these forces 
 acting at a is p w. 
 Similarly, the weight of 
 the water in the long 
 arm produces a down- 
 ward pressure at 
 represent this by w' 
 The resultant of these 
 forces acting at d is 
 p w'. These two re- 
 sultants act against 
 each other, pw being 
 the greater. The result- 
 ant of these resultants 
 is their difference ; (p w) (p w')=w f w. Thus we 
 see that the liquid is pushed through the tube by a net 
 force equal to the weight of a liquid column whose height 
 is the difference between the two arms of the siphon. 
 
 (a) Suppose the siphon to have a cross-section of 1 sq. cm. ; that 
 db = 10 cm. ; that cd = 22 cm. Then the upward pressure at a and at d 
 will be 1,033 g. ; the downward pressure at a will be 10 g. ; the down- 
 ward pressure at d will be 22 g. Then p w = 1,023 g. ; p w' = 
 1,011 g. The resultant of these two upward and antagonistic pres- 
 sures (w' w) is a force of 12 g. tending to push the water from 
 a to d. 
 
 (6) If the downward pressure at a is as great as the atmospheric 
 pressure, the liquid will not flow. Hence, the elevation over which 
 water is to be siphoned must be less than 34 feet. 
 
 FIG. 139. 
 
THE MECHANICS OF GASES. 
 
 193 
 
 Pumps. 
 
 Experiment 93. Every one knows that a liquid may be sucked up 
 through a straw or other tube. Modify the familiar experiment by 
 passing a glass tube snugly through the cork of a bottle. Fill the 
 bottle with water, and close it with the perforated cork. Be sure that 
 no air is left in the bottle. The tube should dip an inch or so into 
 the water. Try to suck water from the bottle. 
 
 172. The Lift Pump or suction-pump consists of a 
 cylinder or barrel, piston, two valves, and a suction-pipe, 
 the lower end of which dips below 
 the surface of the liquid to be raised. 
 The piston works practically air-tight 
 in the cylinder, and has an outlet- valve 
 that opens upward. The inlet-valve is 
 at the upper end of the suction-pipe, 
 and also opens upward. When the 
 piston is drawn upward, its valve 
 is closed by the pressure of the air 
 above, and a partial vacuum is formed 
 in the cylinder below. The elastic 
 force of the air in the cylinder being 
 thus reduced, the atmospheric pres- 
 sure forces water up the suction-pipe, 
 driving the air above it through the 
 lower valve. When the piston is pushed down, the inlet- 
 valve is closed, and the confined air escapes through the 
 outlet-valve. As the piston continues its work, the air is 
 gradually removed from the cylinder and suction-pipe, 
 and the transmitted pressure of the atmosphere pushes 
 the water up to take its place and to restore the disturbed 
 
 equilibrium. 
 13 
 
 FIG. 140. 
 
194 
 
 SCHOOL PHYSICS. 
 
 (a) Theoretically the piston may be 34 feet above the level of the 
 water in the well, but, owing to mechanical imperfections, the prac- 
 tical limit for a pump lifting water by suction is about 28 vertical feet. 
 The height to which water may be lifted above the piston depends 
 only upon the strength of the pump and the power applied. 
 
 173. 
 
 pump 
 
 The Force Pump. The operation of the force- 
 is similar to that of the suction-pump. The outlet- 
 valve generally opens from the cylin- 
 der, the piston being made solid. When 
 the piston is raised, water is forced into 
 the barrel by atmospheric pressure. 
 When the piston is forced down, the 
 inlet-valve is closed, the water being 
 forced through the other valve into 
 the discharge-pipe. When next the pis- 
 ton is raised, the outlet-valve is closed, 
 preventing the return of the water 
 above it, while atmospheric pressure 
 forces more water from below into the 
 barrel. 
 
 FIG. 141. 
 
 (a) For the purpose of securing steadiness 
 for the stream as it issues from the delivery- 
 pipe, the water usually passes into an air-chamber. The elasticity 
 of the confined and compressed air largely takes up the pulsating 
 effect due to the successive pushes of the piston, and forces the water 
 from the nozzle of the delivery-pipe in a continuous stream. Fire- 
 engines and nearly all steam-pumps have such attachments. 
 
 174. The Air Pump is an instrument for removing a gas 
 from a closed vessel. Fig. 142 shows the essential parts 
 of one of the many forms. 
 
 (a) The glass receiver, jR, fits accurately upon the ground plate. 
 The edge of the receiver is often greased to insure an air-tight joint. 
 
THE MECHANICS OF GASES. 
 
 195 
 
 From R, a tube, , leads to the cylinder, C, in which moves a piston, P. 
 Two valves open from the receiver. The outlet-valve, v', is in the 
 piston ; the inlet-valve, v, may be carried by a rod that passes through 
 the piston. Of course the piston, valve, and all sliding parts of the 
 pump, must work air-tight. A down-stroke of the piston carries down 
 the valve-rod, and closes v ; the elastic force of the air confined beneath 
 P opens v', and some of the air escapes to the upper side of the piston. 
 The next up-stroke of the piston closes v' and lifts the valve-rod, and 
 thus opens v. The upward motion of the valve-rod is closely limited 
 by a shoulder near its upper end, the piston sliding upon the rod 
 during the greater part of its up-and-down movements. The air that 
 
 FIG. 142. 
 
 passes up through v f is forced out through an opening (preferably 
 closed by a valve) at the top of the cylinder, and the elastic force of 
 the air in R and t fills again the lower part of C. By the continued 
 working of the piston, the mass and the elasticity of the air in R are 
 reduced, a vacuum being approached more and more closely. As only 
 a fractional part of the residual air is removed at each stroke, a per- 
 fect vacuum is out of the question ; moreover, there is a limit arising 
 from the unavoidable imperfections of the apparatus. 
 
 (6) In Fig. 142, F is a glass vessel communicating with the re- 
 ceiver. It contains a siphon-barometer or mercurial gauge to indi- 
 cate the degree of rarefaction obtained. A stopcock at S, when 
 turned one way, cuts off communication between C and R, thus 
 
196 
 
 SCHOOL PHYSICS. 
 
 FIG. 143. 
 
 reducing the risk that air will reenter the receiver ; when turned the 
 other way, it readmits air to R. 
 
 175. The Condensing Pump is an instrument for com- 
 pressing a gas into a closed vessel, as in pumping air 
 into a pneumatic tire of a bicycle, or oxygen or hydro- 
 gen into the cylinders commonly used for stereopticon 
 purposes, or charging water with carbon 
 dioxide for sale as "soda water." 
 
 (a) It differs from the air-pump chiefly in the facts 
 that the valves are made strong enough to endure 
 high pressures, and that they open toward the re- 
 ceiver. For some purposes, the piston is made solid, 
 and both valves are placed at the bottom of the 
 cylinder, as shown in Fig. 143. The stopcock at R 
 is closed while the pump is in operation. By con- 
 necting each of the lateral tubes with a closed tank, 
 gas may be transferred from one to the other. 
 
 CLASSROOM EXERCISES. 
 
 1. How high can water be raised by a perfect lift-pump, when 
 the barometer stands at 30 inches ? The density of mercury is 13.6. 
 
 2. If a lift-pump can just raise water 28 feet, how high can it 
 raise alcohol having a density of 0.8 ? 
 
 3. Water is to be taken over a ridge 12.5 m. higher than the surface 
 of the water, (a) Can it be done with a siphon ? 
 
 Why? (6) With a lift-pump? Why? (c) With a 
 force-pump ? Why ? 
 
 4. Will a given siphon carry water over a given 
 elevation more rapidly at the top, or at the bottom, of 
 a mountain? Why? 
 
 5. If water rises 34 feet in an exhausted tube, how 
 high will sulphuric acid (density, 1.8) rise under the 
 same circumstances ? 
 
 6. The "sucker" consists of a circular piece of 
 thick leather with a string attached to its middle. 
 Being soaked thoroughly in water, it is firmly pressed 
 
 upon a flat stone to drive out all air from between the leather and 
 
 FIG. 
 
THE MECHANICS OF GASES. 
 
 197 
 
 the stone. Unless the stone is too heavy, it may be lifted by the 
 string. Is the stone really pulled up, or pushed up ? Explain your 
 answer. 
 
 7. If the capacity of the cylinder of an air-pump is that of the 
 receiver, (a) what part of the air will remain in the receiver at the 
 end of the fourth stroke of the piston? (6) How will its elastic force 
 compare with that of the external air ? 
 
 8. How high can a liquid with a density of 1.35 be raised by a 
 perfect lift-pump -when the barometer 
 
 stands at 29.5 inches? 
 
 9. Over how high a ridge can water be 
 continuously carried in a siphon, the mini- 
 mum standing of the barometer being 69 
 cm. ? 
 
 10. What is the greatest pull that can 
 be resisted by Magdeburg hemispheres 
 (a) 4 inches in diameter? (&) 8 cm. in 
 diameter ? 
 
 11. How can you arrange a single lift- 
 pump to raise water from the bottom of 
 a well 50 feet deep ? 
 
 12. Construct the apparatus shown in 
 Fig. 145, filling each of the three bottles 
 half full of water. Be sure that all joints 
 made by the corks of the three bottles are 
 
 FIG. 145. 
 
 air-tight. Blow into the tube, /, until a jet is formed at n. 
 plain the continued action of the apparatus. 
 
 EX- 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Small test-tube; pen-filler; sulphuric 
 ether ; pinchcock ; lead counterpoise. 
 
 1. Partly fill two bottles with water. Con- 
 nect them by a bent tube that fits closely into 
 the mouth of one, and loosely into the mouth of 
 the other. Place the bottle under the receiver 
 and exhaust the air. Note and record what 
 takes place. Admit air to the receiver. Note 
 and record what takes place. Write an explana- 
 tion of the phenomena. 
 
 FIG. 146. 
 
198 SCHOOL PHYSICS. 
 
 2. Fill a test-tube with water and invert it in a tumbler of water. 
 With a pen-filler, introduce a few drops of sulphuric ether, a very 
 volatile and extremely inflammable liquid, into the test-tube. The 
 ether will rise to the top of the tube. Place the tumbler and the test- 
 tube under the receiver and exhaust the air. The water in the test- 
 tube falls. Readmit air to the receiver, and note the contents of the 
 test-tube. Record your conclusions concerning the effect of pressure 
 upon the molecular condition of sulphuric ether. 
 
 3. With a short piece of rubber tubing, connect the short arms of 
 two |_-shaped glass tubes, and set up the apparatus as a siphon. While 
 the water is flowing, perforate the rubber wall between the glass tubes. 
 Note and explain the effect. 
 
 4. With apparatus like that used in Experiments 88 and 89, and 
 noting the reading of the mercurial barometer at the time, verify 
 Boyle's law between the limits of half an atmosphere and two atmos- 
 pheres, by showing the constancy of the product of volume into 
 pressure. 
 
 5. Fill the U'tube used in Experiment 63 with mercury to a 
 depth of about 30 cm., and attach a rubber tube about 40 or 50 cm. 
 long firmly to one end of the tube. Force air steadily from the lungs 
 through the rubber tube ; pinch the tube tightly ; rest ; increase the 
 pressure on the mercury if you can without injury or pain ; close the 
 rubber tube with a pinchcock; and compute your maximum "lung 
 power " in pounds per square inch. 
 
 6. With the same apparatus, suck air from the tube, and compute 
 your maximum "force of suction " in pounds per square inch. Explain 
 the use of quotation marks in the last sentence. 
 
 7. With the same apparatus, measure the pressure under which 
 illuminating gas is delivered at the laboratory. Will you get more 
 accurate results by using mercury, or water ? 
 
 8. What objection is there to using the same apparatus for measur- 
 ing the pressure under which water is supplied at the laboratory? 
 Devise some means for that problem, and solve it. 
 
 9. Repeat Experiment 73. Determine the capacity of the vessel 
 used. Compare the reading of the pressure-gauge of the air-pump 
 with that of the barometer at the time of the experiment, and deter- 
 mine what part of the air in the vessel was removed. Determine 
 the density of air under the thermometric and barometric conditions 
 of the experiment. If you have no vessel like that mentioned in 
 Experiment 73, use a 2-liter bottle, connecting its rubber stopper 
 
THE MECHANICS OF GASES. 199 
 
 with the pump by a thick-walled rubber tube. After exhaustion, 
 close the tube with a pinchcock. Make all connections air-tight, 
 using glycerin for that purpose. Be sure not to omit any of the 
 apparatus from one weighing, that is included in the other. 
 
 10. Fill with mercury the tube used in Experiment 81, and by 
 direct weighing and measurement, determine the weight of the mer- 
 cury per centimeter of the length of the tube. Measure the length of 
 the barometric column in the same tube and compute the weight 
 of the mercury supported by atmospheric pressure. 
 
 11. Make a siphon with parallel arms, each about 50 cm. long, by 
 bending a piece of glass tubing twice at right angles. Place one 
 branch of the tube in a large vessel of water at least 40 cm. deep, and 
 support the siphon so that its short arm shall be 10 cm. long. (See 
 170.) Start the siphon by suction, and measure with a graduate the 
 water that flows in two minutes. Determine the difference between 
 the lengths of the two arms. Raise the siphon until its short arm is 
 15 cm. long. Set the siphon in action. Measure the water that flows 
 in two minutes, and determine the difference between the lengths 
 of the two arms, as before. As this difference decreases, does the 
 amount of water delivered also decrease? Continue the work, 
 successively testing with short arm lengths of 20, 25, 30, 40, and 
 45 cm. Tabulate your results. What is the relation between rate 
 of flow and the difference in the lengths of the two arms of the 
 siphon ? 
 
 12. Using the differences in lengths of the arms as ordinates, and 
 the rate of flow as abscissas, map the line that represents this relation. 
 From this line, measure the abscissa of the point that has an ordinate 
 corresponding to a length of 35 cm. for the short arm of the siphon, 
 and determine the rate of flow that it represents. Set the siphon used 
 in Exercise 11 so that its short arm shall measure 35 cm., and by 
 direct experiment test the accuracy of the result computed from the 
 curve. 
 
 13. With the apparatus used in Experiment 88, measure the com- 
 pression of the air confined under different pressures until the excess 
 of mercury in the long arm is about equal to the barometric column. 
 Avoid touching the short arm, or in any way changing the tempera- 
 ture of the confined air. From the data thus obtained, map upon 
 cross-section paper a line representing the relation between volume 
 and pressure. Let each vertical division of the paper represent a 
 pressure of 2 cm. of mercury, and each horizontal division a com- 
 
200 
 
 SCHOOL PHYSICS. 
 
 pression of 0.5 cm. 
 
 Is the line thus mapped a straight line? If so, 
 what does that show? If the line is 
 curved, what does the .varying down- 
 ward slope indicate ? From the line 
 as drawn, do you conclude that equal 
 increments of pressure produce equal 
 compressions, or otherwise? 
 
 14. Using a lead ball as shown in 
 Fig. 147, counterpoise the globe of Ex- 
 periment 73, "filled with air and with 
 stopcock closed. Cover the apparatus 
 with a bell-glass and exhaust the air. 
 The globe seems to be heavier than 
 the ball which previously balanced 
 it. Record a description and explana- 
 tion of what you do and of what fol- 
 lowed. 
 
 FIG. 147. 
 
CHAPTER III. 
 
 ACOUSTICS: MASS PHYSICS. 
 I. THE NATURE OF SOUND, ETC. 
 
 176. Sound is the mode of motion that is capable of affect- 
 ing the auditory nerve. 
 
 (a) We have to deal with sound only as a physical phenomenon ; 
 not as a physiological or psychological process. 
 
 Cause of Sound. 
 
 Experiment 94. Suspend a small pith-ball so that it shall rest 
 lightly against the edge of a bell or bell-jar. Strike the bell so that 
 it will give forth a sound. Such a bell or a tuning-fork may be 
 sounded by tapping it with a hammer made by slipping a piece of 
 rubber tubing over a stout iron wire, or by thrusting the handle of a 
 cheap tapering pen-holder into the hole at the center of a circular 
 eraser. A better way, however, is to make it vibrate by drawing a 
 resined violin-bow across the edge or end. Xotice that the ball acts 
 as if the edge of the bell was in vibration. Touch the edge of the 
 sounding bell lightly with the finger-nail. 
 
 Experiment 95. Sound a tuning-fork and just touch a water 
 surface with one of its prongs. Notice the spray. 
 
 Experiment 96. The chimneys of student-lamps often break at 
 
 the contracted part near the 
 
 bottom. Close such a broken 
 chimney at the broken end 
 with cork or wax. At the 
 toy store, buy a wooden whis- 
 tle like that shown in the 
 
 rIG. 14o. 
 
 upper part of Fig. 148, and 
 
 cut it off at the point indicated by the dotted line between the first 
 
 201 
 
202 
 
 SCHOOL PHYSICS. 
 
 and second finger-holes. Fit the end of the whistle into the opening 
 of a cork that will tightly close the open end of the broken chimney. 
 Inside the tube, place a small quantity of precipitated silica, a very 
 light powder that you can buy from a dealer in chemical supplies, or 
 a like quantity of the dry dust obtained by filing a cork. Close the 
 tube with the cork and whistle, hold the tube horizontal and shake 
 it endwise so as to distribute the powder evenly, and then blow the 
 
 whistle. The powder is agitated in 
 a peculiar manner, rising in thin ver- 
 tical plates, and coming to rest in 
 little piles transverse to the axis of 
 the tube. Was the motion of the air 
 in the tube one of vibration, or one 
 of translation? 
 
 Experiment 97. Grasp one end 
 of a straight spring made of hickory 
 or steel in one end of a vise, as shown 
 in Fig. 149. Pluck the free end of 
 the spring so as to produce a vibra- 
 tory motion. If the spring is long 
 enough, the vibrations may be seen. 
 Lower the spring in the vise to 
 shorten the vibrating part of the rod, 
 and pluck it again. The vibrations 
 are reduced in amplitude, and in- 
 creased in rapidity. Continued shortening of the spring will render 
 the vibrations invisible and audible ; they are lost to the eye, but re- 
 vealed to the ear. 
 
 177. Cause of Sound. From these experiments, it is 
 reasonable to conclude that sound is caused by the rapid 
 vibrations of a material body. In fact, all sounds may be 
 traced to such vibrations. Bodies that emit sounds are 
 called sonorous. 
 
 (a) A glass plate that has been blackened by holding it over a 
 petroleum or a camphor flame maybe arranged so as to slide easily in 
 the grooved frame, F. A triangular piece of tinsel or a short piece 
 
 FIG. 149. 
 
THE NATURE OF SOUND, ETC. 
 
 203 
 
 of the hairspring of a watch attached by wax to the end of one of 
 the prongs of the fork will make a good style for our purpose. When 
 the fork is made to vibrate, the style placed against the smoked plate, 
 
 150. 
 
 and the plate drawn along rapidly in the grooves, the undulating line 
 traced on the glass represents the vibratory movement of the prong. 
 
 Wind or Wave? 
 
 Experiment 98. Provide a tube four or five yards long, and about 
 four inches in diameter. A few lengths of .common spout from the 
 tinner's will answer. Furnish it with a funnel-shaped piece, having 
 an opening about an inch in diameter. Place the tube on a table with 
 a candle flame opposite the opening at B. With a book, strike a 
 
 FIG. 151. 
 
 sharp blow upon the table opposite the opening at A. The flame will 
 be agitated and perhaps blown out. Something went from A to B. 
 Did it go through the tube ? 
 
 Experiment 99. Close the opening at A and repeat the experi- 
 ment; the flame is not put out. Remove the tube and repeat the 
 blow; the flame is not put out. 
 
 Experiment 100. Replace the tin tube by a rubber tube of the same 
 length and with an internal diameter of about 10 or 15 mm. Insert 
 the neck of a funnel at the end of the tube at A. Get a few inches 
 of glass tubing that will fit snugly into the rubber tubing. Heat the 
 
204 
 
 SCHOOL PHYSICS. 
 
 middle of the glass in a flame until it softens. Slowly draw the ends 
 asunder until the softened part is reduced to a diameter of about 
 2mm. Break the tube at this narrow neck and push the large end of 
 one piece into the rubber tube at B. Place a small flame opposite the 
 small opening of the glass tube. Strike a blow in front of the funnel 
 at A and notice that a puff or pulse of air blows the flame. Make a 
 loose loop in the rubber tube and repeat the experiment. Clap the 
 hands at A and notice the series of puffs at R. While an assistant is 
 clapping his hands at A, pinch the rubber tube. Notice that the puffs 
 at B cease while the tube is thus pinched, and reappear as soon as the 
 tube is released. The tube is necessary. Whatever agitated the 
 candle flame did go through the tube. Was this something a wind, 
 or a wave ? 
 
 Experiment 101. Replace the tin tube. Dissolve as much potas- 
 sium nitrate (saltpeter) as you can in half a cupful of hot water. 
 Soak a piece of blotting-paper in this liquid and dry it. This "touch- 
 paper " burns with much smoke but no flame. Burn the paper in the 
 tube near A, filling that end of the tube with smoke. Repeat Experi- 
 ment 98. No smoke issues at B ; it ivas not a wind that passed through 
 the tube. 
 
 178. Propagation of Sound. Sound is ordinarily propa- 
 gated through the air. Tracing the sound from its source 
 to the ear of the hearer, we may say that the first layer of 
 air is struck by the vibrating body. The particles of this 
 
 layer give their mo- 
 tion to the particles 
 of the next layer, 
 and so on until the 
 particles of the last 
 layer strike upon 
 the drum of the 
 
 FIG. 152. 
 
 ear. 
 
 (a) This idea is beautifully illustrated by Professor Tyndall. He 
 imagines five boys placed in a row, as shown in Fig. 152. "I sud- 
 
THE NATURE OF SOUND, ETC. 205 
 
 denly push A ; A pushes B and regains his upright position ; B 
 pushes C ; C pushes D ; D pushes E ; each boy, after the transmission 
 of the push, becoming himself erect. E, having nobody in front, is 
 thrown forward. Had he been standing on the edge of a precipice, 
 he would have fallen over ; had he stood in contact with a window, he 
 would have broken the glass ; had he been close to a drumhead, he 
 would have shaken the drum. We could thus transmit a push 
 through a row of a hundred boys, each particular boy, however, only 
 swaying to and fro. Thus also we send sound through the air, and 
 shake the drum of a distant ear, while each particular particle of the 
 air concerned in the transmission of the pulse makes only a small 
 oscillation." 
 
 The Medium of Sound. 
 
 Experiment 102. Place a small music box or alarm clock on a 
 thick layer of felt, cotton wool, or other inelastic material on the 
 plate of the air-pump, and cover it with a bell-glass. Exhaust the 
 air and notice that while the motion of the mechanism is plainly 
 visible, the sound is scarcely audible. 
 
 Experiment 103. In a large glass globe provided with a stopcock, 
 suspend a small bell by a thread. Pump the 
 air from the globe ; shake the globe, and notice 
 that the sound of the bell is very faint. Re- 
 admit the air; shake the globe, and notice that 
 the sound of the bell is heard distinctly. A 
 large, wide-mouthed bottle, with a perforated 
 rubber stopper, rubber tubing, and pinchcock, 
 may be substituted for the globe and stopcock. 
 See Experiment 73. 
 
 Experiment 104. Fill a tumbler with water and place it on an 
 empty crayon box. Stick the stem of a tuning-fork into a small 
 wooden disk, sound the fork, and hold it with the disk resting upon 
 the surface of the water. The vibrations will be transmitted by the 
 water, and the sound of the fork will be heard as if coming from the 
 box. Other liquids may be similarly tested. 
 
 Experiment 105. Provide a wooden rod about half an inch square 
 and five or six feet long. Place one end of this rod (preferably made 
 of light, dry pine) agamst the panel of a door; hold the rod hori- 
 
206 SCHOOL PHYSICS. 
 
 zontal, and place the handle of a vibrating tuning-fork against the 
 other end. Notice the sound given out by the panel. The common 
 " string telephone " is a more familiar illustration of the transmission 
 of sound by a solid. 
 
 179. Sound Media. Any elastic substance may be the 
 medium for the transmission of sound. Liquids and solids 
 are better conductors of sound than gases are. The 
 scratching of a pin may be heard through a long wooden 
 beam ; and the gentle tap of a hammer, through a water- 
 pipe a mile or more in length. The nature of the vibra- 
 tions in sound-media demands careful consideration. 
 
 Vibratory Motion. 
 
 Experiment 106. Grip one end of the meter stick in a vise, as 
 shown in Fig. 149. Pluck the free end, and notice that the vibrating 
 end returns periodically to the starting point. Suspend a lead bullet 
 by a long thread, swing it as a pendulum, and notice that the ball 
 returns periodically to the starting point. Swing the ball as a conical 
 pendulum, and notice that the ball, moving in a circular path, returns 
 periodically to the starting point. Twist the torsion al pendulum 
 (Experiment 17), and notice that the index returns periodically to the 
 starting point. 
 
 Experiment 107. Fasten an elastic cord to a ball, or buy a " return 
 ball " at a toy shop. Hold the end of the cord in one hand, and, with 
 the other hand, pull the ball down and let it go. The ball swings up 
 and down in the direction of the length of the cord. Notice that the 
 speed of the ball varies much as does that of a common pendulum, 
 and that the ball returns periodically to the starting point. 
 
 180. Vibrations. When the parts of a body move so 
 that each returns periodically to its initial position, the 
 body is said to be in vibration. The motion made in the 
 interval between two successive passages in the same direction 
 through any position is called a vibration. The vibration 
 may be transverse, torsional, or longitudinal, the classifi- 
 
THE NATURE OF SOUND, ETC. 207 
 
 cation having reference to the direction of the vibration 
 relative to the length of the vibrating body. 
 
 (a) A vibration is analogous to a double or " complete " oscillation, 
 as defined in 114 (a). When the reciprocating movement is com- 
 paratively slow, as that of a pendulum, the term " oscillation " is 
 commonly used ; the term " vibration " is generally confined to rapid 
 reciprocations or revolutions, as that of a sonorous body. The three 
 kinds of vibration have the same manner of moving, the changes 
 in velocity being the same as take place in the swings of a pen- 
 dulum. 
 
 Pendular Motion. 
 
 Experiment 108. Let a pupil take a ball-and-thread pendulum to 
 the further side of the room. With a slight circular motion of the 
 hand that supports the end of the thread, let him cause the ball to 
 move in a circular path, thus forming a conical pendulum. When 
 the speed of the ball has become uniform, count the swings that the 
 ball makes around the circle in 30 seconds. Then place your eye on 
 a level with the ball and observe it ; i.e., look at the ball along a line 
 of sight that is in the plane of the circle. 
 The ball will appear to move from side to side 
 in a straight line that coincides with a diam- 
 eter of the circle, and to vary its velocity as a 
 common pendulum does. Xext, swing the 
 same ball as a common pendulum, and count 
 the vibrations that it makes in 30 seconds. 
 A conical pendulum and a common pendu- 
 lum of the same length have the same period. 
 When the common pendulum is viewed from 
 beneath, i.e., when the line of sight is in the 
 plane of vibration as before, the bah 1 again appears to move in a 
 straight line and with a like varying velocity. This apparent motion 
 and its relation to the real motion are very interesting and instructive. 
 Let the circle shown in Fig. 154 represent the path described by the 
 conical pendulum; then will the diameter, A G, represent the apparent 
 rectilinear path. Suppose that the ball goes around the circle in two 
 seconds. Divide the circumference into any number of equal parts, 
 as 12. The ball will move over each of these equal arcs in of a 
 
208 SCHOOL PHYSICS. 
 
 second. To one who is looking at this motion in the plane of the 
 paper, the ball appears to go from A to B while it really goes from 
 A to b; it appears to go from B to C while it really goes from b to c; 
 etc. When the ball is at d, it is moving across the line of sight, and, 
 therefore, appears to have its greatest velocity, just as a common 
 pendulum does, at the middle of its arc. When it is at A or G, it is 
 moving in the line of sight, and, therefore, appears to be at rest, 
 although it is really moving with its uniform velocity. From a study 
 of the figure, it will be seen that the ball appears to go from A to G 
 and back in the two seconds in which it really goes around the circle. 
 The unequal lengths, AB, BC, . . . FG, give a fair idea of the varying 
 speed of a common pendulum. 
 
 181. Simple Harmonic Motion. If, while a particle 
 moves in the circumference of a circle with uniform ve- 
 locity, a point moves along a fixed diameter of the circle 
 so as always to be at the foot of a perpendicular drawn 
 from the particle to the diameter, as described in Experi- 
 ment 108, the motion of the point along the diameter is 
 called a simple harmonic motion. The radius of the circle, 
 or the distance from the middle to the extremity of the 
 swing, is called the amplitude of vibration ; the time inter- 
 vening between two passages of the particle in the same 
 direction through any point is called the period of vibra- 
 tion. 
 
 Wave Forms. 
 
 Experiment 109. Drop a pebble into a tub of water. Waves will 
 be seen moving on the surface of the water from the center of dis- 
 turbance, and in concentric circles, toward the sides of the tub. A 
 small cork floating on the surface rises and falls with the water, 
 but is not carried along by the advancing waves of troughs and 
 crests. 
 
 Experiment no. Tie one end of a soft cotton rope about 20 feet 
 long to a fixed support, and hold the other end in the hand. Move 
 the hand up and down with a quick, sudden motion, so as to set up a 
 
THE NATURE OF SOUND, ETC. 209 
 
 series of waves in the rope, as shown in Fig. 155, in which each 
 curved line may be considered an instantaneous photograph of a rope 
 thus shaken. 
 
 FIG. 155. 
 
 182. Waves of Crests and Troughs. When a person 
 sees waves approaching the shore of a lake or ocean, 
 there arises the idea of an onward movement of great 
 masses of water. But if the observer watches a piece 
 of wood floating upon the water, he may notice that it 
 merely rises and falls without approaching the shore. 
 Again, he may stand beside a field of ripening grain, and, 
 as the breezes blow, he will see a series of curved forms 
 or waves pass before him. There is no movement of mat- 
 ter from one side of the field to the other ; the grain- 
 ladened stalks merely bow and raise their heads. Most 
 persons are familiar with similar wave movements in 
 ropes, chains, and carpets. Each material particle has a 
 simple harmonic motion, vibratory, not progressive. The 
 only thing that has an onward movement is the pulse or 
 ivave, which is only a form or change in the relative posi- 
 tions of the particles of the undulating substance. 
 
 (a) By fixing a pencil at the end of a lath firmly held at the other 
 end, and vibrating in a horizontal plane, the pencil may be made to 
 mark a nearly straight line, ab, on a sheet of paper or cardboard. By 
 moving the paper while the rod is vibrating, the pencil may be made 
 to trace a sinusoidal curve or wavy line like that shown in Fig. 156. 
 The construction of such a curve, and its relation to the simple har- 
 monic motion of the pendulum, will be further illustrated in the 
 exercises. The distance from crest to crest (1 to 5), or from trough to 
 14 
 
210 
 
 SCHOOL PHYSICS. 
 
 trough (3 to 7), or from any point to the next point at which the 
 vibrating particle was in the same stage of vibration or in the same 
 phase (A to 4, or 2 to 6, or 4 to J3), is called a wave-length. Evidently, 
 
 FIG. 156. 
 
 the disturbance, i.e., the wave, advances just one wave-length in the 
 time required for one vibration; this time is called the vibration- 
 period. 
 
 Experiment in. Make a spiral spring about 12 feet long by 
 closely winding Xo. 18 spring-brass wire on a rod about half an inch 
 in diameter. Fasten one end of the spiral to a hook on the wall, or 
 clamp it in a vise, and tie short pieces of bright-colored strings into 
 
 several of the coils. Holding 
 the other end of the spiral in 
 the hand, insert a finger-nail or 
 knife-blade between two turns 
 FIG. 157. of the wire near the hand, and 
 
 pull one of them further from 
 
 the other. Suddenly release the coil, and a pulse will run along the 
 spiral. Each coil swings to and fro, the coils being crowded closely 
 together at one place, and more widely separated at another, as shown 
 in Fig. 157. 
 
 Experiment 112. Tightly tie a sheet of writing paper over the 
 large end of the tube used in Experiment 98, and hold a candle flame 
 in front of the small end. Tap the paper diaphragm, and notice the 
 consequent flickering of the flame. 
 
 183, Waves of Condensation and Rarefaction. The 
 
 advancing paper diaphragm or other vibrating body 
 crowds the layers of air immediately in its front, thus 
 setting up a condensation or push along the length of the 
 tube, as explained in 178. When the paper swings with 
 
THE NATURE OF SOUND, ETC. 
 
 211 
 
 its pendulum-like motion in the opposite direction, the 
 nearest layers of air follow it, thus setting up a rarefac- 
 tion. As the paper diaphragm continues to vibrate, a 
 series of condensations and rarefactions is sent along the 
 tube, as shown in Fig. 158, which compare with Fig. 154. 
 The air particles are crowded unusually at A and 6r, where 
 their velocity is the least, and are separated more widely 
 at D, where their velocity is the greatest. Just as a water 
 
 FIG. 158. 
 
 wave consists of two parts, the crest and the trough, so a 
 sound wave consists of two parts, a condensation and a 
 rarefaction. The particles in a sound wave move with 
 simple harmonic motion forward and backward in the line 
 of propagation, and not across it. The vibrations are 
 longitudinal, not transverse. 
 
 (a) A series of complete sound waves, such as would be set up in 
 the open air, consists of alternate condensations and rarefactions 
 advancing in the form of concentric spherical shells, at the common 
 center of which is the sounding body. Any radius of the sphere is a 
 line of propagation of the sound. 
 
 (6) The distance from any point to the next point that is in the 
 same phase, as from condensation to condensation or from rarefaction 
 to rarefaction, is a wave-length. The wave advances one wave-length 
 in the time required for one vibration, or in a wave-period. 
 
 (c) A sinusoidal curve like that shown in Fig. 156 is commonly 
 used to represent a sound wave. The parts above the horizontal line 
 represent condensations, while the parts below that line represent 
 
212 
 
 SCHOOL THYSICS. 
 
 rarefactions. Perpendicular distances, from the curve to the line A B, 
 i.e., ordinates, show the relative amount of condensation or rarefac- 
 tion at any point of the curve; but it must not be inferred that ampli- 
 tudes are as great relative to wave-lengths as would be indicated by 
 the curves. The curve is merely a symbol for the sound wave, not a 
 picture of one. 
 
 (d) Fig. 159 represents apparatus devised by Mach for the illus- 
 tration of the pendular motions of the particles of a medium trans- 
 mitting waves of any kind, longitudinal or transverse, stationary or 
 progressive. A wooden framework about 2.2 m. long and 1.2 m. high 
 is arranged to support 17 or more pendulums with bifilar suspensions 
 0.9 m. long. At the top of the frame are two parallel bars joined by 
 
 FIG. 159. 
 
 pivoted crossbars, after the manner of the familiar parallel ruler, and 
 so that they may be separated about 10 cm. One string of the bifilar 
 suspension of each pendulum is fastened to the inner face of the fixed 
 bar, and the other string to the inner face of the movable bar. When 
 the two bars are as far apart as possible (as shown in the figure), the 
 balls can swing lengthwise of the frame ; i.e., longitudinally. When 
 the two bars are brought close together the balls can swing only 
 transversely. 
 
THE NATURE OF SOUND, ETC. 213 
 
 A light frame worked by the foot-lever carries a wave "pattern." 
 The holes in this pattern are at varying distances from each other, 
 one part representing a rarefaction and another part representing a 
 condensation, as is clearly shown in the figure. When the pattern is 
 raised by the lever, the pendulums may be placed in the holes. When 
 the pattern is lowered, the balls swing longitudinally, their relative 
 motions representing a stationary sound wave, such as the wave in an 
 organ-pipe, and giving a vivid idea of the alternate condensations and 
 raref actions. 
 
 A block, shown at the lower right-hand part of the figure, may be 
 drawn along the framework by the string attached to it. This block 
 has upon its upper surface a groove of such depth that, as it is drawn 
 under the balls from one end of the row to the other, each ball is 
 pulled from its position of rest and released as the block passes under 
 it. Thus is produced the form of a progressive wave of condensation 
 and rarefaction. 
 
 The two bars that support the pendulums may be brought together 
 so that the balls can swing only transversely, and the pattern pre- 
 viously used may be replaced by the sinusoidal pattern that represents 
 one complete wave. Such a sinusoidal pattern is shown in the figure. 
 When this pattern is raised by the foot-lever and the balls placed in 
 the holes and the pattern then dropped, the pendular motions give a 
 clear representation of a stationary transverse wave. 
 
 A long board, just wide enough to reach from the pattern supports 
 to the top of the balls may be placed on edge so that all of the balls 
 are pushed about 10 cm. to one side of their positions of rest. 
 When this board is drawn endwise, the balls are successively re- 
 leased, and the pendular motions represent a progressive transverse 
 wave. 
 
 CLASSROOM EXERCISES. 
 
 1. State clearly the difference between a transverse and a longitu- 
 dinal wave. Illustrate. 
 
 2. The velocity of sound being given as 1,145 feet per second, what 
 is the wave-length of a tone due to 458 vibrations per second ? 
 
 3. It is a common experiment for one of two boys in swimming to 
 hold his head under water while another at a distance strikes two 
 stones together under water. The loudness of the sound heard by 
 the first boy is painful and sometimes injurious, even when the dis- 
 
214 SCHOOL PHYSICS. 
 
 tance is so great that the sound would be scarcely heard in the air. 
 Explain. 
 
 4. If a blow is struck with a hammer upon one end of a long iron 
 pipe, a listener at the other end may hear two sounds instead of one. 
 Explain. 
 
 5. What is the difference between the physical and the physiologi- 
 cal definitions of the word " sound " ? 
 
 6. What is the difference between an oscillation and a vibration? 
 
 7. What is the difference between a motion of translation and one 
 of vibration ? Illustrate. 
 
 8. Why is the motion of a particle of the medium through which a 
 sound is passing properly described as " pendular " ? 
 
 9. How does a pendular motion differ from a simple harmonic 
 motion ? 
 
 10. What word accurately describes the curve that is used as a 
 symbol of a sound wave ? 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. A wooden rod about half an inch 
 square and 12 feet long ; cardboard ; India ink ; drawing instruments ; 
 heavy plank and blocks ; hinge ; clock spring ; pocket tuning-fork. 
 
 1. Draw a graphic representation of a series of waves of troughs and 
 crests as follows : With a radius equal to the amplitude of vibration, 
 draw a circle. Draw its vertical diameter, A I. Beginning at A or 7, 
 divide the circumference of the circle into any number of equal parts, 
 say 16. Through these divisions draw horizontal lines intersecting 
 A I at the points B, C, D, E, F, G, and H, and prolong them indefi- 
 nitely. See Fig. 154. Similarly extend tangents to the circle at A 
 and /. On the extension of the line passing through E, the center of 
 the circle, lay off successively 16 equal parts. Consider the beginning 
 of the first of these equal parts as the origin of co-ordinates, and 
 number thence the successive divisions on the axis of abscissas, from 
 1 to 16 inclusive. Through these 16 points, draw vertical lines, ter- 
 minating the successive verticals at the points where they intersect 
 the successive horizontal lines. Mark these successive intersections 
 1', 2', 3', etc., to 15'. Then the ordinates of V and T will be equal to 
 EF; those of 2' and 6' will be equal to EG; those of 3' and 5' will 
 be equal to EH, and that of 4' will be equal to El. The ordinates 
 of 8' and 16' will be zero. The ordinates of 9' and 15' will be nega- 
 
THE NATURE OF SOUND, ETC. 215 
 
 tive and equal to ED ; those of 10' and 14' will be negative and equal 
 to EC ; those of 11' and 13' will be negative and equal to EB; that 
 of 12' will be negative and equal to EA . Join these several loci by 
 drawing a curve through them, and we have the wavy line known as 
 a sinusoidal curve, the outline of the wave as required. What is the 
 distance from O to 16 called? What is the distance from 4 to 4' 
 called ? What is the point 4' called ? What is the point 12' called ? 
 Can you see any connection between the motion of a drop of water in 
 an oscillatory wave and the motion of a pendulum ? 
 
 2. Slightly stretch a solid rubber cord about 0.5 cm. in diameter 
 between a hook in the ceiling and another in the floor. With a ruler, 
 tap the cord near the lower end, timing the blows so that the cord 
 shall vibrate as a whole. Count the number of vibrations made in 
 60 seconds. Repeat the test twice and determine the average of the 
 three trials. 
 
 Tap the cord more rapidly until it vibrates in two segments. 
 Repeat the test and determine as before the average number of 
 vibrations made in 60 seconds. 
 
 Similarly, make the cord vibrate in three and then in four seg- 
 ments, recording the numbers of vibrations as before. Measure the 
 length of the cord between the hooks, tabulate the segment-lengths 
 and the numbers of vibrations per second for each of the four tests. 
 Determine the relation between the segment-lengths and the vibration- 
 numbers. 
 
 3. Hold one end of a slender wooden rod between the teeth, while 
 another pupil holds the stem of a vibrating tuning-fork against the 
 other end of the rod. See if the fork is audible without the inter- 
 vention of the rod. 
 
 4. Cut a slit 1 mm. x 4 cm. in a postal card. Place a ruler below 
 Fig. 156 and parallel with the printed lines. Place the edge of the 
 card against the edge of the ruler, so that the slit shall be at right 
 angles to the line, AB, at its end. AB should show through the slit 
 at its middle point. Slide the card with steady motion along the 
 edge of the ruler, observing the apparent motion of the black line 
 seen through the slit. How does that apparent motion up and down 
 the slit compare with the simple harmonic motion of the pendulum? 
 
 5. From a piece of stiff cardboard, cut a disk 31 cm. in diameter, 
 and from its center draw a circle 0.5 cm. in diameter. Divide the 
 circumference of this little circle into twelve equal parts, and number 
 the points of division consecutively from 1 to 12. With dot 1 as a 
 
216 
 
 SCHOOL PHYSICS. 
 
 FIG. 160. 
 
 center, draw a circle with a radius of 7.5 cm., using the pen-compasses 
 and India ink. With dot 2 as a center, draw a circle with a radius of 
 7.8 cm. With dot 3 as a center, draw a circle with a radius of 8.1 cm. 
 Continue to draw such eccentric circles, using the numbered dots in 
 
 succession as centers and in- 
 creasing the radius by 0.3 cm. 
 each time. Go thus around 
 the little circle twice, when you 
 will have 24 circles drawn upon 
 the cardboard, as indicated in 
 Fig. 160. Cut a hole exactly at 
 the center and mount the disk 
 upon the spindle of a whirling 
 table. Cut a narrow slit about 
 10 cm. long in a card, and hold 
 it so that the slit lies parallel 
 to a radius of the disk and 
 close to it. The short arcs of 
 the circles seen through the 
 slit look like a series of dots, each of which may be taken to represent 
 an air particle. Still viewing the dots through the slit, rotate the disk 
 and you will get a very vivid idea of the way in which air particles 
 actually move when set in motion by a sound wave. 
 
 6. From a two-inch plank, cut a baseboard about 75 x 20 cm. 
 To one edge of this base and about 20 cm. from one end, screw an 
 upright, and at the upper end of the upright support a short hori- 
 zontal shelf, one edge of which 
 shall be over and parallel with 
 the middle line of the base- 
 board. Paste one end of a small 
 strip of stout paper to one end 
 of a piece of glass about 15 cm. 
 long and 10 cm. wide, so that 
 the projecting part of the paper 
 may serve as a handle for mov- 
 ing the glass, which is to be lightly smoked. Provide a wooden 
 block shaped like that shown in Fig. 161, the greatest length of 
 which is about 30 cm. long and the thickness of which at the part 
 marked a is about 2.5 cm. The several faces of the thicker part of 
 this block have holes, into any one of which the handle of a tuning- 
 
 FIG. Nil. 
 
THE NATURE OF SOUND, ETC. 
 
 217 
 
 9 
 
 FIG. 1(>2. 
 
 fork may be driven. The face, i, carries a hinge for fastening the 
 block to the baseboard, and near the end of a is a large screw-eye 
 extending into the baseboard. Fig. 162 shows a pendulum sup- 
 ported from the edge of the shelf already men- 
 tioned. The pendulum is made of a straightened 
 piece of clock-spring with a lead bullet-bob at the 
 lower end. The under side of the bob carries a 
 style. This pendulum will vibrate across a line 
 drawn along the middle of the baseboard. Place 
 the smoked glass on the baseboard so that its 
 length shall be parallel with the length of the 
 board, and so that the pendulum shall hang near 
 the end that carries the paper strip. Drive the 
 handle of the tuning-fork into the hole in the 
 block at the face marked t, and fasten the block 
 at the other end of the smoked glass so that the 
 style at the end of the fork shall come as near as possible to the 
 style of the pendulum, and shall swing parallel with it when prong 
 and pendulum are both in motion. Adjust the height of the shelf 
 so that the pendulum wijl be long enough to make between 100 
 and 150 complete oscillations per minute. Then adjust the pendulum 
 at the clamp on the edge of the shelf so that the style carried by the 
 bob may just touch the glass and cut a line on its smoked surface. 
 Accurately count the number of vibrations that the adjusted pendu- 
 lum makes in a minute. Loosen the screw at the further end of the 
 block that carries the fork, and adjust the height so that the style at 
 the end of the prong just grazes the surface of the glass. Tack a thin 
 strip of wood at the long edge of the glass to serve as a guide for the 
 latter. Set pendulum and fork in vibration and quickly draw the 
 glass lengthwise. From the two traces on the glass, count the num- 
 ber of vibrations of the fork that correspond to one vibration of the 
 pendulum, and thence compute the vibration-number of the fork. 
 
218 ' SCHOOL PHYSICS. 
 
 II. VELOCITY, REFLECTION, AND REFRACTION 
 OF SOUND. 
 
 Experiment 113. Provide three similar rubber tubes, each about 
 3 m. long; fill one of them with sand, and with equal tension stretch the 
 three side by side, suspended between supports at their ends. Strike 
 the two empty tubes simultaneously with a ruler and near one end ; 
 notice that a wave runs along each tube to the other end where it is 
 reflected; the waves return to the starting point at practically the 
 same time; they travel with equal velocities. Increase the tension 
 of one of the tubes and repeat the experiment. The increase of the 
 elastic force increases the velocity of the wave. Similarly, send a 
 wave along the sand-filled tube, and notice that the waves travel per- 
 ceptibly more slowly in the heavier tube. 
 
 184. The Velocity of Sound depends upon two considera- 
 tions, the elasticity and the density of the medium. 
 It varies directly as the square root of the elasticity, and 
 inversely as the square root of the density. 
 
 (a) In solids, elasticity is measured by the modulus of elasticity 
 (E), which is the reciprocal of the coefficient of elasticity (e). In 
 liquids and gases, elasticity is measured by the resistances they offer 
 to compression. 
 
 (6) The velocity of the wave motion may be found by multiplying 
 the wave-length by the number of vibrations per second, or the wave- 
 length may be found by dividing the velocity by the number of vibra- 
 tions. 
 
 (c) Careful experiment has established the fact that the velocity of 
 sound in air at the freezing temperature (0 C. or 32 F.) is about 332 m., 
 or 1,090 feet per second. Oxygen is sixteen times as dense as hydro- 
 gen. Under the same pressure, the elasticity is the same ; hence, 
 sound travels four times as fast in hydrogen as it does in oxygen. A 
 change of pressure on a gas will change elasticity and density equally, 
 and, therefore, will not affect the velocity of sound transmitted by the 
 gas. If a confined portion of any gas is heated, its elasticity is in- 
 
VELOCITY, REFLECTION, AND REFRACTION. 219 
 
 creased without any change of density. Hence, a rise of temperature 
 without barometric change increases the velocity of sound in the air. 
 The added velocity is about 0.6 m., or 2 feet for each degree that the 
 centigrade thermometer rises ; or 0.33 m. or 1.12 feet for each degree 
 that the Fahrenheit thermometer rises. 
 
 (rf) Owing to the high elasticity of liquids and solids as compared 
 with their densities, they transmit sound with great velocities. In 
 water at 8 C., sound travels at the rate of 4,708 feet per second, and 
 the velocity is considerably affected by changes of temperature; in 
 glass, the velocity is 14,850 feet, and in iron it is 16,820 feet ; in lead, 
 a metal of high density and low elasticity, the velocity of sound is 
 4,030 feet per second. 
 
 Reflection. 
 
 Experiment 114. Repeat Experiment 110, and notice that the 
 waves successively started by the hand are turned back at the other 
 end of the rope and meet the advancing waves. When any part of 
 the rope is equally urged in opposite directions by a direct and a re- 
 flected wave, the resultant of the two forces is zero, and the rope at 
 that point remains at rest. 
 
 Experiment 115. Slip the loops at the ends of the wire spiral used 
 in Experiment 111 over hooks screwed into the sides of two boxes. 
 Separate the boxes so as to support and slightly stretch the spiral, 
 fastening the boxes by nailing them down or by loading them with 
 sand. Start a pulse in the spiral, and notice that the wave runs to 
 the other end, is turned back or reproduced in the same medium, 
 moves along the spiral to its starting point, and so continues its jour- 
 neys to and fro until its energy is dissipated. It looks as though a 
 wave motion might be reflected ( 76) as well as a motion of trans- 
 lation. 
 
 Experiment 116. Hold a lamp reflector or other large concave 
 mirror directly facing the sun, so as to bring the rays of light to a 
 focus. Move a piece of paper until you find the place where a spot 
 on the paper is most brilliantly illuminated by the reflected rays, and 
 measure the distance of this focus, F, from A, the center of the re- 
 flector (see Fig. 163). At some point, W, between F and C, the center 
 of curvature of the reflector, hang a loud-ticking watch, and hunt for 
 the point, X, at which the ear can most distinctly hear the ticking. 
 
220 
 
 SCHOOL PHYSICS. 
 
 FIG. 163. 
 
 Use a glass funnel as an ear-trumpet. Keep watch and ear in these 
 positions, and have the reflector removed. The ticking will be faint 
 or inaudible. 
 
 185. Reflection 
 of Sound. When 
 a sound wave 
 strikes an obsta- 
 cle, it is reflected 
 in obedience to the 
 principle given in 
 76. Fig. 164 
 represents two 
 
 parabolic reflectors, mn and op. It is a peculiarity of 
 such reflectors that rays starting from the focus, as F, 
 will be reflected as parallel rays, 
 and that parallel rays falling upon 
 such a reflector will converge at 
 the focus, as P '. Hence, two such 
 reflectors may be placed in such 
 a position that sound waves 
 starting from one focus shall, 
 after two reflections, be converged 
 at the other focus. By such means, the ticking of a 
 watch may be made audible at a distance of two or three 
 hundred feet. Two reflectors so placed are said to be con- 
 jugate to each other. This principle underlies the phe- 
 nomena of whispering galleries. 
 
 186. An Echo is a sound repeated by reflection so as 
 to be heard again at its source. If the direct and 
 reflected sounds succeed each other with great rapidity, 
 as will be the case when the reflecting surface is near, the 
 
 \L 
 
 FIG. 1(54. 
 
VELOCITY, REFLECTION, AND REFRACTION. 
 
 221 
 
 echo obscures the original sound and is not heard dis- 
 tinctly. Such indistinct echoes often interfere with 
 distinct hearing in large halls and churches. Multiple 
 or tautological echoes are due either to independent re- 
 flections by bodies at different distances, or to successive 
 reflections, as between parallel walls. 
 
 (a) The time interval between a sound and its echo is the time 
 required for a sound to travel twice the space interval between the 
 source of the sound and the reflecting body. Suppose that a person 
 can distinctly pronounce five syllables in a second. While one sylla- 
 ble is being spoken, the sound waves that constitute the first part of 
 the syllable will have traveled one-fifth of 1,120 feet or 224 feet. If 
 these waves are to be brought back to the ear of the speaker imme- 
 diately after the syllable is completed, the reflecting surface should 
 be about 112 feet distant. If it is nearer than this, the reflected sound 
 will return before the articulation is complete and confusedly blend 
 with it. If the reflector is 224 feet distant, there will be time to 
 pronounce two syllables before the reflected wave returns. The 
 echo of both syllables may then be heard ; and so on. 
 
 Refraction. 
 
 Experiment 117. Fill with carbon dioxide a large rubber toy bal- 
 loon or other double- 
 convex lens having easily 
 flexible walls. Suspend 
 a watch, and place your- 
 self so that you can just 
 hear its ticking. Have 
 the gas-filled lens moved 
 back and forth in the 
 line between watch and 
 ear until the ticking is 
 much more plainly heard. 
 Use a glass funnel as an 
 ear-trumpet. 
 
 187. Refraction of Sound. As explained in 183 (a), 
 the lines of propagation of sound are ordinarily radial or 
 
 FIG. 
 
222 SCHOOL PHYSICS. 
 
 divergent. When such waves pass obliquely from one 
 medium to another of different density, the line of propa- 
 gation is bent, as will be more fully explained in the 
 chapter on Light. This bending of the lines of propagation 
 is called refraction. Such lines may be made less diver- 
 gent or even converging, as in Experiment 117, and the 
 energy of the waves concentrated at a focus. 
 
 CLASSROOM EXERCISES. 
 
 1. If 18 seconds intervene between the flash and report of a gun, 
 what is its distance, the temperature being C.V 
 
 2. Steam was seen to escape from the whistle of a locomotive, and 
 the sound was heard 7 seconds later. The temperature being 15 C., 
 how far was the locomotive from the observer ? 
 
 3. What is the length of sound waves propagated through air at a 
 temperature of 15 C. by a tuning-fork that vibrates 224 times per 
 second ? 
 
 4. Determine the temperature of the air when the velocity of sound 
 is 1,150 feet per second. 
 
 5. Why will an open hand or a palm-leaf fan held back of the ear 
 often aid a partly deaf person in hearing a speaker ? 
 
 6. A shot is fired before a cliff and the echo heard 6 seconds later. 
 The temperature being 15 C., determine the distance of the cliff. 
 
 7. A musical instrument makes 1,100 vibrations per second. Under 
 what conditions will the sound waves be each a foot long ? 
 
 8. How many vibrations per second are necessary for the formation 
 of sound waves 4 feet long, the velocity of sound being 1,120 feet? 
 Determine the temperature at the time of the experiment. 
 
 9. Taking the velocity of sound as 332 m., determine the length of 
 the waves produced by a body vibrating 830 times per second. 
 
 10. When the velocity of sound is 1,128 feet, determine the rate of 
 vibration of the vocal cords of a man whose voice sets up waves 12 
 feet long. 
 
 11. A person stands before a cliff and claps his hands and hears an 
 echo in | of a second. Determine the distance of the cliff from the 
 man. 
 
 12. A sportsman fires his gun and 2 seconds later hears its report 
 
VELOCITY, REFLECTION, AND REFRACTION. 223 
 
 the second time. The temperature being C., how far away is the 
 reflecting surface ? 
 
 13. A stone is dropped down the shaft of a mine and 5 seconds 
 later is heard to strike the bottom. The temperature being 15 C., 
 what is the depth of the mine ? 
 
 14. Why does sound travel more rapidly through the iron of a pipe 
 than it does through the air contained in the pipe? 
 
 15. From the cyclopedia, cull the story of the prison built by Dio- 
 nysius, the Syracusan tyrant, and explain its remarkable acoustic 
 properties. 
 
 16. Two single-stroke electric bells on the same circuit are made 
 to strike 5 times a second. When the bells are at the same distance 
 from the hearer, 5 strokes per second are heard ; when one of them 
 is about 112 feet further away than the other, 10 strokes per second 
 are heard ; and when one of them is about 22-4 feet further away than 
 the other, only 5 strokes per second are heard. Explain. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. A seconds pendulum; spy glass or opera 
 glass; heavy hammer; long measuring tape; thermometer; two pis- 
 tols ; two or more good watches ; cardboard ; toy trumpet ; a few 
 lengths of tin water-spout. 
 
 1. Let two pupils, A and B, take positions about 900 feet apart, so 
 that each can see the other. Let A set up a seconds pendulum with 
 a heavy bob painted white, so that it shall swing across the line 
 extending from him to B. Drive a stake beneath the pendulum bob, 
 or indicate its lowest position in some other way that may be seen by 
 B. Swing the pendulum, and, just as the pendulum passes the verti- 
 cal, strike a board, stone, or anvil with a hammer that carries a white 
 cloth, so that its motion may be easily visible. B observes these 
 motions through a spy glass and shifts his position from time to time, 
 signaling for other hammer strokes, until his distance from A is such 
 that the sound produced when the pendulum passes the vertical in 
 one direction is heard when the pendulum passes the vertical in the 
 other direction. Mark the position of B. Measure the distance 
 between A and B, and note the reading of the thermometer. If the 
 wind is not blowing, this distance roughly indicates the velocity of 
 sound in air at the observed temperature. It will be well to check 
 the result obtained by reversing the experiment. Let A swing the 
 pendulum. Let B watch it until he feels the motions, and then strike 
 
224 SCHOOL PHYSICS. 
 
 a blow just as the pendulum passes the vertical. If A does not hear 
 the sound just as the pendulum next passes the vertical, let him 
 signal .B to come nearer or go further away, continuing the work 
 until the sound moving from B to A comes in on time. Let B 
 measure the distance between" his two stations, and thence determine 
 the distance of his second position from A. The average of the two 
 distances between A and .B may be taken as the velocity of sound in 
 still air at the temperature observed. If your result differs much 
 from the velocity as computed from the data recorded in 184 (c), 
 you may know that your work has not been well done. 
 
 NOTE. Exercises 1 and 2 may not be practicable in the immediate 
 vicinity of a city school, but it is well worth the effort to make a Sat- 
 urday scientific class-excursion into the country, for the purpose of 
 executing them. If the experiments are performed in the cool air of 
 a frosty morning, and repeated in the warmer air of early afternoon, 
 a change in the velocity of the sound will be observed. 
 
 2. Place two pupils, C and Z>, each of whom has a pistol and a 
 watch, and knows how to take care of them, a long distance apart, 
 but in sight of each other. Let half of the pupils who have watches 
 accompanv C; the others who have watches should go with D. Let 
 C fire his pistol, D and his party noting the interval between the 
 appearance of the flash and the hearing of the report. Take the 
 average of the observations made by the different members of 
 the party, excluding any observation that differs very widely from 
 most of the others. Then let D fire his pistol while C and his party 
 observe the interval and determine their average. Measure the dis- 
 tance between the stations occupied by C and D, and note the read- 
 ing of the thermometer. Record the average of the two averages as 
 the time required for sound to travel that distance at that tempera- 
 ture. From such data compute the velocity of sound per second under 
 the conditions of the experiment. 
 
 3. On opposite sides of the center of a disk of cardboard about 15 
 inches in diameter, cut out two sectors, as shown in Fig. 166. Mount 
 the disk on a whirling table. Sit beside the apparatus, so as to 
 turn the driving wheel with one hand, and with the other hold a. toy 
 trumpet so that its axis shall be inclined to the surface of the disk, 
 about midway between center and circumference. Rotate the disk 
 steadily and sound the trumpet at the same time. Let other pupils 
 take positions in a distant part of the room, as indicated by the law of 
 reflected motion, so that the sound waves from the trumpet reflected 
 
CHARACTERISTICS OF TONES. 225 
 
 by the disk will reach their ears. When the sectors pass before the 
 mouth of the trumpet, the 
 sound will become softer, 
 and when the cardboard re- 
 flector passes, the sound will 
 become stronger. Record a 
 description and explanation 
 of the experiment. 
 
 4. On a table like that 
 shown in Fig. 45, lay two 
 
 tin tubes, each about 150 cm. 
 
 ,' . ,. FIG. 166. 
 
 long and 10 cm. in diameter. 
 
 A few lengths of water-spout will answer. The axes of the tubes 
 should lie on radial lines (like BA and BC) that make equal angles 
 with the radius, BD, drawn perpendicular to the reflecting surface 
 at B. If you have no such table, draw the radial lines on any 
 table-top, and properly place a piece of glass, as at B, to serve as a 
 reflector. Suspend a watch at the outer end of one of the tubes and 
 hold the ear at the outer end of the other tube. Notice the intensity 
 of the sound caused by the ticking of the watch. Shift the inner 
 end of one of the tubes from its position. Listen again and notice 
 the relative intensity of the sound. 
 
 III. CHAKACTEEISTICS OF TONES. 
 
 188. Differences in Tones. Sound waves differ in 
 respect to amplitude, length, and form. These differences 
 in the waves give rise to corresponding differences in the 
 sensations that they produce. Variations in amplitude 
 correspond to differences in intensity or loudness ; differences 
 in wave-length correspond to differences in pitch ; differences 
 in wave-form correspond to differences in timbre or musical 
 quality. 
 
 Intensity. 
 
 Experiment 118. Set a tuning-fork in feeble vibration by striking 
 it gently ; the sound that you hear will be faint. Strike the fork a 
 15 
 
226 SCHOOL PHYSICS. 
 
 harder blow ; its prongs will vibrate with more energy and the sound 
 that you hear will be louder. Gently pluck a guitar string; it vibrates 
 to and fro across its place of rest, striking feeble blows upon the air 
 and sending sound waves to the ear. Pluck the same string more 
 vigorously ; it vibrates with greater amplitude, striking the air with 
 greater energy and sending to the ear sound waves of greater intensity 
 than before. 
 
 189. Intensity and Amplitude. The intensity of a 
 sound depends primarily upon the energy of vibration of 
 the sonorous body, and thence on the amplitude of the 
 vibrating particles of the sound medium. The greater 
 the amplitude, the greater the energy and the louder the 
 sound. 
 
 (a) If the amplitude of the vibration of a sonorous body is doubled, 
 the velocity with which it swings will be doubled, for the vibrations 
 are as strictly isochronous as the oscillations of a pendulum. Since 
 energy varies as the square of the velocity, it follows that the intensity 
 of sound varies as the square of the amplitude. Since energy varies as 
 the mass, it follows that the intensity of sounds generated in gases of 
 little density (see Experiments 102 and 103) will have less intensity 
 than sounds generated in heavier gases like air and carbon dioxide. 
 
 (&) If a smoked glass is drawn very slowly under a style carried 
 by a prong of a vibrating tuning-fork, as shown in Fig. 150, the soot 
 will be scraped from the glass and the area thus cleaned will be tri- 
 angular. As the sound of the fork grows feebler, the swings of the 
 prong become shorter and the trace tapers off. 
 
 Experiment 119. Whisper into one end of a length (50 feet) of 
 garden hose. A person listening with his ear at the other end of the 
 hose can distinctly hear what is said although the sound is inaudible 
 to a person holding the middle of the hose. 
 
 190. Intensity and Distance. In the open air, a sound 
 wave expands as a spherical shell, and its energy is dis- 
 tributed among the increasing number of air particles that 
 constitute these successive shells or spherical surfaces. 
 This number of air particles varies as the square of the 
 
CHARACTERISTICS OF TONES. 227 
 
 radius of the sphere. The energy of any given number of 
 these air particles must, therefore, vary inversely as the 
 square of such radius ; in other words, the intensity of sound 
 varies inversely as the square of the distance from the sonorous 
 body. 
 
 (a) If the sound wave is not allowed to expand as a spherical 
 shell, its energy cannot be thus diffused and its intensity will be 
 conserved. Hence, the efficiency of speaking-tubes and speaking- 
 trumpets. 
 
 (6) The law above given is true only when the distance is so great 
 in comparison with the dimensions of the sounding body that the 
 latter may be considered a center from which sound waves proceed 
 along radial lines. A person 10 feet from a passing railway train 
 does not hear a sound four times as loud as that heard by a person 
 20 feet from the train. 
 
 Experiment 120. Strike a tuning-fork held in the hand. Notice 
 the feeble sound. Strike the fork again and place the end of the 
 handle upon a table. The loudness of the sound heard is remarkably 
 increased. 
 
 Experiment 121. Strike the fork and hold it near the ear, count- 
 ing the number of seconds that you can hear it. Strike the fork 
 again with equal force ; place the end of the handle on the table and 
 count the number of seconds that you can hear it. 
 
 191. Intensity and Area. When a vibrating body is 
 small or thin, the particles of the air readily flow around 
 it instead of being set into vibration by it. Hence, the 
 sound of a small tuning-fork is feebler than that of a large 
 one. When the sonorous lody has a large surface, its vibra- 
 tions set up well-marked condensations and rarefactions, and 
 the consequent sound is correspondingly intense. 
 
 (a) In the sonometer, piano, violin, guitar, etc., the sound is due 
 more to the vibrations of the resonant bodies that carry the strings 
 than to the vibrations of the strings themselves. The strings are too 
 thin to impart enough motion to the air to be sensible at any con- 
 
228 SCHOOL PHYSICS. 
 
 siderable distance ; but as they vibrate, their tremors are carried by 
 the bridges to the material of the sounding apparatus with which they 
 are connected. These larger surfaces throw larger masses of air into 
 vibration and thus greatly intensify the sound. It necessarily follows 
 that the energy of the vibrating body is sooner exhausted. 
 
 (6) The intensity of tones is also affected by resonance and inter- 
 ference, as will be subsequently explained. 
 
 Pitch. 
 
 Experiment 122. Draw a finger-nail across the tips of the teeth 
 of a comb, slowly the first time and rapidly the second time. Xotice 
 the difference in the sounds produced. If one is louder than the 
 other, is that the only difference? 
 
 Experiment 123. The Savart wheel, shown hi Fig. 167, consists 
 of a heavy metal toothed wheel that may be put in rapid revolution 
 by pulling a cord wound upon its axis. Set 
 such a wheel in rapid motion and hold the edge 
 of a card against its teeth. As the speed of the 
 wheel diminishes, the shrill tone produced by 
 the rapid vibrations of the card correspondingly 
 falls in pitch. 
 
 Experiment 124. From a piece of stiff card- 
 board, cut a disk 8| inches in diameter. From 
 FIG. 167?" *h e same center, draw four circles with radii of 
 
 2 inches, 2f inches, 3| inches, and 3f inches 
 respectively. Divide the inner of these circumferences into 24 equal 
 parts, the second into 30, the third into 36, and the fourth into 48. 
 At each division, punch a T 3 g-inch (5 mm.) hole. Cut a hole at the 
 center and mount the perforated disk on the spindle of a whirling 
 table, and you have a simple .form of the siren. See Fig. 168. 
 
 Rotate the disk slowly, blowing meanwhile through a tube of about 
 T Vinch bore, the nozzle of the tube being held opposite the interior 
 ring of holes. As each successive hole comes before the end of the 
 tube, a puff of air goes through the disk. As the speed of the disk 
 increases, the puffs become more frequent, and finally blend into a 
 whizzing sound in which the ear can detect a smooth tone. As the 
 disk is given an increasing velocity, this tone rises in pitch. With a 
 
CHARACTERISTICS OF TONES. 
 
 229 
 
 given rate of rotation of the apparatus, the pitch will rise as the tube 
 is moved outward in succession from the inner to the outer circle of 
 perforations. Does it not 
 appear that the pitch of a 
 sound rises with the fre- 
 quency of the vibrations that 
 produce it? 
 
 192. Pitch is the char- 
 acteristic of a sound or 
 tone by which it is rec- 
 ognized as acute or 
 grave, high or low. It 
 depends upon the rapid- 
 ity of the vibrations by 
 which the sound is 
 produced ; the more 
 rapid the vibrations, the 
 higher the pitch. 
 
 (a) Since, in a given me- 
 dium, all sounds travel with 
 the same velocity, the rate 
 of vibration determines the 
 wave-length. If the sounding body vibrates 224 times per second, 
 224 waves will be started each second. If the velocity of the sound 
 is 1,120 feet, the total length of these 224 waves must be 1,120 feet, 
 or the length of each wave must be 5 feet. If another body vibrates 
 twice as fast, it will crowd twice as many waves into the 1,120 feet ; 
 each wave will be only 2$ feet long. Thus, wave-length may be used 
 to measure pitch ; the greater the wave-length, the lower the pitch. 
 
 (6) If the sounding body and the listening ear approach each 
 other, the sound waves will beat upon the ear with greater rapidity. 
 This is equivalent to increasing the rapidity of vibration of the sound- 
 ing body. The opposite holds true when the sounding body and the 
 ear recede from each other. This explains why the pitch of the whistle 
 of a railway locomotive is perceptibly higher when the train is rapidly 
 approaching the observer than when it is rapidly moving away from 
 him. 
 
 FIG. 168. 
 
230 SCHOOL PHYSICS. 
 
 193. The Range of Hearing of different persons varies. 
 The lower limit for 'most persons is probably represented 
 by about 30 vibrations per second, although some experi- 
 menters place it at 16 vibrations. Similarly, the upper 
 limit varies from 38,000 to 41,000 vibrations per second. 
 Tones of musical value lie between the limits of 27 and 
 4,000 vibrations per second. 
 
 (a) Everybody understands the differences in the range of the 
 human voice, that one can sing bass and another one soprano, the dif- 
 ference depending upon the rate of vibration of the vocal cords. It 
 is equally true, but not equally well known, that some persons are 
 unable to hear low sounds that are distinctly audible to most persons, 
 while the hearing apparatus of others is unable to respond to sounds 
 of high pitch or short wave-length, which are easily heard by the 
 greater number. Some persons whose hearing is considered fairly 
 sensitive have never heard the shrill chirping of the cricket. 
 
 194. An Interval is the difference or distance in pitch 
 between two tones, and is described by the ratio between the 
 vibration-numbers of the two tones. Thus, the interval of 
 an octave is represented by the ratio 2 : 1 ; a fifth, 3:2; 
 a fourth, 4 : 3 ; a major third, 5:4; and a minor third, 
 6:5. 
 
 195. A Musical Scale is a definite, standard series of 
 tones for artistic purposes, and lying within a limiting 
 interval. In constructing such a series, the first step is 
 the adoption of such a limiting interval for the division 
 of the possible range of tones into convenient sections of 
 equal length. In modern music, this limiting interval is 
 the octave. 
 
 196. The Gamut. Starting from any tone arbitrarily 
 chosen, and called the keynote, the interval of an octave 
 
CHARACTERISTICS OF TONES. 
 
 231 
 
 may be traversed by seven definite steps, thus giving a 
 series of eight tones that are very pleasing to the ear. 
 The eighth tone of this group becomes the first tone (i.e., 
 the keynote) of the group or octave above. The inter- 
 vals between these tones are not equal, as will soon appear 
 more clearly. This familiar series of eight tones is called 
 the gamut or major diatonic scale. The series may be 
 repeated in either direction to the limits of audible pitch. 
 The names and relative vibration-numbers of these tones, 
 and the intervals between them, are as follows : 
 
 Relative 
 Absolute 
 Syllables 
 Relative 
 Vibration 
 
 M 
 
 
 
 n 
 
 ^ 
 
 I 
 
 BE 
 
 
 
 m 9 
 
 
 ; 1 
 
 
 1 m 
 
 ff 
 
 
 
 -1 1 
 
 8 
 C 4 
 
 do 
 
 48 
 
 2 
 
 *7 
 names 
 
 J- * ' 
 
 123 
 C 3 D 3 E 3 
 do re mi 
 24 27 30 
 
 1 I 1 
 
 4 
 
 F 3 
 fa 
 32 
 
 f 
 
 i 
 
 5 6-7 
 G 3 A 3 B 3 
 sol la si 
 36 40 45 
 
 t * 
 
 names 
 
 
 vibration- numbers . 
 i-ratios 
 
 Intervals 
 
 t 
 
 (a) The initial tone or keynote of such a series may have any 
 number of vibrations, and whatever pitch is assigned to C, the num- 
 ber of vibrations of any tone may be found by multiplying the 
 vibration-number for C by the vibration-ratios given above. Physi- 
 cists assign to C 3 , sometimes called " middle C," 256 vibrations per 
 second (256 = 2 8 ). Musicians and makers of musical instruments in 
 this country and Europe have adopted the "international pitch," 
 which gives for standard A$, 435 vibrations per second. This cor- 
 responds to 258.6 vibrations for C 3 ( 198). 
 
 (6) When two tones with vibration-numbers as 1 : 2 are sounded 
 together, the character of the combination is the same as that of 
 either tone alone. It is the interval most readily produced by the 
 human voice, and seems to have a foundation in nature ; such an 
 interval is called an octave. When three tones with vibration- 
 numbers as 4:5:6 are sounded together (e.g., C, E, (7), a new 
 
232 SCHOOL PHYSICS. 
 
 quality seems to be added, and the combination produces a very 
 pleasing sensation. The tones are in harmony, or in accord with 
 each other. Such simultaneous sounding of three or more concordant 
 tones constitutes a chord, of which there are several kinds. The three 
 tones above mentioned (i.e., C, E, G) constitute a major chord. A 
 combination of three tones with vibration-numbers as 10 : 12 : 15 
 (e.g., E, 0, B) constitute a minor chord. 
 
 197. Diatonic Scales. The major diatonic scale is built 
 upon three major chords, and the minor diatonic scale upon 
 three minor chords, with the octave of the various tones. 
 
 (a) The method of building up the major diatonic scale is as fol- 
 lows : Assign to Cs, as the first of three tones with vibration-num- 
 bers as 4:5:6, any number of vibrations, as 256 per second. Its 
 octave will have 512 vibrations; and the tones of the major chord 
 will have respectively 256 x f , 256 x f , 256 x f , vibrations per second. 
 Designating these four tones by their absolute names, we have : 
 
 C 3 Z> 3 E s F s G 3 A 3 B 3 C 4 
 256 ? 320 ? 384 ? ? 512. 
 
 Taking Ct as the third tone of another major chord, we have : 
 4:5:6 = ?:?: 512 = 341 : 426| : 512. 
 
 Assigning the two vibration-numbers thus found to Fs and As, we 
 have : 
 
 C s Z> 3 E s F 3 Gs A 3 3 C 4 
 256 ? 320 341| 384 426f ? 512. 
 
 Again, starting with Gz = 384, as the first tone of another major 
 chord, we have the series : 
 
 4 : 5 : 6 = 384 : ? : ? = 384 : 480 : 576 . 
 
 The tone with 480 vibrations will be called Bs, as it lies between ;, 
 those already called A 3 and C. The last tone, having 576 vibrations, ' 
 must be placed beyond C*4, but the tone an octave lower, with a 
 vibration-number half as great, 288, falls between C$ and E s . This 
 lower tone we will call D s . 
 
CHARACTERISTICS OF TONES. 233 
 
 The three chords and the complete series formed from them, in 
 musical notation, with their respective vibration-numbers, which will 
 be found to be in the ratios already given, are: 
 
 s 
 
 
 
 C 3 D 3 E 3 F 3 G 3 A 3 B 3 C 4 
 256 288 320 341.3 384 426.6 480 512 
 
 (6) A minor diatonic scale may be constructed from three minor 
 chords, founded upon any assigned pitch, in the same manner as 
 described above for the major scale. 
 
 198. Chromatic Scale. In music, other tones of the 
 simple scale already described are needed as the beginnings 
 of similar diatonic scales. For instance, D 3 may be used 
 as the keynote. With this, three chords may be formed, 
 using the intervals 4 : 5 : 6, as follows : 
 
 4 : 5 : 6 = 288 : 380 : 432 
 4 : 5 : 6 = 384 : 480 : 576 
 4:5:6 = 432:540:2 x 324. 
 
 The new complete series is : 
 
 A i <> a* <> B, <> D 4 
 
 288 324 380 384 432 480 ,540 576. 
 
 Thus four new tones are introduced by using D 3 as the 
 keynote. Any other tone of the first scale, or any of 
 these new tones, may be used as new keynotes. If we 
 form the twenty-four scales ordinarily used in music, 
 twelve major and twelve minor, no fewer than seventy- 
 two tones, within the limits of the octave, will represent 
 them. To use so many tones in each octave of keyed 
 instruments, such as the piano and organ, is a practical 
 
234 SCHOOL PHYSICS. 
 
 impossibility. As many of these tones differ from each 
 other but little, musicians have agreed to make a com- 
 promise by giving up the simple perfection of the inter- 
 vals of the chords described, and to divide the octave into 
 twelve equal intervals, called semi-tones. The series of 
 thirteen semi-tones, separated by the twelve equal intervals, 
 constitutes the modern chromatic scale. 
 
 (a) The eight tones nearest those already described are named as 
 we have already designated them, while the five interpolated tones, 
 corresponding to the black keys on the piano keyboard, are called 
 sharps of the tones immediately below them or flats of the tones next 
 above them. The compromising process between theory and practice, 
 or the principle by which the octave is divided into twelve equal 
 intervals, is called equal temperament. In this system, the only perfect 
 interval is the octave, and all chords are slightly " out of tune." 
 
 (6) The interval in this scale is ^/o = 1.05946. Any tone being 
 given, the next above is found by multiplying by 1.05946, or the next 
 below by dividing by the same number. The equal tempered chro- 
 matic scale founded upon the international pitch, A 3 = 435 vibrations, 
 as universally used in music, is as follows : 
 
 n u. G & J 
 
 C 3 C 3 3 D 3 D 3 S E 3 F 3 F 3 3 G 3 G 3 S A 3 A 3 S B 3 C 4 
 
 258.6 274.0 290.3 307.5 325.8 345.2 365.8 387.5 410.6 435 460.9 488.3 517.3 
 
 Tones and Overtones. 
 
 Experiment 125. Repeat, Experiment 114, using the soft cotton 
 rope or the long wire spiral used in Experiment 115. By properly 
 timing the motion of the hand, the rope may be made to vibrate as 
 a whole. Doubling the rapidity of motion of the hand, the rope or 
 spiral divides itself into two vibrating segments, separated from each 
 other by a point of apparent rest called a "node." Trebling or 
 quadrupling the rapidity of the motion of the hand causes the rope 
 or spiral to divide into three or four segments separated by a corre- 
 sponding number of nodes. In each case, the period of the hand 
 
UNIVERSITY OF CALfFORWA 
 
 DEPARTMENT OF PHYSICS 
 CHARACTERISTICS OF TONES. 235 
 
 must synchronize with that of the rope or spiral and of the several 
 segments, but by a little practice one may so time the motions of the 
 hand as to bring out the segmental vibrations just described. 
 
 Experiment 126. Bow or pluck the string of a sonometer (see 
 Fig. 171) near its end, thus setting it in vibration as a whole. The 
 
 FIG. 169. 
 
 string will have the appearance of a single spindle as shown in 
 Fig. 169, and will sound the lowest tone that it is capable of produc- 
 
 FIG. 170. 
 
 ing. Lightly touch the wire at its middle point with the tip of the 
 finger or the beard of a quill; the wire will vibrate in halves (Fig. 170) 
 
 FIG. 171. 
 
 and sound a tone an octave above that previously heard. Sound the 
 sonometer again, touch the string as before, and try to distinguish 
 
236 SCHOOL PHYSICS. 
 
 both tones as coming simultaneously from the apparatus. Again set 
 the string in vibration and touch it at one-third its length. The 
 
 vibrating string di- 
 vides into thirds as 
 shown in Fig. 171, 
 v n and emits a tone that 
 
 ==H * == =-B the trained ear recog- 
 
 FlG 172 nizes as the fifth of 
 
 the octave above that 
 
 first sounded. Probably both sounds will be heard at the same time. 
 In similar manner, a string sufficiently long may be made to vibrate 
 in any aliquot part of its whole, as fourths, fifths, ninths, tenths, etc. 
 The string should be touched at n and bowed at v, as shown in 
 Fig. 172. 
 
 199. Fundamental Tones and Overtones. The tone that 
 is sounded by a body vibrating as a whole, i.e., the lowest 
 tone that such a body can produce, is called its fundamental 
 or primary tone. The tones produced by the vibrating seg- 
 ments of sonorous bodies are called overtones, partial tones, 
 or harmonics. The partial tones are named first, second, 
 third, etc., in the order of their vibration-numbers, begin- 
 ning with the fundamental. 
 
 (a) It is customary to regard both ends of the string as nodes. 
 The points of greatest vibration, midway between the nodes, are 
 called anti-nodes. If little A-shaped riders, made of slips of paper 
 bent in the middle, are placed on a string and the string is then 
 made to vibrate in segments, the riders at the nodes will remain in 
 position while those at the anti-nodes will be thrown off as shown 
 in Fig. 171. 
 
 (b) The interval from the fundamental to the first overtone is an 
 octave ; to the second, an octave and a fifth; to the third, two octaves; 
 to the fourth, two octaves and a major third ; to the fifth, two octaves 
 and a fifth, etc. 
 
 200. Quality or Timbre is the characteristic by which 
 we distinguish one tone from another of the same intensity 
 
CHARACTERISTICS OF TONES. 237 
 
 and pitch. The middle C of a piano is essentially different 
 from the same tone of an organ, and any tone of a flute is 
 distinguishable from any tone of a violin. The physical 
 basis of quality is wave-form, and is due to the number, 
 relative intensities, and relative phases of the overtones 
 that accompany the fundamental. 
 
 (a) The well-trained ear can detect several tones when a piano- 
 key is struck. In other words, the sound of a vibrating piano-wire 
 is a compound tone (see Experiment 138) . The sound of a tuning- 
 fork is a fairly good example of a simple sound. By sounding simul- 
 taneously the necessary number of forks, each of proper pitch and 
 with appropriate relative intensity, Helmholtz showed that the com- 
 pound sounds of musical instruments, including even the most 
 wonderful one of all, the human voice, may be produced synthetic- 
 ally. Simple tones lack the richness that is so highly prized in 
 musical instruments. 
 
 (6) The way in which a single string can simultaneously give rise 
 to several tones, i.e., how the segmental vibrations are imposed upon 
 the fundamental, may 
 be explained as fol- 
 lows : In Fig. 173, AB A^^ 
 represents a string Fio. 173. 
 
 which, when vibrating 
 as a whole, sounds its fundamental, and assumes the form A CB. 
 
 Fig. 17-i represents the same string sounding its fundamental and 
 its first overtone. In this case the fundamental is represented by 
 
 the dotted line, while 
 
 -U^ _ the resultant com- 
 
 ^ ""^>>g pound tone is repre- 
 F m sented by the continu- 
 
 ous line, *A CB. While 
 
 AB vibrates as a whole, its halves, AC and CB, vibrate in opposite 
 directions, and with doubled rapidity. 
 
 Fig. 175 represents the compounding of the same fundamental 
 with its second over- 
 tone. The fundamental 
 is represented by the 
 dotted line as before, FlG - 175 - 
 
288 SCHOOL PHYSICS. 
 
 while the resultant compound tone is represented by the continuous 
 line, ADD'B. While A B vibrates as a whole, its thirds, AD, DD', 
 and D'J3, vibrate in alternately opposite directions, and with trebled 
 rapidity. The difference in the three wave-forms is manifest in the 
 figures. Such combinations may be made in almost endless variety, 
 each combination representing a compound tone that varies from all 
 of the others. 
 
 201. The Graphic Method of studying sounds, which 
 fairly meets even the exacting demands of physicists, and 
 
 is largely used by them, 
 may be briefly explained 
 thus: Suppose the 
 smoked plate of Fig. 150 
 to be a sheet of smoked 
 paper fastened upon the 
 surface of a cylinder that 
 is so mounted that, when 
 it is turned by a crank, 
 the screw cut upon the 
 
 FIG. 176. . ,, ,. , 
 
 axis moves the cylinder 
 
 endwise, as shown in Fig. 176. Such an instrument is 
 called a vibroscope. 
 
 (a) When the style *of a vibrating tuning-fork just touches the 
 paper, and the crank is turned, the vibrations will be traced in the 
 form of a sinusoidal spiral upon the smoked surface, the amplitude, 
 length and form of each wave being truthfully recorded. The cylin- 
 der may be turned by clockwork. By counting the number of waves 
 traced in one second, we obtain directly the vibration-number of the 
 fork. By various ingenious and delicate devices, the wave-forms that 
 correspond even to a very complex tone may thus be secured for study 
 or illustration. Such a record may be written parallel with that of a 
 tuning-fork of known frequency (i.e., vibration-number), and com- 
 parative study thus facilitated. For instance, if the record of a 
 phonautograph (see dictionary) shows that while the fork recorded 
 
CHARACTERISTICS OF TONES. 239 
 
 70 vibrations, a singing voice recorded 180, and the vibration-number 
 of the fork is known to be 100, a simple proportion (70 : 180 : : 100 : x) 
 shows that the vibration-number of the voice was 257i, indicating 
 
 FIG. 177. 
 
 a tone almost identical with that of middle C of the pianoforte. 
 Fig. 177 shows traces of several compound tones, each written below 
 the sinusoidal tracing of the tuning-fork. 
 
 Manometric Flames. 
 
 Experiment 127. From an inch board, cut a strip, A, 2 inches 
 wide and 10 inches long. Cut another block, B, 2 inches square. 
 Placing the point of an inch center-bit an inch from the end of A, 
 bore a shallow hole, about |- of an inch deep, in one side of the 
 strip. Bore a similar hole at the middle of one side of B. Place 
 the point of a |-inch center-bit at the center of the shallow hole 
 in A, and bore a hole through the wood. Bore two T 3 g-inch holes 
 from the bottom of the shallow hole in B and through the wood, one 
 directly through the block at the center, and the other obliquely 
 downward from the lower edge of the hole. Stretch a piece of gold- 
 beater's skin, or of the thinnest sheet rubber you can find (toy balloon) 
 over the mouth of the shallow hole in B, gluing it there. Spread 
 glue over the face of A around the shallow hole and screw A and B 
 together, so that the two shallow holes shall come face to face with 
 the elastic membrane between them. The " manometric capsule " is 
 complete. Xail the other end of .4 to a base board, as shown in 
 Fig. 178. Set a glass tube, e, into the i-inch hole of A, making the 
 joint tight with a strip of paper smeared with glue and wrapped 
 about the end of e before it is forced into the hole. Attach one end 
 of a piece of large-sized rubber tubing to the glass tube, 6, and the 
 other end to a trumpet made by rolling up a piece of cardboard into 
 
240 
 
 SCHOOL PHYSICS. 
 
 a cone about 8 inches long and 2 inches across the mouth. Into the 
 T 3 g -inch hole at the middle of B, tightly fit a glass tube, bent and 
 drawn to a jet at the outer end. Into the other T 3 g-inch hole of B, 
 tightly fit a straight glass tube, c, that may be connected with the 
 house supply of illuminating gas. Turn on the gas and light it at 
 the jet. If the air of the room is still, the flame will be compara- 
 tively steady. Hold a vibrating tuning-fork at the mouth of the 
 trumpet, and notice the flickering of the flame. This flickering of 
 the flame is the thing that we are to study, and its cause ought to be 
 clearly apparent to the pupil. 
 
 From a board of an inch thick, 4 inches wide, and a foot long, cut 
 a square piece marked M, and the tw r o attached spindles, H and K. 
 
 Taper the spindles so that 
 the whole piece may be 
 easily twirled, as shown in 
 the figure. The blunt 
 point of the shorter spin- 
 dle should rest in a shal- 
 low pit, on a firm support. 
 To the opposite sides of M, 
 fasten, with tacks at the 
 lower edge and with thread 
 
 wound along the top and 
 bottom borders, two pieces 
 of thin silvered glass, thus 
 completing the "revolving 
 mirror." The support of 
 the mirror should be at 
 su,ch a height that the 
 flame may be seen reflected 
 from the middle of the 
 mirror. 
 
 Rotate the mirror and notice that the steady flame appears as a 
 luminous ribbon of uniform width. If the flame is agitated by the 
 wind from the mirror, shield the flame with a lamp chimney. While 
 twirling the mirror, sing into the mouth of the cone, and notice that 
 the image becomes indentated, each tongue indicating an increase of 
 pressure on the diaphragm of the capsule. Each projection of the 
 image corresponds to the condensation of a sound wave, and each 
 depression to the rarefaction. 
 
 FIG. 178. 
 
CHARACTERISTICS OF TONES. 
 
 241 
 
 FIG. 179. 
 
 FIG. 180. 
 
 The vibration of the flame may be seen without using the mirror, 
 by quickly turning the head from side to side while looking at the 
 flame, an interesting experiment. 
 
 Experiment 128. While the mirror is rotating, sound a tuning- 
 fork at the mouth of the 
 trumpet, and notice that the 
 image resembles Fig. 179. 
 Then sound a tuning-fork 
 that is an octave higher and 
 notice that the image resem- 
 bles Fig. 180, in which twice as many tongues as before are crowded 
 into the same space. 
 
 Experiment 129. Remove the large rubber tubing and connect e 
 
 with two trumpets, using a 
 T-pipe or a Y-tube. Sound 
 the two forks just used, and 
 hold each at the mouth of a 
 trumpet, so that their respec- 
 tive waves may be blended 
 before they reach the diaphragm of the capsule. The image will re- 
 semble that shown in Fig. 181. Evidently this figure could not have 
 been made by a simple vi- 
 bration. The alternate con- 
 densations sent out by the 
 fork of higher piteh unite 
 with the condensations sent 
 out by the fork of lower 
 pitch, thus making the flame jump higher by their combined action 
 on the diaphragm. 
 
 NOTE. By singing different vowels to different tones, many dif- 
 ferent images may be produced in the rotating mirror. 
 
 202. The Optical Method of studying sounds is well 
 illustrated by Mayer's adaptation of Koenig's manometric 
 flames, as employed in Experiment 127. This method, 
 like the graphic, has the advantage of being independent 
 
 of the sense of hearing. When the "manometric cap- 
 16 
 
 FIG. 181. 
 
242 SCHOOL PHYSICS. 
 
 sule " is connected by the tube, e, with a Helmholtz 
 resonator ( 205, <#,), the flame will respond to the tone that 
 affects the resonator. By using a series of such resona- 
 tors in connection with the flame and mirror, the analysis 
 of compound tones is made possible even for one who is 
 deaf. 
 
 CLASSROOM EXERCISES. 
 
 1. If a musical sound is due to 144 vibrations, to how many vibra- 
 tions will its third, fifth, and octave, respectively, be due ? 
 
 2. If a tone is produced by 264 vibrations per second, what number 
 will represent the vibrations of the tone a fifth above its octave ? 
 
 Ans. 792. 
 
 3. A given tone is found to be in unison with the tone emitted by 
 the inner row of holes of the siren described in Experiment 124 when 
 the disk is turned at the uniform rate of 640 times in 30 seconds. 
 Assigning 256 vibrations for middle C, name the given tone. 
 
 4. The vibrations of two tuning-forks are simultaneously recorded 
 by avibroscope. Comparison shows that 9 waves of one occupy the 
 same space as 15 waves of the other. If the fork of lower tone is 
 marked D, what should the other fork be marked? 
 
 5. Determine the vibration-number for each tone of a gamut the 
 keynote of which has 261 vibrations. 
 
 6. Is there any difference in the pitch of a locomotive whistle when 
 the locomotive is standing still, when it is rapidly approaching the 
 observer, and when it is rapidly moving from him? If so, describe 
 and explain it. 
 
 7. What is the vibration-number of the tone G next preceding that 
 of a " violin- J. " fork of 440 vibrations ? 
 
 8. Why does the sound of a circular saw cutting through a board 
 fall in pitch as the saw enters the board? 
 
 9. If an observer should approach a sounding organ-pipe with the 
 velocity of sound, what would be the effect upon the pitch of the 
 tone ? 
 
 10. If an observer should recede from the source of a musical 
 tone with a velocity a little less than that of sound, what would 
 be the effect upon the pitch of the tone? 
 
 11. Suppose that when an orchestra has nearly finished a per- 
 
CHARACTERISTICS OF TONES. 243 
 
 formance, an observer should move away from the orchestra with a 
 velocity twice that of sound. Describe his relation to the sounds 
 previously executed by the orchestra. 
 
 12. A tube about 6 feet long is mounted at its middle on an axis 
 that is perpendicular to the length of the tube. A reed is fixed at 
 one end of the tube and may be sounded by air forced into the tube 
 through an aperture at its axis of rotation. The tube is sounded 
 while in rotation. An observer standing in a prolongation of the 
 axis of rotation hears a tone of constant pitch. An observer standing 
 in the plane of rotation hears a tone of varying pitch. Explain the 
 difference. 
 
 LABORATORY EXERCISES. 
 Additional Apparatus, etc. Cardboard ; punch. 
 
 1. Using the graphic method, show that the two prongs of a tuning- 
 fork are moving in opposite directions at any given instant. 
 
 2. Make another disk for the siren used in Experiment 124, making 
 eight circles of holes, each circle having in order the number of holes 
 indicated by the relative vibration-numbers given in 196. Put this 
 disk upon the whirling table and rotate it at such a uniform speed 
 that the puffs made by the inner circle of twenty-four holes shall give 
 a smooth musical tone. Move the nozzle of the tube through which 
 you blow over the several circles in succession and name the familiar 
 series of tones that you hear. 
 
 3. Figure 182 represents two sets of sound waves with like periods 
 and phases but dif- 
 ferent amplitudes. 
 
 Draw a single curve 
 
 to represent the re- 
 
 sultant of the two 
 
 series, remembering to make the ordinates of the resultant equal to 
 
 the algebraic sum of the corresponding ordinates of the constituents. 
 
 4. Figure 183 represents two such wave systems meeting in opposite 
 
 phases. Draw the 
 resultant curve and 
 tell how the sound 
 it represents corre- 
 FIG. 183. sponds to the sound 
 
 represented by the resultant drawn in Exercise 3, and how it differs. 
 
244 SCHOOL PHYSICS. 
 
 5. Figure 184 represents two wave systems of equal periods and 
 
 amplitudes but of 
 ,B opposite phases. 
 Draw the resultant 
 FlG - 184 - and describe in a 
 
 single word the sonorous effect that it represents. 
 
 6. Bow a sonometer-string vigorously, and while it is sounding 
 lessen the tension. Explain the discordant groan-like sound that is 
 produced. 
 
 7. Arrange apparatus as required by Exercise 4, page 225. To the 
 outer end of one of the tubes connect, by a funnel, a piece of large- 
 sized rubber tubing about a yard long and thrust the shank of a glass 
 funnel into the outer end of the rubber tubing. At the outer end 
 of the other tube, place the tube, e, of the manometric capsule and 
 arrange apparatus as described in Experiment 127. Light the flame 
 and rotate the mirror. Have a vibrating tuning-fork at the mouth of 
 the glass funnel, and notice, directly and by reflection, the agitation 
 of the flame. Shift the position of one of the tubes so that the angles 
 of incidence and reflection shall be unequal, and repeat the experiment. 
 
 IV. CO-VIBRATION. 
 
 Experiment 130. Support a soft cotton rope several yards long 
 between two fixed supports, as the opposite sides of the room, or the 
 floor and the ceiling. With a ruler, strike the rope a blow near one 
 end so as to form a 
 crest, as shown in 
 Fig. 185. Vary the 
 tension of the rope if 
 necessary, until the 
 crest is easily seen. 
 Notice that the crest, 
 
 c, travels from A to B, where it is reflected back to A as a trough, t. 
 Strike the rope from above and thus start a trough which will be 
 reflected as a crest. 
 
 Experiment 131. Start a trough from A. At the moment of its 
 reflection as a crest at B, start a crest at A as shown in Fig. 186. The 
 
CO-VIBRATION. 245 
 
 two crests will meet near the middle of the rope. The crest at the 
 
 point and moment of 
 
 meeting results from L<HI^x ^ "x| A 
 
 two forces acting in 
 
 the same direction ; ^IG. 186- 
 
 their resultant is greater than either of the components. 
 
 Experiment 132. Using the rope as previously described, start a 
 crest at A. At the moment of its reflection at B as a trough, start 
 
 a second crest at ^4. 
 The trough and crest 
 will meet near the 
 middle of the rope. 
 
 Vary the experiment by using the rope as shown in Fig. 155, timing 
 the movements of the hand so that an advancing crest shall meet 
 a returning trough near the middle of the rope. The rope particles 
 at this point, being thus simultaneously acted upon by opposite 
 forces, will remain at rest or nearly so. The resultant will be the 
 difference of the components. Thus, one wave may be made to destroy 
 another wave. 
 
 203. Coincident Waves. Just as, when one crest coin- 
 cides with another, the wave has an increased height, and 
 when a crest coincides with a trough, the wave disappears, 
 so, when the condensation of a sonorous wave coincides 
 with another condensation, the actual motions of the par- 
 ticles of the sound medium are increased, and, when a 
 condensation coincides with a rarefaction, said motions are 
 reduced or destroyed. Such increased resultant motions 
 of the material particles imply an increased loudness of 
 the sound. Such diminished resultant motions imply an 
 enfeebled sound or perhaps silence. 
 
 Sympathetic Vibrations. 
 
 Experiment 133. Repeat Experiment 13, and vary it by setting 
 the heavy pendulum in motion by the cumulative action of well-timed 
 puffs of air from the mouth or from a hand-bellows. 
 
246 SCHOOL PHYSICS. 
 
 Experiment 134. Suspend several pendulums from a frame as 
 shown in Fig. 66. Make two of equal length, so that they will vibrate 
 at the same rate. Be sure that they will thus vibrate. The other 
 pendulums are to be of different lengths. Set a in vibration. The 
 swinging of a will produce slight vibrations in the frame, which will, 
 in turn, transmit them to the other pendulums. As the successive 
 impulses thus imparted by a keep time with the vibrations of &, this 
 energy accumulates in b, which is soon set in perceptible vibration. 
 As these impulses do not keep time with the vibrations of the other 
 pendulums, there can be no such marked accumulation of energy in 
 them, for many of the impulses will act in opposition to the motions 
 produced by previous impulses, and thus weaken if not destroy them. 
 
 Experiment 135. Tune the two strings of a sonometer to perfect 
 unison. Place two or three paper " riders " upon one of the strings, 
 and gently bow the other. The "riders" will be dismounted from 
 the first string, even if the vibrations of the second string are not 
 audible. The vibrant energy was carried from one string through 
 
 FIG. 188. 
 
 the bridges of the sonometer to the other string and there accumu- 
 lated. Change the tension of one of the strings, thus destroying the 
 unison, and try to repeat the experiment. Notice that the sympa- 
 thetic vibrations are not produced. 
 
 Experiment 136. Place two mounted tuning-forks that are in per- 
 fect unison several feet apart, and with the openings of their resonant 
 boxes facing each other. Sound one of the forks, and notice its pitch. 
 After a second or two, touch the prongs to stop their motion. It will 
 be found that the second fork has been set in motion and is giving 
 forth a sound of the same pitch as that originally produced by the 
 
CO-VIBRATION. 
 
 247 
 
 first fork. With wax, fasten a small weight to one of the prongs of 
 the second fork. An attempt to repeat the experiment will fail. 
 When the two forks are in uni- 
 son, their periods are the same. 
 The second and subsequent 
 pulses sent out by the first fork 
 strike the second fork, already 
 vibrating from the effect of the 
 first pulse, in the same phase of 
 vibration, and thus each adds 
 its effect to that of all its pre- 
 decessors. If the forks are not 
 in unison, their periods will be 
 different, and but few of the 
 successive pulses can strike the 
 second fork in the same phase 
 
 FIG. 189. 
 
 FIG. 190. 
 
 of vibration ; the greater number will strike it at the wrong instant. 
 
 Experiment 137. Fig. 190 represents Mayer's "sound-mill," which 
 consists of four small resonators attached to the ends of a small cross. 
 The cross is carefully balanced on a ver- 
 tical pivot. The resonators are made of 
 aluminium (a very light metal), and accu- 
 rately tuned to unison with a mounted 
 tuning-fork. When the "sound-mill" is 
 placed in front of the opening of the res- 
 onant box of the fork with which it is in 
 unison, and that fork sounded, the four resonators turn upon their 
 pivot, a veritable acoustic reaction wheel. 
 
 204. Sympathetic Vibrations. It has been shown 
 repeatedly that the motion of a body may produce 
 sound. The last few experiments show that sound may 
 produce motion. The most important feature now to 
 be noticed is that the sonorous body accumulates only 
 the particular kind of vibration that it is capable of 
 producing. 
 
 (a) By the aid of sympathetic vibrations we are able to analyze 
 compound tones, as is shown by the following experiment : 
 
248 
 
 SCHOOL PHYSICS. 
 
 Experiment 138. Take your seat before the keyboard of a piano. 
 Press and hold down the key of " middle C," marked 1 in Fig. 191, 
 which represents part of the keyboard. This will lift the damper 
 from the corresponding piano wire, and leave it free to vibrate. 
 Strongly strike the key of C 2 , an octave below. Hold this key down 
 for a few seconds, and then remove the finger. The damper will fall 
 upon the vibrating wire and bring it to rest. When the sound of C 2 
 has died away, a sound of higher pitch is heard. The tone corre- 
 sponds to the wire of 1, which wire is now vibrating. These vibra- 
 tions are sympathetic with those that produced the first overtones of 
 the wire that was struck. These vibrations in the wire of 1 prove the 
 
 FIG. 191. 
 
 presence of the first overtone in the vibrating wire of C 2 . In similar 
 manner, successively raise the dampers from the wires of 2, 3, 4, and 
 5, striking C 2 each time. These wires will accumulate the energy 
 of the waves that correspond to the respective overtones of the wire 
 of C 2 , and give forth each its proper tone. Thus we analyze the 
 sound of C 2 , and prove that overtones are blended with the funda- 
 mental. 
 
 Some of these tones of higher pitch, thus produced by vibrations 
 sympathetic with the vibrations of the segments of the wire of C 2 , 
 are feebler than others. This shows that the quality of a tone 
 depends upon the relative intensities as well as the number of the 
 overtones that blend with the fundamental. 
 
 Resonance. 
 
 Experiment 139. Hold a vibrating tuning-fork over the mouth of 
 a cylindrical jar about 15 or 18 inches deep, and notice the feebleness 
 of the sound. Pour in water, as shown in Fig. 192, and notice that, 
 when the liquid reaches a certain level, the sound suddenly becomes 
 
CO-VIBRATION. 
 
 249 
 
 much louder. The water has shortened the air-column until it is 
 
 able to vibrate in unison with the fork. If more water is added, the 
 
 sound will become weaker. 
 
 If a fork of different pitch 
 
 is used, the length of the 
 
 resonant air-column will be 
 
 changed, said length being 
 
 about one-fourth the length 
 
 of the wave produced by the 
 
 fork. 
 
 205. Resonance. The 
 
 increase of sound by the 
 sympathetic vibrations of 
 a body other than that 
 by ivhich it was originally 
 produced is called res- 
 onance. The apparatus 
 used to produce such an 
 effect is called a reso- 
 nator. 
 
 FIG. 192. 
 
 (a) Resonance occurs more or less prominently in connection with 
 all sound, and is carefully utilized in musical instruments. Sounding- 
 boards like that of the piano, and diaphragms like those of the phono- 
 graph and telephone, have a general resonance by virtue of which 
 they are sensitive to any vibratory motion within the limits of 
 ordinary audition. The audiphone is another illustration of the 
 same fact. When the lower prong of the tuning-fork used in Experi- 
 ment 139 vibrated outward, it started a condensation down the tube. 
 This condensation and the succeeding rarefaction were reflected 
 upward from the bottom of the tube, and returned to unite with 
 other waves sent out by the prong. When the air-column was made 
 of the right length, the reflected waves coincided with the other waves 
 in like phases ; i.e., condensation with condensation, and rarefaction 
 with rarefaction. Under different circumstances, the direct and 
 reflected waves may combine in different phases, and thus cause 
 an enfeeblement of the sound. 
 
250 
 
 SCHOOL PHYSICS. 
 
 (6) It is found by experiment that the diameter of the tube affects 
 the length of the resonant air-column, so that an arbitrary correction 
 has to be made. For a cylindrical vessel, the experimental column 
 shortens as the diameter increases. The theoretical column equals 
 the experimental column increased by about one-fourth of the 
 diameter. 
 
 (c) Fig. 193 represents a Savart bell and resonator. The length 
 of the resonant air-column is changed by means of the movable bot- 
 tom of the resonator, which 
 is to be adjusted by trial for 
 resonant effect. When the 
 bell is sounded, and its tone 
 is just audible, the approach 
 of the tube produces a marked 
 reinforcement of sound. 
 
 (c?) Helmholtz constructed 
 a series of resonators, each 
 one of which responds pow- 
 erfully to a single tone of 
 certain pitch or wave-length. They are metallic vessels, nearly 
 spherical, having an opening, as at A in Fig. 194, for the admis- 
 sion of the sound-waves. The funnel-shaped projection at B has 
 a small opening, and is inserted in the 
 outer ear of the observer. Such resonators 
 are largely used in the analysis of complex 
 tones. 
 
 Musical tones may thus be picked from 
 sounds that are commonly reckoned as 
 noises ; e.g., the roar of the tempest or the 
 hum of a busy street, or even from an at- 
 mosphere apparently in silence. p IG 194. 
 
 FIG. 193. 
 
 Interference. 
 
 Experiment 140. Hold a vibrating tuning-fork near the ear, and 
 slowly turn it between the fingers. During a single complete rota- 
 tion, four positions of full sound and four positions of silence will be 
 found. When a side of the fork is parallel to the ear, the sound 
 is plainly audible ; when a corner of a prong is turned toward the 
 
CO- VIBRATION. 
 
 251 
 
 ear the waves from one prong destroy the waves started by the 
 other. 
 
 Experiment 141. Hold a vibrating tuning-fork at the mouth of 
 a resonator, and slowly turn it upon its axis. Notice that, in certain 
 positions of the fork, 
 its tone is nearly 
 inaudible. While 
 the tube is in one of 
 these positions, slip 
 a paper tube over 
 one of the prongs, 
 as shown in Fig. 195, 
 being careful not to 
 touch it. The sound 
 will be restored, be- 
 cause the interfering 
 sound has been re- 
 moved. When, by 
 removing the paper 
 tube, we restore the 
 sound of the second 
 prong, we demon- 
 strate the almost par- 
 adoxical fact that sound added to sound may produce silence. 
 
 FIG. 195. 
 
 206. Interference. The mutual action of waves upon 
 one another so that the effects of their vibratory motions 
 are increased, diminished, or neutralized is called inter- 
 ference. Thus, resonance is, properly speaking, a variety 
 of interference. But, as a general thing, interference sig- 
 nifies the coming together of different systems of tvaves in 
 different phases, so that the vibratory motion of the resultant 
 ivave is less than that of the components. In this sense, 
 interference of sound signifies the union of two or more 
 systems of sound waves in such a way as to weaken or 
 destroy the sound. 
 
252 
 
 SCHOOL PHYSICS. 
 
 (a) If, while a tuning-fork is vibrating, a second fork is set in 
 vibration, the waves from the second, must traverse the air already 
 vibrant from the effects of the first. When two forks that have the 
 same pitch are any number of whole wave-lengths apart, their waves 
 will unite in like phases, and a reinforcement of sound will ensue, as 
 
 FIG. 196. 
 
 indicated by Fig. 196. When the forks are an odd number of half 
 wave-lengths apart, their waves will unite in opposite phases, and a 
 
 FIG. 197. 
 
 silence, perfect or partial, will ensue, as indicated by Fig. 197. 
 ference is the leading characteristic property of wave motion. 
 
 Inter- 
 
 Beats. 
 
 Experiment 142. Simultaneously sound two large tuning-forks 
 that are in unison, and notice that the sound is as smooth as if only 
 one fork was sounding. Load one of the prongs of one of the forks 
 with wax, sound both forks, and notice that the sound is not smooth, 
 but that a series of palpitations or beats is easily perceptible. 
 
 Experiment 143. In a quiet room, strike simultaneously one of the 
 lower white keys of a piano, and the adjoining black key. A similar 
 series of beats will be heard. 
 
 207. Beats. If two tuning-forks, A and B, vibrating 
 respectively 255 and 256 times a second, are set in vibra- 
 
CO-VIBRATION. 253 
 
 tion at the same time, their first waves will meet in like 
 phases, and the result will be an intensity of sound greater 
 than that of either. After half a second, B having gained 
 half a vibration upon A, the waves will meet in opposite 
 phases, and the sound will be weakened or destroyed. 
 At the end of the second, we shall have another reinforce- 
 ment ; at the middle of the next second, another interfer- 
 ence. This peculiar pulsation arising from the successive 
 reinforcement and interference of two tones differing slightly 
 in pitch is called a beat. The number of beats per second 
 equals the difference of the two vibration-numbers. 
 
 (a) In Fig. 198, the high crests and deep troughs represent, in the 
 conventional manner, the phases where the two tones reinforce each 
 
 ^A/VV^^^/X/XA^ 
 
 FIG. 198. 
 
 other, while the intermediate portions of the curve similarly symbol- 
 ize the interference phases. 
 
 208. Noise and Music. A noise is a sound so complex 
 that the ordinary powers of the ear fail to resolve it into 
 its constituent tones. A simple tone is incapable of 
 resolution, by reason of its simplicity. A combination of 
 sounds that may be easily resolved into simple tones is a 
 musical sound. The distinction is often difficult. The 
 combination of sounds heard in a boiler-shop is surely 
 a noise, while the sound of a tuning-fork mounted on a 
 resonant box is very nearly a simple tone. 
 
254 SCHOOL PHYSICS. 
 
 CLASSROOM EXERCISES. 
 
 1. How can a deaf person determine whether a given tone is simple 
 or compound ? 
 
 2. If two tuning-forks, vibrating respectively 256 and 259 times 
 per second, are simultaneously sounded near each other, what phe- 
 nomena will follow ? 
 
 3. A musical string, known to vibrate 400 times a second, gives a 
 certain tone. A second string, sounded a moment later, seems to 
 give the same tone. When sounded together, two beats per second 
 are noticeable. Are the strings in unison? If not, what is the rate 
 of vibration of the second string ? 
 
 4. How many beats per second will be produced by the simultane- 
 ous sounding of two tones having vibration-numbers of 297 and 308 
 respectively ? 
 
 5. Show that the length of a resonant air-column must be about \ 
 the wave-length of the tone that it reinforces, or some odd multiple 
 of that length. 
 
 6. The notion is very common, but without foundation in fact, that 
 the sound heard when a conch shell is held to the ear is a lingering 
 remnant of the roar of the ocean from which the shell came. Explain 
 the sound that is thus heard. 
 
 7. A tuning-fork produces a strong resonance when held over a jar 
 15 inches long, (a) Find the wave-length of the fork. (&) Find 
 the wave-period. Ignore the influence of the diameter of the jar. 
 
 8. A tuning-fork held over a tall glass jar, into which water is 
 slowly poured, receives its maximum reinforcement of sound when 
 the resonant air-column is 64.8 cm. long. Assuming that the fork is 
 accurately tuned to give an exact number of vibrations per second, 
 noting the fact that the thermometer records a temperature of 16 C., 
 and keeping in mind the probability of slight experimental error, 
 determine the vibration-number of the fork. Ans. 132. 
 
 9. Refer to 205 (6), and show that, representing the velocity of 
 sound in air by y, the length of the resonant air-column by I, the 
 diameter of the resonant column by d, and the number of vibrations 
 of the fork by n, 
 
 10. If a tube 4 cm. in diameter and 50 cm. long responds most 
 
CO-VIBRATION. 255 
 
 loudly to a certain fork, what is the wave-length of the tone of that 
 fork? 
 
 11. One of two tuning-forks, each tuned to 512 vibrations per 
 second, is loaded with wax. The forks are simultaneously sounded, 
 and 20 distinct beats are heard in 10 seconds. What is the vibration- 
 number of the loaded fork ? 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Resonant-tube and two tuning-forks, 
 as described ; wooden rod ; piano ; music-box and wraps for the same ; 
 guitar; glass funnel; "["- tubes. 
 
 1. In a manner similar to that employed in Exercise 1, page 214, 
 represent two series of waves. Draw the second circle immediately 
 under the first and with equal diameter. Divide the circumference 
 of the first circle into eight, and that of the other into twelve, equal 
 parts. Use the same scale in laying off the equal parts on the axes of 
 abscissas for the two curves. When the two curves of sines are drawn, 
 prolong the vertical lines downward and draw a third axis of abscissas. 
 Construct a curve that will represent the form of the wave formed by 
 compounding the two waves represented by the curves previously 
 drawn ; i.e., make each ordinate equal to the algebraic sum of the two 
 corresponding ordinates. 
 
 2. Using a resonant jar and a tuning-fork the vibration-number 
 of which is known, determine the velocity of sound in air. (Apply 
 the formula developed in the solution of Exercise 9, on page 254.) 
 
 3. Stretch a string horizontally between two fixed supports. From 
 this string suspend two bullet pendulums by threads about a meter 
 long. Swing one of these pendulums across the direction of the hori- 
 zontal string. Describe and explain the result that you think the 
 exercise was intended to bring to your notice. 
 
 4. Remove the cover from a piano, depress the pedal so as to lift 
 the dampers from all the wires, hold the lips near the wires, and sing 
 the vowel, a, with the sound it has in "fate," and prolong the tone. 
 Listen for the sympathetic response of the piano. Repeat the experi- 
 ment, singing the same vowel with the sound it has in " father," and 
 then the vowel, 0, with the sound it has in " tone." 
 
 5. Fig. 199 represents two series of sound waves traveling together. 
 The full line represents one series and the dotted line another. What 
 phenomenon would result from such a combination of tones as is here 
 
SCHOOL PHYSICS. 
 
 represented? Describe the condition of affairs as represented at A, 
 B and C respectively. Draw a single curve to represent the resultant 
 of combining these two tones. 
 
 / 
 
 FIG. 199 
 
 6. Fig. 200 represents two systems of sound waves having equal 
 amplitudes and periods that are as 1:2. In the first diagram, the 
 waves start together; in the second, the 
 shorter wave is a quarter of a wave-length 
 behind; in the third, it is a half wave- 
 length behind; in the fourth, it is three- 
 fourths of a wave-length behind. Draw 
 curves representing the compound waves 
 resulting from these combinations, and re- 
 peat each form twice, thus getting four 
 curves, each representing a series of three 
 compound waves. Carefully note the dif- 
 ferences in the wave-forms that result 
 from combining like waves in different 
 phases. 
 
 7. Construct a single curve that shall 
 represent the form of sound waves com- 
 posed of the combined motions of the 
 harmonics represented in Fig. 201. 
 
 8. Get a glass tube about f of an inch in 
 FIG. 200. diameter and 12 inches long. Into this 
 
 V 
 
 T\ 
 
 FIG. 201. 
 
CO-VIBRATION. 
 
 257 
 
 FIG. 202. 
 
 tube thrust a neatly fitting cork. Move the cork with a ramrod 
 until, by trial, you have adjusted the tube for maximum resonance 
 with a tuning-fork, e.g., one marked "Philharmonic A." Support 
 the tube with its mouth close to the disk 
 of the siren shown in Fig. 168, and 
 facing one of the circles of holes. Hold 
 the nozzle of the tube on the other side of 
 the disk and just opposite the mouth of 
 the resonant tube. Turn the tube with 
 gradually increasing speed, and blow air 
 through the tube. When the sound is 
 at its maximum, the siren-tone will be in unison with the tone of the 
 fork by which the resonant tube was tuned. Determine the vibration- 
 number of the fork. 
 
 9. Support a wooden rod about an inch square and three feet long 
 with its lower end resting upon the cover of a music-box that is sound- 
 ing. Wrap the music-box in cotton-wool and manifold layers of 
 woolen cloth, until no sound from the box can be heard. Carefully 
 balance a guitar or violin upon the top end of the rod. Describe and 
 explain the consequent phenomenon. 
 
 10. Place two tuning-forks having frequencies of 512 and 516 
 respectively upon the table, and sound them together. They will 
 give four beats per second. Make sure of the fact by trial. Place 
 your ear in a line with the forks, and have one of the sounding forks 
 steadily moved toward the other at the rate of two feet per second. 
 How many beats per second do you hear? Then have one of the 
 sounding forks moved directly away from the other at the uniform 
 rate of two feet per second. How many beats per second do you 
 hear? Explain. 
 
 11. With glass funnel and T-tubes and rubber tubing, arrange 
 apparatus as shown in Fig. 203. A sound wave entering at o will 
 
 divide its energy, part 
 passing by way of a 
 and part by c, and 
 uniting at e. If the 
 two paths between b 
 and e are of equal 
 lengths, the waves 
 will unite at e in like phases, and the ear at s will hear the sound 
 without serious diminution. If, however, one path is longer than 
 17 
 
 FIG. 203. 
 
258 SCHOOL PHYSICS. 
 
 the other by a half wave-length of the sound entering at o, or any 
 odd multiple thereof, the waves will unite, at e in opposite phases, 
 and an interference more or less nearly complete will result. Pro- 
 vide a tuning-fork with a frequency of about 512 ; determine, by 
 experiment or computation, the length of its waves at the tempera- 
 ture of the room, and make one branch of the apparatus a half wave- 
 length longer than the other. This difference will be about a foot. 
 Sound the fork at o and hold the ear at s, and slip one end of c back 
 and forth over the glass tubing, until the adjustment is such that the 
 sound heard at s is very feeble or nil. When a good interference is 
 secured, sound the fork again, and pinch the rubber tubing at a or c. 
 Two Y-tubes may be used instead of the T-tubes, and the tube 
 between b and e may consist in part of a bent glass tube that will 
 slide inside the rubber tube. 
 
 V. THE LAWS OF VIBBATIOK 
 
 209. Vibrations of Strings. The laws of the vibrations 
 that give rise to musical tones are most conveniently 
 studied by means of stringed instruments, especially the 
 sonometer (Fig. 204). The vibrations maybe transverse, 
 
 FIG. 204. 
 
 torsional, or longitudinal, as stated in 180. Of these, 
 the transverse vibrations are the most important. When 
 used for the production of musical tones, strings are 
 
THE LAWS OF VIBRATION. 259 
 
 fastened at their ends, stretched to proper tension, and 
 then made to vibrate by bowing, as in the violin ; by 
 plucking, as in the guitar or banjo ; or by striking them 
 with a light hammer, as in the piano or dulcimer. The 
 manner of producing the vibrations has little effect upon 
 the tone, which is chiefly determined by the length, diame- 
 ter, density, and tension of the string itself. 
 
 Experiment 144. Remove the sliding bridge of the sonometer, 
 stretch one of the strings and pluck or bow it near its end. Xotice 
 the pitch of the tone. Place the sliding bridge at the middle of the 
 scale on the sonometer box so as to halve the length of the string ; 
 then bow as before. Xotice that the pitch of the tone is an octave 
 higher. If desirable, the experiment may be modified by tuning the 
 string until its tone is in unison with a certain tuning-fork or with 
 the tone of the siren when the air-stream is directed against the 
 inner row of holes. Then the tone of the half string will be in 
 unison with another fork an octave higher in pitch or with the siren- 
 tone when the air stream is directed against the outer row of holes, 
 the speed of rotation being the same. 
 
 Experiment 145. Stretch two wires of the same diameter and 
 material with unequal but known weights, and, with the movable 
 bridge, shorten the wire that carries the smaller weight until it sounds 
 in unison with the other. Xotice that the lengths of the strings vary 
 as the square roots of the weights or tensions. 
 
 Experiment 146. Stretch two iron wires of different diameters, 
 upon the sonometer, with equal tension. With the sliding bridge, 
 shorten the heavier wire until it is in unison with the other wire. 
 From the scale on the sonometer box, read the length of the vibrating 
 part of the heavier wire. Measure the diameters of the two wires and 
 notice that the diameters of the wires are inversely proportional to 
 their lengths. 
 
 Experiment 147. Stretch, with equal tension, a brass and a steel 
 wire of the same diameter, and, with the sliding bridge, shorten one 
 of the wires until the two are in unison. Ascertain, in the easiest 
 way, the densities of brass and steel, and notice that the lengths of 
 
260 SCHOOL PHYSICS. 
 
 the strings vary inversely as the square roots of the densities of the 
 materials. 
 
 210. Laws of Vibrations of Strings. These experi- 
 ments indicate the following facts relative to musical 
 strings : 
 
 (1) Other conditions being the same, the vibration-numbers 
 vary inversely as the lengths. 
 
 (2) Other conditions being the same, the vibration-numbers 
 vary directly as the square roots of the tensions. 
 
 (3) Other conditions being the same, the vibration-numbers 
 vary inversely as the diameters. 
 
 (4) Other conditions being the same, the vibration-numbers 
 vary inversely as the square roots of the densities. 
 
 (a) The third and fourth laws may be consolidated as follows : 
 Other conditions being the same, the vibration-numbers vary inversely 
 
 as the square roots of the weights per linear unit. 
 
 (&) In instruments like the piano, the length, diameter, and density 
 
 of the strings are determined once for all by the manufacturer, the 
 
 tension being adjusted by the piano tuner. 
 
 Air Columns. 
 
 Experiment 148. Make a reed-pipe by cutting a piece of wheat 
 straw eight inches (20 cm.) long so as to have a knot at one end. 
 At r, about an inch from the knot, cut inward about a quarter of the 
 straw's diameter ; turn the knife blade flat and draw it toward the 
 
 FIG. 205. 
 
 knot. The strip, rr' , thus raised is a reed ; the straw itself is a reed- 
 pipe. When the reed is placed in the mouth, the lips firmly closed 
 around the straw between r and s and the breath driven through the 
 apparatus, the reed vibrates and produces vibrations in the air-col- 
 umn of the wheaten pipe. Notice the pitch of the tone thus produced. 
 Cut off two inches from the end of the pipe at s. Blow through the 
 
THE LAWS OF VIBRATION. 261 
 
 pipe as before and notice that the pitch is raised. Cut off two inches 
 more, sound the pipe, and notice that the pitch is still higher. 
 
 211. Vibrations of Air Columns. Experiments 96, 139, 
 and 148 show that when gases are confined in tubes they 
 may be made to vibrate as sonorous bodies. The air- 
 column may be set in vibration by a vibrating tongue, as 
 in the reed-pipe of Experiment 148, or in reed instru- 
 ments like the melodeon, accordion, clarinet, etc., or by 
 the fluttering of air particles driven against the edge of 
 an opening in a tube, as in the whistle, fife, flute, or 
 organ-pipe. Whatever the way of producing the vibra- 
 tions, the dimensions of the air-column itself determine 
 the tone. In Experiment 148, we saw that the air- 
 column, and not the straw tongue, determined the pitch. 
 
 Experiment 149. Fit a cork loosely as a piston into the end of a 
 glass tube about 2 cm. in diameter and 30 cm. long. Blow across the 
 open end of the tube so as to produce a steady tone. It may be more 
 easy to do this if you use a mouthpiece made by flattening the end 
 of a piece of brass tubing. Xotice the pitch of the tone produced, 
 and measure the length of the air-column in the tube. By trial, 
 determine the lengths of the air-columns that will give the tones of 
 the gamut, and compare the relative lengths with the relative 
 vibration-numbers given in 196. 
 
 Experiment 150. Provide two glass tubes of the same diameter 
 (about 2.5 cm.), one being half as long as the other (e.g., 10 cm. and 
 20 cm.). Blow across the end of the longer tube so as to produce its 
 lowest tone while the other end of the tube is open. Xotice the 
 pitch. Stop one end of the shorter tube with the hand, ard blow 
 across the open end so as to produce the lowest tone. Xotice that 
 the pitch of the short stopped-pipe is the same as that of the long 
 open-pipe. Of course, if the school is provided with an assortment 
 of organ-pipes (as is desirable), it is better to use them. 
 
 Experiment 151. Procure an open organ-pipe, at least one side of 
 which is made of glass. While the pipe is emitting its fundamental 
 
262 
 
 SCHOOL PHYSICS. 
 
 tone, lower a small ring with a paper bottom, on which a little tine 
 sand has been strewn, as shown in Fig. 206. 
 Just inside the upper part of the pipe, the sand 
 dances right merrily, its motion becoming less 
 energetic as the ring approaches the middle of 
 the pipe. When the ring is lowered below this 
 point, the agitation of the sand steadily in- 
 creases. Vary the experiment by closing the 
 open end of the pipe with a cover or plug per- 
 forated for the thread and moving the sand- 
 strewn membrane up and down as before. The 
 only place where the sand is not agitated is at 
 the closed end of the pipe. 
 
 212. Laws of Vibrations of Air-Columns. 
 
 Careful and elaborate tests have veri- 
 fied what is suggested by our rude ex- 
 periments, namely, that 
 
 (1) The vibration-numbers of air- 
 columns vary inversely as their lengths. 
 
 (2) The pitch of a closed-pipe is an 
 octave below that of an open-pipe of the 
 same length. 
 
 FIG. 206. 
 
 (a) The two ends of an open-pipe sounding its fundamental are 
 places of maximum motion, i.e., the middle points of ventral seg- 
 ments ; while at the middle of the pipe, where the direct and 
 reflected pulses cross each other, there is no motion. This middle 
 point is a node. The length of the air-column is half the wave- 
 length. In the stopped-pipe sounding its fundamental, the node is 
 at the end, and the length of the air-column is a fourth of the wave- 
 length. 
 
 (&) By increasing the pressure of the blast that blows the pipe, 
 overtones may be produced. The change of nodes and ventral seg- 
 ments may be shown by the sand-strewn membrane as before. 
 
 (c) If a hole is made in the side of a pipe at a point occupied by a 
 node, the point is at once changed to the middle of a ventral seg- 
 
THE LAWS OF VIBRATION. 263 
 
 ment, and there is a corresponding change of pitch. This action is 
 familiarly shown in the fife and flute. 
 
 Vibrating Rods. 
 
 Experiment 152. Hold a steel rod, a meter in length, at its middle 
 point, and rub one of its halves with a piece of resined leather. The 
 rod will emit its fundamental tone. Repeat the experiment succes- 
 sively with two other steel rods, one having the same length and a 
 
 FIG. 207. 
 
 different diameter, the second rod being just half as long. The 
 second rod will give a tone of the same pitch as the first, while 
 the shorter rod will sound a tone an octave above. 
 
 Experiment 153. That the rubbing of a rod, as in Experiment 
 152, produces longitudinal vibrations in the rod is prettily shown by 
 the apparatus devised by Koenig, and represented in Fig. 208. A 
 brass rod, AB, is 
 supported by a 
 clamp at /its mid- 
 dle point, c. An 
 ivory ball is sus- 
 pended so as just 
 to touch the end of 
 
 the rod. When the -'.< [[^1 T 
 
 rod is rubbed with 
 resined leather at 
 rf, the vibrations FIG. 208. 
 
 thus set up in the 
 
 rod repel the elastic ball in a very energetic manner. The rod may 
 be clamped in a vise, and the ball suspended in any convenient way. 
 
264 
 
 SCHOOL PHYSICS. 
 
 213. The Vibrations of Rods may be transverse, longi- 
 tudinal, or torsional. Transverse vibrations are famil- 
 iarly illustrated in the music-box, jews'-harp, xylophone, 
 tuning-fork, etc. Longitudinal vibrations were illus- 
 trated in Experiment 153. By clasping a vertical glass 
 tube with one hand, and rubbing the upper half with a 
 wetted cloth held in the other, it is possible to produce 
 longitudinal vibrations that will shatter the lower part 
 of the tube. For longitudinal vibrations of rods of any 
 given material, the vibration-numbers are inversely pro- 
 portional to the lengths of the rods. Such rods may also 
 be made to vibrate in segments, and then the vibration- 
 numbers are inversely proportional to the lengths of the 
 segments. If a violin-bow is drawn around a rod that 
 -is clamped at one end, the rod will twist and untwist 
 with vibrations that are as isochronous as those of a 
 tuning-fork, emitting a tone a little lower than that 
 
 produced by longitudinal 
 vibrations of the same rod 
 having the same number of 
 segment al divisions. 
 
 Vibrating Plates. 
 
 Experiment 154. Support, as 
 shown in Fig. 209, a glass or 
 brass plate, square or round, and 
 strew it evenly with fine sand. 
 Place the finger at any point on 
 the edge of the plate (e.g., at the 
 middle of one side) so as to form 
 FIG. 209. a node there, and draw a violin- 
 
 bow at a point properly chosen 
 (e.g., near the adjacent corner). The sand immediately begins to 
 
THE LAWS OF VIBRATION. 
 
 265 
 
 dance on the plate and arrange itself along nodal lines. By chang- 
 ing the nodal points and bowing properly, other sand-figures may be 
 produced, one of which is shown in Fig. 209. 
 
 214. Vibrations of Plates. The method of studying the 
 vibrations of plates as just illustrated is due to Chladni, 
 after whom the plates and figures are named. The 
 arrangement of nodal lines is determined by the relative 
 positions of the point that is bowed and the point that is 
 touched with the finger. The figures may be produced 
 in multitudinous variety. As the complexity of the 
 figures produced on a given plate increases, the pitch of 
 the corresponding tone rises, the same figure always answer- 
 ing to the same tone. 
 
 Experiment 155. Draw a violin-bow across the edge of a large 
 goblet nearly full of water on 
 the surface of which cork dust 
 or powdered sulphur has been 
 evenly sifted. The, glass bell will 
 emit a musical tone and the sur- 
 face of the water will disclose the 
 mode of the vibration. When 
 the bell sounds its fundamental 
 tone, it vibrates in four segments, 
 and the surface of the water tells 
 the story by a record like that 
 shown in Fig. 210. A few vigor- 
 ous strokes of the bow would set 
 up vibrations of amplitude suf- 
 ficient to break the bell. 
 
 FIG. 210. 
 
 215. Vibrations of Bells. Just as a tuning-fork may 
 be looked upon as a rod bent into a U- sna P e i so a bell ma 7 
 be considered as a disk bent into a cup shape. Like a 
 disk, it sounds its fundamental tone when vibrating in 
 four segments, and the number of segments is always even. 
 
266 SCHOOL PHYSICS. 
 
 CLASSROOM EXERCISES. 
 
 1. A musical string vibrates 200 times a second. State what takes 
 place when the string is lengthened or shortened with no change of 
 tension, and what change takes place when the tension is made more 
 or less, the length remaining the same. 
 
 2. A certain string vibrates 100 times a second, (a) Find the 
 vibration-number of a similar string, twice as long, stretched by the 
 same weight. (6) Of one that is half as long. 
 
 3. A string sounding C 3 is 18 inches long. Must it be lengthened 
 or shortened and how much to give the tone D 3 ? 
 
 4. A certain string vibrates 100 times per second. Find the vibra- 
 tion-number of another string that is twice as long, and weighs four 
 times as much per foot, and is stretched by the same weight. 
 
 5. A certain string sounds the tone C 2 when it is stretched by 
 a weight of four pounds. What weight must it carry to give the 
 tone F 2 . 
 
 6. A musical string five feet long emits a tone in unison with that 
 of a fork that is known to vibrate 256 times a second. What will 
 its vibration-number be when it has been shortened two feet? 
 
 7. A sonometer string is stretched by a load of 16 pounds. What 
 load must be given to it so that it may sound a tone an octave lower ? 
 
 8. A tube open at both ends is to produce a tone corresponding to 
 32 vibrations per second. Taking the velocity of sound as 1,120 feet, 
 find the length of the tube. If the number of vibrations is 4,480, find 
 the length of the tube. 
 
 9. Find the length of an organ-pipe the waves of which are four feet 
 long, the pipe being open at both ends. Find the length, the pipe 
 being closed at one end. 
 
 10. What will be the relative vibration-numbers of two strings of 
 the same length, diameter, and tension, one being made of catgut and 
 the other of brass, the density of brass being nine times that of catgut? 
 
 11. If three organ-pipes of the same dimensions are filled respec- 
 tively with gases of different densities, e.g., air, hydrogen, and carbon 
 dioxide, would the several tones emitted agree or differ in pitch? 
 Why? 
 
 12. How would you experimentally determine whether a vibrating 
 tuning-fork has nodes or not ? 
 
THE LAWS OF VIBRATION. 267 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Two spring-balances, each of which will 
 carry a load of 30 pounds ; four hard wood triangular prisms, each 
 about 5 cm. long and with a triangular altitude of 2.5 cm. ; spring- 
 brass wire, No. 24 and No. 27 ; a tuning-fork with pitch of middle C, 
 and another an octave lower ; a glass tube and a brass rod as described 
 belo\v ; mercury cup ; two electromagnets ; voltaic cell. 
 
 1. Set two screws horizontally into the end of a table-top, and about 
 15 cm. apart. Anneal the two ends of a piece of No. 24 spring-brass 
 wire, about 150 cm. long, and fasten one of the ends to one of the 
 screws, and the other end to the hook of one of the spring-balances. 
 To the ring of the balance, attach a stout, soft iron wire, about 50 cm. 
 long. Within easy reach of the free end of this second wire, set a 
 stout screw, so that its head shall project about 2.5 cm. above the top 
 of the table, and fasten the free end of the wire to it. In similar 
 manner, stretch a No. 27 spring-brass wire parallel with the No. 24 
 wire. Prop the dynamometers so that they will He flat on their 
 backs, and slip one of the hard wood prisms under each end of each 
 of the two brass wires. Put the No. 24 wire under a tension of 20 
 pounds, and move the prism away from the dynamometer hook until 
 the wire, when plucked midway between the prisms, gives a tone that 
 is in unison with the fork of lower tone. In doing this, press the 
 wire lightly against the ridge of the moved prism, hold the ear near 
 the wire and let the rough overtones die away, leaving the funda- 
 mental which is to be tested. Measure the distance between the two 
 ridges ; i.e., the length of the vibrating wire. Shift the prism again 
 and determine the length of the wire when its tone is in unison with 
 the fork of tone an octave higher. Reduce the tension of the wire to 
 5 pounds, and determine the length of the wire when it is in unison 
 with the fork of lower tone. Put the No. 27 wire under a tension of 
 10 pounds, and determine the lengths of the wire when it is in unison 
 with each of the forks. Consult the table of wire gauges in the 
 appendix, and notice that the area of cross-section for No. 24 wire is 
 almost exactly twice that of No. 27 wire, and remember that the 
 weight per linear unit varies as the area of cross-section. How do 
 your results correspond to the laws given in 210? 
 
 2. Replace the No. 27 wire of Exercise 1 with a second No. 24 
 wire like the first, and put it under a tension of 6 pounds. Increase 
 the tension of the first wire to 24 pounds. Move the bridge until the 
 
268 SCHOOL PHYSICS. 
 
 second wire gives a musical tone. Move the other bridge until 
 the other wire has the same length. With the siren, determine the 
 vibration-numbers of the two shortened wires, and see how the ratios 
 between them compare with the ratios between the two tensions. 
 
 3. Bring the siren into unison with a tuning-fork. Turning the 
 wheel regularly for 10 seconds at the rate that gives unison, deter- 
 
 "mine the number of puffs per second, and thus determine the 
 vibration-number of the fork. 
 
 4. Close one end of a glass tube about 1.5 m. in length and 4 cm. 
 in internal diameter, with a stopper. Scatter along the length of the 
 tube a small quantity of precipitated silica or cork dust. Fasten a 
 thin cork that neatly fits into the glass tube to one end of a brass 
 rod or tube about 2 m. in length and 1 cm. in diameter. Lay the 
 glass tube on the table, and push the cork at the end of the brass rod 
 about 50 cm. into it. Clamp the rod between two grooved blocks at 
 its middle so that it shall "lie along the axis of the glass tube. Rub 
 the outer end of the rod with resined leather so as to produce a shrill 
 sound and to agitate violently the powder in the tube. Change the 
 length of the air-column by moving the glass tube endwise until 
 the powder divides into segments separated by clearly marked nodes. 
 From the distance between these nodes, determine the wave-length of 
 the sound in the air. From the length of the rod, determine the 
 wave-length of the sound in brass. From these results, determine 
 the relative velocities of sound in brass and in air. 
 
 5. Solder a wire pointer to the under side of a steel sonometer-wire 
 at its middle. Place a small cup of mercury below the wire so that 
 
 FIG. 211. 
 
 the pointer shall just touch its surface. Cover the surface of the 
 mercury with a thin layer of mixed alcohol and glycerin to keep 
 the metal surface clean. Place the end of an electro-magnet, E, a 
 
THE LAWS OF VIBRATION. 269 
 
 little above the wire and midway between the pointer and the end, 
 and another electro-magnet, M, at a distance of several feet. Put the 
 apparatus into circuit with a voltaic cell, as shown in Fig. 211, and 
 vibrate the wire. Support a tuning-fork that is nearly in unison 
 with the wire so that the face of one of its prongs shall be near the 
 end of M. Adjust the tension or the length of the wire until the 
 response of the fork shows that the wire and the fork are in unison. 
 
 6. Select two tuning-forks of the same tone, and, by means similar 
 to those used in Exercise 5, cause one to respond to the other. Notice 
 the persistence of the vibrations. 
 
CHAPTER IV. 
 
 HEAT: MOLECULAR PHYSICS. 
 
 I. NATURE OF HEAT, TEMPERATURE, ETC. 
 
 216. Heat is a form of energy into ivhich all other forms 
 of energy are convertible. It consists in the agitation of the 
 molecules of matter, and is generally recognized by the sensa- 
 tion of warmth to which it gives rise. 
 
 (a) When the molecular agitation of a body is increased, the body 
 is heated; when it is lessened, the body is cooled. See 6 (c), 8, 
 and 51. 
 
 217. The Temperature of a body is its state considered 
 with reference to its ability to communicate heat to other 
 bodies. When two bodies are brought together, there is a 
 tendency toward an equalization of temperature. If there 
 is an actual transfer between them, the one that gives the 
 greater amount of heat has the higher temperature, and the 
 one that receives it has the lower temperature , 
 
 (a) Water flows from a point of high to one of low level. Electrifi- 
 cation flows from a point of high to one of low potential. Heat flows 
 from a point of high to one of low temperature. 
 
 (&) An addition of heat may increase the velocity of the molecular 
 motion or it may do another kind of work. When a body receives 
 heat, its temperature generally rises, but sometimes a change of con- 
 dition results instead. When a body gives up heat, its temperature 
 falls or its physical condition changes. 
 
 Experiment 156. Into one basin put hot water; into a second 
 basin put ice-cold water ; into a third basin put water at the tempera- 
 ture of the room. Put the" right hand into the hot water and the left 
 
 270 
 
NATURE OF HEAT, TEMPERATURE, ETC. 
 
 271 
 
 hand into the cold water, and hold them there for some time. Trans- 
 fer the right hand from the hot water to the water in the third basin, 
 and that water will seem cold. Transfer the left hand from the cold 
 water to the water in the third basin ; the water that felt cold to the 
 right hand will feel warm to the left hand. 
 
 218. An Unsafe Standard. Experiment 156 shows that 
 our sensations may not be trusted as a measure of tempera- 
 ture. They are of even less value in the measurement of 
 heat. A body feels hot when it is imparting heat to us ; 
 it feels cold when it is drawing heat from us. 
 
 Experiment 157. Provide a ring (or a sheet of tin with a hole cut 
 in it) and a metal ball that, at the 
 ordinary temperature, will just pass 
 through the opening. Heat the ball 
 and it will no longer pass through. 
 
 Experiment 158. Connect, by a 
 perforated cork, a piece of glass tub- 
 ing about 50 cm. long to a Florence 
 flask. Put water that has been 
 colored with red ink into the appa- 
 ratus so that it partly fills the upright 
 tube. Mark the level of the water 
 in the tube by a rubber band or in 
 some other convenient way. Im- 
 merse the flask in hot water and 
 carefully observe the level of the 
 water in the tube. 
 
 FIG. 212 
 
 219. Expansion. Experiments 157 and 158 show that 
 one effect of heating a body is to increase its volume. 
 This increase is the immediate result of the increase of the 
 molecular motions ; the amount of the expansion is defi- 
 nitely related to the increase of temperature. 
 
 220. A Thermometer is an inst? i ument for measuring 
 temperatures. In its most common form, it consists of a 
 
272 
 
 SCHOOL PHYSICS. 
 
 liquid-filled bulb and a tube of uniform bore, as illustrated 
 in Experiment 158. The liquid generally used is mercury 
 or alcohol. The upper part of the tube is freed from air 
 and hermetically sealed. A scale of equal parts is added 
 for the measurement of the rise or fall of the liquid in the 
 tube. 
 
 (a) An air thermometer consists essentially of a large glass bulb at 
 the upper end of a tube of small but uniform bore, the lower end of 
 which dips into colored water. When the bulb is heated, 
 some of the expanded air escapes in bubbles through the 
 liquid ; when the bulb cools, some of the liquid rises in 
 the tube. Of course, the tube has its scale of equal parts. 
 Any slight change of temperature affects the elastic force 
 of the air in the bulb and changes the height of the liquid 
 column. For a small change of temperature, the movement 
 of the index is comparatively large; i.e., the instrument has 
 great sensitiveness. 
 
 (6) The differential thermometer shows the difference in 
 FIG 213 temperature of two neighboring places 
 by the expansion of air in one of two 
 bulbs that are connected by a bent glass tube con- 
 taining some liquid not easily volatile. It is an 
 instrument of simple construction and great sen- 
 sitiveness. 
 
 (c) Mercury freezes at about- 39 C.. For 
 temperatures lower than - 38 C., an alcohol 
 thermometer is generally used. Mercury boils at 
 about 350 C. Temperatures higher than 300 C. 
 are generally measured by the expansion of a 
 metal rod or by using an air thermometer with a 
 porcelain or platinum bulb. FlG 214 
 
 221. Graduation of the Thermometer. In every ther- 
 mometer there are two fixed points called the freezing- 
 point and the boiling-point. The first of these indicates 
 the temperature of melting ice ; the other, the temperature 
 
NATURE OF HEAT, TEMPERATURE, ETC. 273 
 
 of steam as it escapes from water boiling under an atmos- 
 pheric pressure of 76 centimeters of mercury. The dis- 
 tance between the fixed points is divided into equal parts 
 according to different arbitrary scales. 
 
 (a) The two scales chiefly used in this country are the centigrade 
 (or Celsius) and Fahrenheit's. For these scales, the fixed 
 points, determined as just explained, are marked as fol- ^4 
 lows : 
 
 Centigrade. Fahrenheit. 
 
 Freezing-point, 32 
 
 Boiling-point, 100 212 
 
 The tube between these two points is divided into 100 
 equal parts for the centigrade scale, and into 180 for Fah- 
 renheit's. Either scale may be extended beyond either fixed 
 point as far as is desired. The divisions below zero are* 
 considered negative ; e.g., 10 signifies 10 degrees below 
 zero. The scales are designated by their respective initial 
 letters, as 5 C., or 41 F. In the Reaumur scale, which is 
 little used in this country, the freezing-point is marked 
 and the boiling-point, 80. Unless otherwise stated, 
 the thermometer readings given in this book are in cen- FlG - 215 -. 
 tigrade degrees. 
 
 (ft) Since 0C. corresponds to 32 F., and an interval of 1 centi- 
 grade degree equals an interval of 1.8 Fahrenheit degrees, we may 
 reduce centigrade readings to Fahrenheit readings by multiplying the 
 number of centigrade degrees by 1.8 and adding 32. Similarly, we 
 may reduce Fahrenheit degrees to centigrade degrees by subtracting 
 32 from the number of Fahrenheit degrees and dividing the re- 
 mainder by 1.8. 
 
 222. Absolute Zero of Temperature. The temperature 
 at which the molecular motions constituting heat wholly cease 
 is called the absolute zero. It has never been reached, but 
 theoretical considerations indicate that it is 273 below 
 the centigrade zero. ( 232, a.) It is often convenient 
 as an ideal starting-point or standard of reference. 
 18 
 
274 SCHOOL PHYSICS. 
 
 (a) Temperature, when reckoned from the absolute zero, is called 
 absolute temperature. Absolute temperatures are obtained by add- 
 ing 273 to the readings of a centigrade thermometer, or 460 to the 
 readings of a Fahrenheit thermometer. 
 
 CLASSROOM EXERCISES. 
 
 1. The difference between the temperatures of two bodies is 36 
 Fahrenheit degrees. Express the difference in centigrade degrees. 
 
 2. The difference between the temperatures of two bodies is 35 
 centigrade degrees. Express the difference in Fahrenheit degrees. 
 
 3. (a) Express the temperature 68 F. in the centigrade scale. 
 (6) Express the temperature 20 C. in the Fahrenheit scale. 
 
 4. What is the corresponding centigrade reading for 50 F. ? 
 
 5. How would it affect the readings of the school thermometer 
 (mercurial) if the bulb should permanently contract? 
 
 6. How would the readings of a mercury thermometer be affected 
 if the tube was gradually enlarged from the bulb upward ; i.e., if the 
 bore of the tube was made slightly conical ? 
 
 7. When a centigrade thermometer indicates a temperature of 15, 
 what should be the reading of a Reaumur thermometer hanging by 
 its side ? 
 
 8. Suppose that one of the flat faces of a tin can was painted with 
 a mixture of lampblack and oil, the opposite face of the can being 
 left bright ; that the can thus prepared was filled with hot water and 
 hung between the bulbs of the differential thermometer with the 
 painted side facing one of the bulbs; and that the liquid moved 
 toward the bulb that was opposite the bright face of the can. What 
 inference would you draw concerning the effect of the paint on the 
 facility with which tin at a given temperature emits heat? 
 
 9. Suppose that when the Florence flask used in Experiment 158 
 was immersed in hot water, the level of the liquid in the tube fell a 
 little before it began to rise. How would you explain such an effect? 
 
 10. What effect would a diminution of the bore of a thermometer 
 tube have upon the sensitiveness of the instrument ? 
 
 11. What is in the upper part of a thermometer tube? 
 
 12. What relation has a flow of heat between two bodies to the 
 relative temperatures of the two bodies ? 
 
 13. Describe very briefly the molecular agitations of a body at a 
 temperature of -273. 
 
 14. What is the absolute temperature of this room at this time? 
 
NATURE OF HEAT, TEMPERATURE, ETC. 
 
 275 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. One or two chemical thermometers 
 (Fig. 215) graduated from to 100 ; Bunsen burner or alcohol lamp ; 
 the boiler apparatus described below ; a tin pail ; ice or snow ; barom- 
 eter. 
 
 1. Hold a chemical thermometer in the right hand as a pen is gen- 
 erally held, but with the bulb uppermost. Strike the right hand 
 against the palm of the left hand so as to separate some of the mercury 
 in the stem from the main column. Measure, in divisions of the 
 scale and at different parts of the scale, the length of the mercury 
 thus separated from the main column to determine the accuracy of 
 the calibration of the thermometer. Do not imagine that this experi- 
 ment gives any adequate idea of the tedious painstaking necessary for 
 such calibration as is required for work of precision. 
 
 2. Xearly fill any convenient metal vessel with clean ice in small 
 pieces, the smaller the better. For this and other experiments with 
 heat, snow may be used instead of ice. Fill the spaces between the 
 lumps of ice with water, and insert the lower end of a thermometer 
 until the zero mark is within 1 or 2 mm. of the water surface. Place 
 the eye so that the line of vision cuts the thermometer at right angles 
 at the top of the mercury column. When the mercury has fallen to 
 its lowest point, record the reading of the thermometer, estimating 
 fractions of the divisions of the scale with the eye as closely as possible. 
 
 3. Make, of sheet-copper, a boiler with a diameter of 10 cm. and a 
 height of 15 cm. The top of the cylinder should 
 
 not be wired, but should be left flexible. About 
 2 cm. from the top, insert a sheet-copper tube, , 
 about 5 cm. long and about 6 mm. in diameter, so 
 that it shall slope slightly upward from the boiler. 
 Provide three reliable legs, ^r other means of sup- 
 porting the boiler about 20 cm. above the table. 
 Make a sheet-copper conical cover that fits the 
 top of the boiler snugly and internally (as a tin 
 pail cover fits), and that tapers upward for 30 cm. 
 ^o an opening about 2.5 cm. in diameter. This 
 opening at the top of the cover should be so con- 
 structed that it may be closed with a cork, c. About 
 2 cm. below the top of the cover, insert a tube, 6, like 
 that inserted in the boiler proper, but only 2 cm. 
 long. 
 
 FIG. 216. 
 
276 SCHOOL PHYSICS. 
 
 Fill the boiler with water to the depth of 3 or 4 cm. Cork the 
 tube, a. Pass a centigrade thermometer through a perforated cork 
 that closes c, and push it down until the point marked 100 is not 
 more than 2 or 3 mm. above the cork, unless that would bring the 
 bulb close to the water. In that case, adjust the thermometer so 
 that its bulb shall be about 3 cm. above the water. Boil the water 
 (but not violently), guarding against the streaming of the flame up 
 the sides of the boiler. When the mercury has risen as far as it will, 
 record the reading of the thermometer. Note the reading of the 
 barometer, and correct the reading of the thermometer by allowing 
 1 for each 27 mm. that the barometer column exceeds 760 mm., 
 or falls short of it. Hold a wadded handkerchief over the mouth 
 of the tube, b, and note the effect of added pressure upon the boiling- 
 point of the water. 
 
 Allow the thermometer to cool in air, and then redetermine its 
 freezing-point, as in Exercise 2. If that point varies from the one 
 previously found, consider the newly found point as the true one. 
 Heat the ice or snow, stirring it with the thermometer during lique- 
 faction, and observing the thermometric reading. 
 
 If the tests of the thermometer develop an error of 1 or more in 
 the fixed points, get another thermometer, or correct subsequent read- 
 ings for the observed errors. In the estimation of such errors, the 
 error at the 50 mark may be taken as the mean between the errors 
 at and 100 ; at 25, three times as much influence should be 
 allowed for the error at as for that at 100. 
 
 II. THE PRODUCTION AND TRANSFERENCE OF 
 HEAT, ETC. 
 
 223. Sources of Heat. The sun is the great source of 
 thermal energy, but man is able to transform other forms 
 of energy into heat. 
 
 Experiment 159. Rub a metal button on the floor or carpet. It 
 soon becomes uncomfortably warm. 
 
 Experiment 160. Place a nail or coin on an anvil or stone and 
 hammer it vigorously. It soon becomes too hot to handle. In this 
 way, blacksmiths sometimes heat iron rods to redness. 
 
PRODUCTION AND TRANSFERENCE OF HEAT, ETC. 277 
 
 Experiment 161. Hold a piece of iron or steel against a dry grind- 
 stone or an emery-wheel in rapid revolution. The shower of sparks 
 noticeable is due to the fact that the small particles of metal torn off 
 by the grindstone are heated to incandescence. 
 
 Experiment 162. Half fill a stout four-ounce bottle with mercury 
 at the temperature of the room. Cork the bottle, wrap it in several 
 thicknesses of paper to protect it from the heat of the hand, and 
 shake it vigorously. Remove the cork, insert the bulb of the ther- 
 mometer, and see if there has been any change in the temperature of 
 the mercury. Cork the bottle and shake it as before, but longer and 
 more vigorously. Take the temperature of the mercury again. 
 
 Experiment 163. Place a bit of tinder in the cavity at the end of 
 the piston of the " fire-syringe " represented 
 in Fig. 217. Put the piston into the open 
 end of the cylinder and force it in, com- 
 pressing the confined air as abruptly as 
 possible. Promptly remove the piston. The 
 tinder will probably be on fire. 
 
 Experiment 164. Cut a thin slice from 
 a stick of phosphorus under water. Carry 
 the slice 011 the knife-blade, and press it 
 between the folds of a handkerchief to dry 
 it. Moving it again upon the knife-blade, 
 place it upon a brick. Carefully place a 
 single crystal of iodine upon the phosphorus. 
 Some of the potential energy of chemical 
 separation wi^l be transformed into the 
 kinetic energy of heat. 
 
 224. Production of Heat. The 
 experiments just given illustrate 
 some of the methods by which other 
 forms of energy are transformed into 
 heat. The ignition of a common 
 
 FIG. 217. 
 
 friction-match illustrates the trans- 
 formation of mechanical energy and of chemical action 
 into heat. Such transformations are continually taking 
 
278 SCHOOL PHYSICS. 
 
 place, and the attention has only to be called to the 
 subject that they may be recognized. 
 
 (a) The fire in the lamp or stove or grate affords familiar illus- 
 tration of the transformation of chemical action into heat. The 
 heating of saws and other tools by use, and of carriage or car axles 
 when not properly lubricated ; the warming of hands by rubbing them 
 together ; the conversion of the energy of the electric current into heat 
 by the electric lamp ; the old process of striking fire with flint and 
 steel, are a few of the many illustrations that may be drawn from 
 common life. 
 
 Diffusion of Heat. 
 
 Experiment 165. Thrust an iron poker into the fire. The end of 
 the poker that is held in the hand soon grows warm. If it is not a 
 familiar fact that the rod has been heated through its whole length, 
 and that there is a gradual rise of the temperature of the successive 
 parts from the end held in the hand to the end that is in the fire, test 
 the rod for the acquisition of such information. Hold the hand over 
 the stove and it is warmed by the ascending current of heated air. 
 Hold the hand in front of the stove and, in some way that we shall 
 understand better by and by, it receives heat from the fire. 
 
 225. Diffusion of Heat. Heat is transferred from one 
 point to another in two ways, conduction and convection. 
 
 (a) It is often said that heat is transferred in a third way, viz., by 
 radiation. A heated body, like the sun, may communicate periodic 
 disturbances to a medium called the ether, and another body, like the 
 earth, may absorb these disturbances and be heated thereby. The 
 energy thus transmitted is often called radiant heat, although it is not 
 heat at all, simply radiant energy that may be transformed into heat 
 by absorption by ordinary matter. This so-called radiant heat will be 
 considered in the next chapter. 
 
 Conductivity of Solids. 
 
 Experiment 166. Turn up the four sides of a sheet of writing- 
 paper and, without cutting the corners, make a basin about 2 cm. 
 deep. Half fill the paper pan with water and place it on the top of a 
 hot stove. You can boil the water without burning the paper. 
 
 Experiment 167. Instead of the iron poker of Experiment 165, 
 use a glass rod or a wooden stick. The end in the fire may be melted 
 or burned without rendering the other end uncomfortably warm. 
 
PRODUCTION AND TRANSFERENCE OF HEAT, ETC. 279 
 
 Experiment 168. Put a silver and a German-silver spoon into the 
 same vessel of hot water. The handle of the former will become hot 
 much sooner than that of the latter. 
 
 Experiment 169. Place a bar of iron and a similar one of copper 
 end to end so as to be heated equally by the flame of a lamp. 
 Fasten small balls (or nails) by wax to the under surfaces of the bars 
 at equal distances apart. More balls will be melted from the copper 
 
 FIG. 'J18. 
 
 than from the iron. Give plenty of time and consider the number of 
 balls that are melted off, and not the promptness with which a ball or 
 two may fall at an early stage of the experiment. 
 
 Experiment 170. Modify Experiment 169, by providing two stout 
 wires of iron and of copper, each 40 or 50 cm. long. Twist them to- 
 gether for about 10 cm., and spread the untwisted parts so as to form 
 a fork with a twisted handle. Balance this fork on a coverless crayon 
 box, and place a lamp flame under the overhanging handle. After 
 several minutes, test the two metals with similar friction-matches and 
 ascertain the respective distances at which the matches will be ignited 
 by simple contact without rubbing. 
 
 226. Conduction is the mode by which heat is transmitted 
 from points of high temperature to points of low temperature 
 by passing from one particle to the next particle, or by which 
 it is transmitted to a distance by raising the temperature 
 of the intermediate particles without any sensible motion 
 of them. The conduction of the heat is very gradual and 
 as rapid through a crooked as through a straight bar. 
 
 (rt) The power of conducting heat is called thermal conductivity. 
 Some of the preceding experiments show that different substances 
 
280 
 
 SCHOOL PHYSICS. 
 
 have different conductivities, although part of the differences observed 
 may have been due to the facts that equal quantities of some sub- 
 stances require unequal additions of heat for equal increments of tem- 
 perature, and that some substances part with their heat by radiation 
 more rapidly than others. 
 
 (6) Among solids, metals are the best conductors both of heat and 
 of electricity. Owing to lack of continuity, powdered substances have 
 low conductivities, as have wood, leather, flannel, and organic sub- 
 stances generally. The relative thermal conductivities of some metals 
 are as follows : 
 
 Silver 100 
 
 Copper 74 
 
 Gold 53 
 
 Brass 24 
 
 Tin . 15 
 
 Iron 12 
 
 Lead 
 
 Platinum 8 
 
 German silver 6 
 
 Bismuth . . 2 
 
 Conductivity of Liquids. 
 
 Experiment 171. Fasten a piece of ice at the bottom of an ignition 
 tube. A loosely wound coil of soft wire that snugly fits the tube 
 will hold it in place. Cover the ice to the depth of several inches with 
 water. Hold the tube obliquely and apply the flame of a lamp below 
 the upper part of the water. The water there may be made to boil 
 without melting the ice below. Instead of using ice and water, pack 
 the tube full of moist snow if you can get it. 
 
 Experiment 172. Pass the tube of an air thermometer or of an 
 inverted mercury thermometer through a cork 
 in the neck of a funnel. Cover the thermom- 
 eter bulb to the depth of about half an inch 
 with water. Upon the water, pour a little sul- 
 phuric ether and ignite it. The thermometer 
 below will scarcely be affected, although the 
 water above may be boiling. Stir the water 
 and note the prompt movement of the ther- 
 mometer index. To prevent the downward 
 conduction of the heat by the funnel, the ether 
 may be placed in a small porcelain cup sup- 
 ported by a wire frame so that its bottom dips 
 into the water directly over the bulb. 
 
PRODUCTION AND TRANSFERENCE OF HEAT, ETC. 281 
 
 227. Conductivity of Fluids. Experiments 171 and 
 172 indicate that water has a very low conductivity, a 
 fact that applies to liquids generally. The one marked 
 exception to this rule te the liquid metal, mercury. The 
 conductivity of copper is about five hundred times that of 
 water. Gases have still less, if any, thermal conductivity. 
 
 Fluid Currents caused by Heat. 
 
 Experiment 173. Put a small quantity of oak filings or fine saw- 
 dust into a glass vessel of water. Heat the water by a lamp placed 
 below, and notice the liquid currents as indicated by the motion of. 
 the oak particles. 
 
 Experiment 174. With a lamp chimney or other large glass tube, 
 a perforated cork, two pieces of glass tubing 4 and 15 inches long 
 respectively, a bit of rubber tubing, a small 
 lamp or a candle, and two coverless crayon 
 boxes, arrange apparatus as shown in 
 Fig. 220. Partly fill the apparatus with 
 water, and add a small quantity of fine 
 paper raspings or of a paste made by moist- 
 ening some aniline dye with a drop of 
 water. Carefully heat the tube as shown 
 in the figure, and explain any observed 
 movement of the water. 
 
 Experiment 175. Cut a square of stiff 
 writing paper, 15 cm. on each edge, and 
 draw its diagonals. From the four corners, 
 cut the paper along the diagonals to within 
 1.5 cm. of the middle of the square. 
 From the corners, bring four alternate 
 paper tips together and thrust a pin through 
 
 them and the middle of the square and into the end of a penholder 
 or lead pencil. Hold the paper wind-wheel thus made over a stove 
 or metal plate that is very hot, the wooden handle being vertical 
 and above the paper. One of the components into which the force 
 of the ascending current of heated air is resolved sets the wheel in. 
 rotation. 
 
 FIG. 220. 
 
282 SCHOOL PHYSICS. 
 
 228. Convection. When a portion of a fluid is heated 
 above the temperature of the surrounding portions, it ex- 
 pands and thus becomes specifically lighter. It then rises, 
 while the cooler and heavier portions of the fluid rush in 
 from the sides and descend from higher points. In this 
 way, all of the fluid becomes heated. This mode of trans- 
 ferring heat by the mechanical motion of heated fluids is 
 called convection, and the currents thus established are 
 called convection currents. 
 
 (a) Convection currents are applied to the heating of houses, etc., 
 by hot-water pipes or hot-air furnaces, and constitute the basis of the 
 most common forms of house and mine ventilation, the draft of 
 chimneys, etc. The Gulf Stream and the trade-winds are grand con- 
 vection currents. 
 
 CLASSROOM EXERCISES. 
 
 1. Why are hot metal utensils commonly handled with cloth 
 " holders " ? 
 
 2. Why does oil-cloth on a cold floor feel colder to bare feet than 
 carpet does, both being at the same temperature ? 
 
 3. Is a good conductor of heat or a non-conductor preferable for 
 keeping a body warm ? For keeping it cool ? 
 
 4. Explain the non-conducting character of hollow walls, double 
 doors, and double windows. 
 
 5. Why is water heated more quickly when placed over a fire than 
 when placed under one ? 
 
 6. Fur and clothing of loose texture enclose much air in their 
 structure. What bearing, if any,' has this on their warmth? 
 
 7. Why are tin tea-kettles and boilers often given copper bottoms V 
 
 8. Draw a diagram illustrating the heating of a house by hot- 
 water pipes. Explain your diagram. 
 
 9. Draw a diagram showing how a house is supplied with hot 
 water from a boiler connected with the kitchen range or stove. 
 Explain your diagram. 
 
 10. Draw a diagram showing how a house is heated by a hot-air 
 furnace, representing the furnace, cold-air duct, and hot-air pipes. 
 Explain your diagram. 
 
EFFECTS OF HEAT. 283 
 
 III. EFFECTS OF HEAT. 
 
 229. Expansion is the first visible effect of heat upon 
 bodies. 
 
 Expansion of Solids. 
 
 Experiment 176. With a hack-saw, cut a piece from one side of a 
 large link of an iron chain, and force the ends of the opened link 
 slightly together so that the small piece may be pressed hard enough 
 to hold it in place. Heat the opposite side of the link. The metal 
 will expand and the piece will fall out of its place. 
 
 Experiment 177. Grip one end of an iron rod about 1 cm. in 
 diameter and 30 cm. long so that the rod shall be horizontal. Pass 
 a pivot through the hole near the end of the meter stick used in 
 Exercise 8, p. 126, and into a board. The iron rod should lightly 
 touch the vertical edge of the stick a little below the level of the 
 pivot. Heat the iron rod. The motion of the lower end of the 
 meter stick indicates that the rod is increasing in length. 
 
 Experiment 178. Get a straight, compound bar consisting of a 
 strip of brass and a strip of iron, each 2 or 3 mm. thick, 2 cm. 
 wide, and about 20 cm. long, 
 
 bound face to face with wire, or tX . . J j J J tt'j 
 riveted together at intervals of 
 about 2.5 cm. Move the bar back 
 
 and forth in a hot flame so that the two metals may be heated in 
 their whole length and equally. As the bar becomes curved, notice 
 which of the metals has expanded the more. Cool the bar to the 
 temperature of the room and examine its form. Bury it for a few 
 minutes in a freezing mixture of ice and salt, and again examine its 
 form. 
 
 230. Expansion of Solids. Almost without exception, 
 solids expand when heated and contract when cooled, the 
 amount of expansion varying with the increase of the 
 temperature and the nature of the substance. 
 
 (a) The energy of the expansion and contraction of solids is very 
 great and enables many industrial applications. 
 
284 SCHOOL PHYSICS. 
 
 Expansion of Fluids. 
 
 Experiment 179. Xearly fill a Florence flask with water and place 
 it upon the ring of a retort stand. Support a long straw by a thread 
 tied near one end, so that a light weight hung from the short arm 
 may float upon the liquid surface in the neck of the flask and support 
 the long arm of the straw in a horizontal position. Heat the water 
 in the flask. Its expansion will be shown by the motion of the long 
 arm of the straw. 
 
 Experiment 180. Close by fusion one end of each of three similar 
 glass tubes, 15 or 20 cm. long. Put water into one, alcohol into 
 another, and glycerin into the third, using equal quantities of the 
 liquids. Place the three tubes in a vessel of hot water and notice 
 that the liquids expand unequally. 
 
 Experiment 181. Partly fill a toy balloon with air and tightly tie 
 the opening. Hold the balloon over a hot stove. The expanded air 
 fills the balloon. (See 168.) 
 
 Experiment 182. Close a bottle with a cork through which passes 
 a glass tube of small bore and about 30 cm. long. Warm the bottle 
 between the hands, and place a drop of ink at the end of the tube. 
 As the air in the bottle contracts, the ink will move down the tube, 
 forming a liquid index. By heating or cooling the bottle, the index 
 may be made to move up or down. 
 
 Experiment 183. To a Florence flask, fit air-tight a delivery-tube 
 that terminates under water as shown in Fig. 22. Heat the air in 
 the flask, and, in a graduated test-tube, " collect over water " the air 
 driven from the flask. Do not let the flask cool until the delivery- 
 tube has been removed from the water. 
 
 Experiment 184. Fill two Florence flasks of the same size and 
 shape, one with air, and the other with coal-gas. Arrange them as 
 described in Experiment 183, and immerse them to the same depth 
 in hot water, collecting separately the gases driven out by expansion. 
 Compare the volume of the gases thus collected. 
 
 231. Expansion of Fluids. As illustrated by the ex- 
 periments just given, liquids and gases expand when 
 heated, and contract when cooled, the amount of expan- 
 
EFFECTS OF HEAT. 285 
 
 sion varying with the increase of temperature. In the 
 case of liquids, the amount of expansion also varies with 
 the nature of the substance. The rate of expansion is 
 practically the same for all gases, and greater than it i& 
 for solids or liquids. 
 
 (a) Substances that crystallize on cooling, expand as they approach 
 the temperature of solidification ; i.e., a given quantity of matter 
 occupies more space when it has a crystalline structure than it does 
 when it has a liquid form. Ice is a good example of such a sub- 
 stance. 
 
 Experiment 185. Pour recently boiled water into the apparatus 
 of Experiment 182, until the tube is half full. Pack the bottle in 
 a mixture of salt and finely broken ice. Observe the liquid level 
 in the tube. The water contracts, then expands, then freezes and 
 expands. 
 
 232. Coefficient of Expansion. The elongation per unit 
 of length -for each degree that the temperature is raised 
 above 0, is called the coefficient of linear expansion. Simi- 
 larly, the increase in volume per unit of volume for a change 
 of one degree of temperature, is called the coefficient of 
 cubical expansion. It is generally determined by dividing 
 the increment of volume by the original volume as above 
 indicated. It may be taken as three times the coefficient 
 of linear expansion. 
 
 (a) For solids, the coefficient is nearly constant for different tem- 
 peratures. For liquids, the coefficient is more variable. That of 
 mercury, for example, is regular between 36 and 100, but for 
 higher temperatures it gradually increases in value. Water exhibits 
 the most remarkable variation from regularity. As water is heated 
 from to 4, it gradually contracts, so that 4 is the temperature of 
 maximum density for water. As the temperature is raised above 4, 
 the water expands, slightly at first, but more and more rapidly as it 
 approaches the boiling point. For gases under constant pressure, the 
 coeflacient is nearly constant, with a value of -fa or 0.00366. (See 
 
286 SCHOOL PHYSICS. 
 
 222.) For solids, the linear expansion is the more conveniently 
 measured ; for fluids, the -cubical. 
 
 CLASSROOM EXERCISES. 
 
 1. Why do wheelwrights heat the tires of wheels before setting 
 them? 
 
 2. The bulging walls of buildings are often straightened by pass- 
 ing iron rods from one wall to the opposite wall, placing nuts at 
 the ends of the rods, heating the rods, and tightening up the nuts. 
 Explain. 
 
 3. Why is at least one end of a long iron bridge generally sup- 
 ported upon rollers ? 
 
 4. Why is a gallon of alcohol worth more in cold than in warm 
 weather, the market price being the same? 
 
 5. Explain the draft of a lamp chimney. 
 
 6. What is the temperature of the surface water of a pond that 
 is just about to freeze? Of the water at the bottom of the pond? 
 
 7. A certain quantity of gas is measured at 0. To what tempera- 
 ture must it be heated, the pressure being constant, so that its volume 
 may be doubled ? 
 
 8. A mass of air at 0> and under an atmospheric pressure of 30 
 inches, measures 100 cubic inches; what will be its volume at 40, 
 under a pressure of 28 inches? 
 
 Solution : First suppose the pressure to change from 30 inches 
 to 28 inches. The air will expand, the two volumes being in the 
 ratio of 28 to 30 ( 171). 100 cu. in. x f f = 107} cu. in. Next, 
 suppose the temperature to change from to 40. The expansion 
 will be $$ of the volume at ; the volume of the air at 40 will 
 be l/^ times its volume at 0. 
 
 107^ x !/,% = 122fff. Am. 122fff cu. in. 
 
 Alternate Solution : 28 : 30 1 
 
 273 : 273 + 40 j : 
 
 9. At 150, what will be the volume of a gas that measures 10 cu. 
 cm. at 15? 
 
 273 + 15 : 273 + 150 : : 10 : x. Ans. 14.69 cu. cm. 
 
 10. If 100 cu. cm. of hydrogen is measured at 100, what will be 
 the volume of the gas at - 100? 
 
 273 + 100 : 273 - 100 : : 100 : x. Ans. 46.37 cu. cm. 
 
 11. A liter of air is measured at and 760 mm. What volume 
 will it occupy at 740 mm. and 15.5? 
 
EFFECTS OF HEAT. 287 
 
 740- 760 + ! :: 1,000 :*. Ans. 1,085.34 cu. cm. 
 
 12. A rubber balloon that has an easy capacity of a liter contains 
 900 cu. cm. of oxygen at 0. What will be the volume of the oxygen 
 when it is heated to 30? Ans. 998.9 cu. cm. 
 
 13. A certain weight of air measures a liter at 0. How much will 
 the air expand on being heated to 100? Ans. 366.3 cu. cm. 
 
 14. A gas has its temperature raised from 15 to 50. At the latter 
 temperature, it measures 15 liters. What was its original volume ? 
 
 Ans. 13,374.6 cu. cm. 
 
 15. A gas measures 98 cu. cm. at 185 F. W r hat will it measure at 
 10 C. under the same pressure? Ans. 77.47 cu. cm. 
 
 16. A certain quantity of gas measures 155 cu. cm. at 10, and 
 under a barometric pressure of 530 mm. What will be the volume at 
 18.7, and under a barometric pressure of 590 mm. ? 
 
 17. A gallon of air (231 cubic inches) is heated, under constant 
 pressure, from to 60. What is the volume of the air at the 
 latter temperature? Ans. 281.77 cu. in. 
 
 18. The bulb and tube of an air thermometer were filled with boil- 
 ing water. The bulb being placed in water that contained ice, the 
 level of the water in the tube fell for a time and then rose. Explain. 
 At what temperature did the contraction cease and the expansion 
 begin ? 
 
 Liquefaction. 
 
 Experiment 186. Place snow or finely broken ice and a thermom- 
 eter in a vessel of watea The thermometer will fall to the freezing- 
 point, but no further. Apply heat, so as to melt the ice very slowly, 
 and stir the mixture constantly. The temperature does not rise until 
 all of the ice is melted, or it rises so little that we may feel sure that 
 there would be no rise if each particle of water could be kept in 
 contact with a particle of ice. 
 
 Experiment 187. Put a little water into a beaker, and determine 
 its temperature. Add a small quantity of sodium sulphate, and stir 
 with a thermometer. Notice the fall of temperature during the 
 process of solution. Repeat Experiment 26. 
 
 233. The Liquefaction of a solid is effected by fusion or 
 by solution. In either case heat is required to overcome 
 
288 SCHOOL PHYSICS. 
 
 the force of cohesion, and disappears in the process. 
 Sometimes the absorption of heat involved in the lique- 
 faction is disguised by the evolution of heat due to 
 chemical action between the substances used. 
 
 () The action of freezing-mixtures, e.g., one weight of salt and 
 two or three of snow or pounded ice, depends upon the fact that heat 
 is absorbed or disappears in the solution of solids. 
 
 Solidification. 
 
 Experiment 188. Place a thermometer in a small glass vessel 
 containing water at 30, and a second thermometer in a large bath of 
 mercury at 10. Immerse the glass vessel in the mercury. The tem- 
 perature of the water gradually. falls to 0, when the water begins to 
 freeze, and its temperature becomes constant. The temperature of 
 the mercury rises while the water is freezing. 
 
 234. Solidification. When a liquid changes to a solid, 
 the energy that was employed in maintaining the charac- 
 teristic freedom of molecular motion against the force of 
 cohesion is released and appears as heat. The amount 
 of heat that reappears during solidification is the same as 
 that which disappears during liquefaction. 
 
 235. Laws of Fusion. It has been found by experi- 
 ment that the following statements are true : 
 
 (1) A solid begins to melt at a certain temperature that 
 is invariable for a given substance under constant pressure. 
 This temperature is called the melting-point of that sub- 
 stance. In cooling, such liquids solidify at the melting- 
 point. 
 
 (2) TJie temperature of a melting solid or of a solidify- 
 ing liquid remains at the melting-point until the change 
 of condition is completed. 
 
EFFECTS OF HEAT. 
 
 289 
 
 (3) Substances that contract on melting have their melt- 
 ing-points loivered by pressure, and vice versa. 
 
 (a) It is possible to reduce the temperature of a liquid below the 
 melting-point without solidification, but when solidification does 
 begin, the temperature quickly rises to the melting-point. 
 
 Vaporization. 
 
 Experiment 189. Pour a few drops of ether upon the bulb of a 
 thermometer, or into the palm of the hand, and notice the rapid fall 
 of temperature. See that there is no flame near enough to ignite the 
 inflammable vapor. 
 
 Experiment 190. Wet a block of wood and place a watch-crystal 
 upon it. A film of water may be seen under the central part of the 
 glass. Half fill the crystal with sulphuric ether, and evaporate it 
 rapidly by blowing over its surface a stream of air from a small 
 bellows. So much heat disappears that the watch-crystal is frozen to 
 the wooden block. 
 
 Experiment 191. In a vessel of sulphuric ether, place a test-tube 
 containing water. Force a current of air through the ether. (Fig. 
 222.) Rapid evaporation is thus produced and, in a few minutes, 
 the water is frozen. See 
 Exercise 2, page 198. 
 
 236. Vaporization is 
 the process of converting 
 a substance, especially a 
 liquid, into a vapor. 
 This change of con- 
 dition may be effected 
 by an addition of heat, 
 or by a diminution of 
 pressure, or both. When 
 it takes place slowly and 
 quietly, the process is 
 called evaporation. When it takes place so rapidly that 
 19 
 
 FIG. 
 
290 SCHOOL PHYSICS. 
 
 the liquid mass is visibly agitated by the formation of 
 vapor bubbles within it, the process is called ebullition^ 
 The heat that produces the change of condition disappears 
 in the process. 
 
 237. Condensation. The liquefaction of gases and va- 
 pors is effected by a withdrawal of heat or by an increase 
 of pressure, or both. In either case, the energy that was 
 employed in maintaining the aeriform condition is released 
 and appears as heat. The amount of heat that reappears 
 during liquefaction is the same as that which disappears 
 during vaporization. 
 
 238. Laws of Evaporation. Experiments show that 
 the rapidity of evaporation 
 
 (1) Increases with a rise of temperature. 
 
 (2) Increases with an increase of the free surface of the 
 liquid. 
 
 (3) Increases as the atmospheric or other pressure upon 
 the liquid decreases, it being very rapid in a vacuum. 
 
 (4) Increases with the rapidity of change of the atmos- 
 phere in contact with the liquid. 
 
 (5) Decreases with an increase of the vapor of the same 
 substance in the atmosphere in contact with the liquid. 
 
 (a) Water may be frozen by its own rapid evaporation under a 
 low pressure. When liquefied carbon dioxide is relieved from pres- 
 sure, it evaporates very rapidly ; the correspondingly rapid absorption 
 of heat reduces the temperature to about 90, and freezes much of the 
 gas to a snow-like solid. By evaporating liquefied hydrogen, a tem- 
 perature of 243 has been obtained. 
 
 239. Dew-Point. A space is said to be in a state of 
 saturation with respect to a vapor when it contains as 
 
EFFECTS OF HEAT. 291 
 
 much of that vapor as it can hold at that temperature. 
 The vapor then has the maximum elastic pressure for that 
 temperature. The quantity of vapor required for satura- 
 tion increases rapidly with the temperature. When a 
 body of moist air is cooled, the point of saturation is 
 gradually approached; when it has been reached, any fur- 
 ther cooling causes a condensation of the vapor to dew, 
 fog, or cloud, according to circumstances. The tempera- 
 ture at ivhich this condensation occurs is called the dew- 
 point. An instrument for determining the ratio between 
 the actual amount of water vapor present in the air, and 
 that required for saturation is called a hygrometer. The 
 branch of physics that relates to the determination of the 
 humidity of the atmosphere is called hygrometry. 
 
 (a) The ratio between the amount of watery vapor present in the 
 air and the quantity that is required for saturation at the temperature 
 of observation is called the relative humidity. This ratio is generally 
 expressed in percentages, as 75 per cent, or 0.75. 
 
 Boiling-Point. 
 
 Experiment 192. In a beaker half full of water, place a thermom- 
 eter and a test-tube half filled with ether. Heat the water. When 
 the thermometer shows a temperature of about 60, 
 the ether will begin to boil. The water will not boil 
 until the temperature rises to 100. The temperature 
 will not rise beyond this point. 
 
 Experiment 193. Place a thermometer in a metal 
 dish half filled with water, and place a lamp beneath 
 the dish. Be careful that the bulb of the thermometer 
 is covered with water, and that it is not less than FIG. 223. 
 4 or 5 cm. above the bottom of the vessel. Notice the 
 rise of the thermometer. Soon the formation and condensation of 
 minute steam-bubbles in the liquid will produce the peculiar sound 
 known as singing or simmering, the well-known herald of ebullition. 
 
292 SCHOOL PHYSICS. 
 
 Finally, the water becomes heated throughout, the bubbles increase 
 in number, grow larger as they ascend, burst at the surface, and 
 disappear in the atmosphere. Notice that the temperature remains 
 stationary after ebullition begins. 
 
 Experiment 194. When the water used in Experiment 193 has 
 partly cooled, dissolve in it as much common salt as possible, heat it 
 again, and notice that it does not boil until the temperature is notice- 
 ably higher than before. 
 
 240. Laws of Ebullition. It has been found by experi- 
 ment that the following statements are true : 
 
 (1) A liquid begins to boil at a certain temperature that is 
 invariable for a given substance under constant conditions. 
 This temperature is called the boiling-point of that substance. 
 In cooling, such vapors liquefy at the boiling-point. 
 
 (2) The temperature of the boiling liquid or of the lique- 
 fying vapor remains at the boiling-point until the change of 
 condition is completed. 
 
 (3) An increase of pressure raises the boiling-point, and 
 vice versa. 
 
 (4) The boiling-point is affected by the character of the 
 surface of the vessel containing the liquid, an effect of 
 cohesion. 
 
 (5) The solution of a salt in a liquid raises its boiling- 
 point, additional energy being required to overcome the cohe- 
 sion involved in the solution. 
 
 (a) It is possible to heat water above its true boiling-point without 
 ebullition, by confining the steam and thus increasing the pressure, 
 but when the pressure is relieved, the superheated vapor immediately 
 expands and its temperature is reduced. Hence, in determinations 
 of the boiling-point, the thermometer is never immersed in the liquid 
 but in the vapor just above it. Strictly speaking, the boiling-point is 
 the temperature at which the elastic force of the vapor is equal to the pres- 
 sure of the atmosphere. 
 
EFFECTS OF HEAT. 
 
 293 
 
 (&) The temperature of the water in a steam-boiler is higher than 
 100 whenever the pressure (recorded by the gauge) is greater than 
 one atmosphere. At ten atmospheres, the temperature is about 180. 
 Owing to the effect of atmospheric pressure upon the boiling-point of 
 water, the latter may be used in the determination of altitudes above 
 the sea-level. A thermometrical barometer for this purpose consists 
 of a portable apparatus for boiling water, and a very sensitive ther- 
 mometer, and is called a hypsometer. 
 
 (c) A drop of water on a smooth metal surface at a high tempera- 
 ture may rest upon a cushion of its own vapor, without coming into 
 contact with the metal. A liquid in this spheroidal state is at a tem- 
 perature below its boiling-point. When the metal cools so that the 
 vapor pressure will not support the globule, the liquid comes into 
 contact with the metal surface, and is converted into steam with great 
 rapidity. Many boiler explosions are due to such causes. 
 
 (d) Whenever the boiling-point of a substance is lower than its 
 melting-point, the substance vaporizes directly without previous lique- 
 faction. Such a change is called sublimation. The pressure at which 
 the melting-point and the boiling-point of any substance coincide is 
 called the fusing-point pressure. If the fusing-point pressure of a solid 
 substance is greater than the atmospheric pressure, it will sublime 
 when heated unless the pressure upon it is increased. Carbon dioxide 
 sublimes under any pressure less than three atmospheres. Conversely, 
 if the fusing-point pressure is less than the atmospheric pressure, sub- 
 limation may be secured by reducing the pressure. Iodine sublimes 
 at pressures less than 
 
 90 mm. of mercury, and* 
 ice can not be melted at 
 a pressure of less than 
 4.6 mm. Such sub- 
 stances evaporate at tem- 
 peratures below their 
 melting-points. 
 
 Distillation. 
 Experiment 195. 
 Partly fill with strong 
 brine a Florence flask the 
 cork of which carries a 
 delivery-tube and a ther- 
 
 FIG 9 
 
294 SCHOOL PHYSICS. 
 
 mometer. Pass the delivery-tube through a " water jacket/' J, kept 
 cool substantially as shown in Fig. 224. Heat the liquid in the flask 
 until it just boils, and taste the distilled water that collects in R. 
 
 Experiment 196. Place a teaspoonful of alcohol in a saucer and 
 apply a flame; the alcohol burns. Mix 50 cu. cm. of alcohol and 
 50 cu. cm. of water. Test a teaspoonful of the mixture as before ; it 
 does not burn. Place the rest of the mixture in the flask of the appa- 
 ratus described in Experiment 195, and heat the mixture to about 
 90 C. See if the liquid that collects in R will burn. If it will not/ 
 empty the contents of R into F, and interpose between F and / a 
 bottle that is partly immersed in a bath of boiling water and repeat 
 the experiment. 
 
 241. Distillation is an application of volatilization and 
 subsequent condensation for various purposes, such as the 
 extraction of the essential principle of a substance from 
 the liquid in which it has been macerated. 
 
 (a) The most common distillation process consists in placing the 
 distillable liquid in a metal retort, generally made of copper. When 
 heat is applied, vapors rise into the movable head of the retort, the 
 neck of which is connected with a spiral tube called the "worm." 
 The worm being kept cool by flowing water, the vapors of the more 
 easily volatile constituents of the liquid pass into it, are condensed, 
 and make their exit as a liquid, while the solid and non-volatile liquid 
 constituents remain behind in the retort. The whole apparatus is 
 called a " still." 
 
 (b) Fractional distillation is the process of separating liquids that 
 have different boiling-points. The mixture is heated in a retort that 
 allows constant observation of the temperature, and the distillates 
 obtained between certain temperatures are collected separately. The 
 most volatile constituent of the mixture will be found chiefly in the 
 " fractions " first collected. By redistillation of the first fraction, this 
 more volatile liquid may be obtained in comparative or absolute 
 purity. 
 
EFFECTS OF HEAT. 295 
 
 CLASSROOM EXERCISES. 
 
 1. At high elevations, water boils at temperatures too low for ordi- 
 nary culinary purposes. How may persons living there heat water 
 sufficiently for boiling meats and vegetables ? 
 
 2. For the extraction of gelatine from bones by the action of hot 
 water, a higher temperature than 100 is required. How may the 
 water be heated sufficiently for such purposes ? 
 
 3. In sugar refining, it is desirable to evaporate the saccharine 
 liquid at a temperature considerably lower than 100. Indicate a 
 way in which this may be done. 
 
 4. Under ordinary pressure can ice be made warmer than ? 
 
 5. Solid type-metal floats on melted type-metal. Does melted 
 type-metal expand or contract on solidifying? What effect has this 
 quality upon the use of the metal in making type ? 
 
 6. At the summit of Mount Washington, water boils at a tempera- 
 ture of about 94 ; at the summit of Mont Blanc, at 86 ; at the level 
 of the Dead Sea, at 101. Explain these differences in the boiling- 
 points of water. 
 
 7. If the smooth, dry surfaces of two pieces of ice are pressed 
 together for a few seconds, the pieces will be frozen together when the 
 pressure is removed. Explain this result, which is called regelation. 
 
 8. When the air of a room is artificially heated, the temperature 
 may become considerably higher than the dew-point of the air in the 
 room. Under such circumstances, the rapid evaporation of moisture 
 from the person causes a disagreeable sensation in the lips, tongue, 
 skin, etc. How may sucfi results be avoided ? 
 
 9. Sulphur begins to melt at 115. At what temperature does 
 melted sulphur begin to solidify ? 
 
 10. How may sea-water be made fit for drinking? 
 
 11. A drop of water may be placed on a very hot platinum plate, 
 and the plate so held that a candle-flame may be seen between the 
 water and the plate. Explain. 
 
 12. How may a thermometer, a fire, and a dish of water, be used to 
 determine the elevation of a place above the sea-level ? 
 
 13. Water standing in a slightly porous vessel acquires a tempera- 
 ture lower than that of the surrounding atmosphere. Explain. 
 
 14. The temperature of islands and of the borders of the ocean 
 and great lakes is more equable than that of inland regions of the 
 same latitude. Point out the dependence of this fact upon the physi- 
 cal properties of water. 
 
296 SCHOOL PHYSICS. 
 
 15. The inner surface of the upper part of a bottle that contains 
 iodine or gum-camphor is generally covered with minute crystals. 
 What conclusion concerning the physical properties of iodine and 
 camphor do you draw from this fact ? 
 
 16. What effect has the humidity of the atmosphere upon the 
 dew-point ? 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Two air thermometers; kerosene; hy- 
 drometer jar with perforations and jacket; candle; expansion appa- 
 ratus as described below ; one of the thin, nickel-plated, brass vessels, 
 larger at the top than at the bottom, such as are sold at hardware 
 stores as lemonade " shakers." 
 
 1. Connect a small glass funnel by rubber tubing to the stem of an 
 air thermometer. (Fig. 224.) The diameter of the bulb should be 
 4 or 5 cm. and the bore of the stem, 3 or 4 mm. Pour water into the 
 funnel and work it down with a wire until the bulb is full and the 
 liquid stands at the height of about 2 cm. in the stem. Similarly, fill 
 a like bulb with kerosene. Immerse both bulbs in water almost boil- 
 ing-hot. Notice the liquid levels in the stems at the instant of im- 
 mersion and a few minutes later. Record all of your conclusions from 
 the observed phenomena, not omitting to state what was measured by 
 the rise of the liquids in the stems. 
 
 2. Drill a hole through the wall of a tall hydrometer jar near its 
 top and another near the bottom. Close the holes with perforated 
 corks carrying thermometers, so that the bulbs of the thermometers 
 shall be inside the jar. Fill the jar with ice-cold water and notice 
 that the thermometers give like readings. As the water is warmed 
 to the temperature of the room, observe the thermometers, record your 
 observations, and explain any change in the thermometric readings, 
 and any difference between the readings of the two thermometers. 
 
 3. Around the middle of the hydrometer jar mentioned in Exer- 
 cise 2, place a jacket and fill the jacket with a mixture of finely 
 broken ice and salt. Record and explain changes in thermometric 
 .readings as before. 
 
 4. On a day when the doors and windows are closed, ascertain the 
 temperature of the laboratory near the ceiling and near the floor. 
 Record your observations and explain any difference that you find. 
 
 5. On a day when the air in the laboratory is warmer than that 
 outside, stand an outer door slightly ajar, and with a candle flame, 
 
EFFECTS OF HEAT. 
 
 297 
 
 seek for inward and outward air-currents. If you find them, explain 
 their production and show that they have an important relation to 
 artificial ventilation. 
 
 6. Half fill a Florence flask with water. Boil the water until the 
 steam drives the air from the upper part of the flask. Cork the flask so 
 that no air can enter, and quickly remove the lamp. Support the 
 inverted flask upon the ring of a retort stand and place a pan below 
 it. By this time, the water will have stopped boiling. Pour cold 
 water upon the flask. Record and explain the consequent phe- 
 nomena. Without again heating the water, repeat the drenching 
 several times and finally immerse the flask in cool water. 
 
 7. Get a cylindrical tube, cd (Fig. 225), made of " galvanized " iron 
 or other sheet metal. It should be about 2.5 cm. in diameter and about 
 60 cm. long. Near each end of the tube, insert a tube about 6 mm. in 
 diameter and about 3 cm. long, as shown at a and i. At the middle of 
 the main tube, insert a tube about 1.5 cm. in diameter and about 1 cm. 
 long, as shown at e. Get a brass tube about 6 mm. in diameter and 
 about 6 mm. longer than the tube, cd. Solder a fine steel wire in a 
 
 FIG. 225. 
 
 diametral position across one end of the brass tube. Accurately 
 measure the length of the brass tube and place that tube inside the 
 larger tube so that it shall be supported by short perforated corks 
 that close the ends of the latter. The end that carries the steel wire 
 should be at the end of the jacket marked c. Upon a baseboard 
 about 1 m. long and 15 cm. wide, erect five posts, s, x, m, n and w. As 
 m and n are to carry the brass tube and its jacket, they have V-shaped 
 notches at their upper ends ; m is made a few millimeters longer than 
 n, so that the water of condensation will run out at i. A common flat- 
 headed screw is set in the vertical face of w so that, when the jacket is 
 in position, the end of the brass tube will rest against the head of 
 the screw. The distance between w and x is such that the latter may 
 carry a right-angled lever, I, with its short arm resting in a vertical 
 
298 SCHOOL PHYSICS. 
 
 position against the wire soldered to the end of the brass tube. This 
 lever may be made of a tapering piece of wood about 1.5 cm. square 
 
 near the fulcrum end. A " machine " 
 screw set into the face of x makes a 
 good fulcrum. The short arm of 
 the lever should be faced with a 
 metal strip, the free surface of which 
 lies in a vertical line through the 
 center of the fulcrum when the long 
 arm is horizontal. A metal casting 
 of the shape indicated by Fig. 226, 
 
 Fi 226 t ~" J * S Desirable f r carrying the index- 
 
 arm of the lever. The lever should 
 turn upon the fulcrum screw by its own weight but without looseness. 
 The post, s, carries a millimeter scale over which the long arm of the 
 lever moves. The large tube may be kept from turning upon its axis 
 by a peg inserted in x, to which the tube at a may be tied. 
 
 Place the large tube in position. Adjust the brass tube so that it 
 projects about 3 mm. at each end and so that the steel wire is hori- 
 zontal. When the short arm of the bent lever rests against the steel 
 wire, adjust the screw in w until the long arm of the lever is hori- 
 zontal. Pass the bulb of a thermometer through a perforated cork 
 that closes the short tube at e; do not let it touch the brass tube. 
 Place a tumbler below the exit tube at i. Connect the inlet tube 
 at a, by a piece of rubber tubing 75 or 80 cm. long, to the boiler 
 described in Exercise 3, page 275, and shield the adjusted apparatus 
 from the heat of the lamp and boiler. Then measure the horizontal 
 distance from the center of the fulcrum screw to the edge of the 
 millimeter scale from which readings are to be taken, and the verti- 
 cal distance from the center of the same screw to the steel wire at 
 the end of the brass tube, and find the ratio between the two dis- 
 tances. This ratio should be not less than 20. Note the reading of 
 the scale and the temperature inside the jacket. Generate steam in the 
 boiler and let it flow through the jacket for a few minutes after the 
 mercury has ceased to rise in the thermometer. When the movement 
 of the long arm of the lever ceases, take the readings of the millimeter 
 scale, the thermometer, and the barometer. Test the accuracy of the 
 thermometric reading by the temperature as computed from the boil- 
 ing-point of water at the observed atmospheric pressure. Detach the 
 rubber tube at a and allow the apparatus to cool. Press the brass 
 
THE MEASUREMENT OF HEAT. 299 
 
 tube against the head of the screw in w and see if the index returns 
 to its original position, as it should. From the data obtained, calcu- 
 late the coefficients of linear and cubical expansion for brass. 
 
 Represent the actual elongation of the bar by e ; the temperature 
 observed at the beginning of the experiment by t ; the highest tem- 
 perature by t' ; the length of the brass tube before heating by I; 
 and the coefficient of linear expansion by k. Then we have, by 
 definition : 
 
 * = (t'-t)i' whence e = k (i '~ lm 
 
 This last algebraic expression shows why k is called a coefficient. 
 
 8. Determine the boiling-point of a saturated solution of saltpeter. 
 
 9. Put a little water at the temperature of the laboratory into a 
 nickel-plated cup, the outer surface of which should be brightly 
 polished. Breathe upon the polished surface, and notice that the 
 moisture-film is evanescent. Place the bulb of a thermometer in 
 the water and add ice. Stir the mixture continually. Note the 
 temperature of the cooling water at the moment when the moisture- 
 film clearly appears on the outer surface of the cup at a point that 
 cannot be affected by your breath. K the ice is not all melted, 
 remove the residue from the cup. As the water slowly warms, note 
 the temperature at which the moisture-film begins to disappear. 
 Take the mean of the two observed temperatures and call it the 
 "dew-point." To your other records, add your observation of the 
 weather and the out-door temperature. 
 
 IV, THE MEASUREMENT OF HEAT. 
 
 242. Calorimetry is the process of measuring the 
 amount of heat that a body absorbs or gives out in 
 passing through a change of temperature or of physical 
 condition. 
 
 243. A Thermal Unit, or a heat-unit, is the quantity 
 of heat required to raise the temperature of unit mass of 
 water one degree. The unit most commonly used is the 
 
300 SCHOOL PHYSICS. 
 
 quantity of heat required to raise the temperature of one 
 gram of water from to 1. This water-gram-degree unit 
 is called a therm, or a small calory. 
 
 (a) A large calory is the quantity of heat required to raise the 
 temperature of a kilogram of water from to 1. Unless otherwise 
 specified, the calory mentioned in this book is the small calory. 
 
 244. Latent Heat. In considering changes of condition 
 of matter, we have spoken of the disappearance and re- 
 appearance of heat. When heat thus disappears, molec- 
 ular kinetic energy is transformed into the potential form ; 
 when it reappears, the reverse transformation takes place. 
 Because this molecular kinetic energy affects temperature, 
 it is called sensible heat. Because this molecular potential 
 energy does not affect temperature, it is called latent heat. 
 
 (a) So much of the added heat as is used to increase the rapidity 
 of molecular motions is kinetic and appears as sensible heat. So 
 much of it as is used to oppose cohesion (disgregation) and to 
 overcome pressure becomes potential, and disappears as latent heat. 
 When ether evaporates, the potential energy needed to establish the 
 aeriform condition is obtained by the transformation of kinetic energy 
 and at the expense thereof; hence, the disappearance of sensible heat, 
 or the fall of temperature. When steam is condensed, the potential 
 energy that is no longer required to maintain the aeriform condition 
 is transformed into kinetic energy; hence, the increase of sensible 
 heat. These terms, " sensible " and " latent," are reminiscences of the 
 old theory that heat is a kind of matter. 
 
 Experiment 197. Add a kilogram of finely broken ice (0) to a 
 kilogram of water at 80. The ice will melt, and the temperature of 
 the two kilograms of water will be about 0. The 80,000 calories 
 given out by the hot water were used in simply melting the ice. 
 
 245. The Latent Heat of Fusion of a substance is the 
 quantity of heat that is required to melt one gram of the 
 substance without raising its temperature ; i.e., the quantity 
 
THE MEASUREMENT OF HEAT. 301 
 
 of heat that is expended in the molecular work involved 
 in the change from the solid to the liquid condition. 
 The latent heat of fusion of ice is about eighty calories. 
 Ice at + latent heat of fusion = water at 0. 
 
 (a) From the above statement it necessarily follows that the heat 
 required to melt any weight of ice would warm 80 times that weight 
 of water one degree, or the same weight of water 80 degrees, provided 
 there was no change of physical condition. 
 
 Experiment 198. To the end of the delivery- tube of a Florence 
 flask containing water, attach a " trap " like that shown in Fig. 227, 
 so that the water that condenses in the delivery-tube may be retained 
 in the trap. (Instead of using the trap, th'e delivery-tube may be kept 
 hot by a steam-jacket, for which purpose the apparatus shown in Fig. 
 224 or Fig. 225 may be easily adapted.) Boil the water, and when 
 steam passes rapidly from a, the lower tube of the trap, dip a into a 
 beaker of known weight and containing water of known 
 weight and temperature. The temperature of the water in 
 the beaker should be considerably lower than that of the room, 
 and the end of the tube that leads steam from the trap to the 
 beaker should not dip into the w r ater so much that the con- 
 densation of the steam may not be plainly heard. The beaker 
 should be covered with a piece of cardboard, perforated for 
 the admission of the tube, a, and of the thermometer, and 
 should be shielded from the heat of the lamp and flask. 
 After the flow of steam has been continued for some time, 
 remove the beaker, stir its contents with the thermometer FIG. 
 
 227 
 
 thoroughly, and take the temperature quickly but carefully. 
 Ascertain the exact increase in the weight of the water in the 
 beaker, and compute the amount of heat derived from the conden- 
 sation of each gram of steam. Suppose that at the beginning of the 
 experiment the water in the beaker weighed 400 g., and had a tem- 
 perature of 0, and that at the end of the experiment the weight 
 ,was 420 g., and the temperature 30. The 400 g. of water received 
 12,000 calories that came from the 20 g. of steam. In cooling from 
 100 to 30, the condensed steam parted with 1,400 calories. The 
 remaining 10,600 calories came from the latent heat of the steam ; 
 i.e., each gram of steam at 100 gave out 530 calories in condensing 
 to water at the same temperature. This result is subject to correc- 
 tion for radiation, absorption, etc. 
 
302 SCHOOL PHYSICS. 
 
 246. The Latent Heat of Vaporization of a substance is 
 the quantity of heat that is required to vaporize one gram 
 of that substance without raising its temperature. The 
 latent heat of the vaporization of water is about 537 
 calories. 
 
 Water at 100 -f latent heat of vaporization = steam at 
 100. 
 
 (a) From the above statement it necessarily follows that the heat 
 required to vaporize any weight of water would warm 537 times that 
 
 weight of water one degree, or n times that weight of water - 
 degrees, provided there was no change of physical condition. 
 
 Experiment 199. Cut a piece of sheet lead about 5 x 30 cm., wind 
 it into a loose roll, and suspend it by a thread in a vessel of boiling 
 water. In a few minutes the lead will have the temperature of 100. 
 Transfer the lead to a thin metal vessel, containing a weighed quantity 
 of water sufficient to cover the lead, and of known temperature. Stir 
 the water with a thermometer, and note the temperature of the water 
 when it reaches its maximum. Multiply the weight of the warmed 
 water by its increase of temperature, to ascertain the number of 
 calories transferred by the lead. Divide the number of calories by 
 the fall of the temperature of the lead, to find the heat capacity of the 
 lead roll. Divide this capacity by the weight of the lead, to find 
 the specific heat of lead. Remember that, for work of precision, such 
 results would have to be corrected for radiation, absorption by the 
 vessel, etc. 
 
 247. The Specific Heat of a substance is the ratio between 
 the amount of heat required to raise the temperature of any 
 weight of that substance one degree, and the amount of heat 
 required to raise the temperature of the same weight of water 
 one degree. It indicates the number of calories absorbed 
 or emitted by one gram of that substance while under- 
 going a change of one degree of temperature. 
 
THE MEASUREMENT OF HEAT. 303 
 
 (a) The force of cohesion differs considerably for different sub- 
 stances. Consequently, when heat is added, the part thereof that is 
 employed against cohesion in giving new positions to the molecules, 
 and that is thus transformed from kinetic to potential energy (i.e., 
 from sensible to latent heat), is different for different substances. 
 The quantities of sensible heat remaining after such transformations 
 being thus different, the several substances have different specific 
 heats. 
 
 (b) The specific heat of hydrogen is 3.409 ; of ice, 0.505; of steam, 
 0.48; of oxygen, 0.2175; of iron, 0.1138; of lead, 0.0314. Water in 
 its liquid form has a higher specific heat than any other substance 
 except hydrogen. 
 
 Experiment 200. Pour 400 cu. cm. of water at the temperature 
 of 20 into 400 cu. cm. of water at the temperature of 60, and con- 
 tained in a thin liter flask. The temperature of the mixture will not 
 vary much from 40. Remember that allowance must be made for 
 loss of heat by radiation and for absorption of heat by the vessel. 
 The cool water gains and the warm water loses equal amounts of 
 heat; i.e., 8,000 calories; the thermal capacity of water is practically 
 the same at different temperatures. 
 
 248. The Thermal Capacity of a body is the number of 
 calories required to raise its temperature one degree. It is 
 the product of the mass into the specific heat, and has 
 direct reference to the amount of heat the body absorbs 
 or gives out in passing through a given range of tempera- 
 ture. 
 
 CLASSROOM EXERCISES. 
 
 1. One kilogram of water at 40, 2 Kg. at 30, 3 Kg. at 20, and 
 4 Kg. at 10, are thoroughly mixed. Find the temperature of the 
 mixture. Ans. 20. 
 
 2. One pound of mercury at 20 was mixed with one pound of 
 water at 0, and the temperature of the mixture was 0.634. Calcu- 
 late the specific heat of mercury. 
 
 3. What weight of water at 85 will just melt 15 pounds of ice 
 at 0? Ans. 14.117 pounds. 
 
SCHOOL PHYSICS. 
 
 4. What weight of water at 95 will just melt 10 pounds of ice 
 at - 10? Am. 8.947 pounds. 
 
 5. What weight of steam at 125 will melt 5 pounds of ice at - 8, 
 arid warm the water to 25 V 
 
 6. How many grams of ice at can be melted by 1 g. of steam at 
 100? 
 
 7. Equal masses of ice at and hot water are mixed. The ice is 
 melted, and the temperature of the mixture is 0. What was the 
 temperature of the water ? 
 
 8. Ice at is mixed with ten times its weight of water at 20. 
 Find the .temperature of the mixture. Ans. 11 nearly. 
 
 9. One pound of ice at is placed in 5 pounds of water at 12. 
 What is the result? 
 
 10. What temperature will be obtained by condensing 10 g. of 
 steam at 100 in 1 Kg. of water at 0? 
 
 11. A gram of steam at 100 is condensed in 10 grams of water at 
 0. Find the resulting temperature. A ns. 58 nearly. 
 
 12. If 200 g. of iron at 300 is plunged into 1 Kg. of water at 0, 
 what will be the resulting temperature? Ans. C.67. 
 
 13. A body with a weight of 80 g., and a temperature of 100, is 
 immersed in 200 g. of water at 10, and raises the temperature of the 
 water to 20. What is the specific heat of the body ? 
 
 14. How many pounds of steam at 100 will just melt 100 pounds 
 of ice at 0? Ans. 12.55 + pounds. 
 
 15. What will be the result of mixing 5 ounces of snow at with 
 23 ounces of water at 20? 
 
 16. What weight of steam at 100 would be required to raise the 
 temperature of 500 pounds of water from to 10 ? A ns. 7.97 pounds. 
 
 17. What weight of mercury at will be warmed one degree by 
 placing in it 150 g. of lead at 300? 
 
 18. If 4 pounds of steam at 100 is mixed with 200 pounds of water 
 at 10, what will be the resultant temperature ? 
 
 19. A pound of sulphur can melt only one-fifth as much ice as a 
 pound of water at the same temperature. What does this show con- 
 cerning the specific heats of water and sulphur ? 
 
 20. Explain the difference between thermal capacity and specific 
 heat. 
 
 21. If there was no water on the earth, would the differences in 
 temperature between day arid night, and between summer and winter, 
 be greater or less than they now are ? Why ? 
 
THE MEASUREMENT OF HEAT. 305 
 
 22. From a good dictionary or any other available source of infor- 
 mation, get an idea of the operation of an ice-machine or of a 
 refrigerating machine, and then show that when work is done upon 
 a gas there is an increase of sensible heat, and that when work is 
 done by a gas there is a decrease of sensible heat. 
 
 23. Tubs of water are sometimes placed in cellars to "keep the 
 frost away " from vegetables, the f reezing-point of which is a little 
 below 0. Explain the effect of the water in this respect. 
 
 24. The cylinder of a pump that forces air into the pneumatic tire 
 of a bicycle is heated in the process. Explain. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. 1.5 Kg. of mercury; 5 balls of dif- 
 ferent metals, each about an inch in diameter ; a cake of beeswax ; a 
 copper dipper as described below; 1 pounds of Xo. 13 shot; ice 
 or snow. 
 
 1. Pour quickly, and through the shortest possible air space, 1.5 
 Kg. of mercury at 100, into 500 g. of water at 0. Stir the liquids 
 thoroughly together with a thermometer, and, from the resultant 
 temperature, determine the specific heat of mercury. 
 
 2. Place small and similar balls made severally of iron, copper, tin, 
 lead, and bismuth, in a bath of linseed oil, and heat them to a tem- 
 perature of 180, or 200. When they have all had time to acquire 
 the temperature of the bath, wipe them dry, place them upon a 
 cake of beeswax about half an inch thick, and, from what you see, 
 arrange the five metals in. the order of their several specific heats. 
 
 3. Provide a sheet-copper dipper, 4 cm. in diameter, and 10 cm. 
 deep, and encircled about 2 cm. from the top by a flat flange of the 
 same material, and about 4 cm. wide. A handle 
 
 should be fastened to this flange. Accurately deter- 
 mine the weight of the " shaker " used in Exercise 9, 
 page 299, which we shall hereafter call a calorimeter. 
 
 H*T OOft 
 
 Into the dipper, put about 500 g. of very fine shot 
 that has been accurately weighed. Fill the cylindrical part of 
 the boiler described in Exercise 3, page 275, to the depth of about 
 6 cm. with water, and cork the side tube, a. Place the dipper in the 
 boiler, the flange of the dipper resting upon the top of the boiler. 
 Cover the dipper with a piece of cardboard that has a hole, through 
 which push the bulb of a thermometer down into the shot. Boil the 
 20 
 
306 SCHOOL PHYSICS. 
 
 water, stir the shot frequently and thoroughly with any convenient 
 instrument, and observe the rise of temperature of the shot. 
 
 Put about 100 cu. cm. of water into the calorimeter. Cool the 
 water with ice or snow until its temperature is 7 or 8 degrees below 
 that of the laboratory. When the mercury column of the thermome- 
 ter becomes stationary, note the temperature of the shot. Remove 
 the thermometer, and allow it to cool in air to about 40, and then 
 ascertain the temperature of the water in the calorimeter, stirring the 
 water with a thermometer until the thermometer and all parts of the 
 water have a uniform temperature. In the meantime, stir the shot at 
 frequent intervals. Bring the mouth of the dipper to the mouth of 
 the calorimeter, and quickly pour the shot into the water, being care- 
 ful not to spill the shot or to splash the water. Stir the' shot and 
 water quickly and thoroughly, and take the temperature of the con- 
 tents of the calorimeter. Weigh the calorimeter and its contents, 
 and, deducting the weights of the vessel and the shot, ascertain the 
 weight of the water heated by the shot. From the data now secured, 
 calculate the specific heat of lead. Remember that for work of pre- 
 cision, corrections would have to be made for the loss of heat by 
 radiation, and by absorption by the calorimeter, etc. 
 
 4. Repeat Exercise 3, using brass-filings instead of shot. 
 
 V. THE RELATION BETWEEN HEAT AND WORK. 
 
 249. Correlation of Heat and Mechanical Energy. - 
 
 When heat is produced, some other kind of energy 
 disappears, and vice versa. The most important of these 
 transformations are those between heat and mechanical 
 energy. We are able to effect a total conversion of 
 mechanical energy into heat, but we are not able to 
 bring about a total conversion of heat into mechanical 
 energy. 
 
 Experiment 201. Pass a bent glass tube through the air-tight 
 cork of a flask half full of water, and let it dip beneath the surface of 
 
THE RELATION BETWEEN HEAT AND WORK. 307 
 
 the water. Heat the flask. The heat will raise some of the water to 
 the end of the tube, where it may be 
 caught as shown in Fig. 229. 
 
 Experiment 202. To the spindle 
 of a whirling-table, attach a brass tube 
 about 10 cm. long and closed at the 
 lower end. Partly fill the tube with 
 alcohol and cork the open end. Press 
 the tube between two pieces of board 
 hinged together as shown in Fig. 230. 
 The grooves on the inner faces of the 
 boards should be faced with leather. 
 Rotate the apparatus, pressing with 
 the clamp upon the tube. Friction 
 transforms the mechanical energy 
 into heat, and the vapor from the 
 alcohol thus boiled may drive out the cork with explosive violence. 
 
 FIG. 229. 
 
 FIG. 230. 
 
 250. Joule's Principle. The disappearance of a definite 
 amount of mechanical energy is accompanied by the produc- 
 tion of an equivalent amount of heat. 
 
 251. The Mechanical Equivalent of Heat signifies the 
 numerical relation beticeen work-units and equivalent heat- 
 
308 
 
 SCHOOL PHYSICS. 
 
 units. The quantity of heat that will raise the tempera- 
 ture of one pound of water one Fahrenheit degree is 
 equivalent to about 778 foot-pounds. For centigrade 
 degrees the equivalent is 1.8 times as great, or about 1,400 
 foot-pounds. The mechanical equivalent of a calory is 
 about 427 gram-meters, or 4.2 x 10 7 ergs. 
 
 252. The Heat Equivalent of Chemical Union has a 
 
 determinative relation to the comparative fuel-values 
 of substances. 
 
 (a) The numerical values given below indicate that the combustion 
 of a given weight of the substance in oxygen yields heat enough to 
 warm so many times its own weight of water one centigrade degree, 
 or 1.8 times that many Fahrenheit degrees. For example, the com- 
 bustion of a gram of pure carbon develops 8,080 calories : 
 
 Hydrogen . 
 Petroleum 
 
 34,462 
 12,300 
 
 Carbon 8,080 
 
 Alcohol 6,850 
 
 253. The Steam Engine is a powerful device for utiliz- 
 ing the energy involved in the elasticity and expansive 
 
 force of steam as a mo- 
 tive power. It is a real 
 heat-engine, transform- 
 ing heat into mechanical 
 energy. In its modern 
 forms, it has many com- 
 plicated accessories for 
 increasing its efficiency 
 and adapting it to the 
 special uses to which it 
 is put, but the funda- 
 mentally important parts 
 are the cylinder, piston, and slide-valve, diagrammatically 
 
 FIG. 231. 
 
THE RELATION BETWEEN HEAT AND WORK. 309 
 
 represented in Figs. 231 and 232, in which the steam- 
 chest is represented as being at a distance from the 
 cylinder, simply for the purpose of making clear the com- 
 municating steam passages. The piston, P, is moved to 
 and fro in the cylinder by the pressure of the steam 
 which is applied to its two faces alternately. This alter- 
 nate application of the steam pressure is effected by the 
 slide-valve, inclosed in a steam-chest, and moved by the 
 valve-rod, R. The slide-valve covers the exhaust-port, N, 
 and one of the other two ports, A and B. 
 
 (a) Steam from the boiler enters the steam-chest at M. When 
 the valve is in position, as shown in Fig. 231, " live " steam passes 
 through the induction-port, A, 
 
 into the cylinder, and pushes the 
 piston, as indicated by the arrows, 
 forcing out the " dead " or ex- 
 haust steam by the eduction- 
 port, B, and the exhaust-port, N. 
 As the piston nears the end of its 
 journey in this direction, the valve- f\ M 
 rod, R, is moved by an "eccen- 
 trie," or other device, and shifts 
 the valve into position, as shown 
 in Fig. 232. This movement of 
 the slide-valve changes B to an 
 induction-port, by which "live" 
 steam is admitted to the other 
 face of the piston, pressing it in 
 
 the direction indicated by the arrow, and forcing the " dead " steam 
 out through A and N. Then the slide-valve is pushed back to its 
 former position by the rod, R. and the alternating movement of the 
 piston thus continued. The piston-rod and the valve-rod work through 
 steam-tight packing boxes. 
 
 (b) The outer end of the piston-rod carries a transverse bar or 
 cross-head that slides between two guide-bars, so that the motion of 
 the piston-rod is always along the axis of the cylinder. The same 
 
 FIG. 232. 
 
310 SCHOOL PHYSICS. 
 
 end of the piston-rod is pivoted to a pitman or connecting-rod, the 
 other end of which is attached to a crank on the shaft. The pitman 
 receives the reciprocating motion of the piston-rod, and imparts a 
 rotary motion to the crank-shaft. This shaft carries a heavy fly- 
 wheel, the accumulated energy of which carries the shaft across the 
 two " dead-points " when the piston is at one end or the other of the 
 cylinder. The fly-wheel otherwise tends to steadiness of motion, and 
 often serves as a belt-pulley. In large engines, the length of the 
 cylinder is generally horizontal. 
 
 (c) When the exhaust steam escapes through N into the air, the 
 engine is said to be a "high-pressure " or a "non-condensing" engine; 
 when it is led to a chamber and there condensed by a spray of cold 
 water for the purpose of removing the back pressure of the atmos- 
 phere, the engine is said to be a "low-pressure" or a "condensing" 
 engine. As the water is pumped from the condenser, a partial 
 vacuum is maintained. Sometimes the engine expands its steam in 
 two, three, or four successive stages, and in two, three, or four distinct 
 cylinders, the first taking steam directly from the boiler, and the 
 others taking it from the exhaust-port of the cylinder working at 
 the next higher pressure. Such engines are called respectively, 
 "double-expansion," "triple-expansion," and "quadruple-expansion" 
 engines. The live steam may be cut off from the cylinder during the 
 latter part of the travel of the piston, leaving the steam in the cylin- 
 der to expand with decreasing pressure to the end of the stroke. The 
 point of " cut-off " may be fixed, as at three-fourths of the stroke, or it 
 may be variable with the nature of the work. In the latter case, the 
 cut-off device may be adjusted automatically. 
 
 (d) More heat is carried to the cylinder of a steam-engine than is 
 carried from it. The piston does work at every stroke, and every 
 stroke annihilates heat. With a given supply of steam, the engine 
 will give out less heat when it is made to labor than when it runs 
 light. 
 
 () With all of its merits and all of its improvements, the modern 
 steam-engine utilizes less than 15 per cent of the heat energy devel- 
 oped by the combustion of the fuel. 
 
 (y*) Good steam-engines are now easily accessible from nearly every 
 school, and should be studied in detail, and by direct inspection. 
 The action of the pitman, the crank, the crank-shaft, the fly-wheel, 
 and the dead-points may be illustrated by almost any sewing- 
 machine. 
 
THE RELATION BETWEEN HEAT AND WORK. 311 
 
 CLASSROOM EXERCISES. 
 
 1. Show that the high latent heat of water has an important rela- 
 tion to the fact that when the temperature of the atmosphere rises 
 above 0, all the ice and snow of winter do not melt in a single day. 
 
 2. If a cannon ball weighing 192.96 pounds, and moving with a 
 velocity of 2,000 feet per second, could be suddenly stopped and all its 
 kinetic energy converted into heat, to what temperature would that 
 heat warm 100 pounds of ice-cold water ? 
 
 Solution : K.E. = f^ = 192.96 x2000 = 12j000)000) the number of 
 
 'g oi.oz 
 
 foot-pounds. Division of the number of foot-ponnds by 778 gives the 
 number of heat-units (pound-Fahrenheit) developed. This number 
 divided by 100 gives the number of heat-units for each pound of the 
 water, and consequently the number of Fahrenheit degrees that it will 
 raise the temperature. This, added to 32, the initial temperature, 
 will give the temperature called for. 
 
 3. A steam-engine raises 8,540 Kg. to a height of 50 m. How 
 many calories are thus expended ? 
 
 4. One gram of hydrogen is burned in oxygen. To what tempera- 
 ture would a kilogram of water at be raised by the combustion ? 
 
 5. From what height must a block of ice at fall that the heat 
 generated by its collision with the earth would just melt it if all of 
 the heat was utilized for that purpose ? 
 
 6. Show that to raise the temperature of a pound of iron from 
 to 100 requires more energy than to raise 7 tons of iron a foot high. 
 
 7. To what height cpuld a ton weight be raised by utilizing all 
 the heat produced by burning 5 pounds of pure carbon ? 
 
 Ans. 28,280 feet. 
 
 8. Find the height to which it could be raised if the coal had 
 the following percentage composition : 
 
 carbon, 88.42 ; hydrogen, 5.61 ; oxygen, 5.97. 
 
 9. With what velocity must a leaden bullet strike a target that its 
 temperature 'may be raised 100 by the collision, supposing all its 
 energy of motion to be spent in heating the bullet ? (Specific heat of 
 lead, 0.0314; </ = 980 cm.) 
 
 10. The specific heat of tin is .056 and its latent heat of fusion is 
 25.6 Fahrenheit degrees. Find the mechanical equivalent of the 
 amount of heat needed to heat 6 pounds of tin from 374 F. to its 
 melting point, 442 F., and to melt it. 
 
CHAPTER V. 
 RADIANT ENERGY: ETHER PHYSICS. 
 
 I. NATURE OF RADIATION. 
 
 254. The Ether. Physicists are generally of the opin- 
 ion that all space is filled with an incompressible medium 
 of extreme tenuity and elasticity. TJiis hypothetical me- 
 dium is called the ether. The variety of the phenomena 
 for which the ether hypothesis offers the only explanation 
 that modern science can accept (see 10) is so great that 
 the unproved existence of the ether is confidently ac- 
 cepted. 
 
 (a) It has been estimated that the density of the ether is 9.36 
 x 10~ 19 , which is enormously great as compared with that which air 
 would assume in interstellar space. It has been estimated that its 
 rigidity is about 0.000,000,001 that of steel, so that masses of ordinary 
 matter readily pass through it. Its structure is assumed to be con- 
 tinuous instead of granular like that of ordinary matter (see 3). 
 It is regarded as an incompressible substance pervading all space and 
 penetrating between the molecules of all ordinary matter wh^ch are 
 embedded in it and connected with one another by its means. It has 
 been compared to an impalpable and all-pervading jelly through 
 which the particles of ordinary matter move freely ; through which 
 heat arid light waves are constantly throbbing ; which is constantly 
 being set in local strains and released from them, and being whirled 
 in local vortices, thus producing the various phenomena of electricity 
 and magnetism. 
 
 255. Radiant Energy. Since the ether fills all inter- 
 molecular spaces, it follows that the vibrating molecules 
 
 312 
 
NATURE OF RADIATION. 313 
 
 of a body must communicate their motion to it. The 
 periodic disturbances thus communicated to the ether are 
 propagated through it in the form of waves that are 
 assumed to be transverse, and with a velocity of about 
 186,000 miles per second. Conversely, when these ether- 
 disturbances reach a body, they may communicate their 
 energy to the molecules of that body, and thus increase 
 the total energy of that body. The transference of energy 
 by means of periodic disturbances in the ether (without re- 
 gard to the precise nature of those disturbances) is called 
 radiation. The energy thus transferred is called radiant 
 energy. 
 
 (a) The mechanism of radiation involves two correlative processes, 
 emission and absorption, the former term referring to the communi- 
 cation of disturbances to the ether, and the latter to the reception of 
 disturbances from the ether. Any increase in the vibratory molecular 
 energy of a body increases its total radiation. Any increase in the 
 rapidity of those molecular vibrations correspondingly increases the 
 number of the ether disturbances in a unit of time, i.e., increases 
 the wave-frequency. There is, therefore, an evident analogy between 
 the phenomena of radiation and those of sound. 
 
 (b) The energy of radiation is measured by totally absorbing it 
 and determining the heating effect produced by it. Lampblack is the 
 most efficient substance known for such absorption. 
 
 256. A Ray is a line along which radiant energy is prop- 
 agated ; i.e., the straight line perpendicular to the wave- 
 front. A collection of parallel rays is called a beam. A 
 collection of converging or diverging rays is called a 
 pencil. 
 
 (a) The expressions, rays, beams, and pencils, are traces of an 
 exploded theory. So far as they pertain to the wave theory, they 
 are merely convenient geometrical conceptions, having no material 
 existence. 
 
314 SCHOOL PHYSICS. 
 
 257. Incident Radiation may be transmitted, reflected 
 or absorbed by the body upon which it falls. When a 
 body absorbs radiant energy, it is heated thereby. 
 
 Experiment 203. Take a white-hot poker into a dark room. You 
 are conscious of the sensations of heat and light, and readily attribute 
 both sensations to the energy radiated by the poker ; i.e., you say that 
 the poker emits heat and white light. The light gradually becomes 
 reddish, and finally fades from view. There is a continuous change 
 from the emission of white light and much heat to that of no light 
 and less heat. 
 
 258. Radiant Energy is Recognized by its phenomena, 
 which may be classified as luminous, thermal, and chem- 
 ical. 
 
 (a) Not even in theory can we assign limits to the length of the 
 ether undulations. Some of these waves are competent to excite the 
 optic nerve and to produce vision ; some are not. This ability and 
 inability are matters of wave-length. The variety of the effects must 
 not be permitted to obscure the identity of the cause. All of these 
 ether vibrations are of the same nature. Most of the properties and 
 phenomena of radiant energy are most conveniently studied by 
 luminous effects, which constitute the chief subject-matter of this 
 chapter. 
 
 II. LIGHT: VELOCITY AND INTENSITY. 
 
 259. Light. The portion of radiant energy that is 
 capable of producing the effect of vision constitutes light. 
 
 (a) The longest recognized ether wave is 3,000 x 10~ 6 cm. ; the 
 shortest is 18.5 x 10~ 6 cm. These wave-lengths correspond respectively 
 to vibration frequencies of 10 x 10 12 and 1,622 x 10 12 . The radiant 
 energy that constitutes light lies within the comparatively narrow 
 limits of 7.6 x 10~ 6 cm., and 3.9 x 10~ 5 cm., wave-lengths that respec- 
 tively correspond to vibration-frequencies of 392 x 10 12 and 757 x 10 12 . 
 
LIGHT: VELOCITY AND INTENSITY. 315 
 
 While the total range already observed is more than seven octaves, 
 the range within the limits that correspond to light is little more 
 than one octave. 
 
 260. Visible Bodies are visible because of the light that 
 they send to the eye of the observer. This is true whether 
 the body shines by its own or another's light, i.e., whether 
 it is self-luminous like a " live " coal, or illuminated like a 
 " dead " coal. 
 
 (a) Light makes luminous bodies visible but is itself invisible. 
 The illumination of the path of a sunbeam entering a darkened room 
 is due to the reflection of light by the dust motes floating in the air. 
 When a sunbeam is sent through moteless air, its path is imper- 
 ceptible. 
 
 XOTE. For many experiments in light, a darkened room is desir- 
 able. The windows should be provided with opaque curtains so 
 arranged that the sunlight may be quickly and completely excluded 
 from the classroom and laboratory. 
 
 Rectilinear Propagation. 
 
 Experiment 204. Provide six blocks H x 2| x 3^ inches, and three 
 other pieces of wood each } x 3| x 4 inches. Place three postal cards 
 one over the other on a board and perforate them with a stout needle 
 about half an inch below the middle of one end. Pare off the rough 
 edges of the holes with a sharp knife, and again pass the needle 
 through each hole to make its edge smooth and even. From these 
 materials, make three screens like that shown at A or B in Fig. 242. 
 Place the three screens parallel to each other and with their blocks 
 separated by two of the other blocks. Pass a thread through the holes 
 in the screens and carefully put it under tension to be sure that the 
 perforations are in a straight line. If necessary, adjust the screens 
 for that purpose. Remove the thread without disturbing the adjust- 
 ment. On the remaining block, place a lighted candle of such length 
 that its flame is at the height of the perforations in the cards. Place 
 eye and candle so that the flame may be seen through the screen per- 
 forations. Move one of the screens a little so that the three holes 
 are not in a straight line ; the candle flame cannot be seen as it was 
 before. 
 
316 SCHOOL PHYSICS. 
 
 261. Radiant Energy is Propagated along straight lines 
 when the medium is homogeneous, i.e., when it has a uniform 
 composition and density. 
 
 (a) The familiar experiment of " taking sight " depends upon 
 this fact, for \ve see objects by the light that they send to the eye. 
 A small beam of light that enters a darkened room illuminates a 
 straight path. The use of fire-screens and sunshades illustrates the 
 same fact. 
 
 262. Transparency, etc. According to the freedom with 
 which they transmit light, bodies are classified as trans- 
 parent, translucent, and opaque. Transparent bodies, as 
 glass, transmit light so freely that objects may be seen 
 through them distinctly. Translucent bodies, as oiled 
 paper, transmit light so imperfectly that objects seen 
 through them appear indistinct. Opaque bodies cut off 
 the light entirely, and prevent objects from being seen 
 through them at all. No sharp line of separation can 
 be drawn between these classes. 
 
 (a) When light falls upon a mass of small particles or thin films 
 of substances that are usually transparent, as finely-pounded glass or 
 ice, or froth, or foam, or cloud, most of the light is reflected. What 
 passes through one particle or film is reflected by another. Such 
 masses are brilliantly white in sunlight. As the light is reflected and 
 not transmitted, such masses are opaque. 
 
 Shadows. 
 
 Experiment 205. Hold a lead pencil between the flame of an ordi- 
 nary lamp and a sheet of paper about two feet distant from the lamp, 
 first with the edge of the flame toward the pencil, and then with the 
 side of the flame toward the pencil. Notice the difference in the 
 appearance of the screen. 
 
 Experiment 206. Coat with asphaltum varnish the lower half of 
 the outer surface of the chimney of a lamp that has a large flat flame. 
 
LIGHT: VELOCITY AND INTENSITY. 
 
 317 
 
 At the height of the flame, scrape the varnish from a spot 3 or 4 mm. 
 in diameter. Place the chimney on the lighted lamp with the clear 
 spot opposite the middle of a screen of light-colored paper and about 
 2 in. from it. Instead of being varnished, the chimney may be 
 smoked, or a sheet of cardboard may be rolled into a hollow cylinder 
 large enough to surround the lamp; a hole may be cut in the card- 
 board at the proper height. Hang a croquet ball midway between the 
 lamp and the screen. If the room is not darkened, place the ball and 
 the screen between 
 the lamp and the 
 window. Prick a pin- 
 hole through the 
 darkened section of 
 the screen and look 
 through it toward 
 the lamp. From the 
 further side of the FIG. 233. 
 
 screen, prick a series 
 
 of such holes about an inch apart and in a straight line, looking 
 through each hole before another is pricked. When you have pricked 
 a hole through w 7 hich you can see the luminous spot on the lamp- 
 chimney, examine the other side of the screen and notice that the pin- 
 hole is outside the darkened section. 
 
 Experiment 207. Replace the chimney used in Experiment 206 
 by one that is clear, and see that the side of the flame is turned 
 toward the ball. Examine the darkened section on the screen 
 
 i 
 
 FIG. 234. 
 
 and notice that its central disk is equally dark in all its parts, 
 and surrounded by a ring of varying darkness. Beginning at the 
 middle of the disk, prick pin-holes as before, examining each in suc- 
 cession, and avoiding those pricked in Experiment 206. Notice that 
 
318 SCHOOL PHYSICS. 
 
 you cannot see the flame through any hole in the central disk, that 
 you can see part of the flame through any hole in the annular space, 
 and that you can see the whole of the flame through any hole outside 
 the annular space. 
 
 263, A Shadow is the darkened space from which an 
 opaque body cuts off light. If the source of light has con- 
 siderable magnitude there will be a region of complete 
 shadow, called the umbra, surrounded by a partial shadow, 
 called the penumbra. No light enters the umbra ; the 
 penumbra receives light from a part of the luminous 
 surface. 
 
 264. An Image is an optical counterpart of an object and 
 may be formed by passing light through a small aperture, 
 by reflecting it with a mirror, or by refracting it with a 
 lens. When the light actually comes from the image to 
 the eye, the image is real. Such an image may be re- 
 ceived on a screen. When the light seems to come from 
 the image to the eye but does not, the image is virtual. 
 All virtual images are optical illusions. 
 
 Inverted Images. 
 
 Experiment 208. Place the opened end of an empty tin fruit-can 
 upon a hot stove and leave it there just long enough to melt off the 
 mutilated cover. Make a good sized nail-hole at the center of the other 
 end. Cover the nail-hole with tin-foil, anu the other end of the can 
 with thin tracing cloth or paper. Prick a pin-hole in the tin-foil, and 
 turn it toward a candle flame. Upon the paper may be seen an in- 
 verted image the size of which will depend upon the distance of the 
 flame from the pin-hole. The image will be seen more plainly if the 
 room is darkened, or a dark cloth used (after the manner of a pho- 
 tographer) to shut the outside light from the eyes and the screen. 
 
 Experiment 209. Bore a hole about 3 cm. in diameter in the side 
 of a wooden box, paste or tack tin-foil over the hole, and prick the 
 
UHIVERS1TY OF CALIFORNIA 
 
 DEPARTMENT OF PHYSICS 
 LIGHT : VELOCITY AND INTENSITY. 319 
 
 tin-foil with a pin. Invert the box over a lighted candle of such 
 height that its flame will be at the level of the pin-hole. The box 
 should be so large that the candle cannot set it on fire. Darken the 
 room, and hold a paper screen before the hole in the tin-foil. Move 
 the screen backward and forward and notice that, in any position, the 
 length of the flame is to the length of the image of the flame as the 
 distance from the pin-hole to the flame is to the distance from the pin- 
 hole to the image. Replace the tin-foil by another piece from which 
 has been cut a triangle 1 or 2 mm. on a side. Notice that the change 
 in the shape of the aperture does not make much difference with the 
 form of the image. Replace this tin-foil by another piece from which 
 has been cut a triangle about 2 cm. on a side. Notice that the image 
 is brighter and that its outline is less distinct. 
 
 265. Images by Apertures. If light from a highly 
 luminous body is admitted to a darkened room through 
 a small hole in the shutter and there received upon a 
 white screen, it will form an inverted image of the object. 
 
 FIG. 235. 
 
 As the rays are straight lines, they cross at the aper- 
 ture ; hence, the inversion of the image. The darkened 
 room constitutes a camera obscura of simple form. The 
 image of the school playground at recess is very interest- 
 ing, and is easily produced. 
 
 (a) When the aperture is circular, each point of the luminous sur- 
 face sends a cone of rays to the screen, and illuminates a circular spot 
 
320 SCHOOL PHYSICS. 
 
 upon it. When the aperture is triangular, or square, each point sends 
 a pyramid of rays, and illuminates a triangular or a square spot. In any 
 case, there will be an image of the aperture thrown upon the screen 
 for every point in the luminous surface. As these superposed images 
 of the aperture are symmetrically placed with reference to the corres- 
 ponding points of the luminous surface, and as they overlap each other, 
 they build up an image of the luminous body regardless of the shape 
 of the aperture. The idea may be more easily comprehended by 
 imagining the building up of a star-shaped figure by using small, 
 round wafers. The smaller the wafers, the sharper the outline of the 
 star. Remembering that the size and shape of our analogic wafer 
 depend upon the size and shape of the aperture, it ought not to be 
 difficult to understand the phenomena presented by images like those 
 now under consideration. The aperture or the wafer may be so large 
 as to destroy all resemblance between the image and the luminous 
 object, and to substitute therefor a resemblance to the aperture or 
 wafer itself. 
 
 266. The Velocity of Light is about 186,000 miles 
 (3 x 10 10 cm.) per second. For terrestrial distances, the 
 passage of light is, therefore, practically instantaneous. 
 
 (a) At equal intervals of 42 h. 28 min. 36 s., the nearest of Jupiter's 
 satellites passes within his shadow and is thus eclipsed. This phe- 
 nomenon would be 
 seen from the 
 earth at equal in- 
 tervals if light trav- 
 eled instantane- 
 ously from planet 
 
 FIG. 236. to P lanet In 1675 > 
 
 a Danish astron- 
 omer noticed that the interval between successive eclipses as ob- 
 served was longer during the half year when the earth was passing 
 from conjunction to opposition, as from E to E', than it was when the 
 earth was passing over the other half of its orbit, as from E' to E. 
 If, when the earth was at E, the time of successive eclipses was com- 
 puted a year in advance, the eclipse observed six months later when 
 the earth was at E', seemed to be 16 min. 36 sec. behind time, the time 
 apparently lost being regained in the next six months. This led irre- 
 
LIGHT : VELOCITY AND INTENSITY. 
 
 321 
 
 sistibly to the conclusion that it requires 16 inin. 36 sec. for light to 
 pass over the diameter of the earth's orbit from E to E'. This dis- 
 tance being approximately known, the velocity of light is easily com- 
 puted. The velocity of light has been measured by other means, 
 giving results that agree substantially with that above recorded. 
 
 Intensity of Illumination. 
 
 Experiment 210. Make three cardboard screens, A, , and C, 
 respectively 5 cm., 12 cm. and 17 cm. on a side. Draw a line parallel 
 to each edge of B and C, and at a distance of 1 cm. therefrom, thus 
 inscribing squares 10 cm. and 15 cm. on a side. Divide the smaller in- 
 scribed square into four squares, each the size of -4, and the larger 
 inscribed square into nine such squares. Mount the three screens so 
 
 FIG. 237. 
 
 that they stand upright with their middle points at the height of the 
 cleared spot on the lamp-chimney used in Experiment 206. Instead 
 of the asphaltum coat on the lamp-chimney, a perforated cardboard 
 screen may be used as sl/own in Fig. 237. The screens may be con- 
 veniently supported by soft-wood rods, each having a fine slit sawed 
 in one end and a sewing-needle thrust half-way into the other end. 
 Place A about 30 cm. from the perforation. Set C, parallel to A and 
 at such a distance that the shadow of A just covers its nine squares. 
 Then place B so that the shadow of A just covers its four squares. 
 Determine the relative distances of A, B, and C from the source of 
 light. Remove A and notice that the light that previously fell upon 
 it now falls upon B. Remove the second screen and notice that the 
 light that previously fell upon A and B now falls upon C. 
 
 267. The Intensity of Radiation that falls upon a sur- 
 face 
 
 21 
 
322 
 
 SCHOOL PHYSICS. 
 
 (1) Varies inversely as the square of the distance betiveen 
 this surface and the source of radiation. 
 
 (2) Varies with the angle that the incident radiation makes 
 with this surface, being at a maximum when the surface is 
 perpendicular to the direction of propagation. 
 
 (a) In Experiment 210, the light that fell upon A was diffused 
 over four times the area at B, at twice the distance ; and nine times 
 the area at C, at three times the distance. With the same quantity 
 of light diffused over nine times the area, the intensity of the illumi- 
 nation, i.e., the quantity of light per unit of surface, is only 1 as great. 
 
 Photometry. 
 
 Experiment an. Arrange apparatus in a darkened room as shown 
 in Fig. 238, where S represents a screen of white paper or cardboard, 
 and jR, a small rod placed upright a few inches from S (a cheap pen 
 and pen-holder, or a lead pencil held by a bit of wax on the table will 
 answer). The two flames should be on opposite sides of a plane per- 
 pendicular to the screen and passing through R, and at equal angular 
 distances from it ; they should be at the same level, and the flat lamp- 
 
 FIG. 238. 
 
 wick should stand diagonally to the screen. Place C about 20 inches 
 from S, and move L until the two shadows upon S nearly touch and 
 are of equal darkness. The candle and the lamp are now throwing 
 equal amounts of light upon the screen. If the distance from S to 
 L is twice that from to C, then L is four times as powerful a light 
 as C ; if the distance is three times as far, L is nine times as powerful. 
 Apparatus thus used constitutes a Rnmford photometer. 
 
LIGHT : VELOCITY AND INTENSITY. . 323 
 
 Experiment 212. Drop some melted paraffine upon a piece of 
 heavy, unglazed white paper, making a spot about an inch in diameter. 
 Remove the excess of paraffine with a knife, and heat the spot with a 
 flat-iron or can of water. Support the paper as a vertical screen. 
 When the paraffined disk is viewed by transmitted light, it appears 
 brighter than the surrounding paper ; when viewed by reflected light, 
 it appears darker. Place a lighted standard candle (see 268) at one 
 end of a table, and a lamp or gas-flame at the other end. Place 
 the screen between them, and arrange the pieces so that the middle 
 points of the candle flame, the translucent disk, and the lamp-flame 
 are in a straight line that is perpendicular to the screen. If the lamp- 
 flame is flat, set it diagonally to the screen. Move the screen along 
 the line between the candle and the lamp until its two sides are 
 equally illuminated ; i.e., until the paraffined spot is invisible, or until 
 the contrast between it and the rest of the screen is the same on both 
 sides when viewed at the same angle. Find the ratio between the 
 distances of candle and lamp from the screen, and square the ratio to 
 find the candle-power of the lamp. Apparatus thus used constitutes a 
 Bunsen photometer. 
 
 268. Photometry is the measurement of the relative 
 amounts of light emitted by different sources. The usual 
 process is to determine the relative distances at which 
 two sources of light produce equal intensities of illumina- 
 tion. The standard in general use is the light given by a 
 sperm candle (of the size known as " sixes ") when burn- 
 ing 120 grains per hour. The result is expressed by say- 
 ing that the light tested has so many candle-power. 
 
 CLASSROOM EXERCISES. 
 
 1. Describe the shadow cast by a wooden ball (a) when the source 
 of light is a luminous point ; (6) when the source of light is a white- 
 hot iron ball smaller than the wooden ball; (c) when it is of the same 
 size ; (e?) when it is larger. 
 
 2. Do sound waves or water waves the more closely resemble waves 
 of light? Why? 
 
 3. State clearly your idea of the carrier of radiant energy. 
 
324 SCHOOL PHYSICS. 
 
 4. Explain the formation of inverted images by small apertures. 
 
 5. Draw figures to illustrate the effect that doubling the distance 
 of an opaque body from a source of light has upon the shadow of the 
 former. 
 
 6. A coin is held 5 feet from a wall and parallel to it. A luminous 
 point, 15 inches from the coin, throws a shadow of it upon the wall. 
 How does the size of the shadow compare with that of the coin ? 
 
 7. An opaque screen, 3 inches square, is held 12 inches in front of 
 one eye ; the other eye is shut ; the screen is parallel with a wall 
 100 feet distant. What area on the wall may be concealed by the 
 screen ? 
 
 8. A standard candle is 2 feet and a lamp is 6 feet from a wall. 
 The shadows on the wall are of equal intensity. What is the candle- 
 power of the lamp V 
 
 9. An electric arc lamp 100 feet north of me and one 200 feet south 
 of me illuminate opposite sides of a sheet of paper in my hand and 
 render invisible a grease spot on the paper. How do the illuminating 
 powers of the lamps compare ? 
 
 10. If you hold a sheet of paper with a greased spot on it between 
 you and the light, the spot will look lighter than the rest of the sheet. 
 Why is this ? 
 
 11. If you hold the sheet in front of you when you are turned away 
 from the light, the spot will look darker than the rest of the sheet. 
 Why is this ? 
 
 12. Study the shadows cast by an electric arc lamp, and write a 
 very brief description of the penumbra of the shadows. 
 
 13. Describe the shape in space of the umbra and the penumbra of 
 the moon's shadow. Draw an illustrative figure. 
 
 14. When has an umbra an infinite length, and when a finite 
 length ? 
 
 15. The length of the umbra of the moon's shadow is a little longer 
 than the radius of the moon's orbit. On the figure drawn for Exercise 
 13, indicate the position in space occupied by your city (a) when a 
 total eclipse of the sun is visible there ; (b) when a partial eclipse of 
 the sun is visible there. 
 
 16. What does the great velocity of light indicate as to the density 
 and the elasticity of the ether ? 
 
LIGHT: VELOCITY AND INTENSITY. 325 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. A chalk-line; a standard candle; five 
 " Christmas" candles ; cardboard, 20 x 30 cm. ; a slender wooden rod ; 
 two small kerosene lamps ; two pieces of looking-glass, 10 cm. square, 
 tied to the vertical faces of two rectangular blocks. 
 
 1. Place a yardstick vertically against the wall of the room. Hold 
 one end of a foot rule at the eye, sight along the upper side of the rule, 
 and bring it into line with the lower end of the yardstick. Keeping 
 the rule in this position, hold a lead pencil vertically across its further 
 end so that the upper end of the pencil is in line with the upper end 
 of the yardstick. Carefully measure the length of the part of the 
 pencil that projects above the rule, and compute the distance of your 
 eye from the yardstick. 
 
 2. From a point on a blackboard or floor, draw two lines that 
 diverge 1 inch in 10 feet, and make them as long as possible. It will 
 be convenient to use a chalked line for this purpose. The included 
 angle will represent (fairly well) the angle subtended by the diam- 
 eters of the moon and the sun as observed from the center of the 
 earth. "With the apex of the angle as a center, draw a circle 4 inches 
 in diameter to represent the earth . At the distance of 10 feet, draw 
 a circle 1 inch in diameter to represent the moon. Imagine the long 
 lines extended until they have diverged sufficiently to include between 
 them a circle 400 inches in diameter to represent the sun. Compute 
 the distance of the center of this circle from the apex of the angle. 
 Assume the diameter of the earth to be 8,000 miles. From the figure 
 as thus completed in imagination, compute the diameters of the moon 
 and of the sun, and their distances from the earth. Shade the tri- 
 angular space between the moon and the center of the earth. Is it 
 possible for the moon's umbra to envelop the whole earth ? Under the 
 assumed conditions, what phenomenon would be seen by an observer 
 looking toward the inoon from the portion of the earth's surface 
 included in the shaded triangle? By an observer on the earth's 
 surface just outside that shaded part? 
 
 3. Arrange a Rumford photometer by setting up a rod 20 cm. long 
 and 1 cm. in diameter, 5 cm. in front of a white cardboard screen 
 20 cm. tall and 10 cm. wide. Mount a short candle upon a wooden 
 block, and four other candles of the same kind and length in a straight 
 row upon another block. Place the block with the single candle on 
 one side of the median plane, and the block with the four candles 
 
326 SCHOOL PHYSICS. 
 
 on the other side. The outside candles of the set of four should be 
 equally distant from the rod. After the candles have burned for 
 some minutes, carefully trim their wicks so that the flames shall be of 
 the same size. Stand in the median plane and so adjust the distance 
 of the single candle as to get shadows of equal intensity as described 
 in Experiment 211. Measure and record the distances of the two 
 sources of light from the screen and compare the result with the 
 statements of 267. 
 
 4. Instead of the candles of Exercise 3, use two small kerosene 
 lamps. Place them at equal distances from the rod, and turn the 
 edges of their flames toward the rod. Turn one of the flames down 
 until the shadows are of equal darkness. Turn one lamp so that the 
 side of its flame is toward the rod. Fix the attention on the middle 
 of the blurred shadow. If the two shadows are of equal darkness, 
 record the fact. If they are not, move one of the lamps until they 
 are. Then measure and record the distance of each lamp from its 
 shadow. Record your conclusions as to the perfect transparency of a 
 lamp-flame. 
 
 5. Using a Bunsen photometer, compare the illumination of the 
 four candles used in Exercise 3 with that of a standard candle. 
 Interchange the positions of the lights, and record the average 
 distances. 
 
 6. Place two plane mirrors so that an observer standing in the 
 plane of the screen can simultaneously see the images of both faces 
 of the paraffined spot, and compare them for equality of illumination. 
 Thus, determine the candle-power of a kerosene lamp. 
 
 III. REFLECTION OF RADIANT ENERGY. 
 
 Experiment 213. Paint the outside of a pint tin-pail with lamp- 
 black, and fill the vessel with hot water. Support the pail a few inches 
 above the table and, on the table near by, lay a sheet of tin-plate. Be- 
 tween the pail and the sheet, place a glass or wooden screen that has 
 an aperture about 2 cm. in diameter so that radiant energy from the 
 pail may pass through the aperture and fall upon the tin reflector 
 on the table. Place one bulb of a differential thermometer so that 
 the energy radiated directly from the pail will be cut off by the screen, 
 while that reflected by the sheet of tin, in accordance with the law 
 
REFLECTION OF RADIANT ENERGY. 
 
 327 
 
 FIG. 239. 
 
 stated in 76, will fall upon it. Notice the effect of the reflection. 
 Move the bulb out of the line of reflection, and notice the effect. 
 
 Experiment 214. About two feet from an air thermometer, place 
 an inverted flower-pot. Midway between the two, place a board or 
 glass screen that reaches 
 from the table to a height 
 of several inches above the 
 bulb of the air thermometer. 
 Upon the flower-pot, place a 
 very hot brick. Notice that 
 the heat of the brick has 
 little effect upon the ther- 
 mometer. Then hold a sheet 
 of tin-plate over the screen so 
 that energy radiated oblique- 
 ly upward from the brick 
 may be reflected obliquely downward toward the thermometer. By 
 properly adjusting the position of the reflector, the thermometer may 
 be quickly affected. 
 
 269. Reflection of Radiant Energy is the sending back of 
 incident ether waves by the surface on which they fall into 
 the medium from which they come. The reflection may be 
 irregular or regular. 
 
 (a) The proportion of the incident energy that is reflected in- 
 creases with the angle o incidence and with the degree of polish of 
 the reflecting surface, and varies according to the nature of the 
 reflecting substance. 
 
 NOTE. The laboratory should be provided with a porte-lumiere, 
 which consists of a plane mirror so mounted and fitted with adjust- 
 ing appliances that the direction of light reflected from the mirror 
 may be easily controlled. The mirror is placed on the outside of 
 the shutter of a darkened window and operated from within, sunlight 
 being reflected through the aperture in the shutter. 
 
 Experiment 215. Let a beam of light pass through an opening in 
 the shutter of a darkened room, and fall upon a sheet of drawing 
 paper lying on the table-top. The light will be scattered, and will 
 illuminate the room. With a hand mirror, reflect the beam down- 
 ward into a tumbler of water into which a teaspoonful of milk has been 
 
328 
 
 SCHOOL PHYSICS. 
 
 stirred. The milky water will scatter the light, and illuminate the 
 room as if it was self-luminous. 
 
 270. Irregular Reflection or Diffusion results from the 
 
 incidence of radiant energy 
 upon an irregular surface, as is 
 illustrated by Fig. 240. Bodies 
 are made visible to the eye 
 mainly by the light that they 
 thus diffuse. 
 
 FIG. Li.). 
 
 Experiment 216. Repeat Experi- 
 ment 215, allowing the beam of light 
 to fall upon a mirror instead of drawing paper. Most of the light 
 will be reflected in a definite direction, and will brilliantly illuminate 
 a small part of the enclosing wall. Reflect the beam downward 
 into a tumbler of clear water ; the tumbler will be visible but the 
 room will not be illuminated as it was by the milky water. 
 
 271. Regular Reflection results from the incidence of 
 radiant energy upon a polished surface. When a beam of 
 light falls upon a mirror, the 
 greater part of it is reflected in 
 a definite direction as is illus- 
 trated by Fig. 241, and forms 
 an image of the object from 
 which it came. A perfect mir- 
 ror would be invisible. FIG. 241. 
 
 Law of Reflection. 
 
 Experiment 217. Provide a semi-circular table like that shown in 
 Fig. 45. With a sharp knife, cut a line on the silvered surface of a 
 piece of looking-glass about 5 x 10 cm., perpendicular to one of the 
 long edges, and at its middle point. With a thread or fine rubber 
 band, fasten the reflector to the vertical face of the block at B so that 
 the lower end of the line on the looking-glass shall rest upon the 
 normal line, DB. Place a lighted candle at one end of a radius, 
 
REFLECTION OF RADIANT ENERGY. 329 
 
 as at j4, and set one of the postal card screens used in Experiment 
 204, near the edge >f the table, and so that light from the candle 
 will pass through the hole and fall upon the line marked on the 
 mirror. Similarly, place a like screen on the other side of BD, 
 and move it about until, when looking through the hole in it, an 
 image of the hole in the screen near A is seen in the mirror directly 
 in line with the knife-mark on the mirror. Mark the points on the 
 table directly under the perforations in the screens, and through them 
 draw radial lines. From the graduated edge of the table or with a 
 protractor, ascertain which of these radii makes the greater angle 
 with the radius, BD, perpendicular to the face of the mirror. 
 
 Experiment 218. Using the screens and blocks provided for 
 Experiment 204, arrange apparatus as shown in Fig. 242. At the 
 middle of the middle block, place a bit of window glass, m, painted 
 on the under side with black varnish. On the blocks that carry the 
 screens, place bits of glass, n and o, of the same thickness as the black 
 mirror. Light from the candle will pass through A, be reflected at 
 m, and pass through B. Place the eye in such a position that the 
 spot of light in 
 the mirror may be 
 seen through B. 
 Mark this spot 
 with a needle held 
 in place by a bit 
 of wax. Place a 
 piece of stiff writ- 
 ing paper upright FlG L>42 
 upon m and n, 
 
 mark the positions of B and of m, and draw on the paper a straight 
 line joining these two points. The angle between this line and the 
 lower edge of the paper coincides with the angle Bmn. Reverse the 
 paper, placing it upon m and o. It will be found that the same angle 
 coincides with A mo. The complementary angles, A mo and Bmn, 
 being thus equal, the angle of incidence equals the angle of reflection. 
 
 272. Law of the Reflection of Radiant Energy. The 
 angle of incidence and the angle of reflection are equal, and 
 lie in the same plane. 
 
330 
 
 SCHOOL PHYSICS. 
 
 273. Explanation of Reflection. Consider a beam of 
 light as made up of a number of ether waves moving for- 
 ward in air and side by side, as represented by the rays 
 A, B, and C. Imagine a plane, MN, normal to these rays, 
 attached to the waves and moving forward with them. 
 Such a plane is called a wave-front. It continues parallel 
 to itself and moves forward in a straight line. As the 
 wave-front advances beyond MN, the ray, A, strikes the 
 reflecting surface, RS, and is turned back into the air in 
 accordance with the law just given. In the interval of 
 time that passes before the ray, (7, arrives at P, the ray, 
 
 FIG. 243. 
 
 A, traveling with unchanged speed as before, passes over 
 the distance, MO, equal to the distance, NP. This 
 changes the direction of the plane that is attached to 
 the waves, and sets it in the new position indicated by 
 OP. Lines drawn from M, Q, and P, perpendicular to 
 OP, will represent the new direction of propagation, i.e., 
 the paths of the reflected rays. From Fig. 243, it may 
 easily be proved that the angles of incidence and of reflec- 
 tion are equal. 
 
 274. Apparent Direction of Bodies. Every point of a 
 visible object sends a cone of light to the eye. The pupil 
 of the eye is the base of the cone. The point always 
 
REFLECTION OF RADIANT ENERGY. 
 
 331 
 
 appears at the real or apparent apex of the cone. If the 
 path of the light from the point in question to the eye 
 is straight, the apparent position of the point is its real 
 position. If the path is bent by reflection, or in any 
 other manner, the point appears to be in the direction 
 of the light as it enters the eye. 
 
 Experiment 219. Place a jar of water 10 or 15 cm. back of a pane 
 of glass placed upright 011 a table in a dark room. Hold a lighted 
 candle at the same distance in front of the glass. The jar will be 
 seen by light transmitted through the glass. An image of the 
 candle will be formed by light reflected by the glass. The image will 
 be seen in the jar, giving the appearance of a candle burning in water. 
 The same effect may be produced in the evening by partly raising a 
 window, and holding the jar on the outside and the candle on the 
 inside. This experiment suggests an explanation of many optical 
 illusions, such as " Pepper's ghost," etc. 
 
 275. Plane Mirrors. If an object is placed before a 
 plane mirror, a virtual image ap- 
 pears behind the mirror. Each 
 point of this image seems to be 
 as far behind the mirror as the 
 corresponding point o'f the object 
 is in front of the mirror. Hence, 
 images seen in still, clear water 
 are inverted. 
 
 (a) In Fig. 244, AB and AC repre- p IG 244. 
 
 sent any two luminous rays proceed- 
 ing from A and incident upon the plane mirror, MR. From the points 
 of incidence, draw the perpendiculars, BG and CF. Draw BE so that 
 the angle, GBE, is equal to the angle, GBA . Then will BE represent 
 the path 'of the light reflected at B ( 272). Similarly, draw CD to 
 represent the path of the light reflected at C. Prolong DC and EB 
 
332 
 
 SCHOOL PHYSICS. 
 
 until they intersect at a. Draw A a. From this figure, it may be 
 proved geometrically that A IB is a right angle and that A I = al. 
 
 276. The Construction for the Image produced by a 
 plane mirror depends upon the fact that the image of an 
 
 object may be located by locat- 
 ing the images of a number of 
 well chosen points in the sur- 
 face of the object. 
 
 (a) In Fig. 245, OB represents an 
 arrow in front of the mirror, MR. 
 From the ends of the arrow, draw OC 
 and BD perpendicular to the face of 
 the mirror, and prolong them indefi- 
 nitely. Take oC equal to OC and bD 
 
 equal to BD. Join o and h. The image is virtual, erect (i.e., not 
 
 inverted), and of the same size as the object. 
 
 Experiment 220. Hinge together two rectangular pieces of look- 
 ing-glass, each about 7x10 cm., by pasting cloth along two short 
 edges, and set them on the table with an angle of 906 between them. 
 Set a " Christmas " candle or a bright-headed pin between the mirrors 
 and about 3 cm. from the apex of the angle, and count the visible 
 images. Reduce the angle to 60, and count the images. Reduce the 
 angle to 45, and count the images. 
 
 277. Multiple Images. By placing two plane mirrors 
 facing each other, we may produce an indefinite series of 
 images of an object between them. Each image acts as a 
 material object with respect to the other mirror, in which 
 we see an image of the first image, etc. When the 
 mirrors are placed so as to form with each other an angle 
 that is an aliquot part of 360 degrees, the number of 
 images is one less than the quotient obtained by dividing 
 four right angles by the included angle, provided that 
 quotient is an even number. 
 
REFLECTION OF RADIANT ENERGY. 
 
 383 
 
 (a) The mirrors will give three images when placed at an angle of 
 90 ; five at 60 ; seven at 45. 
 When the mirrors are placed 
 at right angles, the object and 
 the three images will be at 
 the corners of a rectangle as 
 shown at A, a, a' and a". 
 
 Experiment 221. Let a 
 small beam of light fall per- 
 pendicularly upon a concave 
 mirror. Strike two black- F! G 24(5. 
 
 board erasers together in 
 
 front of the mirror, and notice that the light converges at a point 
 not far from the mirror. 
 
 278. A Focus is a point at which light converges, in 
 which case it is called a real focus ; or it is a point from 
 which light appears to proceed, in which case it is called 
 a virtual focus. 
 
 279. Concave Mirrors are generally spherical; i.e., the 
 reflecting surface is a small part of the inner surface of a 
 spherical shell. The center of the sphere, (7, is the center 
 of curvature of the mirror. J., the middle point of the 
 
 mirror, is called the center or vertex 
 of the mirror. Any straight line 
 passing through C to or from the 
 mirror is called an axis of the mir- 
 ror. ACX, the axis that passes 
 through J., is called the principal 
 FIG. 247. ax * s > a ^ other axes are called 
 
 secondary axes. The angle, MCR, 
 is called the aperture of the mirror. A concave mirror 
 
334 
 
 SCHOOL PHYSICS. 
 
 increases the convergence or decreases the divergence of 
 light that falls upon it, as is shown in Fig. 248. 
 
 iiilffllllllllllllllllllllllil 
 
 FIG. 248. 
 
 Experiment 222. Arrange conjugate parabolic reflectors of pol- 
 ished brass as shown in Fig. 164. Place a hot iron ball at one focus, 
 and a bit of gun-cotton that has been blackened with lampblack at 
 the other focus. Repeat the experiment, holding a differential ther- 
 mometer so that one bulb will be at the focus, the second bulb being 
 in a direct line with the ball and, therefore, nearer to it. Notice 
 which bulb receives the more heat. 
 
 280. The Foci of Concave Mirrors may be in front of 
 the mirror, in which case they are real; or they may be 
 behind the mirror, in ivhich case they are virtual. 
 
 (a) The location of these foci gives rise to several cases : 
 
 (1) The incident rays may be parallel to the principal axis, as they 
 
 will be when the radiating point is 
 at an infinite distance. Solar rays 
 are practically parallel. Suppose a 
 spherical mirror of small aperture 
 to be held facing the sun. The 
 ray that follows the principal axis 
 will fall upon the mirror perpen- 
 dicularly at A , and be reflected back 
 upon itself. Other rays will be re- 
 flected as shown in Fig. 249, inter- 
 secting at F, a point midway between C and A. This focus of rays 
 
 
 JI 
 
 
 >\ \ 
 
 ,-A 
 
 
 ^C 
 
 
 
 c*^s 
 
 S^J 
 
 
 ^ / 
 
 '~^J 
 
 FIG. 
 
 / 
 249. 
 
 / 
 
REFLECTION OF RADIANT ENERGY. 
 
 335 
 
 FIG. 250. 
 
 parallel to the principal axis is called the principal focus of the mirror. 
 The distance, FA, is called the principal focal length or distance of the 
 mirror. 
 
 (2) When the rays diverge from the center of curvature they strike 
 the mirror perpendicularly, and are reflected back upon themselves. 
 The radiant point and the focus coincide. 
 
 (3) When the rays diverge from a point beyond the center of 
 curvature, as B, the focus 
 
 falls on the same axis, 
 at a distance from the 
 mirror greater than that 
 of the principal focus, and 
 less than that of the cen- 
 ter of curvature. If the 
 radiant point is at B, 
 the focus falls at 6, as 
 shown in Fig. 250. 
 
 (4) When the rays diverge from a point at a distance from the 
 mirror greater than that of the principal focus and less than that of 
 the center of curvature, we have the converse of the third case. The 
 focus falls on the same axis beyond the center of curvature. If the 
 radiant point is at b (Fig. 250), the focus falls at B. Foci that are 
 thus interchangeable are called conjugate foci. (See 185.) This 
 illustrates " the principle of reversibility." 
 
 (5) When the rays diverge from a point at a distance from the 
 
 mirror less than that of the 
 principal focus, the reflected 
 rays diverge as if from a point 
 back of the mirror. This 
 point, 6, is a virtual focus. 
 
 (6) When the rays diverge 
 from the principal focus, the 
 reflected rays are parallel and 
 there is no focus, real or vir- 
 tual. This is the converse of 
 the first case. 
 
 (6) The convergence of parallel rays at the principal focus is only 
 approximately true with a spherical mirror ; it is. strictly true with a 
 parabolic mirror. In order thaj the difference between the spherical 
 and the parabolic mirror may be reduced to a minimum, the aperture 
 
336 SCHOOL PHYSICS. 
 
 of the former should be small. The light from a luminous point at 
 the focus of a parabolic mirror is reflected in truly parallel lines. 
 The head lights of railway locomotives are thus constructed. Para- 
 bolic mirrors would be more common if they were less expensive. 
 
 (c) The sum of the reciprocals of the conjugate focal distances is 
 equal to the reciprocal of the principal focal distance. Representing 
 the radius of curvature by r, the distance of the luminous point from 
 the mirror by/, and the distance of the focus from the mirror by/', 
 
 1 1 2 
 
 Concave Mirror Images. 
 
 Experiment 223. In a dark room, hold a candle between the eye 
 and the concave side of a bright silver spoon held a little ways in 
 front of the face. Notice that the inverted image of the flame is in 
 front of the spoon. Place the spoon between the flame and your face 
 but so as to allow the face to be illuminated by the candle. Notice 
 the image of the observer. 
 
 Experiment 224. Place a concave mirror facing the sun, and hold 
 a bit of paper so that its illumination by the reflected light is of the 
 greatest intensity obtainable, thus locating the principal focus of the 
 mirror. Measure this focal distance. Then stand directly in front of 
 the mirror and at a considerable distance from it. Notice that the 
 image of yourself is inverted, diminished and real. If you are not 
 sure that the image is real, have some one hold his outspread fingers 
 between the image and the mirror. Approach the mirror, and notice 
 that your image increases in size until your eye is at the center of 
 curvature. Continue your approach, and notice that when your eye 
 is between the center of curvature and the principal focus, no image is 
 to be seen. The image is behind you and, therefore, invisible. When 
 your eye is between the principal focus and the center of the mirror, 
 your image is erect, magnified and virtual. 
 
 Experiment 225. In front of a concave mirror, and at a distance 
 equal to the radius of curvature, place a box that is open on the side 
 toward the mirror. Within this box, hang an inverted bouquet of 
 bright-colored flowers. The observer should stand in front of the 
 mirror and some ways back of the box. By giving the mirror a cer- 
 tain inclination, easily determined by trial, an image of the invisible 
 
REFLECTION OF RADIANT ENERGY. 
 
 337 
 
 bouquet will be seen just above the box. A glass vase may be placed 
 upon the box to hold the imaged flowers. 
 
 Experiment 226. Place a lighted candle in front of a concave 
 mirror so that the flame is in a secondary axis of the mirror, and at a 
 distance greater than the focal length and less than the radius of 
 curvature. Place a tracing-cloth or oiled-paper screen as shown in 
 Fig. 252, and, with a blackened card, shield it from the direct light of 
 the candle. Adjust the positions of the candle and the screen until a 
 
 FIG. 252. 
 t 
 
 good image of the former is projected on the latter. If the outer 
 edge of the image is indistinct, place before the mirror a paper cur- 
 tain with a circular opening of such size that the aperture of the 
 exposed part of the mirror does not exceed 10. Xotice that the 
 image is less intensely illuminated, but that its outline is more sharply 
 defined. 
 
 281. Images formed by Concave Mirrors consist of the 
 conjugate foci of the several points in the surface of the 
 object presented to the mirror and may, therefore, be real 
 
 or virtual. The construction of figures to illustrate the 
 22 
 
338 
 
 SCHOOL PHYSICS. 
 
 FIG. 253. 
 
 formation of images under different conditions may be 
 easily performed by selecting a few determinative points, 
 as the ends of an arrow, and determining the foci of those 
 points under the given conditions. 
 
 (a) The focus of each point chosen may be determined by tracing- 
 two rays from the point, and locating their real or apparent inter- 
 section after reflection by the mirror. The two rays most convenient 
 for this purpose are the one that lies along the axis of the point, and 
 the one that lies parallel to the principal axis of the mirror. The 
 
 first of these is reflected back 
 V NJif upon itself, and the focus 
 ^ r must, therefore, lie in that 
 line. The other is reflected 
 through the principal focus, 
 and the construction of equal 
 angles of incidence arid reflec- 
 tion is, therefore, unnecessary. 
 The process is illustrated in 
 Fig. 253. Following the order of the cases discussed in 280, it will 
 be found that : 
 
 (1) When the object is at a distance so great that the incident rays 
 may be considered parallel (e.g., solar rays), the image is formed at 
 the principal focus. 
 
 (2) When the object is at the center of curvature, the image is 
 real, inverted, of the same size as the object, and at the center of 
 curvature. 
 
 (3) When the object is at a distance from the mirror somewhat 
 greater than the center of curvature, as beyond C, the image is real, 
 inverted, smaller than the object, and at a distance from the mirror 
 greater than that of the principal 
 
 focus and less than that of the center 
 of curvature, as between F and C. 
 
 (4) When the object is at a dis- 
 tance from the mirror greater than 
 that of the principal focus and less 
 than that of the center of curvature, 
 as between F and C, the image is real, 
 
 inverted, larger than the object, and FIG. 254. 
 
REFLECTION OF RADIANT ENERGY. 
 
 339 
 
 at a distance from the mirror greater than that of the center of 
 curvature, as beyond C. This is the converse of the third case. 
 
 (5) When the object is at a distance from the mirror less than that 
 of the principal focus, as between F and A, the image is virtual, erect, 
 and larger than the object. 
 
 (6) When the object is at a distance from the mirror equal to that 
 of the principal focus, the reflected rays are parallel and no image is 
 formed. This is the converse of the first case. 
 
 282. The Spherical Aberration of a concave mirror is 
 the deviation of some of the reflected light from the focus, 
 
 FIG. 255. 
 
 as is shown in Fig. 255. It arises from the curvature of 
 the mirror, and causes an indistinctness or blurring of 
 the image. Parabolic mirrors are free from this defect ; 
 spherical mirrors are partly freed from it by reducing 
 their apertures so that the curvature conforms closely to 
 the curvature of a paraboloid. 
 
 Experiment 227. Hold the convex side of a bright silver spoon 
 toward you, and bring the spoon and a candle into the positions de- 
 scribed in Experiment 223. Xotice that the erect image of the flame is 
 back of the spoon. Place the spoon between the flame and your face 
 but so as to allow the face to be illuminated by the candle. Notice 
 the image of the observer. 
 
340 
 
 SCHOOL PHYSICS. 
 
 L' x 
 
 283. A Convex Mirror is generally a part of the outer 
 surface of a spherical shell. It increases the divergence, 
 
 or decreases the con- 
 vergence of light that 
 falls upon it. The foci 
 are virtual ; the prin- 
 cipal focus is midway 
 between the center of 
 >.<? the mirror and the "cen- 
 ter of curvature. The 
 foci may be located and 
 the images determined 
 by processes closely 
 similar to those used 
 FIG 256 for concave mirrors, as 
 
 is sufficiently illustrated 
 
 by Fig. 256. Such an image is erect, diminished, and 
 virtual. 
 
 CLASSROOM EXERCISES. 
 
 1. What must be the angle of incidence that the angle between the 
 incident and the reflected rays shall be a right angle ? 
 
 2. Copy Fig. 245, and add lines to show that the rays that form the 
 image for the right eye of the observer are different from the rays that 
 form the image for the left eye. 
 
 3. With a radius of 4 cm., describe ten arcs of small aperture to 
 represent the sections of spherical concave mirrors. Mark the centers 
 of curvature, and the principal foci, and draw the principal axes. Find 
 the conjugate foci for points in the principal axis designated as 
 follows : (a) At a distance of 1 cm. from the mirror ; (&) 2 cm. from 
 the mirror; (c) 3 cm. from the mirror; (d) 4 cm. from the mirror; 
 (e) 6 cm. from the mirror. Make five similar constructions for points 
 not in the principal axis. Notice that each effect is in consequence of 
 the equality between the angle of incidence and the angle of reflection. 
 
 4. Illustrate by a diagram the image (a) of an object placed at the 
 
REFLECTION OF RADIANT ENERGY. 
 
 341 
 
 FIG. 257. 
 
 principal focus of a concave mirror ; (6) of one placed between that 
 focus and the mirror ; (c) of one placed between the focus and the 
 center of the mirror. 
 
 5. Write a brief discussion of the formation of images by concave 
 mirrors under six different 
 
 conditions, following the 
 
 order of the cases discussed 
 
 in 280. Draw carefully 
 
 constructed diagrams for ^^ \ ^-<T^~M/ 
 
 the cases not illustrated in 
 
 answering Exercise 4. 
 
 6. Rays parallel to the 
 principal axis fall upon a 
 convex mirror. Draw a 
 diagram to show the course 
 of the reflected rays. 
 
 7. Why do images formed by a body of water appear inverted ? 
 
 8. (a) What kind of a mirror always makes the image smaller than 
 the object? (b) What kind of a mirror may make it larger or smaller, 
 and according to what circumstances? 
 
 9. A man stands before an upright plane mirror and notices that 
 he cannot see a complete image of himself, (a) Could he see a com- 
 plete image by going nearer the mirror? Why? (b) By going further 
 from it? Why? 
 
 10. When the sun is 30 above the horizon, its image is seen in a 
 tranquil pool. W r hat is the angle of reflection ? 
 
 11. A person stands before a common looking-glass with the left 
 eye shut. He covers the image of the closed eye with a wafer on the 
 glass. Show that when, without changing his position, he opens the 
 left and closes the right eye, the wafer will still cover the image of 
 the closed eye. 
 
 12. The distance of an object from a convex mirror is equal to the 
 radius of curvature. Show that the length of the image will be one- 
 third that of the object. 
 
 13. From the formula given in 280 (c), deduce an algebraic ex- 
 pression for the value of one of the conjugate focal distances in terms 
 of the principal focal distance and the other conjugate focal distance, 
 and write its significance in words. 
 
 14. Similarly show that as one of the conjugate focal distances 
 increases, the other decreases, and that when one of them becomes 
 
342 SCHOOL PHYSICS. 
 
 infinite, the other coincides in value with that of the principal focal 
 distance. 
 
 15. Considering the same formula, notice that if /is less than half 
 
 the radius, - is greater than the principal focal distance, and that f, 
 
 therefore, has a negative value. What would such a negative value 
 indicate as to the positional character of the focus ? 
 
 16. Given three points, A, B and C, not in a straight line. Show, 
 by a diagram, how to place a plane mirror at C so that light proceed- 
 ing from A shall be reflected to B. 
 
 17. Show by a figure how, with the aid of plane mirrors, one can 
 see around, or apparently see through an opaque object. 
 
 18. How should a plane mirror be placed so that the images seen 
 in it shall have their natural positions relative to the horizon ? 
 
 19. Study a description of a kaleidoscope in a dictionary or cyclo- 
 paedia, and determine the number of mirrors used in such an instru- 
 ment that gives pentagrammatic designs. 
 
 20. Refer to Fig. 255, and show that the aberration of a spherical 
 mirror may be lessened by reducing its aperture. 
 
 21. Determine the position of the image of a vertical object formed 
 by a plane mirror placed at an angle of 45 with the horizon. 
 
 22. The sun's rays are straight and practically parallel. How then 
 does daylight reach every nook and corner of a room from which the 
 sun is never visible, e.g., a room that has only a northern exposure ? 
 
 23. Remember that watery particles in the air may reflect light as 
 well as does suspended crayon-dust, and explain the production of the 
 halos often seen around the street lamps upon foggy nights. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Bright tin-plate, 8 x 30 cm.; plane and 
 curved mirrors ; shawl-pins; cardboard; several large sheets of Ma- 
 nila paper, and one of thin white paper; a wooden cube, 4 or 5 cm. on 
 an edge. 
 
 1. Lay a sheet of paper on the table top, and draw on it a straight 
 line, AB, about 15 cm. long, and mark its middle point C. From C, 
 draw CD at right angles to AB, and 10 or 15 cm. long. Through D, 
 draw MN, a line parallel to AB. Place the rectangular block and 
 mirror used in Experiment 217 so that the back of the mirror (the 
 silvered side) is exactly over AB, while the lower end of the vertical 
 
REFLECTION OF RADIANT ENERGY. 343 
 
 line that is marked on the mirror rests upon CD. Much of the suc- 
 cess of the exercise depends upon the correct placing of the mirror. 
 If the block is 1 or 2 cm. shorter than the mirror, it will be easier to 
 place the mirror properly. Set a shawl-pin upright at E, about 3 cm. 
 from D toward N. Bring the eye nearly to the level of the paper on 
 the other side of D, and into such a position that the image of the pin 
 shall be in line with the line scratched on the mirror. If the scratched 
 line and the image are not parallel, straighten up the pin. Set another 
 shawl-pin upright in this line of vision and in DM, and mark its posi- 
 tion F. Draw the lines, CE and CF. Measure DE and DF, and see 
 how they compare. If your work has been done accurately, they will 
 be equal, but accurate work must not be expected. The mirror may 
 not be a perfect plane; certain lines may not be perfectly straight, 
 and others may not be perfectly parallel ; the right angles called for 
 may vary a little from 90 ; and, with all the rest, a personal error is 
 nearly inevitable. Therefore, determine the ratio that DF bears to 
 DE, shift E to & new position a little further from D, and repeat the 
 work. Then shift the position of E again, and repeat the work. 
 The average of the three ratios for DF and DE will be pretty close to 
 unity if your work has been well done. With DF and DE equal, the 
 work establishes the equality of the angles of incidence and of reflec- 
 tion. Measure the angles with a protractor. 
 
 2. Continue working with apparatus and diagram as in Exercise 1. 
 Move the pin from F to G, 2 or 3 cm. toward M. In line with G and 
 the image of the pin at E and near AB, set a pin, and mark its position 
 G'. Move the pin from G to H, 2 or 3 cm. toward M. In line with 
 H and the image of the pin at E, and near AB, set a pin (that may 
 be moved from G'), and mark its position H'. Remove the pins from 
 H and H'. Bring the eye to the other side of D, and place it so that 
 the pin at E covers its image. Set a pin near AB, and in line with the 
 pin at E and its image. Mark the position of this pin 0. Remove 
 the block, the mirror, and the pins at E and 0. Draw a line through 
 the pinholes at E and O, and produce it indefinitely back of AB. 
 The part that lies back of AB should be broken or dotted, and so in all 
 similar cases (see Figs. 244 and 245). Similarly, produce FC and the 
 lines drawn through the pinholes at G and G', and at H and H'. The 
 four dotted lines should intersect at a common point which mark e. 
 The fact that the image remained at e whether the eye was in line 
 with E, or F, or G, or H, shows clearly that the image has a definite 
 location as long as the object and the mirror remain stationary. If 
 
344 SCHOOL PHYSICS. 
 
 AR is perpendicular to Ee, as it should be, tell what that fact signi- 
 fies. If AB bisects Ee, as it should, tell what that fact signifies. 
 
 3. Draw a straight line, AB, across a 30 x 50 cm. sheet of thin 
 white paper midway between its shorter edges. Set the block and 
 mirror used in Exercise 1 with the foot of the line on the mirror at C, 
 the middle point of AB. Draw on the paper in front of the mirror a 
 triangle, EFG, no side of which is less than 10 cm. long, and no corner 
 of which is less than 7 or 8 cm. from the mirror. Let one corner of 
 the triangle come 1 or 2 cm. nearer the edge of the paper than the end 
 of the mirror does. Paste white paper over one face of a cubical 
 wooden block about 4 cm. on an edge, and draw a vertical ink-mark 
 across the middle of the papered face. This ink-mark is to replace 
 the shawl-pins used in Exercises 1 and 2. Place this block with its 
 papered face toward the mirror, and with the foot of the- inked line 
 over E. Place a school rule or other straight-edge on the paper and, 
 sighting along its horizontal edge, bring the edge into line with the 
 eye and the image of the vertical line. Be sure that the mirror or the 
 wooden cube has not been moved from its proper position, and try 
 the alignment of the edge of the rule again. If it is correct, hold the 
 rule in place and, with a well sharpened pencil, tiace a line on the 
 paper along that edge of the rule that is just under the edge used in 
 taking sight. Mark this line E l E r Move the rule into a new posi- 
 tion as far as possible from the line just drawn, bring its edge into 
 alignment with the image of the vertical line as before, and trace 
 along its edge a line which mark E 2 E 2 . Then place the rule about 
 midway between the two lines drawn on the paper, bring its edge into 
 alignment with the image as before, and trace, as before, a third line 
 which mark E 3 E 3 . Be sure that the mirror and the wooden clibe are 
 still in their original positions; if they have been moved, test the 
 accuracy of the work already done. 
 
 Place the wooden cube with the foot of its vertical line over F and, 
 in like manner, draw three lines which mark F^F V F 2 F 2 and F 3 F S . 
 Similarly, place the vertical mark over G, trace three lines toward its 
 image, and mark them G 1 G V G 2 G 2 , and G S G 3 . 
 
 Remove the \vooden cube and the mirror with its block, and pro- 
 long the lines E v E* and E s back of the mirror as in Exercise 2. They 
 should intersect at a common point which mark e, the location of the 
 image of the point, E. Similarly, determine the points, / and g, the 
 location of the images of F and G. Draw the triangle, efg. Fold 
 the sheet of paper along the line AB, and hold the folded sheet against 
 
REFLECTION OF RADIANT ENERGY. 345 
 
 the window ; compare the size and shape of the two triangles, and 
 their positions relative to the line AB. Compare your results with 
 276. 
 
 4. Balance the block and mirror upon a rule so that the face of 
 the mirror crosses the rule at its middle. Place the eye so that the 
 further end of the rule may be seen by looking obliquely downward 
 and over the upper edge of the mirror. If the block back of the 
 mirror is visible, move the mirror up until it conceals the top of the 
 block, or use a thinner block. Adjust the mirror so that the further 
 end of the image of the rule as seen in the mirror coincides with the 
 end of the rule as seen over the mirror. The length of the rule is 
 now perpendicular to the face of the mirror. Look at the images of 
 the several divisions of the scale in front of the mirror and notice the 
 distance of each image back of the mirror. 
 
 5. On a sheet of paper, draw two lines, AB and CD, that bisect 
 each other at right angles at E. Make each line about 30 cm. long. 
 Place the block and mirror with its reflecting surface over AB, and 
 with its middle over E. See that the image of DE visible in the 
 mirror is in line with the part of EC that is visible back of the 
 mirror, as in Exercise 4. This is a delicate adjustment for the nor- 
 mal position of the mirror. Set the face of the mirror so that it 
 crosses AB at E making acute angles with AB. Xotice that the 
 image of DE is turned more than the mirror is. Set a shawl-pin 
 upright back of the mirror, and in line with the image of DE as seen 
 in the mirror. Mark its position 0. Draw a line along the face of the 
 mirror through E, and mark it MR. Remove the block and mirror. 
 Draw the line, EO. Measure the angles, A EM and CEO, and see 
 how they compare. Place the mirror again across AB at E, increas- 
 ing the angle, A EM. Construct the two angles that measure the 
 rotation of the mirror and of the image as before. Measure and com- 
 pare them. Once more, place the mirror across AB at E, and turn it 
 until the image of DE coincides with EB. Mark on the paper the 
 position of the face of the mirror, and compare the magnitude of the 
 angle that it makes with A E with the magnitude of CEB. State in 
 general but exact terms the effect that the deflection of a plane 
 mirror has upon the deflection of an image seen in it. 
 
 6. With a radius of 12.5 cm., draw MR, the arc of a circle, and 
 through its middle point, C, draw a tangent, AB, extending about 5 
 cm. each way from C. Draw the radius Cc. Cut a rectangular 
 piece of bright tin-plate about 8 x 30 crn., and mark a line across its 
 
SCHOOL PHYSICS. 
 
 face parallel to the two short edges and midway between them. Bend 
 the tin until its long edge coincides with the circular arc on the paper, 
 and hold it in that shape by tying a string around it. Take pains to 
 have the marked line on the concave side, to avoid " kinking " the 
 tin, and to secure a uniform curve. Place this curved reflector over the 
 circular arc with the foot of its marked line at C, and with the con- 
 cave side toward the light. To test the accuracy of the mirror, see 
 that the image of cC is in a straight line with cC itself. Notice the 
 caustic curves reflected on the paper, compare them with Fig. 255, and 
 remember them when you come to the consideration of Exercise 13. 
 About 4 cm. from C, and 2 cm. from cC, set a pin upright, as in 
 Exercise 1. Mark its position E. Bring the eye to the level of the 
 paper and near the reflector, and set a second pin at about the same 
 distance from C, and in line with C and the image of the pin at E. 
 Mark this position F. Remove the curved mirror, and place the 
 rectangular block and plane mirror used in Exercise 1 as therein 
 directed. The pin at F, the line over C, and the image of the pin at 
 E should be in a straight line. Remove the block and mirror. From 
 C and through E and F, draw lines of equal length, CO and CH. 
 Draw GH intersecting Cc at D. With a protractor, measure the 
 angles, DCG and DCH-, they should be about equal. Measure fche 
 lengths of DG and DH, and find the ratio between them ; it should be 
 nearly unity. Shift E successively to two new positions, and repeat 
 the work for each. Find the average of the three ratios between 
 DG and DH; it should be about unity. If it is, the work shows that 
 the relation between the angles of incidence and reflection is the 
 same for a concave mirror that it is for a plane mirror. See the 
 remarks made under Exercise 1. 
 
 7. Repeat Exercise 6, using the convex side of the mirror. 
 
 8. Place a cardboard screen close behind a candle-flame. Hold a 
 concave mirror so that a sharp image of the flame is projected on the 
 screen, making image and flame coincide as nearly as possible. Image 
 and flame will be nearly at the center of curvature of the mirror. 
 Describe the image. Determine the focal length of the mirror. 
 
 9. Place the flame between the center of curvature of the mirror 
 used in Exercise 8 and its principal focus, and adjust the screen so 
 that the image is sharply outlined on it. Determine the distances of 
 the flame and image from the mirror. Change positions of the flame 
 and screen, holding them so that an image may still be formed on the 
 screen. Does the principle of "reversibility" hold good in this case? 
 
REFRACTION OF RADIANT ENERGY. 347 
 
 10. Place the flame as near as possible to the mirror used in Exer- 
 cise 8 and still get an image on the screen. What is the limiting dis- 
 tance, expressed in general terms? 
 
 11. Support the mirror used in Exercise 8 in a vertical position at 
 one end of a long table. Directly in front and at the other end of 
 the table (the distance being greater than the radius of curvature), 
 place a lighted candle. Place a small paper screen so that a clearly 
 denned image of the flame may be projected upon it. Measure the 
 distances of the object and the image from the mirror, and describe 
 the image. Move the candle successively into new positions nearer 
 the mirror, projecting and describing the image, and making meas- 
 urements as above directed for each position. Compare your results 
 with the statements of your answer to Exercise 5, page 341. 
 
 12. In similar manner, experimentally determine the effect that 
 the position of the object has upon the character of the images 
 formed by a convex mirror, and write a brief discussion of the 
 results attained. 
 
 13. Put a pint of milk into a shallow circular dish of bright tin 
 that will hold a quart or more, and hold a lamp so that a catacaustic 
 curve is formed on the surface of the milk. Account for the exist- 
 ence of the curve, and determine the relation that the reflected rays 
 bear to the caustic. 
 
 IV. REFRACTION OF RADIANT ENERGY. 
 
 f 
 
 Experiment 228. Hold a double-convex lens in the sun's rays, so 
 that the bright focus on the side opposite the sun shall fall upon 
 some easily combustible material like the tip of a friction-match. A 
 spectacle-glass will answer, but a larger lens, like that of a reading- 
 glass, is desirable; the larger the lens, the better. Compare the 
 effects when dark-colored paper and white paper are held at the 
 focus. Then compare the effects with white paper that is clean, and 
 the same paper after it has been blackened with a lead pencil, or 
 smeared with lampblack. A lens thus used is called a "burning- 
 
 Experiment 229. Fill a large glass globe with water: An aqua- 
 rium globe will answer. Hang the filled globe in the bright sun- 
 
348 
 
 SCHOOL PHYSICS. 
 
 shine and, at the focus of the liquid lens, hold a bit of gun-cotton that 
 has been blackened with lampblack. The gun-cotton may be thus 
 ignited. The experiment will work equally well if a large double- 
 convex lens of ice is used instead of the globe of water. 
 
 Experiment 230. Place a coin on the bottom of a tin pan 15 cm. 
 or more in diameter and 4 or 5 cm. deep, and lay a slender straight 
 rod across the top of the pan. Hold the eye vertically above the coin, 
 bring the rod nearly into the line of vision, and note the apparent 
 distance of the coin below the rod. Have water poured into the pan, 
 and estimate the apparent displacement of the coin if any is noticed. 
 Empty the pan and replace the coin. Rest the head against the edge 
 of a shelf or other convenient fixed support, close one eye, and have 
 the pan adjusted so that its side just hides the coin from view. Have 
 water poured carefully into the pan until the coin is visible. The 
 light coming from the coin to the eye is bent downward somewhere 
 and somehow. Note the depth of water in the pan. Empty and 
 wipe the pan, and repeat the experiment using kerosene instead of 
 water, and compare the depths of the two liquids. 
 
 Experiment 231. Procure a clear 
 
 FIG. 258. 
 
 lass bottle with flat sides not 
 less than 10 cm. broad. The 
 larger the face of the bottle 
 the better; a rectangular 
 glass battery-jar is still bet- 
 ter. Cover one face of the 
 bottle with paper, and then 
 cut out as large a circle as 
 possible. On this clear cir- 
 cular space, mark horizontal 
 and vertical diameters inter- 
 secting at i, as shown in 
 Fig. 258. With a protrac- 
 tor, graduate the four quad- 
 rants from at the ends of 
 the vertical diameter to 90 
 at the ends of the horizontal 
 diameter. Fill the bottle 
 with clear water to the level 
 of i, and hold it so that a 
 
REFRACTION OF RADIANT ENERGY. 349 
 
 horizontal sunbeam passes through the clear sides of the bottle above 
 the water. Xotice that the path of the beam through the bottle is 
 straight. The path may be made plainly visible by clapping together 
 two blackboard erasers so as to scatter dust through the air around 
 the bottle. Turn the bottle with its clear face to the front, and raise 
 it so that the beam passes through the water. Put a sheet of black 
 paper back of the bottle, and notice that the beam is still straight. 
 In a card, cut a slit about 5 cm. long and 1 mm. wide. Place the card 
 against the bottle as shown in the figure. Reflect the beam through 
 this slit so that it falls upon the surface of the water at i. Xotice 
 that the reflected beam is straight until it reaches the water, but that 
 it is bent as it obliquely enters the water. From the scale on the 
 paper, read the angles that the beam makes with the vertical diameter, 
 above and below /. 
 
 Experiment 232. Repeat Experiment 231, using a rectangular 
 paper-weight of glass instead of the bottle of water, and notice 
 whether the deviation of the light from its straight path is more or 
 less in the glass than it was in the water. 
 
 284. Refraction of Radiant Energy signifies a retarda- 
 tion of the ether waves, and may be manifested by a change 
 of direction. When light is incident on the surface of a 
 transparent medium, part of it is reflected as already 
 explained. Another part of the incident light enters the 
 medium, and generally pursues therein a changed direc- 
 tion. J?his part is said to be refracted. 
 
 (a) There is a change of direction, i.e., the radiant energy is 
 deviated, when it falls obliquely upon the interface that separates 
 two media, as air and water, and passes from one to the other; or 
 when it passes through a medium the density of which is not uniform, 
 as the atmosphere. 
 
 (&) In Fig. 259, LA represents a ray of light propagated in 
 air, falling obliquely upon the surface of water at A, and deviated 
 by the water from AE to AK. Draw CD perpendicular to the 
 refracting surface at the point of incidence. LAC is the angle of 
 incidence ; KAD, the angle of refraction ; and KAE, the angle of 
 
350 
 
 SCHOOL PHYSICS. 
 
 deviation. From A as a center and with unity as a radiu&j describe 
 
 a circle, and draw mn and pq perpen- 
 dicular to CD. Then mn is the sine 
 of the angle of incidence; pq is the 
 sine of the angle of refraction. 
 
 (c) For any two media, the quo- 
 tient arising from dividing the sine 
 of the angle of incidence by the sine 
 of the angle of refraction is constant, 
 and is called the index of refraction. 
 The following table gives the indices 
 of the substances named : 
 
 Air (0and 760 mm.) . . 1.00029 
 
 Water 1.3324 
 
 Alcohol 1.3638 
 
 Carbon disulphide . . . 1.6442 
 
 Crown-glass .... 1.515 to 1.563 
 
 Flint-glass 1.541 to 1.710 
 
 Diamond 2.44 to 2.755 
 
 Lead chromate . . 2.974 
 
 The relative index of refraction for any two of these media may 
 be found by dividing the index of one as given above, by the index of 
 the other. For ordinary purposes, the index of refraction of gases 
 may be neglected ; the index of refraction for light passing from air 
 may be considered as 1^ for water; lj for crown-glass; If for flint- 
 glass; 2 for diamond; and 3 for lead chromate. In this sub-para- 
 graph, refraction has been discussed as if light was homogeneous, i.e., 
 had but one wave-frequency. Subsequently, proper consideration will 
 be given to the fact that light is complex in this respect. 
 
 (</) The following propositions are often given as the " laws of 
 refraction " : 
 
 (1) When radiant energy passes obliquely from one medium to another 
 of greater refractive power, it is bent, at the point of incidence, toward a 
 line that is perpendicular to the surface that separates the two media. 
 
 (2) When radiant energy passes obliquely from one medium to an- 
 other of less refractive power, it is bent from the perpendicular. 
 
 (3) The incident and refracted rays are in a plane that is perpendicular 
 to the refracting surface. 
 
 (4) For any two media, the sine of the angle of incidence bears a con- 
 stant ratio to the sine of the angle of refraction. 
 
 (e) The determination of the direction of the refracted ray may be 
 illustrated as follows: Let LA represent a ray passing from air into 
 
REFRACTION OF RADIANT ENERGY. 
 
 351 
 
 water at A. Through A, draw CD perpendicular to the refracting 
 surface. The index of refrac- 
 tion for the two media is f. 
 From A as a center and with 
 radii that are to each other as 
 4:3, draw concentric circles. 
 Prolong LA to E. From y, the 
 intersection of AE with the 
 circumference of the inner cir- 
 cle, draw vp parallel to CD. 
 Through />, the intersection of 
 this line with the circumfer- 
 ence of the outer circle, draw 
 A K, the line sought. Drawing 
 pq, vw, and mn perpendicular to 
 CD, it may be shown geomet- 
 rically that 
 
 sin LAC mn 4 
 
 TT-TT; : o' the index of refraction for air and water. 
 
 sin KAD pq 3 
 
 (/) If the ray passes in the opposite direction, i.e., from water into 
 air, the process is the reverse of that just indicated. Let KA repre- 
 sent the incident ray. Through p, draw pv. Through u, draw EA 
 and prolong it to L. AL is the direction sought. In some cases 
 it will be more convenient to use the equivalent process of continuing 
 KA to 0, drawing oi parallel to CD, and drawing the refracted ray 
 from A through {. 
 
 ((7) According to the forms and relative positions of their refract- 
 ing surfaces, there are thDee kinds of refractors ; plates, prisms and 
 lenses. 
 
 Total Reflection. 
 
 Experiment 233. Place the bottle used in Experiment 231, upon 
 a block on the table. Invert the card so that its horizontal slit is 
 near the bottom of the bottle. Place a mirror on the table and close 
 to the card. With a hand-mirror, reflect a sun-beam downward upon 
 the mirror on the table so that it will be reflected obliquely upward, 
 passing through the slit in the card and through the water toward i. 
 Diffuse crayon-dust through the air near the bottle, and notice the 
 refraction of the beam as it leaves the water. Bring the slit gradually 
 higher, changing the position of the hand mirror so that, as the rays 
 
352 
 
 SCHOOL PHYSICS. 
 
 pass through the slit and upward through the water to i, the angle of 
 incidence is gradually increased. Notice that the angle of refraction 
 increases more rapidly than the angle of incidence. As the angle 
 of incidence changes from 47 or 48 to 49 or 50, closely observe 
 the refracted light which approaches the refracting surface more and 
 more closely. When the angle of incidence has a certain magnitude, 
 the refracted ray coincides with the surface of the water ; i.e., the 
 angle of refraction has reached its maximum value, 90. If the angle 
 of incidence is still further increased, the light cannot emerge at i, 
 but will be reflected downward as if the plane between the water and 
 the air was a perfect mirror. 
 
 Experiment 234. Place a bright spoon in a tumbler of water with 
 the handle leaning from you. Hold the tum- 
 bler considerably above the level of the eye. 
 Notice that you see not only the lower part of 
 the spoon in the water but also an image of the 
 shank of the spoon above the upper surface of 
 the water. The free liquid surface glistens and 
 reflects as does a mirror. 
 
 285. Total Reflection. When a ray 
 of light passes obliquely from a medium 
 of higher to one of lower refractive 
 power, the angle of refraction is always 
 greater than the angle of incidence. 
 FIG. 201. The angle of incidence may be in- 
 
 creased until the angle of 
 refraction is 90, as repre- 
 sented by the ray, DFM. 
 A further increase in the 
 angle of incidence cannot 
 result in an increase of the 
 angle of refraction. Con- 
 sequently, the ray cannot 
 obey the laws of refraction, 
 
 i^=^^s-<^_ ^ j N 
 
 
 FIG. 262. 
 
REFRACTION OF RADIANT ENERGY. 
 
 353 
 
 but does obey the laws of reflection as represented by the 
 ray, DGrO. It is totally reflected at the point of incidence 
 back into the former medium. The angle of incidence at 
 which the effect changes from refraction to internal re- 
 flection is called the critical angle. 
 
 (a) The magnitude of the critical angle varies with the media 
 employed. For (air and) water, it is about 48^; for crown-glass, 
 about 41 ; for diamond, about 24. The reflection is called " total " 
 because all of the incident light is reflected, which is never the case 
 in ordinary reflection. 
 
 (&) To construct the critical angle, draw concentric circles as in 
 Fig. 260, the ratio of their radii being the index of refraction for the 
 media used. Remember that the emergent ray must graze the surface 
 of the water, and reverse the process described in 284 (/). At the 
 point where AN intersects the inner circle, erect a perpendicular. 
 The point where this normal intersects the outer circle will lie in the 
 prolongation of the ray incident at A. 
 
 286. Cause of Refraction. It is easy to conceive of the 
 motions of the ether as being hindered by the particles of 
 the matter that is 
 permeated by the 
 ether. Thus, when 
 ether waves that 
 constitute light 
 are transmitted 
 through glass, they, 
 are hindered by 
 the molecules of 
 the glass, and im- 
 part some of their 
 motion to those 
 molecules ; i.e., a 
 
 FIG. 263. 
 
 part of the light is absorbed. 
 23 
 
 When a beam of light, as 
 
354 SCHOOL PHYSICS. 
 
 
 
 represented by the rays A, B, and (7, moves forward in 
 the air, the wave-front, JZV(see 273), continues parallel 
 to itself and moves forward in a straight line. As the 
 wave-front advances beyond MN, the ray, A, enters the 
 glass, while B and are still in the air. The advance of 
 A in the glass is retarded by the glass so that, while C is 
 passing in air from NtoP, A traverses the shorter path, 
 MO. This retardation of A and the corresponding re- 
 tardation of B change the direction of the plane that is 
 attached to the waves, and set it in the new position 
 indicated by OP. All of the rays having entered the 
 glass, the wave-front again moves forward in a straight 
 course, normal to OP, representing the new direction of 
 propagation. In passing into the glass the direction of the 
 beam was changed, a direct result of a change of speed at 
 the surface of the glass. This phenomenon is called refrac- 
 tion. The beam was bent toward a perpendicular to the 
 bounding surface, RS. When the beam emerges from 
 the glass, similar changes will take place in inverse order, 
 and the beam will be bent from the perpendicular to the 
 refracting surface. 
 
 () The index of refraction is numerically equal to the ratio 
 between the velocity of the incident light and the velocity of the 
 refracted light. 
 
 Refraction by Plates. 
 
 Experiment 235. Draw a straight line of such length that it ex- 
 tends both ways beyond the ends of a piece of thick plate-glass 
 placed upon it. Look obliquely through the glass and from the 
 side of the line, and notice the apparent displacement of the part 
 of the line seen through the plate. 
 
 287. Refraction by Plates. When radiant energy passes 
 through a medium bounded by parallel planes, the refrac- 
 
REFRACTION OF RADIANT ENERGY. 
 
 355 
 
 tions at the two surfaces are equal and contrary in 
 direction. The direction after 
 passing through the plate is 
 parallel to the direction be- 
 fore entering the plate ; the rays 
 merely suffer lateral aberration. 
 Objects seen obliquely through 
 such plates appear slightly dis- 
 placed from their true position. 
 
 FIG. 264. 
 
 288. A Prism is a transparent body with two refracting 
 surfaces that lie in intersecting planes. The angle formed 
 by these planes is called the refracting angle. 
 
 (a) Let mno represent the principal section of a prism. A ray of 
 
 light from L is refracted 
 
 <^ at a and b, and enters 
 
 I j \^- the eye in the direction 
 
 '\ bE. The object, being 
 
 seen in the direction of 
 the ray as it enters the 
 eye, appears to be at I. 
 An object seen through 
 a prism seems to be 
 moved in the direction of 
 the refracting angle ; the 
 FIG. 265. rays are bent away from 
 
 the refracting angle. 
 
 (&) Cathetal prisms readily yield the phenomena of total reflection 
 as shown in Fig. 266, and are often used when light 
 is to be turned through a right angle. 
 
 v 
 
 Experiment 236. Make a monochromatic light by 
 sprinkling a little table-salt on the wick of an alco- 
 hol lamp. Place the flame on the level of the per- 
 foration in one of the postal card screens used in 
 Experiment 204. Back of this screen, place another so that the 
 
 FIG. 266. 
 
356 SCHOOL PHYSICS. 
 
 light from the lamp passing through the perforation of the first 
 makes a spot on the second. Mark the position of the spot. Behind 
 the first screen and close to it, hold a glass prism with its refracting 
 edge uppermost, horizontal, and parallel to the screen. Adjust its 
 height so that the rays passing through the perforation also pass 
 through the prism. Notice that the spot of light on the second 
 screen is moved downward. Mark the new position of the spot. 
 
 289. The Angle of Deviation of rays thus refracted is 
 the difference in direction between the incident and emer- 
 gent rays. In Experiment 236, this angle may be roughly 
 described as the angle between lines drawn from the 
 perforation in the first screen to the two marked positions 
 of the luminous spot on the second screen. In Fig. 265, 
 imagine La extended until it intersects El at x. The 
 angle Lxl is the angle of deviation. The angle varies 
 with the magnitude of the refracting angle of the prism, 
 its index of refraction, the wave-length of the light used, 
 and the angle of incidence. Other conditions being simi- 
 lar, a prism gives the least deviation when the angles of 
 incidence and of emergence are equal. 
 
 (a) The position of a prism for minimum deviation is easily deter- 
 mined by looking through it at an object, as in Fig. 265, and turning 
 the prism until the changing apparent position, I, comes to a stand- 
 still, and begins to move backward. 
 
 290. A Lens is a transparent body the two refracting 
 surfaces of which are curved, or one of which is curved 
 and the other plane. Lenses are generally made of crown- 
 glass which is free from lead, or of flint-glass which con- 
 tains lead and has greater refractive power. The curved 
 surfaces are generally spherical. 
 
 (a) With respect to their surfaces, lenses are of two classes, with 
 three varieties of each : 
 
REFRACTION OF RADIANT ENERGY. 
 (1.) Double-convex, 
 
 (2.) Plano-convex, 
 
 (3.) Meniscus, converging. 
 
 357 
 
 I Thicker at the middle than at the edges ; 
 
 FIG. 267. 
 
 The double-convex (biconvex or magnifying) lens may be taken as 
 the type of these ; its effects may be considered as produced by two 
 prisms with their bases in contact. 
 
 (4.) Double-concave, ] 
 
 (5.) Plano-concave, [ Thinner at the middle than at the edges ; 
 
 (6!) Concavo-convex, J diver ^ n g' 
 
 The double-concave (biconcave) lens may be taken as the type of 
 these ; its effects may be considered as produced by two prisms with 
 their refracting edges in contact. 
 
 (6) A double-convex lens may be described as the part common to 
 two spheres that intersect each other. The centers of the limiting 
 spherical surfaces, 
 
 as c and C, are ...-" "-, -'"" 
 
 the centers of curva- 
 ture. The straight 
 line, XY, passing 
 through the cen- 
 ters of curvature 
 is the principal axis 
 of the lens. In the 
 piano-lenses, the 
 principal axis is a 
 line drawn from the center of curvature normal to the plane surface. 
 A point on the principal axis so taken that rays passing through it 
 pierce parallel elements of the refracting surfaces is called the optical 
 center. A ray passing through the optical center suffers no change of 
 direction other than a slight lateral aberration that may be disre- 
 garded. When the two spherical surfaces are of equal curvature, thy 
 
358 SCHOOL PHYSICS. 
 
 optical center is at equal distances from the two faces of the lens, i.e., 
 at its center of volume. For the piano-lenses, the optical center lies 
 on the curved surface ; for the meniscus, it lies outside the lens and 
 on the convex side ; for the concavo-convex lens, it lies outside the 
 lens and on the concave side. Any straight line, other than the 
 principal axis, passing through the optical center is a secondary axis. 
 
 (c) To trace a ray through a lens, we have only to apply the prin- 
 ciples already explained. For example, let LN represent a glass bi- 
 convex lens (index of refraction, f) with centers of curvature at C and 
 
 C", and AB, the incident ray. From B as a center, draw the arcs, mn 
 and op, making the ratio of iheir radii equal to the index of refraction, 
 i.e., 2 : 3. Draw the normal, C'B. Draw st parallel to C'B. Draw 
 the straight line tBDy ; BD is the path of the ray through the lens. 
 From D as a center, draw the arcs, uv and wx, using the same radii as 
 for mn and op. Draw the normal, CD. Draw yz parallel to CD. 
 Draw DzA', the path of the ray after emergence. 
 
 Experiment 237. Hold one of the large lenses of an opera glass 
 or optical lantern in the sun's rays. Notice the converging pencil 
 formed by the light (after passing through the lens) as it passes 
 through air made dusty by striking together two blackboard erasers. 
 The focus and its distance from the lens may be seen. Measure this 
 distance. Hold a similar lens by the other, face to face. Notice that 
 the light after passing through both lenses converges more quickly, 
 lessening the distance of the focus from the lens. 
 
 291. The Foci of Convex Lenses may be determined 
 experimentally, but some of their properties are more con- 
 
KEFKACTION OF RADIANT ENERGY. 359 
 
 veniently studied by the diagrammatical tracing of rays in 
 accordance with the principles and processes already 
 studied. To locate the focus for light diverging from 
 any point, it is necessary to determine the point of inter- 
 section of two emergent rays. The problem is much 
 simplified by considering the axis that passes through the 
 point of divergence as the path of one of these rays. 
 
 (a) For converging lenses, the reciprocal of the principal focal dis- 
 tance equals the sum of the reciprocals of any pair of conjugate focal 
 distances. 
 
 1_1 !_ 
 
 f~P + P r 
 
 (6) Experimental work with convex lenses, and a careful study of 
 this formula, develop frequent analogies to the phenomena of concave 
 mirrors, and give rise to several cases as follows : 
 
 (1) When the incident rays are parallel to the principal axis, their 
 focus is called the principal focus. With a biconvex lens of crown- 
 glass (index of refraction, f) the principal focus is. at the center of 
 curvature, i.e., the focal length of the lens is equal to the radius of 
 curvature. With a plano-convex lens, the focal length is twice the 
 radius of curvature. In either case, the focus is real. 
 
 (2) When the incident rays diverge from a point more than twice 
 the focal distance from the lens, a real focus is formed on the other 
 side of the lens, and at a distance greater than the focal length and 
 less than twice the focal length. (See A and A', Fig. 269.) 
 
 (3) When the incident rays diverge from a point at twice the focal 
 distance from the lens, a real focus is formed on the other side of the 
 lens and at the same distance from it. These two points, as c and c' 
 in Fig. 269, are called secondary foci. 
 
 (4) When the incident rays diverge from a point distant from the 
 lens more than the focal length and less than twice the focal length, 
 a real focus is formed on the other side of the lens and at a distance 
 greater than twice the focal length. This is the converse of the 
 second case. Two foci that are thus interchangeable, like A and A' 
 in Fig. 269, are called conjugate foci. The secondary foci are con- 
 jugate. 
 
 (5) When the incident rays diverge from the principal focus, the 
 
360 SCHOOL PHYSICS. 
 
 emergent rays will be parallel, and no focus, real or virtual, will be 
 formed. This is the converse of the first case. 
 
 (6) When the incident rays diverge from a point nearer the lens 
 than the principal focus, the emergent rays are still diverging, and a 
 virtual focus is formed back of the radiant point. 
 
 (7) When the incident rays are converging, a real focus is formed 
 on the other side of the lens at a distance less than the focal length. 
 This is the converse of the sixth case. 
 
 (ft) Each pupil should draw a figure to illustrate each of the fore- 
 going cases. 
 
 292. The Foci of Concave Lenses may be located by 
 processes already studied. Such lenses have their centers 
 of curvature, their primary and secondary axes, and their 
 optical centers the same as convex lenses. 
 
 (a) For diverging lenses, the reciprocal of the principal focal dis- 
 tance equals the difference of the reciprocals of any pair of conjugate 
 focal distances. 
 
 1=1-1 
 
 / P / 
 
 (&) Experimental work with concave lenses, and a careful study of 
 this formula, develop frequent analogies to the phenomena of convex 
 mirrors, and give rise to several cases as follows : 
 
 (1) When the incident rays are parallel to the principal axis, the 
 emergent rays diverge as if they came from a virtual focus, which is 
 called the principal focus. With a biconcave lens of glass (index of 
 refraction, f), the principal focus is at the center of curvature. With 
 a plano-concave lens, the focal length is twice the radius of curvature. 
 
 (2) When the incident rays are diverging, the focus is virtual and 
 at a distance from the lens less than the focal length. As the radiant 
 point approaches the lens, the focus also approaches the lens. 
 
 (3) When the incident rays are converging, the effects are varied 
 according to the degree of convergence. If the point of convergence 
 is nearer the lens than the principal focus, a real focus will be formed 
 at a distance greater than the focal length of the lens. If the point 
 of convergence is at the principal focus, the emergent rays will be 
 parallel, and no focus will be formed. If the point of convergence is 
 further from the lens than the principal focus, a virtual focus will be 
 formed. 
 
REFRACTION OF RADIANT ENERGY. 
 
 361 
 
 (&) Each pupil should draw a figure to illustrate each of the fore- 
 going cases. 
 
 Images. 
 
 Experiment 238. Repeat Experiment 228, and measure the focal 
 length of 'the lens. 
 
 Experiment 239. Place a candle, a convex lens, and a screen in 
 line as shown in Fig. 270, the distance of the candle from the lens 
 
 
 FIG. 270. 
 
 being a little greater than the focal length of the lens. Adjust the 
 position of the screen until a sharply defined image of the candle is 
 projected upon it. Place the eye back of the screen and have the 
 screen removed ; the inverted image may be seen suspended in 
 mid-air. Burn touch-paper under the image, and notice its projec- 
 tion on the screen of smofce. Replace the screen first used. 
 
 Experiment 240. With candle and screen in positions as described 
 in Experiment 239, adjust the position of the lens so that the flame 
 and the image of the flame are of the same size. Measure the dis- 
 tance of the screen from the candle, and compare a quarter of that 
 distance with the focal length of the lens. 
 
 293. Images Formed by Lenses consist of the conjugate 
 foci of the several points in the surface of the object pre- 
 sented to the lens and may, therefore, be real or virtual. 
 The construction for such images is closely analogous to 
 the process employed with mirrors. 
 
362 
 
 SCHOOL PHYSICS. 
 
 (a) The focus of each point chosen may be determined by tracing 
 two rays from the point, and locating their real or apparent intersec- 
 tion after emerging from the lens. The two rays most convenient 
 for this purpose are the one that lies along the secondary axis of the 
 point, and the one that lies parallel to the principal axis of the lens. 
 For example, from A and E, extremities of an arrow, draw the 
 secondary axes, AOa and EOe. From A, draw AB parallel to the 
 
 E 
 
 FIG. 271. 
 
 principal axis, XY. Determine the direction of BD by construction. 
 From D, draw the path of the emergent ray through the principal 
 focus, F. It intersects the secondary axis at a, the conjugate focus 
 of the radiant point, A. In similar manner, the conjugate focus of 
 the point, E, may be located at e. The points, a and e, mark the ex- 
 tremities of the image of the object, A E. 
 
 (b) An examination of Fig. 271 shows that the linear dimensions 
 of object and image are directly as their respective distances from the 
 center of the lens ; they will be virtual or real, erect or inverted, ac- 
 cording as they are on the same side of the lens, or on opposite sides. 
 
 Experiment 241. Select a large biconvex lens, and cut a card- 
 board disk of the same diameter. Punch a ring of small holes near 
 the circumference of the disk, and cut a hole about 2 cm. in diam- 
 eter at its center. Cut a notch in the border of one of the small 
 holes as a distinguishing mark. Place the lens in the path of a 
 beam from the porte lumiere, and cover one of its faces with the 
 perforated disk. Hold a screen near the lens and so that the refracted 
 rays fall upon it. Slowly move the screen away from the lens until 
 you find the focus of the light that passes through the small holes. 
 Moving the screen still further, you will find another focus for the 
 light that passes through the central opening in the disk. Notice 
 
REFRACTION OF RADIANT ENERGY. 363 
 
 that the rays that pass through the marginal holes cross before 
 reaching the screen, and form a ring of luminous spots around the 
 central image. 
 
 294. Spherical Aberration. The rays that pass through 
 a spherical lens near its edge are deviated more than 
 those that pass nearer the center. They, therefore, con- 
 verge nearer the lens. This unequal deviation is called 
 spherical aberration. The indefiniteness of focus causes a 
 blurring of the image. In practice, the marginal rays are 
 often cut off by an annular screen called a diaphragm, or 
 the curvature of the lens is lessened toward its edge. 
 A lens thus corrected for spherical aberration is called 
 aplanatic. 
 
 CLASSROOM EXERCISES. 
 
 1. Remembering the varying density of the earth's atmosphere, 
 draw a diagram showing that the sun may be seen before it has as- 
 tronomically risen, and after the true sunset, i.e., after it has dipped 
 below the western horizon. 
 
 2. (a) Name, and illustrate by diagram, the different classes of 
 lenses. (6) Explain, with diagram, the action of the burning-glass. 
 
 3. Draw circles so that parts of their circumferences may represent 
 the curved surface of a^ meniscus, a biconcave, and a concavo-convex 
 lens. 
 
 4. (a) Describe the phenomena of total reflection. (7>) Show, with 
 diagram, how the secondary axes of a lens mark the limits of the 
 image. 
 
 5. Construct the critical angle for air and water. 
 
 6. Show how a beam of light may be bent at a right angle by a 
 glass prism. 
 
 7. Trace a ray through a biconcave lens, using the process em- 
 ployed in 290 (c) for the biconvex lens. 
 
 8. Trace a ray through a biconvex lens for the location of its 
 principal focus. 
 
 9. Trace a ray through a biconcave lens for the location of its 
 principal focus. 
 
364 SCHOOL PHYSICS. 
 
 10. Through what point does the line joining the conjugate foci of 
 a convex lens always pass ? 
 
 11. Construct the images formed by a convex lens under the six 
 following cases and describe each image : (a) when the incident rays 
 are practically parallel; (6) when the object is a little beyond a 
 secondary focus ; (c) when the object js at a secondary focus ; (e?) 
 when the object is between secondary and principal foci ; (e) when 
 the object is at the principal focus ; (/) when the object is between 
 the principal focus and the lens. 
 
 12. (a) The focal distance of a convex lens being 6 inches, deter- 
 mine the position of the conjugate focus of a point 12 inches from 
 the lens, (b) 18 inches from the lens. 
 
 13. The focal distance of a convex lens is 30 cm. Find the con- 
 jugate focus for a point 15 cm. from the lens. 
 
 14. If an object is placed at twice the focal distance of a convex 
 lens, how will the length of the image compare with the length of the 
 object ? 
 
 15. A small object is 12 inches from the lens; the image is 24 
 inches from the lens and on the opposite side. Determine (by con- 
 struction) the fdcal distance of the lens. 
 
 16. A candle-flame is 6 feet from a wall ; a lens is between the 
 flame and the wall, 5 feet from the latter. A distinct image of the 
 flame is formed upon the wall, (a) In what other position may 
 the lens be placed, that a distinct image may be formed upon the 
 wall ? (6) How will the lengths of the images compare V 
 
 17. Why does a sphere under water look like a spheroid V 
 
 18. When clear glass is pounded into small particles, it becomes 
 opaque. Explain. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Lenses ; spy-glass ; wooden cubes 
 grooved and fitted as described in Exercise 12. 
 
 1. Trace a ray passing obliquely from air into glass (index of 
 refraction, 1.5). 
 
 2. Trace a ray passing obliquely from glass into air. 
 
 3. Trace a ray passing obliquely from air into water (index of 
 refraction, 1.3). 
 
 4. Trace a ray passing obliquely from water into air. 
 
 5. Trace a ray passing obliquely from air into diamond (index of 
 refraction, 2.5). 
 
REFRACTION OF RADIANT ENERGY. 365 
 
 6. Trace a ray passing obliquely from water into glass. 
 
 7. Trace a ray passing through water toward air so that the angle 
 of incidence is 50. (See 285, a.) 
 
 8. Hold a test-tube partly immersed in water so that its length is 
 slightly inclined from a vertical. Look down through the water upon 
 the immersed part of the air-filled tube, and notice that it looks like 
 highly polished silver. Fill the test-tube with water, and write an 
 explanation of the change in its appearance. 
 
 9. Make a concave air-lens and place it in water. Make a con- 
 vex water-lens and place it in air. Compare the effects of the two 
 lenses upon beams of light that pass through them. 
 
 10. Adjust a candle-flame and a screen on opposite sides of a bi- 
 convex lens so that a sharp image of the flame is projected on the 
 screen when flame and screen are at equal distances from the lens. 
 Record the focal length of the lens, the names of the positions occu- 
 pied by flame and screen, and a description of the image. Exchange 
 the positions of the flame and the screen, and test the principle of 
 " reversibility." Slowly diminish the distance between lens and can- 
 dle until it is impossible to place the screen so as to obtain an image. 
 Measure this distance, compare it with the focal distance of the lens, 
 and indicate the significance of the comparison. With the lens at 
 four different distances from the screen, form images. In each case, 
 measure the linear dimensions of flame and image, and the distances 
 from the lens to flame and image. Find the ratio between the dis- 
 tances and the corresponding dimensions, and compare the ratios. 
 
 11. Focus a spy-glass or small telescope on an object a mile or more 
 distant. The rays coming from the object to the eye will be practi- 
 cally parallel. Place a lens, the focal length of which you are to 
 measure, in front of the telescope. Paste a small-type newspaper- 
 clipping on a piece of cardboard, and look at it through the telescope 
 and lens. Adjust the position of the cardboard so that the printing 
 appears distinct. Measure the distance of the cardboard from the 
 lens. Obtain the average of several such trials. Record a discussion 
 of the proposition that this average distance is the focal length of the 
 lens. 
 
 12. Provide two wooden cubes with edges about 4 cm. long and- 
 with the grain of the wood, cut in each block a groove about 2 cm. 
 deep and wide enough to admit the edge of the meter rod as shown 
 in Fig. 272. Provide common screws so that the blocks may be 
 fixed in any position on the rod. Provide a circular biconvex spec- 
 
366 
 
 SCHOOL PHYSICS. 
 
 tacle-lens having a known focal length of not less than 12 cm. and not 
 more than 16 cm. Mount this lens on one of the grooved blocks, e. 
 It may be held in place between slotted brass strips each fastened to 
 the block by a screw. Upon the other block, mount a cardboard 
 screen about 8 cm. square. This screen, s, may be carried in a groove 
 sawed across the block, a. As an object the image of which is to be 
 projected upon the screen, cut a small cross in the varnish on the 
 lamp-chimney or in the paper cylinder mentioned in Experiment 206. 
 Give the top of the cross some distinguishing shape or mark so that 
 you can tell whether its image is erect or inverted. Support the meter 
 rod horizontally so that the center of the lens shall be at the height 
 of the center of the cross, and so that m, the end of the meter rod, 
 shall be just under the cross. Set the screen at a distance from the 
 cross equal to about three times the focal length of the lens. Slide 
 the lens along the rod, seeking for it a position that gives upon the 
 
 screen a clear image 
 of the cross. If no 
 such position for the 
 lens can be found, 
 move the screen 1 or 
 2 cm. further from 
 the object, and renew 
 the search for the 
 desired position of 
 the lens. If neces- 
 sary, move the screen 
 further and further 
 from the object until 
 you are able to place the lens so that a distinct image is obtained. When 
 it is found, record a description of the image, as erect or inverted, and 
 magnified, diminished, or the same size. Read from the rod the dis- 
 tance from the cross to the lens, and enter it as the first number in 
 a second column headed " Object-distances." Make a corresponding 
 entry of the distance from the screen to the lens in a third column 
 headed "Image-distances." Without changing the image-distance, 
 try to secure a distinct image with the lens in any other position. 
 If you can, make the three entries as before. When you have 
 exhausted the possibilities of object-distance with this first image- 
 distance, move the screen 10 cm. further from the cross, secure a good 
 image, and record the description and distances as before. Move the 
 
 FIG. 272. 
 
REFRACTION OF RADIANT ENERGY. 367 
 
 screen 10 cm. further from the cross, adjust the lens, and make the 
 record as before. Continue the work until you have recorded at least 
 five pairs of distances. Compare your results with those of Exercise 
 11, p. 364. To your tabular-record, add a fourth column, each 
 entry in which is the sum of the two recorded distances. Such sums 
 will represent the distances of image from object. Head the column 
 " Total distances." In a fifth column, enter the quotients obtained 
 by dividing the several total distances by the focal length of the lens. 
 Try to get a quotient as small as 3, and if you fail, give a good reason 
 for your failure. 
 
 Using the records made in this exercise, test the accuracy of the 
 statement that the reciprocal of the focal length equals the reciprocal 
 of the object-distance plus the reciprocal of the image-distance, or of 
 the equivalent statement that the product of the object and image 
 distances equals the sum of those distances multiplied by the focal 
 length. 
 
 If you were told that in such an experiment the object-distance 
 was 20 cm. and the image-distance 60 cm., could you theoretically 
 determine any other object-distance and image-distance for the same 
 positions of object and screen? 
 
 13. In similar manner, experimentally determine the effect that 
 the position of the object has upon the character of the images 
 formed by a concave lens, and write a brief discussion of the results 
 attained. 
 
 14. Focus a magnifying glass on a finely divided decimeter scale. 
 Hold a similar scale at the distance of distinct vision (about 25 cm.). 
 With one eye, look through the lens at the first scale and with the 
 other eye look directly at the other scale. By continued trial, the eyes 
 will become accustomed to the unusual conditions, and the two images 
 will appear as if one was superposed on the other. Then count how 
 many divisions of the magnified scale correspond to a certain number 
 of divisions of the other scale. Divide the latter number by the 
 former to determine the magnifying power of the lens. 
 
 15. Determine the focal distance of the lens used in Exercise 14 
 and call it f. Call the distance taken in that exercise as the distance 
 
 of distinct vision, v. Determine the value of --f 1 and compare it 
 with the magnifying power of the lens as determined in Exercise 14. 
 
868 SCHOOL PHYSICS. 
 
 V. SPECTKA, CHROMATICS, ETC. 
 Analysis. 
 
 Experiment 242. Admit a sunbeam through a small opening in 
 the shutter of a darkened room. In the path of the beam, place a 
 prism, as shown in Fig. 273. Instead of the colorless image of the 
 
 FIG. 273. 
 
 sun at E, there appears upon the white screen a many-colored band 
 changing gradually from red at the lower end, through all the colors 
 of the rainbow, to violet at the upper end. 
 
 Experiment 243. Paste a strip of white paper 3 x 0.2 cm. upon a 
 black card. Upon a similar card, paste, end to end, strips of red, of 
 white, and of blue paper, each 1 x 0.2 cm. In a well-lighted room, 
 place the first card with the white strip vertical. Hold a prism with 
 its refracting edges vertical, and look through it at the white strip. 
 On its way to the eye, the beam of white light from the strip will be 
 separated into differently colored parts. You will see a colored band 
 instead of the white strip. Similarly, view the tri-color strip on the 
 other card, and carefully compare the three colored bands that cor- 
 respond to the three parts of the strip. 
 
 295. Dispersion. The separation of differently colored 
 rays by refraction is called dispersion. Experiment 242 
 shows that white or colorless light, like that of the sun, is 
 
SPECTRA, CHROMATICS, ETC. 369 
 
 a mixture of radiations of varying color and refrangi- 
 bility. The differences in deviation arise from differ- 
 ences of wave-length, the angle of deviation increasing 
 as the wave-length diminishes. 
 
 296. Spectra. The many-colored image of the sun pro- 
 jected on the screen in Experiment 242 is called a spectrum. 
 It is called a solar spectrum when the source of light is 
 under consideration, and a prismatic spectrum when the 
 method of producing it is under consideration. Most in- 
 candescent bodies emit light of varying wave-length and 
 refrangibility. 
 
 (a) These prismatic colors are generally described as violet, in- 
 digo, blue, green, yellow, orange, and red. The initial letters of 
 these terms form the meaningless, mnemonic word "vibgyor." 
 
 FIG. 274. 
 
 In fact, the gradations of color are imperceptible. The differently 
 colored images of the sun overlap, as shown in Fig. 274. Conse- 
 quently, such an opening in the shutter gives an impure spectrum. 
 
 Synthesis. 
 
 Experiment 244. Repeat Experiment 242, and hold a second prism 
 in a reversed position close behind the first. The light dispersed by 
 the first prism will be reunited by the second, and emerge as colorless 
 light. The two prisms have the effect of a plate with its refracting 
 faces parallel. 
 
 Experiment 245. Let light that has been dispersed by a prism fall 
 upon an achromatic convex lens as shown in Fig. 275. It will be re- 
 fracted to a focus and recombined to form white light. Hold a card 
 24 
 
370 
 
 SCHOOL PHYSICS. 
 
 between the prism and the lens so as to cut off the red light and 
 notice the focus of what remains. Similarly cut off the violet light, 
 
 FIG. 275. 
 
 and again notice the focus of what remains. A concave mirror may 
 be used to reflect the light to a focus instead of using the lens as 
 above described. 
 
 Experiment 246. Make a "Newton disk," painting the prismatic 
 colors in proper proportion as indicated by Fig. 276, or pasting sectors 
 of properly colored paper 
 upon cardboard. Tt is bet- 
 ter to divide the surface 
 given to each color into 
 smaller sectors arranged 
 alternately as shown in 
 Fig. 277. Fasten this disk 
 to a large top, or to a 
 whirling table, and cause 
 it to revolve rapidly. The 
 1 blends the colors, and the disk appears grayish 
 
 FIG. 276. 
 
 FIG. 277. 
 
 " persistence of vision 
 
 white. 
 
 Disks about 15 or 20 cm. in diameter may be cut from colored 
 
 paper, and a hole cut at the center of each of such size that the disks 
 
 may be slipped over the spindle of the 
 whirling table. By cutting each along 
 a radial line, the several disks may 
 be worked into each other as shown in 
 Fig. 278, and in such a way as to expose 
 the several colors to view in any desired 
 FIG. 278. proportion. 
 
SPECTRA, CHROMATICS, ETC. 371 
 
 Experiment 247. Hold a hand mirror near the dispersing prism 
 so as to reflect the refracted light to a distant wall or ceiling. Give a 
 rapid, angular motion to the mirror so that the spectrum moves to 
 and fro very quickly in the direction of its length. The spectrum 
 changes to a band of white light with a colored spot at each end. 
 
 297. The Composition of White Light. We have now 
 shown, by both analysis and synthesis, that white light is 
 composed of the prismatic colors. We have decomposed 
 white light into its constituents, and recombined these 
 constituents into white light. 
 
 Experiment 248. With a double-convex lens in a darkened room 
 project on the screen an image of the aperture in the shutter. The 
 white image will be fringed with color. 
 
 298. Chromatic Aberration. Because of their greater 
 refrangibility, the focus of the violet rays is nearer the 
 lens than the focus of the red rays, 
 
 as illustrated in Fig. 279. If the 
 screen is as near the lens as the 
 focus marked v, the outer fringe is 
 
 j .j. ,1 . (. - FIG. 279. 
 
 red ; if the screen is as far from 
 
 the lens as the focus marked r, the outer fringe is violet. 
 This difference in the deviation of differently colored rays 
 is called chromatic aberration. 
 
 (a) A double-convex lens of crown-glass may be combined with a 
 plano-concave lens of flint-glass so as to overcome the dis- 
 /v\ persive effect for some of the colors without overcoming 
 
 / \ i the converging effect. As such a compound lens forms 
 an image that is nearly free from the fringe of spectral 
 colors, it is called an achromatic lens. 
 
 Experiment 249. Gradually raise the temperature of 
 FIG. 280. a pi a ti num wire by an electric current. The first radia- 
 tions emitted are those of " obscure heat " ; i.e., they affect the nerves 
 
372 SCHOOL PHYSICS. 
 
 of general sensation only. The vibrations increase in frequency and 
 amplitude with the temperature, and, at about 525, the eye perceives 
 the wire as a dark red line. As the temperature continues to rise, 
 waves of shorter and shorter wave-length are added, while those 
 previously emitted are increased in amplitude. The wire succes- 
 sively appears orange and yellow and then becomes white hot, the 
 light emitted being exceedingly complex. 
 
 299. Color is a property of light, and depends upon wave- 
 length. Thus, the relation between color and light is the 
 same as that between pitch and sound. 
 
 (a) The wave-lengths that correspond to the several prismatic 
 colors as they appear in the solar spectrum are as follows : 
 
 Violet, 4,059 
 
 Indigo (violet-blue), 4,383 
 
 Green, 5,271 
 Yellow, 5,808 
 
 Orange, 5,972 
 Red, 7,000 
 
 Blue (cyan-), 4,960 
 
 These magnitudes are for the middle points of the several colors, and 
 represent ten-millionths of a millimeter. Light of only one wave- 
 length is said to be monochromatic or homogeneous. 
 
 (&) An incandescent body emits light with wave-lengths that grade 
 imperceptibly from values less to values greater than any of those 
 given above. When the wave-lengths are much less or greater than 
 those above given, the radiation is incapable of exciting vision. 
 Within the limits of visibility are an indefinitely great number of 
 wave-lengths, and a correspondingly great number of colors. When 
 light of all grades of refrangibility within these limits is blended, as 
 it is in sunlight, the resultant effect is white or colorless light. When 
 the light that corresponds to some of the prismatic colors is wanting, 
 the resultant effect of blending what is present is colored light. 
 Many artificial lights are deficient in some of these wave-lengths. 
 
 (c) Since the wave-length for the extreme red is approximately 
 twice that of the extreme violet, it may be said that the range of the 
 visible spectrum is only about one octave. The full spectrum, from 
 the extreme ultra-violet to the longest waves yet recognized, embraces 
 more than seven octaves. These invisible spectra have been explored 
 with delicate thermoscopes and by photography. Wave-lengths twenty 
 times that of the visible red, and corresponding to the temperature of 
 melting ice, have thus been detected in the radiation of the surface of 
 
SPECTRA, CHROMATICS, ETC. 373 
 
 the moon. The method of phosphorescence is also employed, while 
 fluorescence is made use of in studying the ultra-violet region. 
 
 (of) Every sensation of light that the human eye experiences is the 
 effect of impressing about five hundred trillion (5 x 10 14 ) waves upon 
 the ether each second. If the frequency of the ether waves is much 
 lower, the result is chiefly heat. 
 
 Color of Bodies. 
 
 Experiment 250. Repeat Experiment 242, and hold a piece of deep 
 red glass between the slit in the shutter and the prism. Notice that 
 the intensity of illumination is reduced less in the red than in any 
 other part of the spectrum. 
 
 Experiment 251. Paste three strips of paper, one white, one 
 vermilion-red, and one aniline-violet, each about 3 x 0.2 cm., upon 
 sheets of black cardboard. Successively place these strips in a strong 
 light, and look at them through a prism held with its refracting edge 
 parallel to the length of the strips. Carefully compare the coloring 
 of the images of the three strips thus viewed. 
 
 Experiment 252. Paint three narrow strips of cardboard, one 
 vermilion-red, one emerald-green, and the other aniline-violet. Be 
 sure that the coats are thick enough thoroughly to hide the card- 
 board. When dry, hold the red strip in the red of the solar spectrum ; 
 it appears red. Move it slowly through the orange and yellow ; it 
 grows gradually darker. In the green and colors beyond, it appears 
 black. Repeat the experiment with the other two strips, and carefully 
 notice the effects. 
 
 Experiment 253. Make a loosely wound ball of candle-wick ; soak 
 it in a strong solution of common salt in water ; squeeze most of the 
 brine out of the ball ; place the ball in a plate, and pour alcohol over 
 it. Take it into a dark room and ignite it. Examine objects of 
 different colors, as strips of ribbon or cloth, by this yellow light. 
 Only yellow objects will have their usual appearance. 
 
 Experiment 254. In a clear tumbler or large beaker of water, 
 dissolve a little white castile soap, or stir a few drops of an alcoholic 
 solution of mastic. Hold the vessel in the hand, and examine the 
 liquid by transmitted sunlight. Notice that it appears yellowish-red. 
 In a small test-tube, either liquid will appear colorless. Place a black 
 
374 SCHOOL PHYSICS. 
 
 screen behind the vessel and examine the liquid by reflected sunlight. 
 Notice that it appears blue. 
 
 300. The Color of a Body depends upon the light that 
 the body reflects or transmits to the eye. The color of the 
 light thus sent to the eye depends partly upon the nature 
 of the incident light, and partly upon the nature of the 
 body. Some bodies have a power that may be described 
 as selective absorption, reflecting or transmitting light of 
 certain wave-lengths, and absorbing the others. When 
 a house is painted yellow, the painters lay on not a yel- 
 low color but a substance that absorbs from sunlight all 
 the colors except yellow. If the light incident upon a 
 body has only the wave-lengths that the body absorbs, 
 the body can send no light to the eye and, therefore, 
 appears black. 
 
 (a) A red ribbon is red because it reflects light of the particular 
 wave-length that corresponds to the sensation of redness, and absorbs 
 the rest. A white ribbon is white because it reflects the same propor- 
 tion of all the light that constitutes sunlight. A piece of blue glass 
 is blue because it transmits or reflects light of the particular wave- 
 length that corresponds to the sensation of blueness, and absorbs the 
 rest. Glass that absorbs none of the incident light is colorless. 
 
 (&) The earth's atmosphere freely transmits yellow and red light, 
 and freely reflects blue light after the manner of the solutions used in 
 Experiment 254. The blue of the sky is due to light thus reflected. 
 When the sun is near the horizon, its light traverses a thicker layer 
 of air than it does at noon. Hence the predominance of yellow and 
 red in the light of the morning and evening hours. 
 
 Complementary Colors. 
 
 Experiment 255. Repeat Experiment 246, and receive the red and 
 orange light upon a prism of small refracting angle placed behind 
 the lens. The prism will deflect the red and orange, and form a 
 reddish colored image at n. The violet, indigo, blue, green, and 
 
SPECTRA, CHROMATICS, ETC. 
 
 875 
 
 FIG. 282. 
 
 yellow light, not caught by the prism, will unite at / to form a 
 greenish image. When the prism is removed, the reddish light that 
 fell at n, and the greenish 
 light that fell at /, unite to 
 form white light. By shifting 
 the position of the prism, other 
 parts of the beam may be de- 
 flected to the side, giving rise 
 to various pairs of colors, as 
 orange and blue, etc. Each of these pairs of colors has this property 
 in common, that when united they form white light. 
 
 Experiment 256. Again repeat Experiment 246, holding a paper 
 
 screen in front of the lens. 
 Mark the positions of the yel- 
 low and blue parts of the spec- 
 trum on the paper, and cut 
 narrow slits across the spec- 
 trum so as to allow the yellow 
 and the blue light to pass 
 
 through the lens. These two simple colors will be blended by the 
 lens, forming a light that is nearly white. The effect of mingling 
 any two colors may be determined in this way. 
 
 Experiment 257. Lay a piece of blue paper and a piece of yellow 
 paper, each about 5 cm. square, jiipon a black horizontal surface and 
 about 5 cm. apart. Hold a piece of plate glass 10 or 15 cm. above 
 the colored papers and in a vertical plane that passes between them. 
 Looking obliquely downward, you may see one of the papers by light 
 that the glass transmits, and an image of the other paper by light that 
 the glass reflects. By trial, you can find positions for the glass and 
 eye such that the object seen by the transmitted light and the image 
 produced by the reflected light overlap each other with a blending of 
 their colors. 
 
 301. Complementary Colors are any two colors the 
 blending of which produces ivhite light. If all the colors 
 of the solar spectrum are divided into two parts and the 
 colors in each part are blended, each resultant color evi- 
 
376 
 
 SCHOOL PHYSICS. 
 
 FIG. 283. 
 
 dently has what the other needs to make white light. 
 Either of such colors is said to be complementary to the 
 other. When complementary colors are placed in prox- 
 imity, each heightens the effect of the other, by contrast. 
 
 (a) Any two colors standing opposite each other in Fig. 283 are 
 complementary to each other. If such 
 colors are blended, the resultant is white 
 light; if any two alternate colors are 
 blended, the resultant will be the color 
 that appears between them in the figure. 
 
 Experiment 258. Cut holes 8 cm. in 
 diameter at the middle of two boards 
 each 18 x 10 cm. and, in each case, re- 
 move part of the strip remaining at 
 the middle of one of the long edges. 
 Thinly coat the circular edges with 
 melted beeswax or paraffine. Provide 
 four pieces of clear window glass, 10 x 18 cm., and fasten one of them 
 with marine glue to each side of each board, thus covering the open- 
 ings. The glue and the surfaces to be joined should be heated. The 
 glue may be thinned, if necessary, with naphtha. Fill one of these 
 " chemical tanks " with a solution of copper sulphate, and the other 
 with a solution of potassium dichromate. Kepeat Experiment 242, 
 and hold the yellow solution between the shutter and the prism. 
 Notice that the solution absorbs the radiations of shorter wave-length 
 and thus cuts the violet, indigo and blue from the spectrum. Change 
 the tanks, and notice that the blue solution absorbs the radiations of 
 greater wave-length and thus cuts the yellow, orange and red from 
 the spectrum. If both solutions are interposed, the green alone will 
 be freely transmitted. 
 
 Experiment 259. With a yellow-colored crayon, draw a broad 
 mark on the blackboard. Along the same line, draw a similar mark 
 with a blue crayon. Also mix a small quantity of chrome-yellow 
 with a like quantity of some ultramarine-blue pigment. The blend- 
 ing of the blue and the yellow colors in Experiment 256, gave a 
 white; the blending of the yellow and the blue pigments gives a 
 green. 
 
SPECTRA, CHROMATICS, ETC. 377 
 
 302. Mixing Pigments is a very different thing from 
 mixing colors, as has just been illustrated. In the ma- 
 jority of cases, the scattering of incident light takes place 
 not only at the surface of bodies but also at distances 
 below the surface. This distance is generally small but 
 in some cases it is considerable. When sunlight falls 
 obliquely upon a piece of blue glass, part of the incident 
 light is reflected at the anterior surface of the glass ; the 
 color of this reflected light is white. Another part of 
 the incident light is reflected from the posterior surface ; 
 the color of this light that has twice traversed the thick- 
 ness of the glass is blue, the radiations of other wave- 
 lengths having been absorbed. The difference in the 
 colors may be seen by receiving the reflected light upon a 
 screen. In the case of pigments, most of the scattered 
 light comes from below the surface. In Experiment 259, 
 the yellow pigment removed most of the violet, indigo 
 and blue by such absorption. The blue pigment similarly 
 removed most of the yellow, orange and red. (Compare 
 Experiment 258.) The radiations that escaped both were 
 of the particular wave-length that constitutes green : 
 
 ffl&tt- 
 
 Experiment 260. Fill the bulb of an air thermometer with clear 
 water. Cut a circular opening (somewhat smaller than the bulb) in 
 a large sheet of cardboard. Reflect a sunbeam into a darkened room 
 so that it shall pass through the opening in the cardboard and fall 
 upon the water-filled bulb. Adjust the position of the bulb until 
 circular spectra are thrown by the bulb back upon the cardboard 
 screen. 
 
 303. A Rainbow is a solar spectrum formed by water- 
 drops. The necessary conditions are : 
 
378 
 
 SCHOOL PHYSICS. 
 
 (1) A shower during sunshine. 
 
 (2) That the observer shall stand with his back to the 
 sun, and facing the falling drops. 
 
 (a) The center of the circle of which the rainbow forms a part .is 
 in the prolongation of a line drawn from the sun through the eye of 
 the observer. This line is called the axis of the bow. 
 
 (b) Often, a second bow is visible. The inner or primary bow is 
 much brighter than the other; the outer or secondary bow has the 
 order of colors reversed, as indicated in Fig. 284. 
 
 (c) The rays of sunlight incident upon the rain-drops are refracted 
 as they enter the drop, internally reflected, and chromatically dis- 
 persed, as illustrated in Experiment 260. The drop at V has an angu- 
 lar distance of 40 from EO, the axis of the bow, and sends violet 
 rays to the eye at E, and red rays below the eye. Other drops, at the 
 
 same angular distance from EO, send vio- 
 let light to the eye and, therefore, form a 
 violet-colored circular arc of which V is 
 the radius of curvature. Similarly, the 
 angle of deviation for red rays is such 
 that the drop, R, at an angular distance 
 of 42 from EO, sends red rays to the eye 
 of the observer and violet rays above the 
 eye. Other drops at the same angular dis- 
 tance send red light to the eye and, there- 
 fore, form a red-colored circular arc, of 
 which OR is the radius of curvature. The primary bow, therefore, 
 has an angular width of 2, the other prismatic colors ranging in 
 regular order between the violet and the red. 
 
 (d) The secondary bow involves two reflections within the rain- 
 drops, as shown at r and v. The drops that send these rays to the eye 
 are at the angular distances of 51 and 54 respectively from EO. As 
 some light is lost at each reflection, the secondary bow is fainter than 
 the primary. 
 
 Pure Spectra. 
 
 Experiment 261. Cut a very narrow slit, 2 or 3 cm. long, in a piece 
 of tin or of tin-foil, and fasten the sheet over the opening in the shutter 
 of a darkened room so that the slit shall be horizontal. Hold a prism 
 about 1.5 m. from the slit and with its edges horizontal. Looking 
 
 FIG. 284. 
 
SPECTRA, CHROMATICS, ETC. 
 
 379 
 
 through the prism at the slit, turn the prism about its axis until the 
 colored image of the slit is at the least angular distance from the slit 
 itself. The colors of the image will show with a greater distinctness 
 than before observed. 
 
 Experiment 262. Change the position of the tin-foil used in Ex- 
 periment 261, so that the slit shall be vertical. Using a convex lens 
 with a focal distance of about 30 cm., project an image of the slit upon 
 a white screen at a considerable distance. Place a glass or a carbon 
 disulphide prism near the lens, and between it and the screen. See 
 that its edges are vertical, and that it is properly placed for mini- 
 mum deviation. Shift the position of the screen so that the rays from 
 the prism fall normally upon it, but keeping it at the same distance 
 from the lens. The spectrum visible upon the screen will be more 
 distinct than any before observed. 
 
 304. A Pure Spectrum is made up of a succession of 
 colored images with little or no overlapping. The first 
 requisite in preventing the overlapping, like that of the 
 impure spectrum described in 296 (a), is that the slit 
 be very narrow. 
 
 (a) A spectroscope is an instrument used to produce a spectrum of 
 the light from any source, and for its study. It affords a delicate 
 means of chemical 
 analysis and is one of 
 the most powerful 
 aids to modern 
 science. In one of its 
 simple forms it con- 
 sists of, 
 
 (1) A collimator, 
 C, a tube with an ad- 
 justable slit with par- 
 allel edges at the outer 
 end through which the 
 light enters, and at the 
 
 other end a collimating lens that brings the rays into a parallel beam. 
 
 (2) A prism, P, or a series of prisms, that receives the radiation 
 from C, and disperses it, thus forming a spectrum. 
 
 FIG. 285. 
 
380 SCHOOL PHYSICS. 
 
 (3) A telescope, jT, through which the magnified image of the spec- 
 trum is viewed. The spectrum is received directly upon the retina of 
 the eye and may be distinctly seen even when the radiation is feeble. 
 
 It is often necessary to determine the position of certain lines that 
 appear in the spectrum ( 307). In such cases, the spectroscope is 
 provided with a third tube that carries a collimatinglens, and a trans- 
 parent plate on which a fine scale has been engraved. Light, as from 
 a candle, enters the outer end of this tube, passes from the collimat- 
 ing lens at the inner end, and is reflected from the face of the prism 
 so that it enters the telescope with the light that is being examined. 
 Thus the spectrum and the image of the scale are viewed simultane- 
 ously and in close juxtaposition. 
 
 A pocket form of the spectroscope, often called a direct-vision 
 spectroscope, has two telescoping tubes. The inner tube carries a 
 series of three or more prisms made of different kinds of glass, and 
 so placed as to overcome the deviation of the light from a straight 
 path and yet to preserve the dispersion. The outer tube carries an 
 adjustable slit for the admission of light which, after dispersion, is 
 received by the eye at the other end of the instrument. Such an in- 
 strument is not very expensive, and may be made to answer for the 
 purposes of this book. 
 
 Spectrum Analysis. 
 
 Experiment 263. Examine a candle-flame with a spectroscope, and 
 notice that the colored spectrum is continuous through all the 
 prismatic colors. Evidently, the radiation is extremely complex. 
 
 Experiment 264. Dip a platinum wire or a strip of asbestos into 
 a solution of sodium chloride (common salt), and hold it in the almost 
 colorless flame of a Bunsen burner. The sodium vapor colors the 
 flame yellow. Examine this sodium flame with a spectroscope, and 
 notice that the spectrum consists of a bright yellow line instead of 
 the continuous multi-colored band. If your spectroscope was of high 
 dispersive power, it would show that the sodium line is really double. 
 These two fine lines represent wave-frequencies of 508.3 x 10 12 and 
 509.3 x 10 12 respectively. If the flame is similarly colored with a 
 solution of chloride of lithium, the bright line spectrum will have 
 a carmine color. If the flame is colored with strontium nitrate, the 
 crimson flame will yield a spectrum composed of bright lines the 
 colors and positions of which are different from those of either of 
 the spectra previously examined. If the flame is colored with a mix- 
 
SPECTRA, CHROMATICS, ETC. 381 
 
 ture of these three substances, the spectrum will show all of the bright 
 lines previously observed. 
 
 305. Spectrum Analysis. It has long been known that 
 when certain substances are heated they give colored 
 flames, the yellow of sodium, the lilac of potassium, etc., 
 being familiar. Each of the chemical compounds used in 
 Experiment 264 has a metallic base, sodium, lithium, or 
 strontium. The vapors of these metals yielded the spec- 
 tra observed. Like tuning-forks, free molecules have 
 definite vibration-periods; e.g., the ether waves set up 
 by incandescent sodium have the same frequency whether 
 the sodium is solar, stellar or terrestrial. The character- 
 istic frequency of the radiation thus established deter- 
 mines the relative position of the corresponding spectrum. 
 As the spectra of such substances are characteristic, i.e., 
 no two of them are alike, they may be used for the identi- 
 fication of the several substances that produce them. 
 This method of analyzing composite radiations, or of iden- 
 tifying substances by the spectra of their incandescent vapors, 
 is catted spectrum analysis. 
 
 (a) As a condition necessary for the production of the spectrum, 
 the temperature must be so high that the substance to be examined 
 may be vaporized, disassociated, and made incandescent. If a com- 
 pound gas or vapor is not disassociated at the temperature employed, 
 it gives its own spectrum instead of the spectra of its constituent 
 elements. Having mapped the spectra of all known substances, the 
 presence of new lines in any spectrum would indicate the presence of 
 a substance previously unknown. The quantity of material required 
 for such examination is exceedingly small, a hundred-millionth of a 
 milligram of strontium giving the spectrum characteristic of that 
 element. The chemist is thus provided with a method of qualita- 
 tive analysis of far greater power than any previously known. By it, 
 the chemistry of the stars has been studied, and the extreme gen- 
 erality of the diffusion of the elements in nature has been shown, 
 
382 SCHOOL PHYSICS. 
 
 and several new elements have been discovered. The method has 
 been successfully applied in the industrial arts. 
 
 Experiment 265. Remove the objective from an optical lantern 
 ( 323). From the lantern, send a beam of electric or calcium light 
 through a narrow vertical slit in a tin screen. Beyond the screen, 
 place a double convex lens to receive the light that passes through the 
 slit. Beyond the lens, place a prism so as to throw a spectrum on a 
 screen still beyond. Place a Bunsen burner or an alcohol lamp be- 
 tween the lantern and the slit and, in its almost colorless flame, hold a 
 bit of sodium. The metal will burn giving an intense yellow to the 
 flame. Notice that the yellow of the spectrum, instead of being more 
 intensely illuminated, is marked by a dark band. Then hold a piece 
 of tin between the lantern and the flame and so as to cut off the light 
 of the lantern from the upper part of the slit. The upper part of the 
 slit is now traversed by light from the sodium-colored flarne, and 
 the lower part of the slit by light from both the lantern and the 
 flame. The image of the slit is inverted, and two parallel spectra are 
 thrown on the screen. One of these is the bright-line spectrum of 
 sodium ; the other shows a dark line on a continuous spectrum. 
 Notice that the bright line of one spectrum falls in the same relative 
 position as the dark line of the other spectrum. 
 
 Experiment 266. Place some common salt on the wick of an 
 alcohol lamp. The sodium of the salfr will give a yellow tinge to the 
 flame. Let a beam of electric or calcium light pass through this 
 yellow flame and fall upon the collimator slit of the spectroscope ; 
 study its spectrum. A dark line crosses the spectrum, which thus be- 
 comes discontinuous. Shut off the lantern light, and the sodium 
 flame again gives its bright-line spectrum as before. Turn on the 
 lantern light, and remove the sodium-colored flame. Notice that the 
 spectrum is continuous. Replace the sodium flame, and notice that 
 the dark line of the discontinuous spectrum falls in the same rela- 
 tive position as the bright line of the sodium spectrum, just as if the 
 sodium vapor absorbed light of the same refrangibility as that it emits. 
 
 306. Kinds of Spectra. From the foregoing, it appears 
 that a spectrum may be continuous or discontinuous, and 
 that a discontinuous spectrum may be a bright-line spec- 
 trum or a dark-line spectrum. For obvious reasons, 
 
UNIVERSITY OF CALIFORNIA 
 
 dark-line spectra are sometimes called reversed spectra, or 
 absorption spectra. 
 
 307. The Fraunhofer Lines. A spectrum of sunlight 
 is crossed by dark lines, many hundreds of which have 
 been counted and 
 accurately mapped. 
 
 The more conspic- 
 uous of these dark 
 v .. ,. FIG. 286. 
 
 lines are distin- 
 guished by letters of the alphabet, as shown in Fig. 286. 
 A few of these dark lines in the solar spectrum are due 
 to absorption in the earth's atmosphere, but by far the 
 greater number originate in the selective absorption of 
 the solar atmosphere itself. 
 
 (a) In accordance with the principles illustrated by the experiments 
 immediately preceding, and as more fully explained in the paragraph 
 immediately following, it is supposed that the nucleus of the sun 
 would give a continuous spectrum if it was not surrounded by gases 
 and metallic vapors that absorb some of the rays to which their own 
 spectra correspond. Just as the D-line corresponds to sodium, so the 
 greater number of the Fraunhofer lines have been identified in the 
 spectra of known terrestrial substances. The presence of at least 
 thirty-six elements in the sun's atmosphere has been thus established, 
 the identity of the absent wave-frequencies indicating the identity of 
 the absorbing media. 
 
 (6) The indices of refraction given in 284 (c) are for light that 
 has the particular wave-frequency that corresponds to the Fraunhofer 
 D-line. 
 
 308. Laws of Spectra. The following laws have been 
 established : 
 
 (1) Incandescent solids and liquids give continuous 
 spectra. This is true of vapors and gases also when they 
 
384 SCHOOL PHYSICS. 
 
 are under great pressures. The spectrum from the flame 
 of a candle, of kerosene, or of illuminating gas is con- 
 tinuous, being due to the incandescent carbon particles 
 suspended in the flame. 
 
 (2) Incandescent rarefied vapors and gases give discon- 
 tinuous spectra consisting of colored bright lines or bands. 
 These lines or bands have a definite position for each sub- 
 stance and are, therefore, characteristic of it. Thus the 
 sodium spectrum consists of bright yellow lines, corre- 
 sponding in position to the D-line as shown in Fig. 286. 
 
 (3) If light from an incandescent solid or liquid passes 
 through a gas at a temperature lower than that of the incan- 
 descent body, the gas absorbs rays of the same degree of 
 refrangibility as that of the rays that constitute its own 
 spectrum. This absorption is somewhat analogous to that 
 mentioned in 204. The result is a spectrum continuous 
 except as interrupted by dark lines that occupy the po- 
 sition that the bright lines in the spectrum of the gas 
 itself would occupy. Thus, the emission spectrum of 
 sodium corresponds in position to the D-line ; the sodium 
 flame absorbs light of the same refrangibility, and its 
 absorption spectrum falls in the same position. 
 
 (a) If the source of radiant energy under spectroscopic examina- 
 tion is approaching the observer, the effect of the motion will be the 
 same as if the wave-length was shortened ; the characteristic lines will 
 be moved toward the violet end of the spectrum. If the source of 
 radiation is moving from the observer, the opposite effects will follow. 
 Compare 192 (6). Such displacement of spectra lines has enabled 
 investigations of the motions of even the " fixed " stars. 
 
 Experiment 267. Hold a pane of glass between the face and a 
 hot stove; the glass shields the face from the heat of the stove. 
 Hold the glass between the face and the sun ; the glass does not 
 shield the face from the heat of the sun. 
 
SPECTRA, CHROMATICS, ETC. 385 
 
 309. Thermal Effects may be detected throughout the 
 length of the visible spectrum and beyond in each direc- 
 tion, i.e., in the infra-red spectrum and in the ultra-violet 
 spectrum. The infra-red radiation is of longer, and the 
 ultra-violet radiation is of shorter wave-length than that 
 of any part of the visible spectrum. The former is 
 present in the spectrum from any hot body ; the latter, 
 in that from a body at a high temperature, as the incan- 
 descent carbons of an arc electric light. When radiant 
 energy is considered with reference to its heating effects, 
 it is sometimes called "radiant heat," a term that is evi- 
 dently misleading, but that has acquired a good foot-hold 
 in the literature of science. Similarly, the radiation of 
 the infra-red region is spoken of as "obscure heat." 
 
 (a) Lenses and prisms of rock-salt are generally" used in the study 
 of the heating effects of radiant energy, as glass absorbs much of the 
 energy of the longer ether waves, as was shown in Experiment 267. 
 When a solar spectrum is produced with a rock-salt prism, the maxi- 
 mum heating effect is found in the infra-red region, but with a normal 
 spectrum (diffraction-spectrum, 315), the maximum heating effect 
 coincides somewhat closely with the maximum luminous effect. 
 
 (6) When the heating effects of radiant energy rather than the 
 luminous effects are under consideration, the ability freely to trans- 
 mit the ether waves constitutes diathermancy ; the corresponding 
 inability constitutes athermancy. In other words, diathermanous 
 corresponds to transparent, and athermanous to opaque. Glass, water 
 and alum transmit light, but absorb nearly all of the energy radiated 
 from a vessel filled with boiling water, i.e., they are transparent and 
 athermanous. A solution of iodine in carbon disulphide is opaque 
 and diathermanous. Dry air is very diathermanous ; watery vapor is 
 decidedly athermanous. 
 
 310. Theory of Exchanges. All bodies at tempera- 
 tures above absolute zero must radiate energy that may 
 be converted into heat. When two bodies at different 
 
 25 
 
386 SCHOOL PHYSICS. 
 
 temperatures are placed near each other, one gains and 
 the other loses heat by radiation until both ha^e the same 
 temperature. Each radiates to the other, but while the 
 inequality of temperature continues, the hotter body gives 
 more than it receives, and vice versa. This is a brief 
 statement of Prevostfs theory of exchanges. 
 
 Absorption, etc. 
 
 Experiment 268. When there is snow on the ground, and the 
 sun is shining, spread a piece of white cloth and a similar piece of 
 black cloth on the snow, and notice whether the snow melts more 
 rapidly under one than under the other. 
 
 Experiment 269. Focus a sunbeam on the clear glass bulb of an 
 air thermometer, and notice the feeble effect produced. Coat the bulb 
 with candle soot, and repeat the experiment. Notice the greatly in- 
 creased effect. 
 
 Experiment 270. Secure two similar pieces of tin-plate at least 
 10 cm. square. Coat one face of one of the pieces with lampblack 
 (candle-soot). Support the two plates, with the painted surface ver- 
 tical, facing the other plate, and about 10 cm. from it. With small 
 bits of shoemaker's wax, fasten a small ball to the middle of the 
 outer face of each plate. Hold a hot bod} T , as a " soldering iron," 
 midway between the plates. Xotice which ball first falls. Repeat 
 the experiment several times to make certain whether the effect 
 was accidental or due to the lampblack. 
 
 Experiment 271. Provide two bright tin cans of the same size 
 and shape. In the cover of each, make a hole and insert the bulb 
 of a chemical thermometer. Blacken the outside of one can with 
 lampblack. Fill both cans with hot water from the same vessel and, 
 consequently, of the same temperature. At the end of half an hour, 
 pass the bulb of the thermometer through the holes in the covers, 
 and ascertain the temperature of the water in each can. It will be 
 found that the blackened can has radiated its heat more rapidly 
 than the other. Fill both cans with cold water, and set them in front 
 of a hot fire or in the sunshine. The temperature of the water in 
 
SPECTRA, CHROMATICS, ETC. 
 
 387 
 
 the blackened can rises more rapidly than that of the water in the 
 other can. 
 
 4 
 
 Experiment 272. Secure a piece of stoneware (Fig. 287) of any 
 black and white pattern. Xotice carefully what parts absorb the 
 most radiant energy. Heat 
 the plate intensely, view it in 
 
 FIG. 287. 
 
 a darkened room, and notice 
 carefully what parts radiate 
 the most energy (Fig. 288). 
 
 FIG. 288. 
 
 311. Radiation, Reflection and Absorption. -- Bodies 
 differ greatly in absorbing power. From the nature of the 
 case, a good absorber is a poor reflector. Lampblack is a 
 substance of maximum absorbing and of minimum reflect- 
 ing power. Further than this, the emission and the ab- 
 sorption of radiant energy go hand in hand, good absorbers 
 being good radiators, and good reflectors being poor 
 radiators, and vice versa. 
 
 312. Chemical Effects may be detected throughout the 
 length of the visible spectrum and beyond in each direc- 
 tion. The chemical changes upon which ordinary pho- 
 tography depends are most stimulated by the violet and 
 ultra-violet rays ; this, however, is not true of all chemical 
 changes, and even infra-red photography has been accom- 
 
388 SCHOOL PHYSICS. 
 
 plished. By exciting molecular agitation of the molecules 
 of sulphide of zinc with an electric current of about 
 10,000 alternations per second, Nikola Tesla demon- 
 strated, in 1894, the actinic value of u cold rays" by 
 taking photographs by phosphorescent light. 
 
 (a) It, therefore, appears that the long-time division of the spec- 
 trum into three parts, heat, light and actinism, was ill founded ; that 
 from one end of the spectrum to the other, the radiation differs intrin- 
 sically in wave-length only; and that the observed diversity of effect 
 is due to the character of the surface upon which the radiation falls. 
 
 (b) Lenses and prisms of quartz are generally used in the study of 
 the chemical effects of radiant energy as they absorb less of the 
 energy of the short ether waves than do those of glass. 
 
 313. Change of Vibration-Frequency. When solutions 
 of certain substances, such as esculin and sulphate of 
 quinine, are exposed to ultra-violet radiation, the solu- 
 tions lower the rate of vibration to that of an opalescent 
 blue light. This property of lowering the vibration- 
 frequency of ultra-violet radiation to the range of vision 
 is called fluorescence. Another class of substances, such 
 as the sulphides of barium, calcium, and strontium, are 
 luminous when carried from sunlight into a dark room 
 and, for a long time after, present the general appear- 
 ance of a hot body cooling. This property of shining in 
 the dark after exposure to light is called phosphorescence. 
 What is correctly termed phosphorescence has nothing to 
 do with phosphorus, the luminosity of which in the dark 
 is due to slow oxidation. The radiations that excite this 
 luminosity are those of high wave-frequency, so that phos- 
 phorescence is a species of fluorescence that lasts longer 
 after the excitation has ceased than the species just 
 described. The property has been taken advantage of for 
 
SPECTRA, CHROMATICS, ETC. 389 
 
 the production of what are called "luminous paints." 
 The luminous rays of an electric arc may be absorbed by 
 a solution of iodine in carbon disulphide, and the residual 
 infra-red rays reflected or refracted to a focus. A piece 
 of platinum or of charcoal at such a focus of non-luminous 
 radiation may be heated to incandescence. This raising 
 of the vibration-frequency of infra-red radiation to the 
 range of vision is called calorescence. 
 
 CLASSROOM EXERCISES. 
 
 1. Why is the rainbow a circular arc instead of a straight 
 band? 
 
 2. What does a wave-length of red light measure in centimeters ? 
 
 3. Taking the velocity of light to be 186,000 miles per second 
 and the wave-length of green light to be 0.00002 of an inch, how 
 many waves per second beat upon the retina of an eye exposed to 
 green light ? 
 
 4. How may spherical and chromatic aberration caused by a lens 
 be corrected? . 
 
 5. What name is given to the differential deviation by refraction 
 of rays of different wave-frequencies? 
 
 6. Why is a rainbow never seen at noon ? 
 
 7. Describe Fraunhofer's lines, and tell how they may be pro- 
 duced. 
 
 8. Under what circumstances will a spectrum be (a) continuous, 
 ( &) bright-line ; (c) dark-line ? 
 
 9. Why do not the sun's rays heat the upper atmosphere of the 
 earth as they pass through it ? 
 
 10. Show that the glass walls and roof of a greenhouse are a trap 
 for solar heat. 
 
 11. Why is it oppressively warm when the sun shines after a sum- 
 mer shower ? 
 
 12. Why is there greater probability of frost on a clear than on a 
 cloudy night ? 
 
 13. Explain the fact that the glass of a window may remain cold 
 while the sun's radiations are pouring through it and heating objects 
 in the room. 
 
390 
 
 SCHOOL PHYSICS. 
 
 14. What is meant by the statement that water is transparent and 
 athermanous ? 
 
 15. What is meant by "radiant heat," and what by "obscure 
 heat"? Why are these terms objectionable? 
 
 16. How can you cut out the short-wave radiations of an arc elec- 
 tric lamp? How can you cut out the long-wave radiations? 
 
 17. Why does a polished tea-urn remain warm longer than a similar 
 one with a roughened surface ? 
 
 18. Explain the apparent unsteadiness of an object seen across 
 the top of a hot stove. 
 
 19. Show that the watery vapor in the atmosphere acts as a blanket 
 for terrestrial objects. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Porte-lumiere or optical lantern ; crown- 
 glass, flint-glass, and carbon disulphide prisms ; a wooden block, 
 grooved and painted black ; cyan-blue and orange colored glass; pic- 
 ric acid ; copper sulphate ; ammonia water ; fine platinum wire ; in- 
 duction tube ; voltaic cell ; Pliicker-tube ; two Leslie cubes ; pane of 
 window glass about 9 x 12 inches; lampblack; India-ink; tin-foil; 
 white-lead; chemical tank; alum; iodine; carbon disulphide. 
 
 lw Cut a very narrow slit with straight, smooth edges in a piece of 
 cardboard. Fasten the cardboard across the opening of a porte- 
 lumiere or an optical lantern, with the slit vertical. With a convex 
 lens that has a focal distance of about 30 cm., project an image of the 
 slit upon a white screen at a considerable distance. Place a prism 
 
 (60) of crown-glass between the lens 
 and screen, close to the lens and with 
 its edges vertical. Turn the prism 
 about its axis until it is in the po- 
 sition of least deviation. Without 
 changing its distance from the lens, 
 set the screen so that the light re- 
 fracted by the prism falls perpendicu- 
 larly upon it. Describe the image and 
 mark on the screen its limits, and the 
 FIG. 289. position of any characteristic points. 
 
 Replace the crown-glass prism succes- 
 sively with flint-glass and carbon disulphide prisms, and note any 
 changes in the spectrum. Set a second prism near the first and with 
 
SPECTEA, CHROMATICS, ETC. 391 
 
 its base turned the same way, as shown in Fig. 289, so that the disper- 
 sion effect of the second may be added to that of the first, and note 
 any changes in the spectrum. 
 
 2. Shorten the slit used in Exercise 1 and hold the second prism 
 with its edges perpendicular to the edges of the first, so that the differ- 
 ently colored light emergent from the first shall be received upon a 
 face of the second, each color by itself. See if these rays of differing 
 wave-lengths are refracted equally by the second prism. 
 
 3. Arrange apparatus as described in Exercise 1, and cut a narrow 
 vertical slit from the screen so that light of some one color may pass 
 through the slit. Receive this light upon a prism behind the screen, 
 and see if there is any further dispersion, or any production of new 
 colors. Explain the result of your experiment. 
 
 4. Cut a slit 2.5 cm. long and 2 mm. wide in each of two pieces of 
 black cardboard, and support the two cards in a groove cut in a 
 blackened piece of wood. The width of the groove should be just 
 twice the thickness of the cards, so that the distance between the slits 
 may be adjusted by moving the cards in the groove. Repeat Experi- 
 ment 245, and hold the perforated cardboard screen between the lens 
 and the prism, and adjust the slits so that light of only two colors falls 
 upon the lens. Note the color of the spot formed by the synthesis 
 of these colors. Try other pairs of colors, and note the resultant color 
 in each case. Especially, try to find as many combinations as possible 
 that yield white light. 
 
 5. Place the three disks represented in Fig. 278 upon the whirling 
 table, and fasten them in position.. Turn the spindle rapidly, and note 
 the color of the blending. Change the proportions of the exposed 
 colors, and blend them again. Continue the work with a view of 
 determining the accuracy of the statement that any color of the spec- 
 trum may be produced by the composition of these three colors. 
 
 6. With a variety of similar disks, demonstrate the effect of blend- 
 ing complementary colors. 
 
 7. Admit two sunbeams to a darkened room, and cause them to 
 overlap on a white screen. Hold a piece of blue glass so that one of 
 the beams passes through it. Pass the other beam through a piece 
 of glass so chosen that the blending of the two colored beams pro- 
 duces a white spot on the screen. Shut off one of the beams, and 
 determine the effect of sending the other through both of the pieces 
 of glass. 
 
 8. While observing the solar spectrum with a spectroscope, hold a 
 
392 SCHOOL PHYSICS. 
 
 piece of cyan-blue glass over the slit of the instrument, and note the 
 effect. Then try a piece of orange-colored glass. Then study the 
 effect when the two pieces are superposed in front of the slit. Suc- 
 cessively try test-tube portions of a solution of picric acid, and of an 
 ammoniacal solution of copper sulphate. 
 
 9. Make a loop about 2 mm. in diameter at the end of a fine 
 platinum wire. Fuse a small bit of common salt into this loop. 
 Place an alcohol flame just beyond the slit of a spectroscope. Hold 
 the bead of salt in the edge of the flame nearest the spectroscope and a 
 little below the level of the slit. Examine the spectrum, and map the 
 position of any bright lines that you observe. Devise some way of 
 producing dark lines that occupy the same positions in the spec- 
 trum. 
 
 10. With an induction coil, illuminate a Pliicker-tube containing 
 some known gas, and examine its spectrum with a spectroscope. 
 Record a description of the spectrum. (See 506.) 
 
 11. Make a cubical metal vessel with edges of about 7 or 8 cm., 
 and vertical faces made respectively of polished brass, sheet lead, 
 bright tin-plate, and tin-plate that has been coated with lampblack. 
 Leave a small opening in the upper face. Such a vessel is called a 
 Leslie cube. Fill it with water, and bring the temperature to 10. 
 Place the cube 3 or 4 cm. from an air thermometer or from one bulb 
 of a differential thermometer, and note the effect upon the thermom- 
 eter. Raise the temperature successively to 20, 30, 40, etc. ; bring, 
 it .within the same distance of the thermometer, and note the effect 
 in each case. Record a comparison of the readings of the mercury 
 thermometer in the cube with the indications of the air thermometer, 
 and a clear statement of the relation between them. 
 
 12. Repeat one of the tests of Exercise 11, and then interpose a pane 
 of window glass between the cube and the thermometer. Explain the 
 effect produced by the screen. 
 
 13. With the same apparatus, test the absorptive powers of tin-foil, 
 lampblack, India-ink, and white-lead by successively coating the bulb 
 of the air thermometer with such substances. 
 
 14. Test the radiating powers of tin, lampblack, India-ink, and 
 white-lead by successively turning faces of the Leslie cube thus coated 
 toward the bulb of the air thermometer, being careful that the tem- 
 perature and the distance of the cube are the same in each instance. 
 Try to find some relation between the absorbing powers and the radi- 
 ating powers of these several substances. Also similarly test the 
 
INTERFEKENCE, DIFFRACTION, POLARIZATION. 393 
 
 radiating powers of faces of the cube that have been coated with 
 unglazed white paper and with white cotton cloth. 
 
 15. Repeat Experiment 228, holding a " chemical tank " (see Ex- 
 periment 258) so that the sun's rays shall pass through the two circu- 
 lar windows before they fall upon the lens. Fill the tank with a 
 solution of alum in water, and repeat the experiment. Determine the 
 effect, if any, that the presence of the tank, empty or filled, has upon 
 the result at the focus. Empty out the alum-water and fill the tank 
 with a solution of iodine in carbon disulphide, and repeat the experi- 
 ment. 
 
 VI. INTERFERENCE, DIFFRACTION, POLARIZATION, 
 
 ETC. 
 
 Experiment 273. In any convenient clamp, firmly press together 
 the centers of two pieces of clean, thick, plate-glass. Look obliquely 
 at the glass, and a beautiful play of colors will be seen surrounding 
 the point of greatest pressure. If the glass is illuminated by the 
 monochromatic light of a sodium flame (see Experiment 253), yellow 
 bands separated by dark bands will be seen. 
 
 314. Interference of Light. We have seen that two 
 wave-motions may combine in such a way as to neutralize 
 each other ( 206), and that such an interference is a 
 peculiarity of wave -motion,. The fact that light may thus 
 neutralize light is strong confirmation of the wave-theory. 
 
 (a) In the historical experiment of which Experiment 273 is a 
 modification, a plano-convex lens of little curvature was pressed upon 
 a flat piece of glass. When looked at 
 
 from above, the center of the lens thus - I ' 
 
 used is surrounded by rainbow-like bands t ^""""" f ( """"' 
 of color, known as Newton rings. Of the 
 light that falls vertically upon the lens, FIG. 290. 
 
 some is reflected at the curved surface, and 
 
 some from the upper surface of the plate under the lens. These 
 latter rays have to traverse twice the wedge-shaped film of air be- 
 tween the lens and the plate. Whenever the thickness of the air- 
 film is such that the two sets of reflected waves unite in opposite 
 
394 
 
 SCHOOL PHYSICS. 
 
 phases, interference is the result. If the apparatus is observed by 
 white light, and the red rays are destroyed at a certain distance from 
 the center of the lens, the color perceived at that distance will be 
 complementary to the destroyed red, and will form a circular green 
 band. If the apparatus is observed by red light, a dark ring will ap- 
 pear at the same distance. At another distance from the center of 
 the lens, the violet rays will be destroyed, and the circular band seen 
 at that distance will be due to the combination of the other constit- 
 uent rays of the light used. 
 
 (&) Interference colors similarly produced by reflection are often 
 seen in soap bubbles, in small quantities of oil that have been spread 
 over large sheets of water, in mica, selenite, ice, and other crystals. 
 Certain striated surfaces, like those of mother-of-pearl, some kinds of 
 shells and feathers, etc., owe their beautiful colors to the interference 
 of reflected light (see 315, 6). 
 
 Diffraction. 
 
 Experiment 274. With a fine needle, rule a number of fine parallel 
 lines upon a piece of glass that has been coated with India-ink. Take 
 pains to cut through the ink to the glass. Cut a slit 2 mm. wide in a 
 black card, and hold it at arm's length in front of a flame. Hold the 
 glass close to the eye and, through the scratched lines, look at the slit. 
 Notice the series of spectra on each side of the slit. 
 
 Experiment 275. Throw a sunbeam through a very small opening 
 in the shutter of a darkened room. Receive the beam upon a convex 
 
 FIG. 291. 
 
 lens of short focal length, placing a piece of red glass between the 
 aperture and the lens. Place an opaque screen with a sharp edge 
 beyond the focal distance of the lens, as at a, so as to cut off the lower 
 part of the cone of homogeneous light, and project the upper part 
 thereof upon a screen at b. A faint light is seen on the screen below the 
 level of a and, therefore, within the geometrical shadow. The part of the 
 screen immediately above the level of a contains a series of dark and 
 light bands, as shown at B, which is a front view of the screen at b. 
 
INTERFERENCE, DIFFRACTION, POLARIZATION. 395 
 
 315. Diffraction. When water waves strike an obstacle, 
 part of the energy of the wave is expended in producing a 
 second set of waves that seem to circle outward from the 
 side of the obstacle as a center. The original wave 
 (primary) passes directly onward, while the secondary 
 waves wind around behind the obstacle. In similar man- 
 ner, sound bends around a corner, but sound-shadows may 
 be produced if the wave-length is sufficiently small, or if 
 the obstacle is of great size compared with the length of 
 the sound waves. So ether waves are modified when they 
 traverse a minute opening or narrow slit, or impinge upon 
 an obstacle, e.g., a hair, so small as to be comparable 
 with the wave-length. The phenomena are identical 
 when the scale of the ex- 
 periment is the same. 
 If a beam of monochro- 
 matic light is passed 
 through a narrow slit 
 
 and received upon a screen in a dark room, a series of 
 alternately light and dark bands or " fringes " is seen ; 
 if white light is employed, a series of colored spectra is 
 obtained. Thus it appears that, under proper conditions, 
 rays may be bent and caused to penetrate into the shadow. 
 The interference-phenomena resulting from this action are 
 called diffraction. 
 
 (a) As the primary and secondary waves cut each other, they 
 unite at some points, crest with crest and, at other points, crest 
 with trough. At the latter points, we have interference of light 
 and the effects of colors produced thereby as explained above. 
 The halos sometimes seen around the sun and moon are due to 
 the diffraction of light by watery globules in the atmosphere. The 
 colors often seen on looking through a feather or one's half-closed 
 
396 
 
 SCHOOL PHYSICS. 
 
 eyelashes at a distant source of brilliant light are also due to 
 diffraction. 
 
 (&) When lines are ruled on the surface of glass, the ruled lines 
 become opaque, the spaces between them remaining transparent. A 
 system of close, equidistant, parallel lines ruled on glass, or on polished 
 (speculum) metal, constitutes a diffraction grating. Lines are ruled 
 for this purpose at the rate of 10,000 to 20,000 or even 40,000 to the 
 inch. Such gratings yield interference or diffraction spectra, which are 
 much used in spectroscopic work, and afford a simple means for 
 measuring the wave-length of ether vibrations. In these spectra, the 
 colors are distributed in their true order and extent according to their 
 differences in wave-length; while, in prismatic spectra, the less re- 
 frangible (red) rays are crowded together, and the more refrangible 
 B C D E F O H,. 
 
 H,H., 
 
 B C D E F G 
 
 FIG. 293. 
 
 (violet and blue) are correspondingly dispersed. For this reason, the 
 diffraction spectrum is called a normal spectrum. The upper part of 
 Fig. 293 represents a normal spectrum, and the lower part, a prismatic 
 spectrum. Comparing the two, the "irrationality of dispersion" of 
 the prismatic spectrum is seen. 
 
 316. Irradiation is the apparent enlargement of a strongly 
 
 illuminated object 
 when seen against a 
 dark ground. Thus, 
 when the two equal 
 circles shown in 
 Fig. 294 are care- 
 fully observed in a 
 FIG. 294. J 
 
 good light, one 
 
 seems to be larger than the other. 
 
INTERFERENCE, DIFFRACTION, POLARIZATION. 397 
 
 (a) Irradiation increases with the brightness of the object, 
 diminishes as the illumination of the object and that of the field of 
 view approach equality, and vanishes when they become equal. This 
 effect is very perceptible in the apparent magnitude of stars, which 
 look much larger than they otherwise would ; also in the appearance 
 of the new moon, the illuminated crescent seeming to extend beyond 
 the darker portion, as if the new moon was holding the old moon in 
 its arms. 
 
 Polarization. 
 
 Experiment 276. While looking through the plates of a pair of 
 tourmaline tongs, turn one of 
 the plates in its wire support. 
 The intensity of the light 
 transmitted will vary as the 
 plate is turned. When little 
 or no light is transmitted, the FIG. 295. 
 
 plates are said to be " crossed." 
 
 Experiment 277. Write your name on a sheet of paper, and cover 
 it with a crystal of Iceland spar. The lines will appear double, as 
 
 shown in Fig. 296. Place 
 the crystal over a dot on the 
 paper, hold the eye directly 
 over the dot, and slowly turn 
 the crystal around ; one of 
 the two images of the dot 
 will revolve about the other 
 image. Prick a pin-hole 
 through a card, and hold the 
 card against one side of the 
 crystal, look through the crystal at the pin-hole, and rotate the crystal 
 as before. 
 
 Experiment 278. Look through one of the plates of the tourmaline 
 tongs (Fig. 295) at the two images of the dot formed by the double 
 refraction of the Iceland spar as described in Experiment 277. One 
 of the images will be much fainter than the other. Turn the tourma- 
 line plate slowly around, and notice that one image grows fainter and 
 the other brighter, the maximum brightness of one being simultane- 
 ous with the extinction of the other. 
 
 FIG. 296. 
 
398 SCHOOL PHYSICS. 
 
 317. Polarization of Light. Common white light is a 
 highly complex form of radiant energy, comprising not 
 only an indefinite number of wave-lengths, but also an in- 
 definite number of modes of ether vibration. When a 
 rope is shaken as described in Experiment 110, the vibra- 
 tions of the wave thus produced will lie in a vertical plane ; 
 when the hand is moved horizontally, the vibrations will 
 lie in a horizontal plane. It thus appears that a transverse 
 wave is capable of assuming a particular side or direction ; 
 a longitudinal wave is not. In like manner, a single row 
 of ether particles engaged in propagating a linear trans- 
 verse wave may describe any one of a variety of paths, 
 each perpendicular to the line of propagation of the radia- 
 tion. For example, each particle may vibrate in a straight 
 line, parallel to the wave-front and indiffer- 
 ently in any plane about the line of propa- 
 gation, as represented in Fig. 297. If all 
 the ether particles in the row under consid- 
 eration successively vibrate along lines lying 
 in the same plane, the radiation is said to be plane- 
 polarized, and the wave thus constituted is called a 
 plane-polarized wave. A change ~by which the transverse 
 vibrations of luminous waves are limited to a single direc- 
 tion is called polarization of light. This change may be 
 produced in several ways. 
 
 (a) Light may be polarized : 
 
 (1) By reflection from the surface of glass, water, and other non- 
 metallic substances. The degree of polarization reaches its maxi- 
 mum when the angle of incidence lias a certain value depending upon 
 the substance, and called the angle of polarization. For glass, this 
 angle is 54^. 
 
 (2) By transmission through a series of transparent plates of 
 
INTERFERENCE, DIFFRACTION, POLARIZATION. 399 
 
 glass placed in parallel position at the proper angle to the inci- 
 dent ray. 
 
 (3) By double refraction, as in the case of Iceland spar or of a plate 
 cut in a certain way from a tourmaline crystal. A beam of light, 
 falling upon such a crystal, is generally split into two parts polarized at 
 right angles. One of these parts obeys the regular law of refraction, 
 and is called the ordinary ray ; the other does not, and is called the 
 extraordinary ray. A prism of Iceland spar prepared in such a way 
 that one beam of polarized light is totally reflected and extinguished, 
 w^hile the other beam passes through as polarized light, is called a 
 Nicol prism. Xicol prisms and tourmaline plates are largely used in 
 experiments with polarized light. 
 
 (6) Light that has passed through a tourmaline plate differs so 
 much from ordinary light that it may be stopped by a similar plate, 
 as was seen in Experiment 276. For the sake of simplicity, imagine 
 the indifferently placed planes of vibration, as represented in Fig. 
 297, to be resolved into two that lie at right angles to each other, as 
 shown in Fig. 298. Then the action 
 of the first tourmaline plate may be 
 compared to that of a vertical-bar 
 grating that allows the vibrations in a 
 vertical plane to pass, but absorbs the 
 vibrations that lie in a horizontal FIG. 298. 
 
 plane. Evidently, the vibrations that 
 
 pass one such grating, as T, will pass others similarly placed, but 
 will be stopped by one that is crossed, as at T' . The part of the 
 beam that lies between T and ^represents plane polarized light. 
 
 (c) Polarized light presents to the unaided eye the same appear- 
 ance as common light. An instrument for producing and testing 
 polarized light is called a polariscope. It consists of two characteristic 
 parts; one, used to produce polarization and called the polarizer ; the 
 other, used to test or to study the polarized light and called the analyzer. 
 Apparatus that serves for either of these purposes will serve for the 
 other. The Xicol prism is generally preferred for both purposes. 
 Some of the color-effects due to the interference of polarized light are 
 very beautiful. 
 
 (rf) The plane of polarization may 'be rotated by passing plane- 
 polarized light through certain substances, some substances producing 
 a right-hand rotation and others a left-hand rotation. This property 
 of polarized light has been applied to the estimation of the commercial 
 
400 SCHOOL PHYSICS. 
 
 value of sugar by the amount of rotation produced by a solution of it 
 of known strength. The devices for the precise measurement of the 
 amount of rotation involve advanced scientific principles. When 
 plane polarized light is passed through a plate of quartz cut perpen- 
 dicularly to the axis, the plane of polarization is turned through an 
 angle that varies with the thickness of the plate and the wave-length 
 of the light. Thus, if a pebble spectacle-lens is placed between 
 crossed tourmaline plates, the dark field is brightened, and generally 
 colored, by the transmitted light. 
 
 (e) Light may be circularly and elliptically polarized as well as 
 plane polarized. 
 
 Note. For a fuller discussion of the polarization of radiant 
 energy, the pupil is referred to some special work on Light. The 
 subject is interesting and the phenomena are beautiful. 
 
 VII. A FEW OPTICAL INSTRUMENTS. 
 
 Experiment 279. Stick two needles into a board about 6 inches 
 apart. Close one eye, and hold the board so that the needles shall be 
 nearly in range with the open eye and about 6 and 12 inches respec- 
 tively from it. One needle will be seen distinctly while the image of 
 the other will be blurred. Fix the view definitely on the needle that 
 appears blurred and it will become distinct, but you cannot see both 
 clearly at the same time. 
 
 Experiment 280. Cover half of a white sheet of paper with a 
 sheet of black paper. Fix the eye intently on the middle of the white 
 surface for fifty or sixty seconds. Keep the eye fixed on the same 
 point, and suddenly remove the black paper. The newly exposed part 
 of the sheet appears more brilliantly illuminated than the other. 
 
 Experiment 281. Stick a bright red wafer upon a piece of white 
 paper. Hold the paper in a bright light and look steadily at the 
 wafer, for some time, with one eye. Turn the eye quickly to another 
 part of the paper or to a white wall, and a greenish spot, the size and 
 shape of the wafer, will appear. The greenish color of the image is 
 complementary to the red of the wafer. If the wafer is green, the 
 image afterwards seen will be of a reddish (complementary) color. 
 
A FEW OPTICAL INSTRUMENTS. 401 
 
 Experiment 282. Close one eye and try to thread a needle. Bend 
 a stout wire at a right angle, and try to pass one end of it through a 
 ring held at arm's length, one eye being closed. 
 
 Experiment 283. Prick a pin-hole in a card, hold it near the eye, 
 and look through the pin-hole at a pin held at arm's length. As the 
 pin is slowly moved toward the eye, the visual angle ( 318, e) increases 
 and the pin seems to grow larger. 
 
 318. The Human Eye, optically considered, is an ar- 
 rangement for projecting inverted, real images upon a 
 screen made of nerve filaments. This image is the origin 
 of the sensation of vision. The luminous waves transfer 
 their energy to the nerve filaments, they transmit it to 
 the brain and, in some mysterious way, the sensation 
 follows. 
 
 (a) The most essential parts of this instrument are contained in 
 the eyeball, a nearly spherical body, about an inch in diameter, and 
 capable of being turned considerably in its socket by the action of 
 various muscles. It is represented in section from front to back 
 by Fig. 299. The greater part of the outer coat is tough and opaque, 
 and is called the " white of the eye " 
 or the sclerotic coat, S ; the front part 
 of the coat is a hard, transparent 
 structure called the cornea, C. The 
 cornea is more convex than the rest 
 of the eyeball, and fits into the scle- 
 rotic as a watch-crystal does into its 
 case. The chief part of the second 
 tunic of the eye is the choroid coat, 
 N, which is opaque and intensely 
 black, and absorbs all internally re- F IG 299. 
 
 fleeted light. The third or inner 
 
 tunic is the retina, R, an expansion of the optic nerve which enters 
 the eyeball from behind. These several tunics or coats form a kind 
 of camera filled with solid and liquid refractive media. The crys- 
 talline lens, L, a solid biconvex body, is suspended in the middle of 
 this camera and directly in the axis of vision. Its shape is shown 
 26 
 
402 SCHOOL PHYSICS. 
 
 in the figure ; it tends to flatten with age. With its capsule, it divides 
 the eye into two compartments, and is chiefly instrumental in bring- 
 ing the rays of light to a focus on the retina. The larger chamber 
 of the eyeball is filled with a transparent, jelly-like substance, F, that 
 resembles the white of an egg, is called the vitreous humor, and is 
 enclosed in the delicate hyaloid membrane, H. The chamber between 
 the cornea and the lens is filled with a more watery liquid, the aqueous 
 humor. This anterior chamber is partly divided into two compart- 
 ments by an annular curtain, /, called the iris. This curtain is 
 opaque, and its color constitutes the color of the eye. The circular 
 opening in the iris is called the pupil The iris acts as a self-regulat- 
 ing diaphragm, dilating the pupil and thus admitting more light 
 when the illumination is weak ; contracting the pupil and cutting off 
 more light when the illumination is strong. 
 
 (ft) That vision may be distinct, the image formed on the retina 
 must be clearly defined, well illuminated, and of sufficient size. With- 
 out our consciousness, the muscular action of the eye changes the 
 curvature of the crystalline lens so that rays from near or distant 
 objects may be focused on the retina. Instead of moving the screen, 
 the refractive power of the lens is changed. This power of " accom- 
 modation," or automatic adjustment for distance, is limited. When a 
 book is held close to the eyes, the rays from the letters are so divergent 
 that the eye cannot focus them upon the retina. The near point of 
 vision is generally about 3| inches from the eye. As parallel rays are 
 generally brought to a focus on the retina when the eye is at rest, the 
 far point for good eyes is infinitely distant. Owing to the small size 
 of the pupil, rays from a point 20 inches or more distant are practi- 
 cally parallel. The near point of some eyes is less than 3J- inches, 
 while the far point is only 8 or 10 inches. Such eyes are myopic and 
 their owners are near-sighted; the retina is too far back, the eyeball 
 being elongated in the direction of its axis. The remedy is in concave 
 glasses. The near point of some eyes is about 12 inches and the far 
 point is infinitely distant. Such eyes are hypermetropic and their 
 owners are far-sighted. In such eyes the retina is too far forward, the 
 eyeball being flattened in the direction of its axis. The remedy is in 
 convex glasses. When the diminished power of accommodation for 
 near objects is an incident of advancing years, and due to the progres- 
 sive loss of elasticity in the crystalline lens, the eyes are presbyopic 
 and their owners are old-sighted. The cause of the difficulty is different 
 from that of far-sightedness, but the remedy is the same. 
 
A FEW OPTICAL INSTRUMENTS. 403 
 
 (c) The impression upon the retina does not disappear instantly 
 when the action of the light ceases, but continues for about an eighth 
 of a second. The result is what is called the persistence of vision. If 
 the impressions are repeated within the interval of the persistence of 
 vision, they appear continuous. This phenomenon is well illustrated 
 by the luminous ring produced by swinging a firebrand around a 
 circle, and in the action of the common toy known as the thaumatrope 
 or the zoetrope. 
 
 (W) The retina is thickly studded with microscopic projections 
 called rods and cones, the terminal elements of the optic nerve. 
 According to a theory that is as yet purely provisional, these end- 
 organs are tuned to sympathetic vibrations with the ether vibrations 
 that severall} T correspond to violet, green, and red ( 299, a), and by 
 combining these effects in suitable proportions, the several color- 
 sensations are produced. When any of these end-organs are inopera- 
 tive or when they are not equally sensitive, the person is affected 
 with color-blindness, i.e., he is unable to recognize certain colors, 
 generally red. Sometimes these terminal elements seem to become 
 tired of vibrating at a given rate and thus to become insensible to a 
 certain color. (See Experiments 280 and 281.) Hence, what is known 
 a subjective color is due to a retinal fatigue. In the middle of the 
 retina and in the axis of the eye is a little rounded elevation called 
 the yellow spot or macula lutea. It is the most sensitive part of the 
 retina. On the nasal side of the yellow spot is the entrance of 
 the optic nerve and its central artery. As this part of the retina 
 lacks the visual function that characterizes the rest of its surface, it 
 is called the blind spot. 
 
 (c) The estimation of distances by the eye is a matter of judgment 
 and is chiefly based upon experience. This experience relates to the 
 amount of muscular effort exerted in adjusting the eye for distinct 
 vision, and in turning the two eyes inward so that their axes meet at 
 the object, thus forming the optical angle (see Experiment 282) ; to the 
 comparison of the angle formed by lines drawn from the extremities 
 of the object to either eye and called the visual angle with the visual 
 angle subtended by objects of known size and distance ; and to the 
 observation of changes of color and brightness produced by the varying 
 thickness of the air through which the object is viewed. 
 
 (/") The estimation of the size of distant objects is also a matter 
 of judgment, based upon the known or supposed distance of the object. 
 The ratio between the size of object and image equals the ratio 
 
404 
 
 SCHOOL PHYSICS. 
 
 between the distance of each from the lens, and the mind uncon- 
 sciously bases its conclusions on this fact. 
 
 Stereoscopic Effect. 
 
 Experiment 284. Close the left eye, and hold the right hand so 
 that the forefinger hides the other three fingers. Without changing 
 the position of the hand, open the left and close the right eye. The 
 hidden fingers become visible in part. It is evident that the images 
 upon the retinas of the two eyes are different. 
 
 Experiment 285. Place a die on the table directly in front of you. 
 Looking at it with only the left eye, 
 three faces are visible, as shown at A, 
 Fig. 300. Looking at it with only the 
 right eye, it appears as shown at B. If, 
 in any way, we combine two such draw- 
 ings, so as to produce images upon the 
 retinas of the two eyes like those pro- 
 duced by the solid object, we obtain the idea of solidity. 
 
 
 
 A. 
 
 r. 
 
 B 
 
 FIG. 300. 
 
 319. The Stereoscope is an instrument for illustrating 
 the phenomena of binocular vision, and for producing from 
 two nearly similar pictures of an object the effect of a 
 single picture with the appearance of relief and solidity 
 that pertains to ordinary vision. 
 
 (a) The stereoscopic view or slide shows, side by side, two pic< 
 tures taken under a slightly different angular view. It is the office 
 of the stereoscope to blend 
 these two pictures. As in 
 ordinary vision, each eye 
 sees only one of the pictures, 
 but the two images conveyed 
 to the brain unite into one. 
 The diaphragm, Z), prevents 
 either eye from seeing both 
 pictures at the same time. 
 Rays of light from B are 
 refracted by the half-lens, FIG. 301. 
 
 E' t so that they seem to come from C, beyond the plane of the 
 
A FEW OPTICAL INSTRUMENTS. 405 
 
 pictures. In the same way, rays from A are refracted by E so that 
 they also seem to come from C. The two slightly different pictures, 
 thus seeming to be in the same place at the same time, are success- 
 fully blended ; the picture " stands out," or has the appearance of 
 solidity. 
 
 320. The Photographer's Camera corresponds to the 
 camera-obscura described in 265. ' A darkened box, 
 DE, adjustable in length, takes the place of the darkened 
 room, and an achromatic convex lens is substituted for 
 the aperture in the shutter. 
 
 (a) A ground-glass plate is placed in the frame at E, which is 
 adjusted so that a well-defined inverted image of the object in 
 front of A is projected upon 
 the glass plate as shown in 
 Fig. 302. This adjustment is 
 completed by moving the lens 
 and its tube by the toothed 
 wheel at />. When the focus- 
 ing is satisfactory, A is cov- 
 ered, the ground-glass plate is 
 replaced by a chemically pre- 
 pared sensitive plate, A is un- 
 covered, and the image pro- 
 jected on the chemical film. - F IG . 302. 
 The chemical changes that the 
 
 light produces in the film are made visible by a process called 
 "developing," and made permanent by a process called "fixing." 
 
 Microscope. 
 
 Experiment 286. Provide two small biconvex lenses about 4 cm. 
 in diameter, one with a focal length of about 3 cm. and the other 
 with a focal length of about 5 cm. Mount each by inserting its 
 edge in a slit in a large cork. Place a small bright object in 
 front of the lens of shorter focal length and close to it, and adjust 
 a screen on the other side of the lens so that a sharp image of 
 the object will be projected on it. Place the other lens back of the 
 screen, and at a distance from it less than the focal length of the 
 
406 
 
 SCHOOL PHYSICS. 
 
 lens. Remove the screen, and look through the second lens toward 
 the first. Adjust the second lens until you can see a virtual image 
 of the real image of the object. 
 
 321. A Microscope consists of a lens or a combination of 
 lenses used to observe small objects, often so minute as 
 to be invisible to the unaided eye. 
 
 (a) The simple microscope is generally a single convex lens, and 
 is often called a magnifying glass. The object is placed between 
 the lens and its principal focus. The lens increases the visual angle. 
 The image is virtual, erect, and magnified. 
 
 (b) The magnifying power of a lens is the ratio between the length 
 of the object and the length of its image. 
 
 (c) The compound microscope consists essentially of two lenses or 
 
 systems of lenses. One of these, 0, 
 called the objective, is of short focus. 
 The object, AB, being placed slightly 
 beyond the principal focus, a real image, 
 cd, magnified and inverted is formed. 
 The other lens, E, called the eyepiece 
 or ocular, is so placed that the image, 
 cd, lies between it and its focus. A 
 magnified, virtual image of the real 
 image, cd, is formed by the eyepiece 
 and seen by the observer at ab. Eye- 
 piece and objective are placed at op- 
 posite ends of a tube and are generally 
 compound, the objective consisting of 
 two or three achromatic lenses, and the 
 eyepiece of two or more simple lenses. 
 The instrument varies widely in con- 
 struction, and is often provided with 
 many accessories or special devices ap- 
 plicable to particular uses. 
 
 Experiment 287. Using a biconvex 
 lens about 10 cm. in diameter and 
 with a focal length of about 40 cm., project a sharp image of a 
 distant object on a screen. Back of the screen, place the lens of 
 
A ^FEW OPTICAL INSTRUMENTS. 407 
 
 3 cm. focal length that was used in Experiment 286. The distance 
 of the lens from the screen should be less than the focal length of 
 the lens. Remove the screen, and look through the second lens 
 toward the first. Adjust the second lens until you can see a virtual 
 image of the real image of the object. 
 
 322. A Telescope is an instrument designed for the obser- 
 vation of distant objects, and consists essentially of an 
 objective for the formation of an image of the object 
 and of an eyepiece for magnifying this image. The 
 optical parts are generally set in a tube so arranged that 
 the distance between the objective and the eyepiece may 
 be adjusted for distinct vision. A telescope is refracting 
 or reflecting according as its objective is a convex lens or 
 a concave mirror, and astronomical or terrestrial accord- 
 ing as it is designed for the observation of celestial or 
 terrestrial objects. 
 
 (a) The astronomical refractor consists essentially of a large convex 
 lens objective of long focus, and a convex lens eyepiece of short focus, 
 
 FIG. 304. 
 
 as is shown in Fig. 304. The objective is made large that it may collect 
 many rays, to the end that its real and diminished image, ab, may be 
 so bright that it may be considerably magnified without too great loss 
 of distinctness. This real image formed by the objective is magnified 
 by the eyepiece, as in the case of the compound microscope. The 
 visible image is a virtual image of the real image. 
 
 (J) The spy-glass or terrestrial telescope avoids the inversion of the 
 image by the interposition of two double-convex lenses, m and n, 
 
408 
 
 SCHOOL PHYSICS. 
 
 between the objective and the eyepiece. The rays diverging from the 
 inverted image at / cross between m and n, and form an erect, magni- 
 fied, virtual image at ab. 
 
 FIG. '305. 
 
 (c) The Galilean telescope has a double-concave eye-lens that inter- 
 cepts the rays before they reach the focus of the objective. The rays 
 from A, converging after refraction by 0, are rendered diverging by 
 
 FIG. 300. 
 
 C; they seem to diverge from a. In like manner, the image of is 
 formed at b. The image, ab, is erect and very near. Two Galilean 
 telescopes placed side by side constitute an opera-glass. 
 
 (e?) The reflecting telescope has as an objective a concave mirror, 
 technically called a speculum. The images formed by the speculum 
 are brought to the eyepiece in several different ways. Sometimes the 
 
 FIG. 307. 
 
 eyepiece consists of a series of convex lenses placed in a horizontal 
 tube, as shown in Fig. 307. The rays from the mirror may be re- 
 
A FEW OPTICAL INSTRUMENTS. 409 
 
 fleeted by a cathetal prism, TOW, and a real image formed at ab. This 
 image is magnified by the eyepiece, and a virtual image formed at cd. 
 The Earl of Rosse built a telescope with a mirror that was six feet in 
 diameter, and had a focal distance of fifty-four feet. 
 
 (e) The magnifying power of a telescope depends upon the ratio 
 between the focal length of the objective and that of the eyepiece, and 
 may be changed by changing one eyepiece for another. 
 
 Optical Projection. 
 
 Experiment 288. Reflect a horizontal beam of sunlight into a 
 darkened room. In its path, place a piece of smoked glass on which 
 you have traced the representation of an arrow, AB (Fig. 308), or 
 written your auto- 
 graph. Be sure that 
 every stroke of the 
 pencil has cut 
 through the lamp- 
 black and exposed 
 the glass beneath. 
 Place a convex lens 
 
 beyond the pane of 
 
 FIG. 308. 
 glass, as at L, so 
 
 that rays that pass through the transparent tracings may be refracted 
 by it, as shown in the figure. It is evident that an image will be 
 formed at the foci of the lens. If a screen, SS, is held at the positions 
 of these foci, a and &, the image will appear clearly cut and bright. 
 If the screen is held nearer the lens or further from it, as at S f or 
 S", the picture will be blurred. 
 
 323. The Optical Lantern is an instrument for project- 
 ing on a screen magnified images of transparent photo- 
 graphs, paintings, drawings, etc. 
 
 (a) The light is placed at the common focus of a concave mirror, 
 and of a convex lens called -the condenser. A powerful beam of light 
 is thus thrown upon 6, the transparent object, technically termed a 
 " slide." A compound objective, TO, is placed at a little more than its 
 fecal distance beyond the slide. A real, inverted, magnified image of 
 the picture is thus projected upon the screen, S, The tube carrying 
 
410 
 
 SCHOOL PHYSICS. 
 
 m is adjustable, so that the foci may be made to fall upon the screen, 
 and thus render the image distinct. By inverting the slide, the image 
 
 FIG. 309. 
 
 is seen right side up. Solar and electric microscopes act in nearly the 
 same way, the chief difference being in the source of light. An opti- 
 cal lantern is often called a magic lantern. 
 
 (6) Two matched lanterns placed so that their images coincide 
 constitute a stereopticon. The use of such an instrument avoids the 
 delay and unpleasant effect of moving the pictures across the screen 
 in view of the audience when the slides are changed, and enables the 
 production of many interesting " dissolving " effects- that are impos- 
 sible with a single lantern. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Two pieces of heavy plate-glass, 
 about 8 cm. square ; a small iron clamp ; three spring clothes-pins ; a 
 spectacle-lens made of quartz, and a similar one made of glass. 
 
 1. In a good light, press together two pieces of clean plate glass 
 with a clamp at their centers, and explain the appearance of colors in 
 the glass. 
 
 2. Spring a clothes-pin upon each of three corners of the glass 
 plates used in Exercise 1, and support the plates by an iron clamp at 
 the fourth corner. Let a beam of sunlight from the porte-lumiere fall 
 upon the face of the plate so as to make the angle of incidence 45. 
 Receive the beam reflected from the plate upon a convex lens so that 
 an image of the opening in the shutter will be projected on the screen. 
 Vary the pressure at the clamp, and explain the change of colors on 
 the screen. 
 
A FEW OPTICAL INSTRUMENTS. 411 
 
 3. Look through the two plates of the tourmaline tongs (Fig. 295) 
 at the bright sky. Turn one of the plates in its supporting ring and 
 observe the changes of brightness. When the plates are so adjusted 
 that the view through them is the darkest, slip successively between 
 them a quartz spectacle-lens and a similar lens made of glass, noting 
 the effect of each, and explaining the effect of one. 
 
 4. Project a solar spectrum upon a white screen, and look at it in- 
 tently for 50 or 60 seconds. Then have some one suddenly cut off 
 the light that yields the spectrum, and turn up the lamp or gas-light. 
 During these changes, keep your eyes fixed on the screen watching for 
 any change that may take place in the appearance of the spectrum. 
 Describe and explain any such change that takes place. 
 
 5. Fasten a thread to a disk of paper of some bright color. Place 
 this disk upon a sheet of white paper and in a strong light. Look 
 intently at the colored disk for 20 or 30 seconds. Suddenly pull away 
 the colored disk without moving the eye. Describe and explain the 
 after-image. 
 
 6. While a friend is looking intently at a distant object, look 
 obliquely into his eye, holding a candle-flame on the other side of it. 
 If the flame is properly held, three images of it will be seen ; one 
 erect and bright, reflected from the cornea; another erect and less 
 bright, reflected from the anterior surface of the crystalline lens ; and 
 a third, inverted, reflected from the posterior-surface of the lens. 
 When the eye that is being studied changes its adjustment for the 
 observation of an object held near it, the first image of the candle- 
 flame is unchanged, while the second and third become smaller, the 
 change being greater in the second than in the third. 
 
 7. Close the left eye and look steadily at the cross below, holding 
 the book about a foot from the face. The dot is plainly visible as well 
 
 * 
 
 as the cross. Keep the eye fixed on the cross and move the book 
 slowly toward the face. When the image of the dot falls on the 
 " blind spot " of the eye, the dot disappears. Hold the book in this 
 position for a moment and see if the changing convexity of the 
 crystalline lens throws the image of the dot off the blind spot, making 
 the dot again visible. 
 
CHAPTER VI. 
 
 ELECTRICITY AND MAGNETISM. 
 
 (Ether Physics continued.) 
 
 I. GENEKAL VIEW. 
 A. STATIC ELECTRICITY. 
 
 324. Electricity is the common cause of a large variety 
 of phenomena, including apparent attractions and repul- 
 sions of matter, heating, luminous and magnetic effects, 
 chemical decomposition, etc. 
 
 (a) The true nature of electricity is not yet well understood. Lit- 
 tle more can be said at this point than that it is the agent upon which 
 certain phenomena depend, and that " it behaves like an incompressible 
 fluid filling all space and yet entangled in an ether that has the 
 rigidity necessary to propagate the enormously rapid and minute 
 oscillatory disturbances that constitute radiation, while, at the same 
 time, it allows the free motion of ordinary matter through it." 
 
 (6) The phenomena of electricity are generally classified as static 
 or dynamic, and considered under the heads, frictional electricity or 
 current electricity. Owing to their common cause and for reasons of 
 convenience, little effort will be made to maintain the distinction in 
 this work. 
 
 (c) "Experiments with electricity produced by friction are very 
 beautiful and of great theoretical interest, but many of them are 
 troublesome to perform, and their practical importance is very small." 
 
 Experiment 289. Draw a silk ribbon about an inch wide and a 
 foot long between two layers of warm flannel and with considerable 
 friction. Hold the ribbon near the wall, and notice the unusual at- 
 traction. Place a sheet of paper on a warm board, and briskly rub it 
 with india-rubber. Hold it near the wall, as you did the ribbon, and 
 
 notice the effect. 
 
 412. 
 
STATIC ELECTRICITY. 
 
 413 
 
 FIG. 310. 
 
 Experiment 290. Cut a number of pith-balls about 1 cm. in di- 
 ameter. Whittle them nearly 
 round, and finish by rolling 
 them between the palms of the 
 hands. Cover one of these 
 balls with gold-leaf, suspend 
 it by a silk fiber, and call it an 
 electric pendulum. Briskly rub 
 a stout stick of sealing-wax with 
 warm flannel, and bring it near 
 the electric pendulum. Xotice 
 the attraction. 
 
 Experiment 291. To the 
 
 middle of a straw about a foot 
 
 long, fasten with wax a short 
 
 piece of straw as shown in 
 
 Fig. 311. Fasten two disks of 
 
 bright-colored paper at the ends 
 
 of the straw, and balance the 
 
 apparatus upon the point of a sewing-needle, the other end of which 
 is thrust into the cork of a glass vial. Rub the 
 
 Q * O sealing-wax as before, and hold it near one of 
 
 the paper disks. The straw may be made to 
 follow the wax round and round. A paper 
 
 hoop or an empty egg-shell may be made to roll after the rubbed rod. 
 
 Experiment 292. Repeat the last two experiments, using a glass 
 
 rod or tube that has been 
 rubbed with a silk pad. 
 The ends of the glass 
 should be rounded or 
 smooth; a long ignition- 
 tube will answer. The 
 effect may be increased by 
 smearing lard on one side 
 of the pad, and applying a 
 coat of the amalgam that 
 may be scraped from bits 
 FIG. 312. of a broken looking-glass. 
 
 Small scraps of paper, shreds of cotton and silk, feathers and 
 
 II 
 
 FIG. 311. 
 
414 
 
 SCHOOL PHYSICS. 
 
 gold-leaf, bran, sawdust, and other light bodies may be similarly 
 attracted. 
 
 Experiment 293. Place an egg in an egg-cup, and balance a yard- 
 stick upon it. The end of the stick may 
 be made to follow the rubbed rod round 
 and round. Place the blackboard pointer 
 or other stick in a wire stirrup (Fig. 313) 
 or stiff paper loop suspended by a stout 
 silk thread or a narrow silk ribbon. It 
 may be made to imitate the actions of the 
 balanced yardstick. 
 
 Experiment 294. Suspend the rubbed 
 sealing-wax or glass rod in the stirrup, 
 and hold the pointer or your hand near 
 it. Evidently the action is mutual, i.e., 
 each body attracts the other. 
 
 FIG. 313. 
 
 325. Electrification. Bodies that are endowed with the 
 power of attracting other bodies as just illustrated are said 
 to be electrified. Any substance may be electrified by suit- 
 able means. The state or condition thus established is 
 called electrification, and may be brought about in a variety 
 of ways. 
 
 Experiment 295. Support a meter stick upon a glass tumbler. 
 Bring an electrified glass rod to one end of the stick, and hold some 
 small pieces of gold-leaf or paper a few centimeters under the other 
 end of the stick. The gold-leaf or paper will be attracted and repelled 
 by the stick as it previously was by the glass itself. The electrifica- 
 tion passed along the stick from end to end. 
 
 326. Conductors and Insulators. Substances that easily 
 permit the transference of electrification along them are said 
 to be good conductors. No substance is so good a conductor 
 as not to offer some resistance to the transfer. No sub- 
 stance is so poor a conductor that the electrification cannot 
 be forced through it, but there are some that offer resistances 
 
STATIC ELECTRICITY. 
 
 415 
 
 Conductors. 
 
 Salt water. 
 
 Metals. 
 Charcoal. 
 
 Vegetables. 
 Animals. 
 
 Graphite. 
 Acids. 
 
 Linen. 
 Cotton. 
 
 so great that they are called insulators, or non-conductors. 
 A conductor supported by an insulator is said to be insu- 
 lated. An insulated body that is electrified is said to have 
 a charge, or to be charged. 
 
 (a) In the following table, the substances named are arranged in 
 the order of conductivity: 
 
 Dry wood. Glass. 
 
 Paper. Sealing-wax. 
 
 Silk. Vulcanite. 
 
 India-rubber. Insulators. 
 Porcelain. 
 
 (6) The fact that a conductor in the air may be insulated shows 
 that air is a non-conductor.* Dry air is a very good insulator (at least 
 10 26 times as good as copper), but moist air is a fairly good conductor. 
 All experiments in static electricity are, therefore, more successfully 
 performed in clear, cold weather when the atmosphere is dry. Resist- 
 ance and conductivity will be 'more specifically considered in subse- 
 quent pages. 
 
 (c) A medium intervening between two electrified bodies, i.e., a 
 substance, solid, liquid or gaseous, through or across which electric 
 force is acting, is called a dielectric. The dielectric plays an important 
 part in the phenomena of electrification. 
 
 Kinds of Electrification 
 Experiment 296. Suspend several pith- 
 balls by fine linen threads from an insu- 
 lating support, and touch them with an 
 electrified rod. The rod repels the balls, 
 and the balls repel each other. 
 
 Experiment 297. Electrify a suspended 
 pith-ball by contact with a rubbed rod. 
 Notice that the ball is repelled by the rod, 
 and attracted by the cloth with which the 
 rod was rubbed. 
 
 Experiment 298. Bring an electrified 
 glass rod near a pith-ball electroscope as 
 before, and notice that, after contact, the 
 
 FIG. 314. 
 
416 SCHOOL PHYSICS. 
 
 ball is actively repelled. Similarly charge a second ball with an 
 electrified rod of sealing-wax. Bring the two balls near each other, 
 and notice their mutual attraction. Charge the two balls as before. 
 Bring the glass rod near the ball that is repelled by the sealing-wax, 
 and notice the attraction. Bring the sealing-wax near the ball that is 
 repelled by the glass rod, and notice the attraction. 
 
 327. Opposite Electrifications. As just illustrated, 
 electrification may be manifested by repulsion as well as 
 by attraction, and is of two kinds, opposite in character. 
 The electrification developed by rubbing glass with silk 
 is called positive ; that developed by rubbing sealing-wax 
 with flannel is called negative. Bodies similarly electri- 
 fied repel each other; bodies oppositely electrified attract 
 each other. 
 
 (a) The statement that there are^ two kinds of electrification does 
 not necessarily imply that there are two kinds of electricity. It is, 
 however, very convenient to speak of one kind of electrification as 
 caused by a charge of one kind of electricity, and the other kind of 
 electrification as caused by a charge of an opposite kind of electricity. 
 
 (&) Any substance mentioned in the following electric series is posi- 
 tively electrified when rubbed with any substance that follows it, and 
 negatively electrified when rubbed with any substance that precedes it 
 in the list : 
 
 1. Cat's fur, 5. Glass, 9. Vrood, 13. Resin, 
 
 2. Flannel, 6. Cotton, 10. Metals, 14. Sulphur, 
 
 3. Ivory, 7. Silk, 11. Caoutchouc, 15. Gutta-percha, 
 
 4. Quartz, 8. The hand, 12. Sealing-wax, 16. Gun-cotton. 
 
 Thus, cat's fur is always positively electrified, and gun-cotton nega- 
 tively, when rubbed with any other substance mentioned in the list. 
 Glass is positively electrified when rubbed with silk, and negatively 
 when rubbed with flannel. 
 
 (c) The electrification of the rubbed body is equal in amount to 
 that of the body with which it is rubbed, but opposite to it in character. 
 
 328. Electrification by Conduction is the process of 
 charging a body by putting it in contact with an electrified 
 
STATIC ELECTRICITY. 
 
 417 
 
 body. The charge thus produced is of the same kind 
 as that of the communicating body. 
 
 329. The Electroscope is an instrument for detecting and 
 testing electrification. The electric pendulum, or the bal- 
 anced straw of Experiment 291, 
 constitutes a simple and efficient 
 electroscope. The gold-leaf 
 electroscope represented in Fig. 
 315 is a common form of a more 
 sensitive instrument. A metal- 
 lic rod passes through the cork 
 of a glass vessel, and terminates 
 on the outside in a ball or a 
 disk. The lower end of the rod 
 carries two strips of gold-leaf 
 or of aluminium-foil that hang 
 parallel and close together. 
 
 When an electrified object is brought near the knob or into 
 contact with it, the metal strips below become similarly 
 charged and are, therefore, mutually repelled. 
 
 (a) A proof-plane may be made by cementing a bronze cent or a 
 
 disk of gilt paper to a thin insulating 
 handle, as a glass tube or a vulcanite 
 rod. Slide the disk of the proof-plane 
 along the surface of the electrified 
 body to be tested, and quickly bring it 
 into contact with the knob of the gold- 
 leaf electroscope, the leaves of which 
 will diverge. Positively charge the 
 proof-plane by contact with a glass 
 rod that has been electrified by rub- 
 bing it with silk, and transfer the 
 
 second charge to the electroscope. If the leaves diverge more widely, 
 27 
 
 FIG. 315. 
 
418 SCHOOL PHYSICS. 
 
 the first charge was positive. If the leaves collapse, repeat the test, 
 using the negative charge from a rod of sealing-wax rubbed with flan- 
 nel instead of the positive charge from the glass rod. If the leaves 
 are thus made to diverge more widely, the first charge was negative. 
 
 330. Electrical Units. There are two systems of elec- 
 trical units derived from the fundamental " C.G.S." units, 
 one set being based upon the attraction or repulsion ex- 
 erted between two quantities of electrification, and the 
 other upon the force exerted between two magnet poles. 
 The former are termed electrostatic units; the latter, elec- 
 tromagnetic units. Distinctive names have not yet been 
 adopted for the electrostatic units. 
 
 331. The Electrostatic Unit of Quantity is the quantity 
 of electrification that exerts through the air a force of one 
 dyne on a similar quantity at a distance of one centimeter. 
 The force may be attractive or repulsive. 
 
 332. Law of Electric Action. The force that is mutu- 
 ally exerted between two charges varies directly as the 
 product of the charges, and inversely as the square of 
 the distance between them. The two charges are supposed 
 to be collected at two points.- 
 
 Distribution of the Charge. 
 
 Experiment 299. Make a conical bag of linen, supported, as shown 
 in Fig. 317, by an insulated metal hoop five or six inches in diameter. 
 Electrify the bag. A long silk thread extending each way from the 
 apex of the cone will enable you to turn the bag inside out without 
 discharging it. Test the inside and outside of the bag, using the 
 proof -plane. Turn the bag and repeat the test. Whichever surface 
 of the linen is external, no electrification can be found upon the in- 
 
STATIC ELECTRICITY. 419 
 
 side of the bag. Vary the experiment by the use of a hat sus- 
 pended by silk threads. Notice that the 
 greatest charge is obtained from the 
 edges; less from a curved or flat sur- 
 face ; none from the inside. 
 
 Experiment 300. Fasten one edge of 
 a large sheet of tin-foil to a horizontal 
 glass rod or tube. Connect a lower cor- 
 ner of the tin-foil by a fine wire to the 
 knob of an electroscope. Charge the 
 tin-foil lightly, and notice the divergence 
 of the leaves of the electroscope. Slowly 
 turn the rod so as to roll the tin-foil upon 
 it. As the area of the electrified surface 
 is reduced, notice the increase in the divergence of the leaves. 
 
 Experiment 301. Prick a pin-hole at each end of an egg, and blow 
 out the contents of the shell. Paste tin-foil or Dutch-leaf smoothly 
 over the entire surface of the empty shell. Fasten the two ends of 
 a white silk thread with wax near the ends of the shell, so that the 
 shell may be suspended with its greater diameter horizontal. Charge 
 this insulated egg-shell conductor. With a proof-plane, carry a 
 charge from the side of the conductor to the knob of the gold-leaf 
 electroscope, and notice the degree of divergence of the leaves. In 
 like manner, carry a charge from the smaller end of the conductor, 
 and notice the greater divergence jpf the leaves. 
 
 Experiment 302. Cement the end of a small glass tube to the 
 middle of a pin, and hold the head of the pin against the knob of a 
 gold-leaf electroscope. Observe the collapse of the leaves. 
 
 333. Distribution of the Charge. As the electrification 
 is self-repulsive, the charge lies wholly upon the outer sur- 
 face. The amount of electrification per unit of surface 
 is called the surface density. Whenever a charge is com- 
 municated to a conductor, the electrification distributes 
 itself over the surface of the conductor until it reaches a 
 condition of equilibrium. A change in the area of the 
 surface works a corresponding change in the surface 
 
420 SCHOOL PHYSICS. 
 
 density, as was shown in Experiment 300. The distri- 
 bution is a function of the surface, independent of the 
 substance of the conductor, and greatest where the curva- 
 ture is the greatest. On a sphere, the density is uniform ; 
 on an egg-shaped conductor, it is greatest at the smaller 
 end. 
 
 (a) Since any charge is self -repulsive, there must be, at every point 
 of the surface of a charged conductor, an outward pressure against 
 the surrounding dielectric. The surface density increases with the 
 curvature, but the repulsion increases still more rapidly, varying as 
 the square of the density. When the density becomes about a 
 hundred electrostatic units per square centimeter, the electrification 
 cannot be retained upon the conductor, and sparks fly into the sur- 
 rounding air. The discharge takes place most readily where the 
 density is the greatest; i.e., where the curvature is the greatest, as 
 at a point. Since the air in contact with such a point is similarly 
 electrified, and, therefore, repelled, an air-current passes from the 
 point, and the charge is dissipated by convection. As a general 
 thing, points and sharp edges are avoided in apparatus for use with 
 static electricity, but they are sometimes purposely provided. 
 
 334. Process of Electrification. When two dissimilar 
 substances are brought into contact and then separated, they 
 are equally and oppositely electrified. If the substances are 
 poor conductors, they must be rubbed together ; i.e., con- 
 tact must be made at every point in order to secure elec- 
 trification over the entire surface. If the substances are 
 good conductors, the opposite and equal electrifications 
 flow to the point last in contact, and pass by conduction 
 from one to the other. Evidently the resultant, in this 
 case, is zero. 
 
 335. Electrification and Energy. When two dissimilar 
 substances are brought into contact, they become oppositely 
 electrified. When they are subsequently separated, work 
 
STATIC ELECTRICITY. 421 
 
 is done against their mutual electric attraction. This 
 work represents the increased potential energy of the 
 system. That energy is at zero when the bodies are 
 in contact, and at its maximum when they are at an infi- 
 nite distance from each other. If the charged bodies are 
 similarly electrified, work is done against their mutual 
 electric repulsion. Then the potential energy of the 
 system varies from zero at an infinite distance between the 
 bodies to a maximum when the two are in contact. 
 
 336. Electrical Field and Lines of Force. The space 
 surrounding an electrified body and through which the elec- 
 trical force acts is called an electrical field of force. We 
 may imagine lines drawn in this field, each indicating the 
 direction in which a unit of electrification would move if 
 placed in the field. Evidently, we may draw an indefi- 
 nite number of such lines, but in order to "map" an elec- 
 trical field and to show the relative intensity of different 
 parts of it, it has been agreed that one line shall be drawn 
 through each square centimeter of surface for each dyne 
 of force exerted in the field. "" If one such line representing 
 a force of one dyne cuts each square centimeter of surface, 
 thp field is said to be of unit intensity; i.e., a unit of 
 electrification in a field of unit intensity would be acted 
 upon by a force of one dyne tending to move it along a line 
 of force. 
 
 (a) We may further imagine two electrified bodies as immersed 
 in an electrical field of force, and connected by elastic lines of force 
 that tend to shorten and that are self-repellent. In such a field, there 
 will be a stress parallel to the lines of force, and of the nature of a 
 tension ; also a stress perpendicular to the lines of force, and of the 
 nature of a pressure. 
 
422 SCHOOL PHYSICS. 
 
 337. Potential. In a general way, it may be said that 
 potential represents degree of electrification, or that it is 
 the relative condition of a conductor that determines the 
 direction of a transfer of electrification to it or from it. 
 The direction of the transfer depends, not upon quantity 
 or upon surface density, but upon relative potential. 
 
 (a) In dealing with masses of matter and the force of gravitation, 
 it is easy to understand that the potential energy of a unit mass at a 
 given point is an attribute of that point, and that the condition at the 
 point is due only to the existence of attracting bodies, and is the same 
 whether the unit mass is actually there or not. This attribute of the 
 point is called the gravitation potential at the point. The potential at a 
 point is zero when a unit particle if placed there would have no 
 potential energy, as when the point is at an infinite distance from 
 all attracting masses. Similarly, if a charge is placed anywhere in 
 an electrical field, it has a potential energy due to the work done 
 upon it in carrying it thither. This attribute of the point is called the 
 electrical potential at the point. The charge thus placed is subject to 
 the action of the electrical force that tends to move it to another 
 point where its potential energy will be less; i.e., to move it from a 
 point of higher to a point of lower potential. An electrostatic unit 
 difference of potential exists between two points when an erg of work is 
 involved in moving unit charge from one point to the other. 
 
 (6) Relative potential is analogous to level. As the sea-level is 
 taken as the zero from which altitudes are measured, so the surface 
 of the earth is taken as the zero of electric potential. As water 
 tends to flow from higher to lower levels, and as heat tends to flew 
 from places of higher to places of lower temperature, so electrification 
 tends to flow from places of higher to places of lower potential until 
 an equalization is reached.^ In the latter case, the flow is called a 
 current of electricity. If the quantity of electrification is limited, the 
 current is temporary, as in the discharge of a Ley den jar. If the 
 difference of potential is maintained, the current is continuous, as in 
 the case of a voltaic cell. 
 
 338. Equipotential Surfaces. Surrounding a unit posi- 
 tive charge as a center, there is a surface such that it will 
 
STATIC ELECTRICITY. 
 
 423 
 
 FIG. 318. 
 
 require the expenditure of an erg of work to carry a unit 
 negative charge from the center to any point of that sur- 
 face, as from A to P. Further from the center, there is 
 
 another surface such that it will 
 
 f s' >., 
 
 require the expenditure of an erg 
 of work to carry a unit negative 
 charge from the first surface to the 
 second, as from P to Q ; i.e., such 
 that there is unit difference of 
 potential between the two surfaces. 
 Such surfaces as these, throughout 
 which the potential is everyivhere the same, are called equi- 
 potential surfaces. Such surfaces are everywhere perpen- 
 dicular to the lines of force that cut the electrical field. 
 
 (a) When a charge is moved from any point to another point in 
 the same equipotential surface, no work is done upon it. When a 
 
 charge is moved from one such surface 
 to another, the work done is indepen- 
 dent of the path of transfer. If such 
 a surface was to be rendered impene- 
 trable, a particle could lie upon it 
 without tendency to move along it in 
 any direction. If any two points in 
 such a surface were to be joined by a 
 conductor, no flow of electrification 
 would take place. The closed lines in 
 Fig. 319 are equipotential lines drawn, 
 of course, upon equipotential surfaces, 
 about two similarly electrified spheres, 
 the quantity of electrification at A 
 being twice that at B. The lines radiating from A and B represent 
 lines of force. 
 
 Experiment 303. Charge a gold-leaf electroscope positively until 
 its leaves diverge slightly. Similarly charge a like electroscope until 
 its leaves diverge widely. The potential of the second charge is 
 
 FIG. 319. 
 
424 SCHOOL PHYSICS. 
 
 higher than that of the first. Connect the knobs of the two electro- 
 scopes by an insulated conductor. The change in the divergence of 
 the leaves shows that electrification has passed from a place of higher 
 to a place of lower potential. 
 
 339. Electromotive Force. Whenever a positive charge 
 is placed upon a conductor, it raises the potential at the 
 point of application, and there is a flow of electrification 
 until the surface of the conductor is an equipotential 
 surface. If two conductors at different potentials are 
 connected by a wire, a transfer of electrification will take 
 place until the difference of potential disappears. What- 
 ever its nature, the agency that tends to produce such a 
 transfer is called electromotive force. 
 
 Electrostatic Induction. 
 
 Experiment 304. Electrify a glass rod by rubbing it with silk, and 
 bring it near the electroscope but without making contact. The 
 leaves diverge. When the rod is removed, the leaves fall together. 
 Repeat the experiment, holding a glass plate between the rod and 
 the electroscope. 
 
 Experiment 305. Bring a metallic sphere positively charged near 
 an insulated cylindrical conductor with hemispherical ends and 
 
 provided with pith-ball and 
 linen thread electroscopes as 
 shown in Fig. 320. The 
 divergence of the pith-balls 
 shows electrification at the 
 FIG. 320. ends but not at the middle 
 
 of the conductor. With the 
 
 proof-plane and gold-leaf electroscope, examine the condition of the 
 conductor at the points A, B, and m, and compare your results with 
 the representations in the figure. Remove the sphere from the vicinity 
 of the conductor, or discharge it by touching it with the hand. All 
 signs of electrification on the conductor disappear, showing that the 
 charges at A and B were opposite and equal. 
 
STATIC ELECTRICITY. 425 
 
 Experiment 306. Electrify the insulated conductor, AB, as in Ex- 
 periment 305. Touch it with the finger, thus connecting it with the 
 earth and making it of indefinite length ; its positive electrification is 
 so diffused as to be insensible. Remove first the finger and then the 
 electrified sphere. The negative electrification being no longer held 
 at A by the attraction of the positive electrification at C, diffuses 
 itself over the cylinder, and the balls at each end of the cylinder 
 diverge, all being charged negatively. 
 
 Experiment 307. Suspend two egg-shell conductors (see Experi- 
 ment 301), as shown in 
 Fig. 321. Be sure that the 
 shells are in contact. Bring 
 an electrified glass rod near 
 one of them, and slide one 
 of the loops along the sup- 
 porting rod until the shells 
 are about 10 cm. apart. 
 Hold the electrified rod be- 
 tween the shells. It will 
 
 attract one and repel the FlG 321 
 
 other, showing that they 
 
 are oppositely electrified. Bring the shells into contact again, and 
 charge them similarly, as indicated in Experiment 306. 
 
 Experiment 308. Charge one of the egg-shells of Experiment 307, 
 and suspend it above the knob of a gold-leaf electroscope and at such 
 a distance that the leaves of the latter diverge but slightly. Provide a 
 plate of beeswax or of sulphur, the thickness of which is a little less 
 than the distance between the shell and the knob, and pass a gas flame 
 over its surface to remove all electrification from it. Hold the plate 
 between the shell and the electroscope without touching either. The 
 leaves of the electroscope diverge more widely, as if the electric force 
 passed more readily through the plate than through the air. 
 
 340. Electrification by Induction. The collapse of the 
 leaves of the electroscope in Experiment 304 showed that 
 there was no transfer of electrification from the rod to 
 the electroscope. Whenever an electrified body is brought 
 into the vicinity of an unelectrified conductor, thus placing 
 
426 SCHOOL PHYSICS. 
 
 the latter in an electrical field, and subjecting the inter- 
 vening dielectric to a condition of strain, the unelectrified 
 conductor becomes electrified. A dissimilar electrification 
 appears on the side nearer the electrifying conductor, and 
 similar electrification upon the further . side. Electrifi- 
 cation produced in this way, by the influence of an electrified 
 body and without contact with it, is called electrification by 
 induction. 
 
 (a) A charged body surrounded by a dielectric (e.g., the air) in- 
 duces an equal and opposite charge on the inner surface of the en- 
 closure containing the charged body and the dielectric (e.g., the walls 
 of the room). An induced charge is opposite in kind to the charge of 
 the inducing body. 
 
 (ft) The amount of inductive effect that takes place across an 
 intervening medium depends upon the nature of that medium ; it is 
 a function of the dielectric. The relative powers of different sub- 
 stances to transmit electrical inductive effects is called specific inductive 
 capacity, or the dielectric constant. The introduction of a dielectric 
 plate increases the inductive effect when the dielectric constant of 
 the plate is greater than that of air. 
 
 Experiment 309. Charge a gold-leaf electroscope to a high poten- 
 tial, i.e., until its leaves diverge widely. Bring the electric pendulum 
 of Experiment 290, or a similar metallic ball similarly suspended, into 
 contact with the knob of the electroscope, and notice the diminished 
 divergence of the leaves. The charge being distributed over a larger 
 surface, the potential is lowered. 
 
 341. The Capacity of a conductor is the amount of elec- 
 trification required to raise its potential from zero to unity, 
 i.e., the ratio of its charge to its potential. The unit of 
 capacity is the capacity of a conductor that requires unit 
 quantity to produce unit difference of potential ; it is 
 called a farad; one-millionth of a farad is called a micro- 
 farad. The capacity of a simple conductor is dependent 
 upon its size and shape, and upon the form and position 
 
STATIC ELECTRICITY. 427 
 
 of neighboring conductors that may act upon it induc- 
 tively. 
 
 (a) Under like conditions, the capacities of spheres are propor- 
 tional to their radii. 
 
 Experiment 310. Spread a sheet of tin-foil upon a pane of glass 
 supported on a tumbler. Charge the tin-foil by repeated sparks from . 
 the electrophorus (404) until it will receive no more. Count the 
 number of sparks that the tin-foil will receive. 
 
 Experiment 311. Lay a sheet of tin-foil upon the table so that it 
 will be in electrical connection with the earth. Over it place the glass 
 and foil used in Experiment 310. ' Charge the upper sheet as before, 
 and notice that it will receive a much greater number of sparks. Touch 
 the lower sheet of tin-foil w r ith a finger of one hand, and the upper sheet 
 with a finger of the other hand, thus discharging the apparatus. A 
 pricking sensation will be caused by the discharge. 
 
 342. A Condenser consists of a pair of conductors slightly 
 separated by a dielectric. If one of these conductors is 
 connected to earth, it requires a much larger quantity of 
 electrification to raise the potential of the other from zero 
 to unity, i.e., the capacity of the other is greatly increased. 
 A condenser is, therefore, a~device for increasing the elec- 
 trical density without increasing the potential, i.e., for 
 accumulating a large charge with a small electromotive 
 force. The smaller the distance between the conducting 
 surfaces, the greater the capacity of the condenser. 
 
 (a) When a charge is given to a conductor on one side of the 
 dielectric, it induces an opposite charge in the conductor on the other 
 side, as in Experiment 305. By their mutual attraction, these op- 
 posite charges are "bound" at the surface of the dielectric, thus leav- 
 ing the first conductor free to receive another charge, which acts 
 inductively upon the second conductor as the original charge did; and 
 so on, successively. This process necessarily results in an increasing 
 strain of the dielectric ; an over-charge may break it. 
 
428 
 
 SCHOOL PHYSICS. 
 
 (6) The nature of the dielectric has a great effect on the capacity 
 of the condenser. The specific inductive capacity of a dielectric may 
 now be defined as the ratio of the capacity of a condenser with air 
 insulation to the capacity of a similar condenser using the dielectric 
 in question. For instance, changing the dielectric from air to ebonite 
 more than doubles the capacity of the condenser. 
 
 (c) Condensers of the flat type (Fig. 322), consisting of tin-foil 
 
 conductors separated by 
 
 thin, flat dielectric sheets 
 
 (usually of mica), are 
 
 much used. To obtain 
 
 large area, and hence 
 great capacity, they are arranged alternately 
 in two series. A condenser of this type 
 (Fig. 323), having a capacity of one micro- 
 farad, weighs 6 or 7 pounds. The plug- 
 serves to connect the coatings when the instrument is not in use. 
 
 Fia. 322. 
 
 FIG. 323. 
 
 343. The Ley den Jar. The most common and, for many 
 purposes, the most convenient form of condenser is the 
 Leyden jar. This consists of a glass 
 jar, coated within and without for 
 about two-thirds its height with tin- 
 foil, and a metallic rod that communi- 
 cates by means of a small chain with 
 the inner coat, and terminates above 
 in a knob or a disk. The upper part 
 of the jar, and the wooden or ebonite 
 stopper that closes the mouth of the 
 jar and supports the rod, are generally 
 coated with sealing-wax or shellac- 
 varnish to lessen the deposition of 
 moisture from the air. Evidently, it may be considered 
 as a flat condenser rolled into cylindrical form. 
 
 (a) The jar may be charged by holding it in the hand as shown in 
 
 FIG. 324. 
 
STATIC ELECTRICITY 
 
 429 
 
 Fig. 324, or otherwise placing the outer coat in electrical connection 
 with the earth, and bringing the knob into contact with a charged 
 body. If the outer coat is insulated so that the repelled electrification 
 cannot pass to the earth, the jar cannot be very highly charged. To 
 discharge the jar, pass a stout wire through a piece of rubber tubing 
 and bend it into a V shape, or. in some other way, provide the wire 
 with an insulating handle. Bring one end of the wire into contact 
 with the outer coat, and then bring the other end into contact with 
 the knob. It is well to provide the wire " discharger " with metal 
 balls at its ends. 
 
 (&) That the phenomenon of electrification pertains to the dielec- 
 tric and not to the conducting plates may be shown with a Leyden jar 
 with movable coats. The parts being put together in proper order 
 and the jar charged, the inner coat, C, is re- 
 moved with a glass rod, and the glass vessel, 
 B, lifted from the outer coat, A. Tests show 
 that A and C are not electrified, and that B is 
 electrified. By placing thumb and forefinger 
 on the inner and the outer surfaces of B, a 
 slight shock may be felt. When the parts are 
 put together, the condenser is highly electri- 
 fied, and may be discharged in the usual way. 
 After a Leyden jar is discharged, a "residual 
 charge " gradually accumulates, as if the glass 
 was strained and slowly returned to its normal 
 condition. The time-interval required for the 
 residual charge is lessened by tapping the jar 
 and thus facilitating the molecular readjust- 
 ments. The metallic coats simply provide the 
 means for the prompt discharge of the super- 
 ficial layers of the molecules of the dielectric. 
 
 (c) A number of Leyden jars having their 
 coats connected constitutes an electric battery. 
 
 FIG. 325. 
 
 344. Nature of Electricity. The phenomena of electrifi- 
 cation indicate that electricity is a perfectly incompres- 
 sible substance of which all space is completely full, and 
 the question arises, is it not identical with the ether? 
 It has recently been suggested that the ether is made up 
 
430 SCHOOL PHYSICS. 
 
 of two equal opposite constituents, each endowed with 
 inertia, and connected to the other by elastic ties which 
 the presence of gross matter generally weakens and some- 
 times dissolves, and that these two constituents of the 
 ether are positive and negative electricity. According 
 to this provisional hypothesis, and the general belief of 
 physicists, electricity is a form of matter rather than a form 
 of energy. A full discussion of the ultimate nature of 
 electricity is beyond the province of this book, but it is 
 safe for us to say that electricity is that which is transferred 
 from one body to another in the process of electrifying them. 
 
 345. Theory of Electrification. When electricity is 
 transferred from one body to another and the bodies are 
 separated (see 334 and 335) against their mutual 
 attraction, the intervening medium is thrown into a state 
 of strain indicated by the lines of force. This state of 
 strain in the dielectric constitutes electrification. Whatever 
 the real nature of electricity, and whether the phenomena 
 of attraction and repulsion are explained on the hypothesis 
 that the elastic ether is strained by the separation of the 
 electrified bodies and tends to recover its normal condition, 
 or on any other hypothesis, electrification results from 
 work done, and is a form of potential energy. 
 
 CLASSROOM EXERCISES 
 
 1 . How can you show that there are two opposite kinds of electri- 
 fication ? 
 
 2. How would you test the kind of electrification of an electrified 
 body? 
 
 3. (a) What is a proof -plane ? (&) An electroscope ? (c) Describe 
 one kind of electroscope, (d) Another kind. 
 
STATIC ELECTRICITY. 431 
 
 4. Why do we regard the electrifications produced by rubbing 
 two bodies together as opposite and equal? 
 
 5. Why is it desirable that a glass rod used for electrification be 
 warmer than the atmosphere of the room where it is used ? 
 
 6. Two small balls are charged respectively with + 24 and 8 units 
 of electrification. With what force will they attract one another 
 when placed at a distance of 4 centimeters from one another? 
 
 Ans. 12 dynes. 
 
 7. If these two balls are then made to touch for an instant and 
 then put back in their former positions, with what force will they act 
 on each other? Ans. Repulsion of 4 dynes. 
 
 8. At what distance from a small sphere charged with 28 units of 
 electrification must you place a second sphere charged with 56 units 
 that one may repel the other with a force of 32 dynes? Ans. 7 cm. 
 
 9. (a) Having a metal globe positively electrified, how could you 
 with it negatively electrify a dozen globes of equal size without 
 affecting the charge of the first? (6) How could you charge posi- 
 tively one of the dozen without affecting the charge of the first? 
 
 10. Suppose two similar conductors to be electrified, one with a 
 positive charge of 5 units and the other with a negative charge of 3 
 units. They are made to touch each other. When they are sepa- 
 rated, what will be the charge of each? 
 
 Ans. One unit of positive electrification. 
 
 11. In what way may an electric charge be divided into three equal 
 parts ? 
 
 12. When a pin or needle is held with its point near the knob of a 
 charged gold-leaf electroscope, the leaves quickly collapse. Explain. 
 
 13. A Leyden jar standing on a plate of glass cannot be highly 
 charged. Why? 
 
 14. Will you receive a greater shock by touching the knob of a 
 charged Leyden jar when it is held in the hand or when it is stand- 
 ing on a sheet of glass? Explain. 
 
 15. Imagine that the knob of a gold-leaf electroscope is connected 
 by wire to the knob of a Leyden jar, and that a given amount of elec- 
 trification is communicated to the knob of the jar. Will the diverg- 
 ence of the leaves of the electroscope be greater when the jar is held 
 in the hand or when it is standing on a sheet of glass ? Explain. 
 
 16. Show by a diagram that electrostatic induction always precedes 
 electric attraction, and explain why the repulsion between the opposite 
 electrifications does not neutralize the attraction. 
 
432 SCHOOL PHYSICS. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. A rubber comb; metal pipe; tin pail. 
 
 1. Quickly pass a rubber comb through the hair and determine 
 whether the electrification of the comb is positive or negative. 
 
 2. Provide an insulated egg-shell conductor as described in Experi- 
 ment 301, which the teacher will electrify by induction, using a glass rod 
 that has been rubbed with silk or with flannel. Determine the kind 
 of electrification of the conductor experimentally, and thence deter- 
 mine theoretically whether the glass rod was rubbed with silk or with 
 flannel. 
 
 3. Show that an electric charge is self -repulsive by blowing a soap- 
 bubble on a metal pipe and then electrifying it. Compare the change 
 in the size of the bubble with that noticed in Experiment 30. 
 
 4. Bring an electrified body near the knob of a gold-leaf electro 
 scope ; touch the knob with the finger ; remove the finger ; remove the 
 electrified body. Bring a rod that is positively charged near the knob 
 and, from the increased or diminished divergence of the leaves, deter- 
 mine whether the electrification of the first body was positive or nega- 
 tive. 
 
 5. Twist some tissue paper into a loose roll about six inches long. 
 Stick a pin through the middle of the roll into a vertical support. 
 Present an electrified rod to one end of the roll, and thus cause the 
 roll to turn about the pin as a horizontal axis. Give this piece of 
 apparatus a scientific name. 
 
 6. From a horizontal glass rod or a tightly stretched silk cord, sus- 
 pend a fine copper wire, a linen thread, and two silk threads, each at 
 least a meter long. To the lower end of each, attach a metal weight 
 of any kind. Place the weight supported by the wire upon the disk 
 of a gold-leaf electroscope. Bring an electrified rod near the upper 
 end of the wire ; the gold leaves diverge instantly. Repeat the experi- 
 ment with the linen thread; the leaves diverge soon. Repeat the 
 experiment with the dry silk thread ; the leaves do not diverge at all. 
 Rub the rod upon the upper end of the silk thread; no divergence 
 follows. Wet the second silk cord thoroughly, and repeat the experi- 
 ment; the leaves diverge instantly. Record the teaching of the 
 experiment. 
 
 7. Prepare two wire stirrups, A and B, like those shown in Fig. 
 313, and suspend them by threads. Electrify two glass rods by rub- 
 bing them with silk, and place them in the stirrups. Bring A near B. 
 
CURRENT ELECTRICITY. 433 
 
 Notice the repulsion. Repeat the experiment with two sticks of seal- 
 ing-wax that have been electrified by rubbing with flannel. Notice 
 the repulsion. Place an electrified glass rod in A, and an electrified 
 stick of sealing-wax in B. Notice the attraction. Give the law illus- 
 trated by these experiments. 
 
 8. Place a gold-leaf electroscope inside an insulated tin pail and 
 electrify the pail. Describe and explain the indications given by the 
 electroscope. 
 
 9. Insulate a tin pail, and run a fine wire from its edge to the knob 
 of an electroscope. Suspend a metal ball by a silk thread, electrify 
 it, and lower it into the pail without contact. Notice and account for 
 the divergence of the leaves of the electroscope. Touch the pail with 
 a finger. Notice and account for the collapse of the leaves. Remove 
 the finger and withdraw the ball. Notice and account for the diver- 
 gence of the leaves. If the ball is negatively charged, what is the 
 final charge of the electroscope? 
 
 B. CURRENT ELECTRICITY. 
 
 Experiment 312. Partly fill a tumbler with a solution made by 
 slowly pouring one part of sulphuric acid into ten parts of water. 
 Place a strip of zinc, 1 x 10cm., in the tumbler of dilute acid, and 
 notice the bubbles that rise. Apply a flame to them as they reach the 
 surface of the liquid, and notice that they burn with slight puffs. 
 Hydrogen is evolved by the chemical action between the zinc and the 
 acid. 
 
 Experiment 313. Take the zinc from the tumbler of acid and, 
 while it is yet wet, rub thereon a few drops of mercury, thus amalga- 
 mating the zinc. The amalgamated surface will have 
 the appearance of polished silver. Replace the zinc 
 in the acid, and notice that no bubbles are given off. 
 Place a copper strip, 2 x 10 cm., in the solution, 
 being careful that it does not touch the zinc. No 
 bubbles appear on either the copper or the zinc. 
 Bring the strips together at their upper ends as 
 shown in Fig. 326. Bubbles now arise from the cop- 
 per. Connect the metals above the liquid by a piece 
 of copper wire about No. 18. The same results are FIG. 326. 
 observed. 
 
 28 
 
434 
 
 SCHOOL PHYSICS. 
 
 NOTE. Always make such connections secure, metal to metal, and 
 with large area of contact. Each metal strip may be bent at the top 
 so as to clasp the edge of the tumbler, leaving the part on the inside 
 long enough to reach very nearly to the bottom. 
 
 346. Suspicion. It seems as though a metallic contact 
 is necessary to bring about this phenomenon of bubbles on 
 the copper. We have a complete circuit of materials, 
 copper strip, wire, zinc strip, and acid. Perhaps we do 
 not see all that is taking place in the system. 
 
 Experiment 314. Solder a wire 50 centimeters long to each strip. 
 This gives a better electrical contact than simply twisting the wire 
 about the strip. Place the strips in the acid, and bring the free ends 
 of the wires into contact with the tongue, one above and one below 
 it, being sure that there is no acid on the wires. A bitter, biting 
 taste is felt. Make sure that this taste disappears when either strip 
 is removed from the solution ; when either wire is disconnected from 
 the tongue ; or when the circuit is broken at any point. 
 
 Experiment 315. Hold the two wires over a compass-needle as 
 shown in Fig. 327. No change appears. Bring the two ends of the 
 
 FIG. 327. 
 
 wire into contact, and thus close the circuit. The needle instantly flies 
 
 around as though it was trying to place itself at right angles to the 
 
 wire. Break the circuit, and the needle 
 
 =^ N swings back to its north and south posi- 
 tion. Twist the wires together, and bend 
 the conductor into a loop so that the cur- 
 rent passes above the needle in one direc- 
 tion and beneath the needle in the other 
 direction, as shown in Fig. 328. The de- 
 FIG. 328. flection of the needle will be greater than 
 before. If the wire is formed into a loop 
 that makes several turns about the needle, the deflection will be 
 
 
CURRENT ELECTRICITY. 
 
 435 
 
 greater still. Continued investigations with this simple apparatus 
 will show that the hydrogen bubbles cling tenaciously to the copper, 
 and that, by this "polarization of the cell," its electrical power is 
 much diminished. 
 
 Experiment 316. Put the cover of a tin spice-box into a fire and 
 thoroughly melt the tin coating from the iron plate. The cover thus 
 prepared is to be used as a mold for casting a zinc plate 6 mm. thick. 
 Place the mold on a fire-shovel and hold it over a hot fire, preferably 
 a gas or gasoline burner. Fill the mold with zinc clippings, and 
 when they have melted, place in the liquid metal a copper wire about 
 
 28 cm. long, bent 
 
 as shown in Fig. 
 
 329. Turn out 
 FIG. 329. the flame and al- FIG. 330. 
 
 low the zinc to 
 
 cool. Remove the zinc plate from the mold. If the work has been 
 properly done, the hook of the wire will be embedded in the zinc, 
 and the straightened wire will support the plate from its edge as shown 
 in Fig. 330. Smooth the rough edges of the plate with a file, and 
 amalgamate the zinc with mercury. 
 
 Invert a ^common tumbler on a square board of soft pine, about 
 1.5 cm. thick, and large enough to serve as a cover for it. Run a pen- 
 cil around the edge of the tumbler and draw the diagonals of the in- 
 scribed and circumscribed squares, as shown in Fig. 331. Bore holes 
 
 FIG. 331. 
 
 FIG. 332. 
 
 as shown at a, &, c, and d just large enough to admit an electric (arc) 
 light carbon. Cut four such carbons to lengths that are equal and less 
 than the depth of the tumbler. If the carbons are copper-coated, 
 
436 
 
 SCHOOL PHYSICS. 
 
 FIG. 333. 
 
 dissolve the copper with nitric acid from all of the rod except 
 1.5 cm. at the upper end. Insert one end of each carbon into one of 
 the holes, and connect the four carbons by a copper wire as shown in 
 Figs. 332 and 333. Pass the wire of the zinc plate through a small 
 hole at the middle of the board, so that the plate may be suspended 
 
 in the tumbler as shown in Fig. 334. 
 Wedge the wire in place. Be careful 
 that the wire from the zinc does not 
 touch the wire from the carbons on the 
 top of the cover. It will be well to 
 insulate the former wire, by slipping 
 over it a piece of soft rubber tubing of 
 very small bore and two or three inches 
 long. The tubing may be held in place 
 by a kink in the wire. Wire that has 
 been insulated with cotton and paramne may be used for supporting 
 the zinc, the end that is to be embedded in the zinc being scraped 
 bare before the casting. 
 
 Prepare a solution as follows : slowly pour 167 cu. cm. of sulphuric 
 acid into 500 cu. cm. of water, and let the mixture cool. Dissolve 
 115 g. of potassium dichromate (bi- 
 chromate of potash) in 335 cu. cm. 
 of boiling water, and pour the hot 
 solution into the dilute acid. When 
 this liquid is cool, fill the tumbler 
 about two-thirds full with it, and 
 place the carbons and zinc therein. 
 Adjust the height of the plate as 
 shown in Fig. 334, and be sure that 
 the zinc does not touch any of the 
 carbons. The zinc and carbon 
 should be kept in the fluid no longer 
 than is necessary. It is well to pro- 
 vide a second tumbler in which to 
 drain them. Each pupil should 
 make at least one of these cells ; he 
 will find three or four of them very useful. The cost of the cell need 
 not exceed twenty-five cents. Using this cell, repeat Experiment 315. 
 Notice the direction of the deflection of the needle. Reverse the 
 cell connections, and notice that the needle deflects in the opposite 
 direction. 
 
 FIG. 334. 
 
CURRENT ELECTRICITY. 437 
 
 347. Certainty. We are now sure that something un- 
 usual is going on in the wire. This something is called a 
 current of electricity. Its exact na- 
 ture is not yet known, but much has 
 
 been learned about its properties and 
 the laws by which it is governed. 
 There is a difference of potential 
 between the plates, and the chem- 
 ical action between the liquid and 
 one or both of the plates, or some 
 other cause, tends to maintain that 
 
 FIG. 335. 
 
 difference. The containing vessel, the 
 
 plates, and the exciting liquid constitute a voltaic cell. 
 
 348. Direction of Current. We cannot conceive a cur- 
 rent without direction. The actual direction of current- 
 flow is not known, but, for the sake of convenience and 
 uniformity, electricians assume that the current flows 
 from the carbon through the wire to the zinc, and from 
 the zinc through the liquid to the carbon. 
 
 349. Plates, Poles, etc. The entire path traversed by 
 the current, including liquids as well as solids, is called the 
 circuit. The plate that is the more vigorously acted upon 
 by the liquid is called the positive plate ; the other is 
 called the negative plate. The free end of the wire 
 attached to the negative plate is called the positive pole 
 or electrode ; that of the wire attached to the positive 
 plate is called the negative pole or electrode. When the 
 two electrodes are joined, the circuit is closed ; when they 
 are separated, the circuit is broken. When several cells 
 are connected so that the positive plate of one is joined 
 
438 
 
 SCHOOL PHYSICS. 
 
 to the negative plate of the next, as zinc to carbon, and so 
 
 on, as shown in Fig. 
 336, they are said to 
 be grouped or joined 
 
 c ' ^- ' *- in series. When all 
 
 z "T" j ( c of the positive plates 
 
 M^O""" are connected on one 
 
 FlG - 336 ' side, and all of the 
 
 negative plates are connected on the other side, as shown 
 
 in Fig. 337, the 
 
 cells are said to be 
 
 joined in parallel, 
 
 or in multiple arc. 
 
 A number of cells 
 
 joined in either 
 
 way is called a vol- 
 taic battery. 
 
 (a) The nomenclature of plates and poles is a little perplexing, 
 but the possible confusion may be avoided by remembering that in 
 any part of an electric circuit, a point from which the current flows 
 is called positive ( + ) and. a point toward which the current flows is 
 called negative ( ). 
 
 NOTE. The representation of the zinc and carbon plates, as at Z 
 and C in Fig. 336, is the conventional way of representing a voltaic 
 cell. 
 
 Experiment 317. Provide a flat piece of soft pine wood about 
 10 cm. square and 3 cm. thick, and 
 wind on evenly one layer of No. 16 
 cotton-covered or insulated copper wire, 
 covering the whole block. Secure the 
 two ends of the wire by double- 
 pointed tacks. Place a small pocket 
 compass upon the block thus wound, 
 and turn the block until the coils of 
 FIG. 338. wire are parallel to the needle when the 
 
 FIG. 337. 
 
CURRENT ELECTRICITY 
 
 439 
 
 circuit is open. Then pass a current through the coil. The deflec- 
 tion of the needle is much stronger than 
 before, although, owing to the weakening 
 of the cell, the deflection falls off after a 
 time. The instrument we have made is 
 called a galvanoscope. If a pocket com- 
 pass can be spared for this exclusive use, 
 it is well to mount it in a grooved block, 
 and to attach the terminals of the wire to 
 the bases of two binding posts, as shown in FIG. 339. 
 
 Fig. 339. 
 
 Experiment 318. Interpose 20 feet of No. 30 (or finer) iron wire 
 in the circuit of a voltaic cell. Connect it so that the current will 
 flow from the carbon through the galvanoscope, through the iron 
 
 FIG. 340. 
 
 wire, and back to the battery. In other words, connect the wire 
 and galvanoscope in series. The deflection will be less than before. 
 Keep the current on just long enough to read the galvanoscope; 
 otherwise, the diminished deflection may be due more to the weak- 
 ening of the cell than to the interposition of the wire. 
 
 350. Resistance. The interposition of the iron wire 
 appears to diminish the electrical effect, or to resist the 
 current flow. This property exists in all substances, and 
 its manifestation is accompanied by a transformation of 
 electrical energy into heat. The property of a conductor 
 
440 SCHOOL PHYSICS. 
 
 by virtue of which the passage of an electric current through 
 it is diminished, and part of the electric energy dissipated is 
 called resistance. 
 
 (a) We know nothing of the nature of electrical resistance, and 
 perhaps can best define it, as we soon shall ( 361, c), in terms of dif- 
 ference of potential and current strength. 
 
 (b) The word " resistance " is also applied to a material device, 
 such as a coil of wire, introduced into an electric circuit on account 
 of the resistance that it offers to the passage of the current. 
 
 Experiment 319. Provide 20 feet of No. 30 iron wire, 20 feet of 
 No. 30 copper wire, 60 feet of No. 30 iron wire, and 20 feet of No. 20 
 
 iron wire. Repeat Experiment 318 
 
 20 FT. NO. 20. USON 
 
 20 FT'. NO. so.' COPPER z^F w ith eacn f these wires, in each 
 BO FT. NO. so.' .RON R o . \ case notin g ^6 deflection of the 
 galvanoscope, G. 
 
 Each wire may be coiled on a 
 board, care being taken that adja- 
 cent coils do not touch. Coiled or 
 
 FIG. 341. uncoiled, the wires may be con- 
 
 nected as in Fig. 341, and the free 
 
 end of F touched at 1, 2, 3, and 4 successively. Give the cell a 
 moment's rest between successive contacts. 
 
 351. The Ohm is the practical unit of resistance. It is 
 the resistance of a column of pure mercury one square mil- 
 limeter in cross-section and 106.3 centimeters long, and at 
 a temperature of 0. A thousand feet of No. 10 copper 
 wire, or 9.3 feet of No. 30 copper wire, has a resistance 
 of very nearly an ohm, an important "rough and ready" 
 standard. 
 
 (a) The ohm has been repeatedly determined by societies and con- 
 gresses of electricians. The British Association determined its mag- 
 nitude with great care, but there was an error in the method that 
 long passed unnoticed. The international ohm, denned above, is 
 equal to 1.013+ B.A. ohms. Resistance boxes and other apparatus 
 measuring in B.A. ohms are common; their results should be cor- 
 rected as above indicated. 
 
CURRENT ELECTRICITY. 441 
 
 (6) A million ohms is called a megohm ; one-millionth of an ohm 
 is called a microhm. 
 
 352. Laws of Resistance. Three important laws have 
 been experimentally established : 
 
 (1) Other things being equal, the resistance of a conductor 
 is directly proportional to its length. 
 
 (2) Other things being equal, the resistance of a conductor 
 is inversely proportional to its area of cross-section, or to 
 the square of its radius or diameter. 
 
 (3) Other things being equal, the resistance of a wire de- 
 pends upon the material of which it is made. At a given 
 temperature, resistance is directly proportional to a con- 
 stant that is different for different substances. 
 
 (a) This constant, K t is called the specific resistance or the resistivity 
 of the material. The specific resistance of a substance is the resistance 
 at C. of a cubic centimeter of the substance, i.e., of a conductor 
 made of the substance, 1 cm. long and 1 sq. cm. in cross-section. It 
 varies widely with temperature and other considerations, and is prac- 
 tically measured in microhms. The reciprocal of resistivity is called 
 conductivity, and is measured in a unit called the mho. Tables of 
 resistances, etc., are given in the appendix. 
 
 (&) The laws of resistance may be expressed algebraically as fol- 
 lows : 
 
 **% 
 
 in which R represents the resistance of the wire in ohms ; K, the resis- 
 tivity of the material; and I and r, the length and radius in centi- 
 meters. 
 
 Experiment 320. Heat a long, fine iron wire to dull redness by 
 an electric current, and dip a loop of the hot wire into ice-cold water. 
 The resistance of the cooled part of the wire is lessened, the current 
 is increased thereby, and the uncooled part of the wire becomes 
 highly incandescent. 
 
442 SCHOOL PHYSICS. 
 
 353. Effect of Temperature on Resistance. The resist- 
 ance of metals and of most other substances increases as 
 the temperature rises. But the resistance of some sub- 
 stances, notably carbon and electrolytes, is lowered by 
 heating. The " cold " resistance of the carbon filament of 
 an incandescent electric lamp is much greater than the 
 resistance of the same filament when the lamp is lighted. 
 
 (a) Suppose a wire at any point to become reduced to half its 
 diameter. The cross-section will have an area as great as in the 
 thicker part. The resistance here will be 4 times as great, and the 
 number of heat units developed will be 4 times as great as in an equal 
 length of the thicker wire. But 4 times the amount of heat spent 
 on \ the amount of metal will warm it to a degree 16 times as great. 
 In other words, the heat developed by a given current in different 
 parts of a wire of uniform material and varying size is inversely pro- 
 portional to the fourth power of the diameters. 
 
 CLASSROOM EXERCISES. 
 
 1. What is the resistance of a No. 10 copper wire 1,000 feet long? 
 (Consult the table in the appendix.) 
 
 2. What is the resistance of 800 feet of German silver wire, No. 4 ? 
 
 3. What is the resistance of 750 feet of iron wire, No. 8? 
 
 4. What is the resistance of 350 feet of silver wire, No. 14? 
 
 5. What is the resistance of 6,050 feet of copper wire, No. 25? 
 
 6. There is a " fault " in a telegraph line 3,590 feet long and made 
 of No. 14 iron wire. By means of electrical instruments, it is found 
 that the resistance of the wire from one end to the fault is 1.75 ohms. 
 How far is the fault from the end of the line ? 
 
 7. What is the resistance of the whole line mentioned in Exer- 
 cise 6? 
 
 .8. How far away would the fault have been, had the line been of 
 No. 14 copper wire ?/ 
 
 9. Determine the diameter of a copper wire that has a resistance 
 of 2 ohms per thousand feet. 
 
 10. What is the resistivity of a wire 50 mils in diameter, 900 feet 
 long and having a resistance of 46.2 ohms? Of what material men- 
 tioned in the table on page 593 might the wire be made ? 
 
CURRENT ELECTRICITY. 
 
 443 
 
 354. Analogy. In many respects, it is convenient to 
 compare the flow of electrification through a wire to the 
 flow of water through a horizontal pipe. Such a compari- 
 son yields the following analogues : 
 
 Functions. 
 Pressure. 
 Quantity. 
 Rate of flow. 
 
 Resistance. 
 
 Work. 
 
 Rate of work. 
 
 Hydraulic Units. 
 
 Head in feet. 
 
 Pound. 
 
 Pounds per second. 
 
 Xo definite unit. 
 Foot-pound. 
 
 Foot-pounds per second, 
 or horse-power. 
 
 Electromagnetic Units. 
 
 Volt. 
 
 Coulomb. 
 
 Coulombs per second, 
 
 or ampere. 
 Ohm. . 
 Joule. 
 Volt-ampere, or watt. 
 
 355. The Volt. Just as a head of water supplies a 
 hydraulic pressure that causes the liquid to flow through a 
 pipe in spite of friction, so there is an electrical pressure 
 that forces a current through a conductor in spite of its 
 resistance. As hydraulic pressure might be called water- 
 moving force, so electrical pressure is called electromotive 
 force (E.M.F.). The unit of electrical pressure is called 
 the volt, and is almost the same as the electromotive 
 force of a cell consisting "of a copper and a zinc plate 
 immersed in a solution of zinc sulphate. . 
 
 (a) The E.M.F. of a Daniell cell is about 
 1.1 volts ; of a fresh chromic acid cell, 2 volts ; 
 and of a Leclanche cell, 1.5 volts. The E.M.F. 
 of a Carh art-Clark standard cell (see Fig. 342) is 
 1.44 volts at 15; conversely, a volt is about 0.7 of 
 the E.M.F. of a Carhart-Clark standard cell at that 
 temperature. A standard cell should never be 
 used on a closed circuit. 
 
 Experiment 321. Prepare a block for a gal- 
 vanoscope, winding it closely with ten layers of 
 No. 34 insulated copper wire, thus making an 
 
 FIG. 342. 
 
444 
 
 SCHOOL PHYSICS. 
 
 FIG. 343. 
 
 instrument of high resistance. Arrange a circuit as shown in Fig. 
 
 343, employing about ten feet of 
 No. 30 iron wire. As the copper 
 wire, /, is slid along the iron wire 
 from a to #, the deflection of the 
 galvanoscope will decrease. 
 
 356. Difference of Potential. 
 
 When the stop-cock of a 
 vessel like that shown in Fig. 344 is closed, water will stand 
 at the same level in the 
 vertical tubes, a, 6, and 
 c. There is no differ- 
 ence of pressure at dif- 
 ferent points along the 
 tube B, and, therefore, 
 no flow of water. When 
 the stop-cock is opened, 
 the pressure at C is relieved, and the greater pressure at the 
 bottom of A results in a flow along the horizontal pipe. 
 I c The variations in liquid 
 
 pressure at different points 
 along B is now shown by 
 the differences of level in 
 C a, b, and c (Fig. 345). The 
 pressure becomes less as 
 we pass from A toward C. 
 The analogous phenome- 
 non is shown in Experiment 321, where the galvanoscope 
 reveals the differences of electric pressure, or potential, at 
 different points of the circuit. 
 
 (a) Difference of potential is a different thing from electromotive 
 force. The electromotive force of a circuit is the total electrical pres- 
 
 FIG. 344. 
 
 FIG. 345. 
 
CURRENT ELECTRICITY. 445 
 
 sure existing therein, while the difference of potential is merely the 
 difference of electrical pressure between two points on the circuit. A 
 generator of electricity for arc lights may have an electromotive force 
 of 3,000 volts, while the difference of potential between the terminals 
 of an arc lamp in circuit with it is only 45 volts. 
 
 Experiment 322. Connect several similar cells in series, as 
 shown in Fig. 346. Put a Xo. 40 
 iron wire, wn, and a larger copper 
 wire, 'ef, in circuit as shown. Slide 
 the end of the copper wire along the 
 iron wire from n toward m until the 
 latter becomes red hot. 
 
 HHhHHH 
 
 357. The Ampere. In Ex- 
 periment 322, we gradually FIG 
 reduced the length of the cir- 
 cuit, and thus reduced its resistance. As the resistance 
 was reduced, the electromotive force of the battery sent 
 a correspondingly increased current through the wire. 
 This increase of current strength was manifested by the 
 increased heating effect. The unit of rate of flow, or cur- 
 rent strength, is the ampere, which may be defined as the 
 current flowing in unit of- time (second) through a wire 
 having unit resistance (ohm), and between the two ends of 
 which unit difference of potential (volt) is maintained. 
 
 (a) A 1-ampere current passes a coulomb of electricity each second, 
 and will electrolytically deposit 0.001118 of a gram of silver, or 
 0.0003287 of a gram of copper in a second. A thousandth of an 
 ampere is a milliampere. 
 
 358. The Coulomb. Just as quantity of water may be 
 measured in pounds, so quantity of electrification is meas- 
 ured in coulombs. The coulomb may be defined as the 
 quantity of electrification carried past any point by a 
 
446 SCHOOL PHYSICS. 
 
 1-ampere current in one second. The unit is rather large 
 for practical purposes, and is but little used. 
 
 359. The Joule is the electrical unit of ^vork, and repre- 
 sents the energy of one coulomb delivered under a pressure 
 of one volt, or the work done in one second in maintaining 
 a current of one ampere against a resistance of one ohm. 
 
 Joules = volts x coulombs. 
 It is equivalent to 10 7 ergs. 
 
 360. The Watt is the unit of electrical activity or power, 
 and represents the rate of working in a circuit when the 
 electromotive force is one volt and the current is one 
 ampere. One horse-power equals 746 watts. 
 
 Watts volts x amperes. 
 It is equivalent to 10 7 ergs per second. 
 
 361. Ohm's Law. Representing current strength by 
 C, voltage by E, and resistance by R, the numerical re- 
 lations of these functions of an electrical current are ex- 
 pressed by the formula, 
 
 T> /~f 
 
 \j O 
 
 Any two of these being known, the third may be found. 
 
 (a) Applied to an electric generator (as a dynamo or voltaic cell), 
 we may represent the resistance of the external circuit by R and the 
 internal resistance of the generator itself by r. Then 
 
 = ^R 
 
 Thus, if the E.M.F. of a chromic acid cell is 2 volts, the internal 
 resistance of the cell is 1.5 ohms, and the wire resistance is 0.5 ohms, 
 
 C= 
 
 1.5 + 0.5 
 The cunrent strength will be 1 ampere. 
 
CURRENT ELECTRICITY. 447 
 
 (6) Representing algebraically the definition of the watt, we have 
 W=ExC. (1) 
 
 Substituting, in this equation, the above given value of E, we have 
 
 W=RxC*. (2) 
 
 Substituting, in the same equation, the above given value of C, we have 
 
 (c) In the light of Ohm's law, resistance might be defined as the 
 ratio between E. M. Y. and current strength, or as electric pressure 
 divided by electric flow. 
 
 362. Joule's Law. The work done by an electric cur- 
 rent is equal to the product of the strength of the current, 
 C; the fall of potential, E; and the time, t. 
 
 W= CEt. 
 
 Since, by Ohm's law, E = (7/2, we have the following 
 equivalent expression : 
 
 W= C*Bt. 
 
 If E is measured in volts, C in amperes, and R in ohms, 
 W will be expressed in joules per second, or watts. 
 Since a small calory equals 4.2 joules, 
 
 in which formula,* H represents the number of small 
 calories. 
 
 Experiment 323. Join equal lengths of iron wires of different 
 sizes end to end, and pass a gradually increasing current through 
 them. The smallest wire will be most heated. 
 
 Experiment 324. Join, end to end, equal lengths of iron and cop- 
 per wires of the same size, and increase the current that passes through 
 
448 SCHOOL PHYSICS. 
 
 them until the iron wire is red-hot. Ascertain the thermal condition 
 of the copper wire. 
 
 Experiment 325. Send the current of a few cells in series through 
 a chain made of alternate links of silver and platinum wires of the 
 same size. The platinum links grow red-hot, while the silver links 
 remain comparatively cool. The specific resistance of platinum is 
 about six times that of silver, and its specific heat is about half 
 as great ; hence, the rise of temperature in wires of equal thickness 
 traversed by the same current is about twelve times as great for 
 platinum as for silver. 
 
 Experiment 326. Pass a suitable current through a long, fine iron 
 wire, and thus heat it to dull redness. By means of a sliding contact, 
 progressively shorten the iron wire part of the circuit, as in Experi- 
 ment 322. As the resistance decreases, the current increases, until 
 the iron wire that remains in circuit is melted. 
 
 363. Distribution of Heat in the Circuit. Since, at any 
 instant, the current strength is uniform at every part of 
 the circuit, it follows from the last formula given in 362 
 that the heat developed in any part of the circuit will be 
 proportional to the resistance of that part of the circuit. 
 As the fall of potential is proportional to the resistance, 
 the heat energy developed in any part of the circuit is pro- 
 portional to the fall of potential through that part of the 
 circuit. 
 
 364. Shunts. When part of a circuit consists of two 
 
 branches, each branch is said to be a shunt to the other. 
 The current flowing through such a circuit will divide, 
 
CURRENT ELECTRICITY. 449 
 
 part of it going one way, and the other part the other 
 way. 
 
 (a) Under such circumstances, the current that flows through the 
 branches will be inversely proportional to the respective resistances 
 of the branches. To illustrate, suppose that the branch that carries 
 the galvanometer, G, has a resistance of 900 ohms, and that the 
 branch that carries the coil, 5, has a resistance of 100 ohms. Then 
 0.9 of the current will flow through 5, and 0.1 through G. 
 
 (b) The introduction of a shunt lessens the resistance of the cir- 
 cuit. The conductivity of the circuit between a and b is the sum of 
 the conductivities of the two branches, and conductivity is the re- 
 ciprocal of resistance. Representing the resistance of the branched 
 circuit by R, that of one branch by r, and that of the other branch by 
 /, we have 
 
 = - H ; whence R = 
 
 R r r' r + r / 
 
 For instance, in the case of the galvanometer and the coil above 
 mentioned, 
 
 R = 90 x 10 = 90, the number of ohms. 
 900 + 100 
 
 CLASSROOM EXERCISES. 
 
 1. A copper wire is carrying a 5-ampere current. The resistance of 
 this wire is 2 ohms. 
 
 (a) How many volts are necessary to force the current through the 
 wire? 
 
 Solution : E = C x R = 5 x 2 = 10, the number of volts. 
 (6) How much energy is consumed in the wire ? 
 
 Solution : W = E x C = 10 x 5 = 50, the number of watts ; or 
 W = R x C 2 = 2 x 25 = 50, the number of watts. 
 
 2. An incandescence lamp is connected with an electric generator 
 (dynamo) 300 feet away by a Xo. 18 copper wire that is carrying a 
 1-ampere current. A fine coil galvanoscope, used as described in Ex- 
 periment 321, would show differences in potential between the ends of 
 the two wires running to the lamp, and between the two terminals of 
 the lamp itself. What is the loss of voltage due to the line? 
 
 29 
 
450 SCHOOL PHYSICS. 
 
 Solution : The table of resistances given in the appendix shows 
 that the resistance of the 600 feet of wire is 3.83466 ohms. 
 
 E=C x R = l x 3.83466 = 3.83466, the number of volts. 
 
 If the lamp took 1 ampere at 100 volts, the line loss would be nearly 
 3.8 per cent. 
 
 3. What would be the proper size of copper wire to supply a group 
 of lamps 400 feet away, and taking 15 amperes, so that the line loss 
 shall be 2 volts. 
 
 Solution : The resistance of the line would be, 
 
 R = = = 0.1333, the number of ohms. 
 C 15 
 
 Itc resistance in ohms per foot must be (0.1333 -=- 800 =) 0.0001666, 
 and the resistance per 1,000 feet, 0.1666 ohms. From the table, we 
 find that No. 2 is the nearest size of wire. 
 
 4. The wire loss of an electric motor is 156 watts. If the resistance 
 of the motor is 2 ohms, what current flows ? 
 
 Solution : 
 
 W = R x C 2 ; C = <%/ = 8.83, the number of amperes. 
 
 5. How many foot-pounds per minute equal a watt? A us. 44.236. 
 
 6. How many horse-power will be absorbed by a circuit of arc 
 lamps, taking 9.6 amperes at 2,900 volts pressure ? 
 
 Ans. 37.32 H.P., nearly. 
 
 7. If the electric generator that develops the current described in 
 Exercise 6 wastes 10 per cent, of the power delivered to it, how much 
 work was done upon it? Ans. 41.46 H.P. 
 
 8. A group of incandescence lamps absorbs 21 amperes. The line 
 loss is limited to 1.5 volts. 
 
 (a) What is the resistance of the line ? Ans. 0.07143 ohms. 
 
 (6) How many watts are lost? Ans. 31.5 watts. 
 
 (c) If the line is 800 feet from source of supply to lamps, what is 
 
 the nearest size of copper wire to use ? Ans. No. 0000. 
 
 9. An incandescence lamp absorbs 0.5 amperes at 110 volts, and 
 gives out 16 candle-power. An arc light absorbs 10 amperes at 
 45 volts, and produces 2,000 candle-power. Which light is the more 
 economical? Determ. ..,5 the electrical energy per candle-power ab- 
 sorbed by each? Ans. Incandescence, 3.4375 watts; arc, 0.225 watts. 
 
 10. Which has the more energy, an arc light generator capable of 
 
CURRENT ELECTRICITY. 451 
 
 delivering 10 amperes t at 900 volts pressure, or an electro-plating 
 machine that produces 1,800 amperes at a pressure of 5 volts ? 
 
 11. What mechanical horse-power is necessary for 50 incandescence 
 lamps, each taking 0.5 amperes at 110 volts, allowing 10 per cent loss 
 for transformation from mechanical into electrical energy ? 
 
 Ans. 4.09 H.P. 
 
 12. What energy is absorbed by a coil of wire of 23 ohms resist- 
 ance, through which 3.5 amperes is flowing? Ans. 281.75 watts. 
 
 13. A coil of wire of resistance 37 ohms is subjected to a pressure 
 of 110 volts. What energy is expended? A ns. 327.02 watts. 
 
 14. A dynamo receives 525 H.P. of mechanical energy, and delivers 
 350,000 watts at a pressure of 10,000 volts. The line that completes 
 the circuit has a resistance of 14 ohms, (a) Determine the current 
 strength. (b) What is the line loss in volts? (c) in watts? 
 (rf) What is the efficiency of the dynamo ? 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Mercury; sulphuric acid; nitric acid; 
 copper sulphate ; glass tumblers ; porous cup ; a zinc and a copper plate ; 
 sheet lead ; sheet iron ; tin-plate ; galvanoscope. 
 
 1. Put the cell described in Experiment 313, with clean and unamal- 
 gamated plates into circuit with a galvanoscope. Xotice the move- 
 ment of the needle, tap the galvanoscope lightly, and record the 
 position in which the needle comes to rest. Observe for a minute 
 what takes place at the surface of .each plate. Amalgamate the zinc 
 plate, carefully remove any adhering mercury drops, replace the zinc 
 in the acid, being careful that it is as far from the copper as it was 
 before. When the circuit is again closed through the galvanoscope, 
 record the deflection of the needle, and observe for a minute what takes 
 place at the surface of the plates. At intervals of two minutes, record 
 the successive deflections of the needle. If any bubbles are visible on 
 either or both of the plates at the end of ten minutes, rub them off 
 without removing the plates from the acid. Take care that no mercury 
 comes in contact with the copper, and record the deflection of the 
 needle. Remove the copper plate from the acid, rub it thoroughly, 
 replace it in the acid, and record the deflection of the needle. Remove 
 the copper plate again, dip it into nitric acid, and amalgamate it. Put 
 it back into the acid, and record the deflection of the needle. Record 
 the teachings of your experiment. 
 
452 SCHOOL PHYSICS. 
 
 2. Solder one end of 50 cm. of insulated copper wire, No. 20, to one 
 end of a zinc plate 10 cm. long, 2.5 cm. wide, and 0.5 cm. thick. 
 Similarly, solder a like wire to a piece of sheet copper 10 cm. square. 
 Weigh the plates and their wires carefully to 0.1 of a gram. Put 
 the zinc plate into a porous cup about 10 cm. deep and 4 cm. wide, 
 and nearly fill the cup with dilute sulphuric acid. Put the cup 
 into a glass tumbler about 10 cm. deep and 8 cm. wide. Pour a satu- 
 rated solution of copper sulphate into the tumbler until it stands at 
 the same level as the acid in the cup. Amalgamate the zinc, and put 
 it back into the acid. Clean the copper plate, bend it so that it will 
 partly encircle the porous cup, and put it into the copper sulphate 
 solution. Put the cell into circuit with a low resistance galvanoscope. 
 Watch carefully for bubbles on this copper plate. Record the deflec- 
 tion of the needle at intervals of five minutes for half an hour. Take 
 the cell to pieces and clean its several parts. Weigh the plates care- 
 fully as before. Name the cell, and compare the constancy of its cur- 
 rent with that of the cell used in Exercise 1. Account for any change 
 in the weight of either plate. 
 
 3. Cut 2 x 10 cm. strips of zinc, lead, iron, copper, and tin-plate, and 
 provide a carbon plate or half of an electric light carbon rod, and 
 attach to each a copper wire 40 or 50 cm. long. Successively use dif- 
 ferent pairs of these as plates of similar voltaic cells, connect each cell 
 with the galvanoscope, determine and record the direction of the cur- 
 rent and the magnitude of the deflection, and make as many different 
 combinations as possible. Arrange the given materials in an electro- 
 motive series, i.e., so that if any two are used as plates of a voltaic cell, 
 the current will flow through the wire from the former to the latter. 
 When the series is completed, using dilute sulpuric acid as the excit- 
 ing liquid, go over the work again using a dichromate solution, and 
 ascertain whether any change in the series is required. 
 
 4. Wind four or five layers of No. 20 insulated copper wire upon the 
 edge of a board 25 cm. square. Slip the wire from the board, and tie 
 together the several turns of the wire at the corners of the rectangle. 
 Bend one end of the wire into a hook and solder it to the middle of the 
 pointed half of a sewing-needle as shown at m in Fig. 348. Straighten 
 the other end at a right angle, as shown at n. Bend a narrow strip of 
 brass at a right angle, and in one arm make an indentation that will 
 hold a globule of mercury. Support the brass L with the indented 
 arm horizontal, and from it hang the wire rectangle. A globule of 
 mercury insures a good connection at m, and the straightened part of 
 
CURRENT ELECTRICITY. 
 
 453 
 
 the wire dips into a cup of mercury at n. Adjust the form of the sup- 
 porting hook so that the sides of the rectangle are vertical or hori- 
 zontal, and place the face of the 
 rectangle in a north and south 
 plane. Pass the current of a bat- 
 tery of 3 cells through the appara- 
 tus, and notice that the rectangle 
 turns into an east and \vest plane. 
 Reverse the current and notice 
 the effect. Make a record of 
 this motion of the wire rec- 
 tangle, and reserve it for future 
 study. 
 
 5. Wind four or five layers of 
 No. 20 insulated copper wire upon 
 the edge of a board 10 x 20 cm. 
 Slip the wire from the board, 
 
 and tie as directed in Exercise 4. FIG. 348. 
 
 Place this coil in the circuit be- 
 tween the battery and the mercury cup at n, Fig. 348. Call the 
 larger wire rectangle A, and the smaller one B. Hold B with one 
 of its 20 cm. sides vertical and near one side of A. Record the effect 
 as manifested by the motion of .4, when the current flows upward 
 through the adjacent sides of the two rectangles ; when the current 
 flows downward through both ; and when it flows upward in one and 
 downward in the other. Formulate a general expression of the ac- 
 tion of parallel currents upon each other, (a) When they flow in 
 the same direction. (&) When they flow in opposite directions. The 
 consideration of the interaction between currents as herein illustrated 
 constitutes the subject-matter of electrodynamics. 
 
 6. Hold the rectangle B of Exercise 5 within A so that a long side 
 of the former makes an angle with the lower side of the latter. Record 
 the effect. Change the angle several times, recording the effect in 
 each case. Formulate a general expression for the mutual action of 
 currents that are not parallel (a) when they flow toward the point of 
 intersection or from it ; (b) when one flows toward the intersection 
 and the other from it. 
 
 7. Wind some Xo. 16 insulated copper wire into a close spiral about 
 4 cm. in diameter and 15 cm. long. Bend its ends as indicated in 
 Fig. 349. Put it into the circuit of the battery as directed for the 
 
454 SCHOOL PHYSICS. 
 
 rectangle of Exercise 4 and hold a bar magnet near one of its 
 
 ends. Trace the current through the 
 solenoid. 
 
 8. Pass two stout copper wires sepa- 
 rately through a cork about 2 cm. in 
 diameter. About 2 cm. from the smaller 
 end of the cork, connect the copper wires 
 with a short piece of very fine iron wire. 
 FIG. 349. Wrap the edge of a strip of paper about 
 
 5 cm. wide around the cork so as to make 
 
 a paper cup with the iron wire inside. Fill the cup with fine gun- 
 powder, and close the other end with a cork or a paper cap. Place 
 this torpedo at a safe distance, connect it by stout copper wires to 
 a voltaic battery, and send through the wires a current that will 
 heat the iron wire and explode the torpedo. State some industrial 
 application of electricity that is illustrated by this exercise. Cut the 
 leading wires at three or four points and join them with short pieces 
 of fine iron wire. Tie the fuse of a fire-cracker around each piece of 
 iron wire, and send a current that shall ignite all of the fuses. 
 
 9. Make a torpedo similar to the one described in Exercise 8. In- 
 stead of interposing the high-resistance iron wire, bend the copper 
 wires until their ends nearly but not quite touch. Place the torpedo 
 at a safe distance, lay leading wires, and explode the torpedo by a 
 spark from an induction coil or an electric machine ( 403, 405). 
 
 C. MAGNETISM. 
 
 Experiment 327. Wrap a piece of writing paper around a large 
 iron nail, leaving the ends of the nail bare. Wind fifteen or twenty 
 turns of stout copper wire around this paper wrapper, taking care 
 that the coils of the wire do not touch each other or the iron. It is 
 well to use insulated wire. Put this spiral into the circuit of a voltaic 
 cell, and dip the nail into iron filings. Some of the filings will cling 
 to the ends of the nail in a remarkable manner. Upon breaking the 
 circuit, the nail instantly loses its newly acquired power, and drops the 
 iron filings. 
 
 Experiment 328. Draw a sewing-needle four or five times from 
 eye to point across one end of the nail of Experiment 327, while the 
 current is flowing through the wire wound upon it. Dip the needle 
 
MAGNETISM. 455 
 
 into iron filings. Some of the filings will cling to each end of the 
 needle. - 
 
 Experiment 329. Cut a thin slice from the end of a vial cork and, 
 with its aid, float the needle of Experiment 328 upon the surface of 
 water. The needle comes to rest in a north and south position. Turn 
 it from its chosen position and notice that, after each displacement, it 
 resumes the same position, and that the same end of the needle always 
 points to the north. 
 
 Experiment 330. Break the tangs from a few flat, worn-out files. 
 Smooth the ends and sides of the files on a grind-stone. Get some 
 good-natured dynamo tender to magnetize these hard-steel bars and 
 three or four stout knitting-needles. You can magnetize the needles 
 yourself by winding upon them successively, evenly, and from end to 
 end, a layer of insulated Xo. 20 wire, and sending a current from a 
 voltaic battery through the wire. Freely suspend these permanent 
 magnets at a considerable distance from each other and so that each 
 can turn in a horizontal plane. The knit- 
 ting-needles may be thrust through two 
 corners of triangular pieces of paper to the 
 third corner of which the end of a horse- 
 hair is fastened by wax. The heavier mag- 
 nets may be placed in stout paper stirrups 
 similarly supported, or they may be floated 
 
 upon water, as shown in Fig. 350. The 
 
 suspended magnets will come to rest in a north and south line. Mark 
 the north-seeking end of each magnet so that it may be distinguished 
 from the % other. 
 
 Experiment 331. Suspend a bar of iron as you did the magnets in 
 Experiment 330. Bring one end of a magnet near one end of the 
 iron bar, and notice the attraction. Try the other end of the iron bar. 
 Bring the other end of the magnet successively near the two ends of 
 the iron bar, noticing the effect in each case. 
 
 365. A Magnet is a body that has the property of attract- 
 ing iron or steel, and that, when freely suspended, tends to 
 take a definite position, pointing approximately north and 
 south. 
 
456 SCHOOL PHYSICS. 
 
 (a) One of the most valuable iron ores is called magnetite (Fe 3 O 4 ). 
 Occasional specimens of magnetite attract iron. Such a specimen is 
 called a lodestone. It is a natural magnet. 
 
 (&) Artificial magnets have all the properties of natural magnets, 
 and are more powerful and convenient. They may be temporary or 
 permanent. Temporary magnets are made by passing electric cur- 
 rents around soft iron, as in Experiment 309, and are called electro- 
 magnets. Permanent magnets are made of hardened steel, as in 
 Experiment 328. The most common forms of artificial magnets are 
 the bar magnet and the horseshoe magnet. The first of these is a straight 
 bar of iron or steel ; the second is U -shaped, 
 as shown in Fig. 351. Several similar thin 
 steel bars, separately magnetized and fas- 
 tened together side by side and with like 
 poles in contact, constitute a compound 
 magnet. A piece of iron placed across 
 
 the two ends of a horseshoe magnet is called an armature. The 
 process of making a magnet is called magnetization. 
 
 366. Magnetic Substances. It appears to be clearly 
 established that all matter is subject to the magnetic 
 force as universally as it is to the force of gravitation. 
 Substances that are attracted, as iron is, are called para- 
 magnetic ; substances that are repelled, as bismuth is, are 
 called diamagnetic. Paramagnetic substances are some- 
 times called magnetic. Diamagnetic substances are more 
 numerous than paramagnetic substances ; diamagnetic 
 effects are more feeble than paramagnetic effects. 
 
 367. Magnetic Poles. When a bar magnet is dipped 
 into iron filings, the magnetic effect is seen to be at maxi- 
 mum at the ends of the bar, and to diminish rapidly 
 toward the middle, at which point no filings are sustained 
 (see Experiment 328). The ends of the freely suspended 
 magnet also point toward the poles of the" earth. These 
 ends of the magnets are called poles, and the magnet is said 
 
MAGNETISM. 457 
 
 to exhibit polarity. A distinguishing mark is put on the 
 end that turns toward the north, and that end is called 
 the marked, north-seeking, or + pole. The other end is 
 called the unmarked, south-seeking, or pole. A unit 
 magnetic pole is a pole that exerts a force of one dyne upon 
 
 a like pole at a distance of one centimeter. 
 
 i 
 
 (a) For purposes of discussion, a theoretical magnet is assumed, 
 long and indefinitely thin and uniformly magnetized. Such a magnet 
 may be looked upon as a pair of poles united by a bar exerting no 
 action, the whole magnetic effect being concentrated at the poles. 
 When it is freely suspended, the line that joins the poles is called 
 the magnetic axis. 
 
 Magnetic Needles. 
 
 Experiment 332. Repeat Experiment 29 using the sewing-needle 
 of Experiment 329. The needle will assume a north and south 
 position. 
 
 Experiment 333. Straighten a piece of watch-spring about 15 cm. 
 long by drawing it between thumb and finger. Heat the middle of 
 this steel bar to redness in a flame and bend it double. Bend the 
 ends back into a line with each other, as 
 shown in Fig. 352. Magnetize each end sepa- 
 rately and oppositely. Wind a waxed thread 
 around the short bend at the middle to form 
 a socket, and balance the needle upon the FIG 352 
 
 point of a sewing-needle thrust into a cork. 
 
 A little filing, clipping, or loading with wax may be necessary to 
 make it balance. The needle will point north and south. 
 
 Experiment 334. Pass a knitting-needle through a small cork 
 from end to end and so that the cork shall be at the middle of the 
 needle. Thrust a sewing-needle or half of a knitting-needle through 
 the cork at* right angles to the knitting-needle to serve as an axis of 
 support. Place* the ends of the axis upon the edges of two glass 
 goblets or other convenient objects. Push the knitting-needle through 
 the cork until it balances upon the axis like a scalebeam. Magne- 
 
458 
 
 SCHOOL PHYSICS. 
 
 tize the knitting-needle, and notice that the marked end seems to 
 have become heavier. 
 
 368. Magnetic Needles. A small bar magnet suspended 
 in such a manner as to allow it to assume its chosen position 
 relative to the earth is a magnetic needle. 
 
 (a) The needle may turn in a horizontal or in a vertical plane. It 
 it turns freely in a horizontal plane, it is a horizontal needle; e.g., 
 
 the mariner's or the surveyor's com- 
 pass. If it turns freely in a vertical 
 plane, it constitutes a dipping-needle 
 (Fig. 353). 
 A magnetized 
 sewing-needle, 
 suspended at 
 its center of 
 mass by a fine 
 thread or hair 
 
 FIG. 354. 
 
 or an u n- 
 
 twisted fiber 
 
 will serve as a 
 
 dipping-needle. Two magnets fastened 
 
 to a common axis and with their poles 
 
 reversed constitute an astatic needle 
 
 (Fig. 354) . An astatic needle assumes 
 
 no particular direction with respect to the earth if the two needles 
 
 are equally magnetized. 
 
 FIG. 353. 
 
 Magnetic Field. 
 
 Experiment 335. Lay a bar magnet on the table between two 
 wooden strips of the same thickness as the magnet. Cover the mag- 
 net with a sheet of paper or cardboard, or a plate of glass. With 
 a dredge-box or muslin bag, sprinkle uniformly over the plate the 
 finest filings of wrought iron that you can obtain. Gently tap 
 the plate to facilitate the movement of the filings. They will 
 arrange themselves in lines that seem to proceed from the poles, to 
 curve outward through the air, and to complete their circuit through 
 the magnet, as shown in Fig. 355. Place a short magnet (e.g., a piece 
 
MAGNETISM. 
 
 459 
 
 of a magnetized sewing-needle suspended by a silk fiber) just above 
 the filings, and move it into different positions. At every point, the 
 
 """' '" V; -'--^--^- : - -".::. ./--;..-::;.;/;.'::;: . l >.>-.iPV:: ;i if 
 
 FIG. 355. 
 
 magnet will place itself parallel to a tangent to the curves, with its 
 marked end always pointing in the same direction relative to the 
 curves. 
 
 Experiment 336. Similarly map out the "magnetic phantom" 
 
 ^^^gvjgp'- 
 
 FIG. 356. 
 
 curves when the opposite poles of two bar magnets are brought near 
 each other. The result will be like that represented in Fig. 356. The 
 
460 SCHOOL PHYSICS. 
 
 lines from one magnet seem to interlock with those from the other as 
 if by mutual attraction. 
 
 Experiment 337. Similarly produce the phantom when the like 
 poles of two bar magnets are brought near each other. The result 
 
 
 will be like that represented in Fig. 357. The lines now seem to 
 repel each other. 
 
 369. Magnetic Field and Lines of Force. The space 
 surrounding a magnetized body and through which the 
 magnetic force acts is called a magnetic field. The iron 
 filings could not have arranged themselves in their definite 
 phantom curves except under the action of some force or 
 forces. We may imagine lines drawn in the magnetic 
 field, each indicating the direction in which a marked pole 
 would move. Such lines are called magnetic lines of force. 
 They are assumed to flow from the marked to the un- 
 marked pole outside the magnet, and in the opposite 
 direction inside the magnet, so as to form closed loops, 
 or complete circuits. By agreement among physicists, as 
 many lines are drawn through each square centimeter 
 
MAGNETISM. 461 
 
 of surface as there are dynes in the force of that part of 
 the field. Each line, therefore, represents a force of one 
 dyne, and the closeness of the lines indicates the intensity 
 of the field. 
 
 (a) A number of lines of force traversing a magnetic field is called 
 a flow or Jinx of force. The unit of Jinx is called a weber, and represents 
 one line of force. A flux of 10,000 lines of force would be a flux of 
 10,000 webers. The unit of strength of field, or intensity of flux, is called 
 a gauss, and represents the number of lines of force per square centi- 
 meter. With a flux of 24,000 w : ebers in 12 square centimeters, the 
 intensity of flux would be 2,000 gausses. A field is of unit strength 
 when a unit magnetic pole placed in it is acted upon with a force of 
 one dyne. A pole which when placed in a field of unit strength, 
 is acted upon by a force of one dyne is sometimes said to be of unit 
 magnetic mass. 
 
 (b) By agreement, the direction in which a marked pole would 
 move in a field is called positive. When a magnet is placed in a 
 magnetic field, the marked pole tends to move in a positive direction, 
 and the unmarked pole in a negative direction. The total effect is 
 that of a couple, and tends to produce rotation. The universal 
 tendency of a magnetic needle thus to turn upon its pivot so as to 
 place its axis in a north and south line indicates that the earth is 
 surrounded by a magnetic field. 
 
 (c) The magnetic action that takes place in a magnetic field has 
 been happily illustrated by supposing the lines of force to be stretched 
 elastic threads that tend to shorten along their lengths, and that 
 are self-repellent. Compare 336 (a). This conception of magnetic 
 lines of force suggests that unlike poles ought to attract each 
 other (see Fig. 356), and that like poles ought to repel each other 
 (see Fig. 357). 
 
 (</) The magnetic lines of force form closed circuits, passing 
 through the air from one pole to the other. The shorter the air- 
 path, the more numerous the lines of force. Hence, the advantage 
 of the U- sna P e d or horseshoe magnet. When a bar of soft iron is 
 placed across the poles, the magnetic circuit is all iron, and the lines 
 of force that traverse it are at a maximum. 
 
 (e) A magrretic pole tends to repel its own magnetization, to 
 develop opposite polarities there, and thus to weaken itself. To 
 
462 SCHOOL PHYSICS. 
 
 maintain the strength of the magnet, an armature is used to connect 
 opposite poles, and thus to provide a closed circuit of magnetic mate- 
 rial. Two bar magnets placed near each other in reversed position 
 may be given a closed magnetic circuit, and thus preserved, by placing 
 two armatures at their ends. 
 
 Experiment 338. Place the end of a bar magnet upon a thin 
 plate of glass, and bring a few tacks to the under side of the plate. 
 The magnetic lines of force seem to pass readily through the glass ; 
 the attraction is not perceptibly weakened. In like manner, try 
 paper, mica, sheet zinc, and sheet iron. The paramagnetic iron seems 
 to act as a magnetic screen ; the other substances do not. 
 
 370. Magnetic Transparency. Substances other than 
 those that are paramagnetic allow the free action of 
 magnetic forces through them. This quality is some- 
 times called magnetic transparency. 
 
 Experiment 339. Suspend one of the bar magnets at a consider 
 able distance from the others. Bring one end of another magnet held 
 in the hand near one end of the suspended magnet, and notice the 
 attraction or repulsion. Also notice the designations of the poles that 
 are brought into proximity. Satisfy yourself that 
 
 N repels X, ' N" attracts S, 
 
 S repels S, S attracts N. 
 
 371. Law of Magnetic Poles. (1) Like magnetic poles 
 repel each other ; unlike magnetic poles attract each other. 
 
 (2) The force exerted at different distances between two 
 poles of the same magnetic mass is inversely proportional to 
 the squares of the distances. 
 
 (3) The force exerted at a given distance between two 
 poles is directly proportional to the product of the magnetic 
 masses of the poles. 
 
 (a) Representing the force acting by F, the magnetic masses by 
 m and m f , and the distance between the poles by d, and measuring 
 
MAGNETISM. 463 
 
 all magnitudes in absolute units, we may summarize the last two 
 
 laws thus : 
 
 P_ mm' 
 
 If, in this equation, we make m, m', and d each equal to unity, F will 
 also be equal to unity ; i.e., a unit pole exerts unit force on a unit 
 pole at unit distance. The absolute C.G.S. unit magnetic pole is, 
 therefore, a pole of such magnetic mass that, when placed a centi- 
 meter distant from another unit pole, the force between them shall 
 be one dyne, as was stated in 367. 
 
 372. Magnetic Potential is essentially analogous to elec- 
 trostatic potential. At any point, it is measured by the 
 work done against the magnetic forces in moving a unit 
 magnetic pole from an infinite distance to the given point. 
 The difference of magnetic potential between two points is 
 measured by the amount of work required to move a unit 
 magnetic pole from one to the other. If this work is one 
 erg, there is unit difference of potential between the two 
 points. See 338. 
 
 Magnetization. 
 
 Experiment 340. Place a short rod of soft iron in a paper stirrup, 
 and suspend it by a thread over and near the poles of a strong horse- 
 shoe magnet that is supported in a vertical plane. Bring first one 
 end of a bar magnet, and then the other end, near one end of the soft 
 iron rod, and determine whether the suspended iron is a magnet or 
 not. If it is, ascertain which of its poles is over the marked pole of 
 the horseshoe magnet. 
 
 Experiment 341. Support a bar magnet in a horizontal position 
 6 or 7 cm. above the table. Bring a quantity of iron tacks to one 
 pole so that as many as possible will be supported. Place a similar 
 magnet on the table, parallel to the first but with its poles in reversed 
 position. Test the upper magnet for increase or decrease of lifting 
 power. 
 
 373. Magnetization. Any magnetic substance is mag- 
 netized by bringing it into contact with a magnet, or 
 
464 SCHOOL PHYSICS. 
 
 simply by placing it in a magnetic field. In the latter 
 case, it is said to be magnetized by induction. If the 
 substance is paramagnetic, its magnetic axis will coincide 
 with the lines of force of the field. The amount of magne- 
 tization developed depends upon the nature of the sub- 
 stance and the strength of the field. 
 
 (a) With a given field, iron receives the greatest amount of mag- 
 netization, steel coming next. As the magnetizing force increases, 
 the magnetization produced also increases, rapidly at first but more 
 and more slowly. When the magnetization ceases to increase, the 
 substance is said to be saturated; the saturation point is, therefore, 
 a function of the magnetizing force. 
 
 Theory of Magnetization. 
 
 Experiment 342. Heat a magnetized needle to redness and, when 
 it has cooled, test it for magnetism. Put a magnetized knitting- 
 needle into active vibration (see Fig. 149), and subsequently test it 
 for magnetism. In each case, the magnetization will be weakened 
 or destroyed. 
 
 Experiment 343. Magnetize a piece of watch-spring about 10 cm. 
 long, and ascertain how large a nail it will support. Bring the two 
 ends of the magnets into contact. The ring thus formed manifests 
 no polarity, thus showing the equality of the opposite poles. Break 
 the magnet at its middle, and test the strength of magnetization of 
 the two new poles developed at the point of fracture. 
 
 Experiment 344. Nearly fill a slender glass tube with steel filings, 
 and close the ends of the tube with corks. Draw the marked pole of 
 a strong magnet from the middle of the tube to one end, and the 
 unmarked pole from the middle to the other end, and repeat the 
 stroking several times. One end of the tube will attract and the other 
 will repel the marked pole of a suspended magnetic needle ; i.e., j;he 
 filled tube has become a magnet. Thoroughly shake up the filings; 
 the tube loses its magnetic properties, as if the actions of the many 
 little magnets in the tube were neutralized through their indiscrimi- 
 nate arrangement. 
 
MAGNETISM. 465 
 
 374. Theory of Magnetic Polarization. When a magnet 
 is broken, each piece becomes a magnet, the newly developed 
 poles being of strength nearly equal to that of the original 
 poles. The subdivision of the magnet may be carried on 
 indefinitely, and with the same results. This suggests 
 that the magnetic property must reside in the smallest 
 particle capable of existing by itself, i.e., the molecule. 
 It is easy to imagine that if the steel particles in the 
 shaken tube of Experiment 344 could be restored to their 
 former positions, the tube would again act as a magnet. 
 It may be assumed that the molecules of a magnetic sub- 
 stance are always magnets; that the substance does not 
 exhibit magnetic properties when the magnetic axes of the 
 molecules are turned indifferently in every direction; and 
 that the process of magnetization consists in turning the mole- 
 cules so that their axes point in the same direction. When 
 the axes of all the molecules have thus been set parallel, 
 the maximum of magnetization has been secured. 
 
 (a) Magnetization changes the length but not the volume of the 
 bar magnetized. When soft iron is rapidly magnetized and demag- 
 netized, it becomes heated, and sometimes a clicking sound is produced 
 at each change. 
 
 Magnetic Properties of Electric Currents. 
 
 Experiment 345. Repeat Experiment 315, and test the accuracy 
 of the following rules : 
 
 (1) To determine the direction of the deflection of the needle, 
 hold the open right hand over or under the conducting wire, but so 
 that the wire is between the hand and the needle, so that the palm 
 of the hand is toward the needle, and so that the fingers point in the 
 direction of the current ; the marked end of the needle will turn 
 in the direction of the extended thumb. 
 
 (2) To determine the direction of the current, hold the open right 
 hand over or under the conducting wire, but so that the wire is 
 
466 
 
 SCHOOL PHYSICS. 
 
 between the hand and the needle, so that the palm of the hand 
 is toward the needle, and so that the thumb is extended in the direc- 
 tion in which the marked end of the needle is deflected ; the fingers 
 will point in the direction of the current. 
 
 Experiment 346. Dip a short part of a stout copper wire that is 
 carrying a large current into fine iron filings. A cluster of the filings 
 will cling to the wire. 
 
 Note. If you cannot obtain an electric-light or a trolley-wire 
 current for the next experiment, connect a number of similar cells in 
 parallel. Make the external circuit of very heavy wire, and have the 
 paper in place around the wire, and the dredge-box ready. Close the 
 circuit and perform the experiment quickly. 
 
 Experiment 347. Around a vertical conductor carrying a heavy 
 current, place a piece of paper cut as shown in Fig. 358, and sprinkle 
 fine iron filings on the paper. Notice that the iron particles arrange 
 themselves in distinct circular whirls around the wire, as shown in 
 Fig. 359. Experimentally establish the tangential relation between 
 a short magnet and these curves, as in Experiment 335. Hold the 
 closed right hand so that the extended thumb points in the direction 
 of the current in 
 the wire ; then the 
 fingers will indi- 
 cate the direction 
 of the lines of 
 force in the sur- 
 rounding field. 
 Bend the upper 
 part of the con- 
 ducting wire, and FIQ 
 pass it vertically downward through the 
 paper. Sprinkle iron filings as before. Notice that the magnetic 
 lines of force around the two parallel parts of the wire circle in 
 opposite directions, clockwise in one case, and counter-clockwise in 
 the other. If the conducting wire is bent into the form shown 
 in Fig. 360, the lines of force will pass around the wire from one face 
 of the loop to the other, and in the direction indicated by the "rule of 
 thumb " just given. 
 
 Experiment 348. Bend a piece of stout copper wire into the form 
 shown in Fig. 360. Suspend it at its highest point by a long thread 
 
 FIG. 358. 
 
MAGNETISM. 
 
 467 
 
 and so that its free ends just dip into mercury contained in sepa- 
 rate, shallow dishes. Put the apparatus 
 into the circuit of a strong electric cur- 
 rent, making connections with the mer- 
 cury cups. Bring a bar magnet near 
 either face of the circular conductor. 
 The loop will turn upon its vertical axis, 
 seeking a position at right angles to 
 the magnet, and acting as if it was a disk 
 magnet with poles at its faces. 
 
 FIG. 360. 
 
 Experiment 349. Coil some No. 12 
 
 copper wire through holes in a board, 
 
 as shown in Fig. 361, and pass a strong 
 
 current through it. Sprinkle iron filings as before and note the 
 
 effect. Such a coil of conducting 
 wire, wound so as to afford a num- 
 ber of equal and parallel circular 
 electric circuits arranged upon a 
 common axis, is called a solenoid. 
 
 Experiment 350. Wind , the 
 middle part of about 3 meters of 
 Xo. 20 insulated copper wire around 
 a rod about 1.5 cm. in diameter, 
 forming thus a solenoid about 
 10 cm. long. Bring the ends of the 
 wire along the axis of the sole- 
 noid, and bend them at right angles 
 near the middle. Solder small 
 plates of sheet copper and amalga- 
 mated sheet zinc to the ends of the wire. Support the solenoid and 
 
 plates by a large flat cork on the surface of 
 
 dilute sulphuric acid, as shown in Fig. 362. 
 
 The floating cell will take position so that the 
 
 axis of the solenoid extends north and south. 
 
 Test the ends of the solenoid for polarity, 
 
 using a bar magnet for that purpose. 
 
 FIG. 3(31. 
 
 Experiment 351. Repeat Experiment 315, 
 
 c z 
 FIG. 362. 
 
468 
 
 SCHOOL PHYSICS. 
 
 using the floating cell of Experiment 350 instead of the compass, 
 needle. 
 
 Experiment 352. Prepare a second solenoid similar to that de- 
 scribed in Experiment 350, omitting the 
 plates. Put it into an electric circuit, and 
 use it as you did the bar magnet in Ex- 
 periment 350. 
 
 375. The Magnetic Character of 
 an Electric Current has been shown 
 
 FIG. 363. . -, -, n P , 
 
 by the deflection of the magnetic 
 
 needle, by the production of phantom curves, and by 
 other experiments. The passage of an electric current 
 through a solenoid gives it many of the properties of a 
 cylindrical bar magnet. 
 
 (a) The polarity of the solenoidal magnet may be determined by 
 holding it in the right hand so that the fingers point in the direction 
 of the current; then the extended 
 thumb will point toward the marked 
 or north-seeking pole of the magnet. 
 The lines of force flow from the 
 marked to the unmarked pole out- 
 side the solenoid, and in the oppo- -jiPL N 
 site direction inside the solenoid. 
 Looking at one end of a solenoid 
 so that the current circles around 
 clockwise, you may imagine that the 
 enclosed lines of force go forward, 
 just as the right-hand turning of a 
 corkscrew is related to its forward 
 motion. .Two solenoids freely sus- 
 pended act toward each other as did 
 the suspended magnets of Experi- p IG 364< 
 ment 339. 
 
 376. Magnetomotive Force. The influence to which 
 these magnetic lines of force are due is called magneto- 
 
MAGNETISM. 469 
 
 motive force (M.M.F.). The magnetomotive force of a 
 magnetic circuit is directly proportional to the number 
 of amperes in the electric circuit surrounding it, and to 
 the number of turns that the electric circuit makes around 
 the magnetic circuit ; i.e., the magnetomotive force is pro- 
 portional to the ampere-turns. The unit of magnetomotive 
 force is called a gilbert, and corresponds to 0.7958 
 ampere-turns. 
 
 Experiment 353. Place a strip of sheet iron in the solenoid of 
 Experiment 350, as shown in Fig. 
 365, and repeat that experiment. 
 Notice that most of the lines of force 
 are gathered into the iron and issue 
 from its ends. Notice that the lines 
 curve outward and tend to return. 
 forming closed loops or complete 
 magnetic circuits. Change the iron 
 from the inside of the solenoid to the 
 outside, and repeat the experiment. 
 Notice that the iron again gathers in 
 the lines of force as if it offered an 
 easier path for them. 
 
 377. Permeability. Some substances are capable of 
 receiving more lines of force than others with the same 
 magnetomotive force. This relative capacity is called 
 permeability, which may be denned as the ratio between 
 the number of lines of force that pass through a given 
 area of the substance and the number of lines of force 
 that pass through a like area of the inducing field alone. 
 It is a sort of magnetic conductivity. 
 
 (a) The permeability of paramagnetic substances is greater than 
 unity; that of diamagnetic substances is less than unity. Bismuth 
 has the lowest permeability of any known substance. When a 
 
470 SCHOOL PHYSICS. 
 
 paramagnetic substance is placed in a uniform magnetic field, its 
 permeability being greater than that of the field, an increased number 
 of lines of force are crowded into it, as shown in Fig. 366. When a 
 
 diamagnetic substance is placed 
 in such a field, its permeability 
 being less than that of the field, 
 the number of lines that pass 
 through it is diminished, as shown 
 in Fig. 367. 
 
 (b) If a small compass is put 
 
 P, ,.[. into a closed bottle, an outside 
 
 magnet will affect it, but if it is 
 put into a hollow iron ball, an outside magnet will not affect it. 
 Soft iron acts as a magnetic 
 screen ( 370) because of its high 
 permeability. Watches are some- 
 times protected from magnetic 
 influence by soft iron shields in 
 the shape of inside cases. 
 
 378. Reluctance and Re- 
 
 FIG. .367. 
 
 luctivity. Like electric 
 
 currents, magnetic lines of force flow in the greatest 
 quantity through paths of least resistance. Magnetic 
 resistance is called reluctance, and its unit is the oersted. 
 Specific magnetic resistance (specific reluctance) is 
 called reluctivity. Reluctivity is the reciprocal of per- 
 meability. 
 
 379. The Analogue of Ohm's Law. In 361, we have a 
 formula that shows the mathematical relations between 
 amperes, volts, and ohms. The corresponding relations 
 for magnetic units is expressed by the equation, 
 
 weber* = &** . (1) 
 
 oersteds 
 
MAGNETISM. 471 
 
 From this we may derive the other two, 
 
 gilberts = webers x oersteds, and (2) 
 
 webers 
 These formulas are much used in magnetic calculation. 
 
 Coercive Force. 
 
 Experiment 354. Prepare three small bars of the same size, one 
 of soft iron, one of soft steel, and one of hardened steel. Bring one 
 end of a good bar magnet into contact with one end of the iron bar, 
 and dip the other end of the iron bar into iron filings. Lift the mag- 
 net and the iron bar without breaking the contact between them. 
 Xotice the quantity of filings lifted by the iron. Break the contact, 
 and notice the quantity of filings dropped by the iron. Repeat the 
 test with the other two bars in succession. It will be found that the 
 iron will lift the most and the hardened steel the least, but that, 
 when the contact is broken, the hardened steel holds the most and 
 the iron the least. 
 
 Experiment 355. With the end of a good bar magnet, write your 
 name upon the blade of a hand saw. The invisible characters may 
 be made visible by sifting fine iron filings upon the blade. 
 
 Experiment 356. Lay a thin piece of well-hardened steel (it 
 may be cut from a saw-blade) in the solenoid, and repeat Experiment 
 353. After the current has been interrupted, jar the solenoid, and 
 notice that some of the filings are still held in their positions. The 
 hard steel has become a permanent magnet. 
 
 380. Coercive Force and Remanance. The persisting 
 magnetomotive force shown by tne steel is due to what 
 is called the coercive force of the steel, which acts as a sort 
 of magnetic inertia, resisting magnetization at the outset 
 and tending to retain it afterward. The number of lines 
 of force per square centimeter in the body of the steel is 
 called its remanance. 
 
472 
 
 SCHOOL PHYSICS. 
 
 (a) Coercive force is measured in gilberts ; remanance, in gausses. 
 
 Experiment 357. Make a helix about 15 era. long by neatly 
 winding three layers of No. 18 insulated copper wire upon a rod about 
 2 cm. in diameter. Remove the rod, pass a few threads through the 
 opening of the helix, and tie them on the outside so as to hold the 
 turns of wire in place. Put the helix into the circuit of a voltaic cell, 
 and bring it near a magnetic needle. The deflection of the needle 
 shows the magnetic power of the helix. Nearly fill the opening in 
 the helix with straight pieces of soft iron wire, and again test its 
 magnetic power. The deflection of the needle will be much greater 
 than before. 
 
 381. 
 
 electric 
 
 An Electromagnet is a bar of iron magnetized by an 
 current, substantially as just shown. When the 
 current was passed through the 
 helix used in Experiment 357, some 
 of the lines of force leaked out at 
 the sides, as indicated by Fig. 368, 
 and few of them extended from 
 end to end. The soft iron core, 
 by reason of its high permeability, 
 diminished this leakage of lines of 
 force, and greatly increased their 
 number, as shown in Fig. 369. 
 
 (a) Since the lines of force are perpen- 
 dicular to the direction of the current, the 
 FIG. 368. i 1011 core * s to be placed at right angles to FIG. 369. 
 
 the wire ; the ^effect is increased by in- 
 creasing the number of turns of the wire. The direction of polarity 
 in the core depends only upon the direction of the current in the 
 helix, and may be determined by the thumb or the corkscrew rule 
 already given. 
 
 (6) When an electromagnet is U- sna P e d> tne co ^ s around the two 
 ends of the bent iron core are so wound that if the coil should be 
 straightened either coil would appear as a continuation of the other, 
 
FIG. 370. 
 
 UNIVERSITY OF CALIFORNIA 
 
 DEPARTMENT OF PHYSJCS 
 
 MAGNETISM. 473 
 
 i.e., the current would circle around the core in the same direction in 
 the two coils. Such magnets are often made by connecting an end 
 of the core of one spool-shaped magnet, 
 by a straight soft iron bar called a 
 yoke, to one end of the core of a sim- 
 ilar magnet, a screw passing through 
 the bar into an end of each straight 
 core. The two spools are then con- 
 nected as above indicated. 
 
 (c) To produce the best effect, the 
 resistance of the electromagnet should 
 be equal to that of the rest of the cir- 
 cuit. If several electromagnets are used 
 on the same circuit, the sum of their 
 
 resistances should equal the resistance of the rest of the circuit. 
 
 (d) If the iron of the magnet core is of commercial quality, it is 
 not wholly demagnetized when the current is interrupted. The mag- 
 netization thus retained after withdrawal from a magnetic field is 
 called residual magnetism. 
 
 382. Ampere's Theory of Magnetism. As an electric 
 current is surrounded by a whirl of lines of magnetic 
 force, so we may conceive a magnetic line of force as 
 surrounded by an electrical current-whirl. This would 
 imply, as Ampere long ago suggested, that magnetism is 
 simply a vortical electric current, and that a magnetic 
 field is something like a whirlpool of electricity. Fig. 371 
 represents a vertical conductor carrying an 
 electric current, and surrounded by a mag- 
 netic line of force, which is in turn sur- 
 rounded by electric whirls ; the magnetic line 
 of force is an electric vortex-ring. It is not 
 difficult to conceive the vortex-ring as made 
 up of ether whirls. As the phenomena of 
 magnetism belong to the molecules, these electrical whirls 
 must be rotations perpendicular to the magnetic axes of 
 
 FIG. 371. 
 
474 SCHOOL PHYSICS. 
 
 the molecules. Ampere's theory supposes that electric 
 currents circle round the molecules of a magnetic sub- 
 stance, thereby polarizing them, and that when all these 
 magnetic axes face in the same direction the substance is 
 magnetically saturated. 
 
 (a) The great importance of the relation between magnetic lines 
 of force and electric currents will appear more plainly in the following 
 section. 
 
 Terrestrial Magnetism. 
 
 Experiment 358. Place a small dipping-needle over the marked 
 end of a long, horizontal bar magnet, and move it slowly toward the 
 other end of the bar, observing the changes in the position of the 
 dipping-needle. Similar changes would be observed if you could 
 carry the dipping-needle from far southern to far northern latitudes. 
 
 Experiment 359. Take a bar of very soft iron about 75 cm. long, 
 and make sure by trial that its ends will not attract bits of soft iron. 
 Then hold the bar in a meridian plane, and with its north end 
 depressed below the horizon a number of degrees approximately 
 corresponding to the latitude of the place of the experiment, i.e., 
 give it the position of a dipping-needle. Tap the rod on its end with 
 a mallet or wooden block, and test it for magnetic polarity. 
 
 383. Terrestrial Magnetism. A magnetic field is recog- 
 nized by the fact that it gives a definite direction to a 
 magnet freely suspended in it. The directive tendency 
 of the compass, and other phenomena, show that the earth 
 is surrounded by such a field. In fact, these phenomena 
 are such as might be expected if we knew that a bar 
 magnet four or five thousand miles long extended nearly 
 north and south through the earth's center. This terres- 
 trial magnetism is explained as being due to equatorial 
 electric currents produced by the action of the sun, and 
 modified by the motion of the earth. 
 
MAGNETISM. 
 
 475 
 
 (a) The angle that the axis of a dipping-needle makes with a 
 horizontal plane is called the inclination or dip of the needle. The dip 
 is 90 at the magnetic poles of the earth, and at the magnetic 
 equator, and, at any given place, does not differ greatly from the 
 latitude. Lines passing through points on the earth's surface where 
 the inclination has the same value are called isoclinic lines. The 
 inclination of the needle is subject at most places to secular, annual, 
 and diurnal changes. 
 
 (6) The magnetic poles of the earth do not coincide with its geo- 
 graphical poles and, consequently, in some places, the magnetic needle 
 does not point to the geographical north. The angle that the axis of 
 a compass-needle makes with the geographical meridian at any place 
 is called the declination or variation of the needle at that place. When 
 the marked end of the needle lies east of the meridian, the variation 
 is easterly, and vice versa. Lines drawn through places on the earth 
 where the declination is the 
 same are called isogonic lines, as 
 is shown in Fig. 372. The par- 
 ticular isogonic line for which 
 the declination is zero is called 
 an agone or an agonic line. 
 These lines are very irregular, 
 being apparently affected by 
 local conditions. The Ameri- 
 can agone, in 1890, entered the 
 United States near Charleston^ 
 passed through the mountains 
 of North Carolina and West 
 Virginia, and near Columbus, 
 Toledo, and Ann Arbor, and is FIG. 372. 
 
 slowly moving westward. The 
 
 declination of the needle is subject to periodic changes, secular, 
 annual, and diurnal, and to irregular variations or perturbations. 
 The mariner or the surveyor must recognize not only the declination 
 of his needle but also the changes in its declination. 
 
 (c) The magnetic intensity of the earth is also an element that 
 varies from point to point at the same time, and from time to time 
 at the same place. Lines drawn through places on the earth where 
 the force of terrestrial magnetism is the same are called isodynamic 
 lines. 
 
476 SCHOOL PHYSICS. 
 
 (d) The determination of these three magnetic elements is the 
 object of governmental magnetic surveys. 
 
 () The observed coincidences between magnetic storms, i.e., sud- 
 den disturbances of the earth's magnetism, and solar storms indicate 
 a connection, the nature of which is not yet well understood. 
 
 CLASSROOM EXERCISES. 
 
 1. What part of a magnet might properly be designated by the 
 term equator ? 
 
 2. Explain the increase of lifting power manifested in Experi- 
 ment 357. 
 
 3. How can the intensity of different parts of a magnetic field be 
 roughly estimated from the behavior of a magnetic needle ? 
 
 4. Show that the influence of the earth's magnetism upon a mag- 
 netic needle is merely directive. 
 
 5. If a wire coil of 220 turns carries a 3-ampere current, what is its 
 magnetomotive force? Ans. 829 + gilberts. 
 
 6. A rectangular bar of steel 1x3 cm. and 30 cm. long, is bent into 
 a circle, and upon it is wound 40 turns of wire. A o-ampere current 
 is passed through the wire, (a) Determine the M.M.F. (6) Assume 
 the reluctance to be 0.00593 oersteds, and divide the M.M.F. by the 
 reluctance to determine the flux of force in webers. (c) Determine 
 the intensity of flux in gausses, (d) Assume the permeability to be 
 1,684 and determine the reluctivity, (e) Divide the M.M.F. by the 
 length of the bar to determine the magnetizing force in gausses. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. A collection of bar magnets ; a hack-saw 
 blade ; several sheets of paper about 50 cm. square ; a compass with a 
 needle 2 or 3 cm. long. 
 
 1. By observations of the North Star or in any other convenient 
 way, mark a true north and south line on the laboratory table. Place 
 a magnetic needle in this line, and determine the direction and mag- 
 nitude of the declination. 
 
 2. Float a magnet on water as shown in Fig. 350. The float should 
 be the lightest that will carry the load with safety, and the body of 
 water should be so large that surface tension will not urge the float 
 toward the side of the vessel. When the magnet is at rest near the 
 
MAGNETISM. 477 
 
 middle of the liquid surface, determine the tendency of the magnet to 
 drift toward the north or south. Repeat the experiment with a 
 variety of magnets, and try to find one that always floats in one 
 direction, i.e., one in which the marked pole is stronger or weaker 
 than the other. If you cannot find such a magnet, strongly magnetize 
 the blade of an old hack-saw, and test it on the float. If you have 
 not yet found that for which you seek, break the blade in the middle, 
 and test each half. If necessary to the success of your search, break 
 one of the halves in two, and repeat the tests. Make very careful 
 notes of any magnet that you find to have more magnetism of one 
 kind than of the other. 
 
 3. Fasten a large sheet of paper upon the table-top. Place a bar 
 magnet about 20 cm. long and 1 sq. cm. in cross-section upon the 
 middle of the paper with its marked end pointing toward the north. 
 Place a small compass on the paper at the northeast corner of the 
 magnet, move it away from the magnet in the direction in which the 
 marked end of the needle points, tracing upon the paper the path of 
 the middle point of the compass, and indicating by arrow-heads upon 
 the line thus traced the direction in which the compass is moved. 
 Continue the movement of the compass, continually changing the 
 direction of the motion of the compass as indicated by the direction 
 in which the marked end of the needle points, until the traced path 
 reaches the edge of the paper or returns to the magnet. Repeat the 
 work, starting near the same corner but 1 cm. nearer the middle of 
 the magnet. Taking the successive starting points nearer and nearer 
 the middle of the magnet, continue to draw such lines until you come 
 within about 3 cm. of the middle of the bar. Similarly, trace an 
 equal number of lines on the other side of the magnet. The curves 
 may be traced in an " off-hand " way, their general character being of 
 more importance than exact details. Trace the outline of the mag- 
 net on the paper, and indicate its polarity. 
 
 4. Place the magnet used in Exercise 3 upon a clean sheet of paper, 
 and with its marked end pointing toward the south. Trace lines as 
 indicated in that exercise. 
 
 5. Place two similar bar magnets on a clean sheet of paper, parallel 
 to each other, about 15 cm. apart, and with their marked ends point- 
 ing toward the north. In manner similar to that prescribed for 
 Exercise 3, trace the lines of force, including several lines between the 
 two magnets. Compare this diagram with those drawn in Exercises 
 3 and 4, specify their characteristic features, and explain their 
 significance. 
 
478 SCHOOL PHYSICS. 
 
 6. Map a magnetic field as in Experiment 335. Carefully remove 
 the rnagnet and wooden strips. Over the filings, carefully place a sheet 
 of printing-paper that has been wet with a solution of tannin. Over 
 this, place a sheet of heavy blotting-paper. Place a board on the 
 blotting-paper and a weight on the board. When the printing-paper 
 is removed, some of the iron filings will adhere to it. When the 
 paper is dry, brush off these filings. The ink-like markings on the 
 paper make a permanent copy of the map. 
 
 II. ELECTRIC GENERATORS, ELECTROMAGNETIC 
 INDUCTION, ETC. 
 
 384. Introductory. We have seen that when two bodies 
 at different electric potentials are connected by a conductor, 
 an electric current transfers along the conductor the state 
 of strain that constitutes electrification. If that strain is 
 reproduced as fast as it is relieved, the difference of poten- 
 tial will be constant, and the current will be continuous 
 and uniform. The devices considered in the preceding 
 section are incapable of producing a current adequate to 
 the demands of the age in which we live. It is the pur- 
 pose of this section to indicate how such currents are 
 produced. 
 
 385. Voltaic Cells are among the most common and 
 important of "electric generators," and have been devised 
 in great variety. Some of them are dry, some have one 
 liquid, and others have two. Some are constant and 
 strong while they last, but require frequent renewals ; 
 others are effective for short periods only, and require 
 time for their own recovery. Each has its advantages 
 
ELECTRIC GENERATORS, ETC. 479 
 
 and its disadvantages, so that one is the better for one pur- 
 pose, and another for another. 
 
 (a) When commercial zinc is used as one of the plates of a cell, 
 the chemical action shown in Experiment 312, and known as local 
 action, contributes nothing to the current. It is probably due to the 
 presence of particles of carbon, iron, etc., in the zinc. The zinc and 
 these foreign particles in the zinc act as the plates of minute voltaic 
 cells, the currents flowing in short circuits from the zinc through the 
 liquid to the foreign particles, and thence back to the zinc. This local 
 action is prevented by using pure zinc, or by amalgamating commercial 
 zinc as in Experiment 313. 
 
 (6) The polarization of the cell, i.e., the accumulation of the hydro- 
 gen film on the negative plate, interferes with the action of the cell 
 and diminishes the available current by increasing the resistance of 
 the circuit, and by setting up a counter electromotive force that may 
 reduce, stop or even reverse the flow of the current. The various 
 devices for removing the hydrogen, or for preventing its accumulation, 
 constitute the most essential differences between the diiferent forms 
 of cells. These devices may be classified as physical (e.g., the mechan- 
 ical agitation of the liquid, or the roughening of the plate to lessen the 
 adhesion of the gas), and chemical (e.g., the use of some agent, like 
 nitric or chromic acid or manganese dioxide, for the oxidation of the 
 hydrogen before it reaches the negative plate). 
 
 Note. The oxidation of hydrogen yields water. 
 
 (c) A few forms of cells are mentioned, although it is impossible to 
 give descriptions of all or many. For such descriptions, the pupil is 
 referred to some technical work on the subject. 
 
 (1) The Smee cell consists of a silver or a lead plate suspended 
 between two zinc plates immersed in dilute sulphuric acid. Polariza- 
 tion is partly prevented by giving the negative plate a rough coat of 
 finely divided platinum. 
 
 (2) The potassium dichromate cell (see Experiment 316) consists 
 of zinc and carbon plates immersed in a solution of potassium 
 dichromate in dilute sulphuric acid. The action of the sulphuric acid 
 on the dichromate liberates chromic acid which oxidizes the hydro- 
 gen, and thus prevents polarization. This cell is very convenient for 
 quick use, and valuable for "all-around" work. It is sometimes 
 called the Grenet cell. A similar cell that employs sodium dichromate 
 
480 SCHOOL PHYSICS. 
 
 instead of potassium dichromate is more enduring in its action. A 
 solution of chromic acid is much used and is more economical than 
 either. 
 
 (3) In the Grove cell, a cylindrical plate of zinc is immersed in 
 dilute sulphuric acid, and carries a porous cup that contains strong 
 nitric acid in which a platinum strip is immersed. The hydrogen 
 evolved at the zinc plate is oxidized by the nitric acid. 
 
 (4) The Bunsen cell differs from the Grove in a substitution of 
 carbon for platinum, and in the larger size of the plates. Like the 
 Grove cell, it is little used, the fumes that come from the nitric acid 
 being choking and corrosive. 
 
 (5) In the Leclanche cell, a zinc rod is immersed in a saturated 
 solution of ammonium chloride (sal-ammoniac). In this solution is 
 also a porous cup that contains a bar of carbon tightly packed in a 
 mixture of granular carbon and manganese dioxide. The hydrogen 
 evolved is oxidized by the dioxide, but so slowly that the cell must be 
 given frequent intervals of rest to recover from polarization. This 
 cell is much used for working telephones, electric bells, etc., i.e., on 
 circuits that are open most of the time. 
 
 (6) The Daniell cell consists of a zinc plate immersed in dilute sul- 
 phuric acid contained in a porous vessel outside of which is a perfo- 
 rated copper plate surrounded by a solution of copper sulphate. The 
 hydrogen is taken up by the sulphate before it reaches the copper 
 plate. Polarization being wholly prevented, this cell is one of the 
 most constant known. 
 
 (7) The gravity cell is a modification of the Daniell. The liquids 
 are kept separate by their different densities, thus dispensing with 
 the porous cup. It is commonly used on closed circuits. This is the 
 form of cell most used for telegraphic purposes in the United States. 
 
 (rf) Every cell has an internal resistance that consists chiefly of the 
 resistance of the liquid or liquids used. The voltage of the cell is 
 largely taken up in overcoming this internal resistance, thus greatly 
 lessening the energy available at the electrodes. If R is the resistance 
 of the circuit outside the cell, and r is the resistance of the cell itself, 
 then Ohm's law becomes 
 
 c -. 
 
 r+R 
 
 Refer to Fig. 335, and notice that the liquid prism between the plates 
 is part of the circuit ; that when the plates are separated, the length 
 of the liquid conductor, and the internal resistance of the cell, are in- 
 
ELECTRIC GENERATORS, ETC. 
 
 481 
 
 creased (see 352) ; that when one of the plates is lifted partly from 
 the liquid, the area of cross-section is reduced, and the resistance 
 increased. 
 
 Experiment 360. Upon each end of a 4-inch piece of soft, round 
 iron-rod 1 inch in diameter, drive a vulcanite or hard-wood collar 
 about 1 inches in diameter. 
 Upon the spool thus formed, 
 wind about 6 feet of No. 8 in- 
 sulated copper wire, being care- 
 ful first to insulate the iron core 
 with paper. Fasten a rectan- 
 gular piece of soft iron, a, to 
 a piece of whalebone and sup- 
 port it, as shown in Fig. 373, 
 over M, the electromagnet just 
 
 described. Place M in the circuit of a battery of six or more similar 
 cells joined in series. The whalebone magnetoscope will enable you 
 to make a rough estimate of the pull of the electromagnet. 
 
 Experiment 361. Connect the cells of the battery in parallel, and 
 repeat Experiment 360. 
 
 Experiment 362. Make an electromagnet similar to that of Experi- 
 ment 360, but using about 250 feet of No. 24 insulated copper wire, 
 and with it, repeat Experiments 360 and 361. 
 
 Experiment 363. Connect the terminals of the high resistance 
 galvanoscope described in Experiment 321 to the poles of a single 
 cell, and record the deflection of the needle. Next, put the galvano- 
 scope in circuit with a battery of six similar cells joined in parallel, 
 and record the deflection of the needle. Then put the galvanoscope in 
 circuit with a battery of the same cells joined in series, and record the 
 deflection of the needle. From the records, determine which method 
 of joining cells is most effective with a high external resistance. 
 
 386. Advantages of Grouping in Parallel. Some of the 
 foregoing experiments indicate what is a general truth, 
 that, \vhen the external resistance is small, the grouping 
 of electric generators in parallel will give a greater cur- 
 rent than will a series grouping of the same generators. 
 31 
 
482 SCHOOL PHYSICS, 
 
 (a) With such a grouping, the available difference of potential 
 between the terminals of the system is not increased, but the internal 
 resistance is diminished (see 448). For instance, with n cells thus 
 grouped, we have j? 
 
 C= 
 
 It is evident that the less the value of R, the greater will be the effect 
 of n in increasing the value of C. 
 
 387. Advantages of Grouping in Series. Our experi- 
 ments also indicate that when the external resistance is 
 great, the grouping of electric generators in series will 
 give a greater current than will a parallel grouping of the 
 same generators. 
 
 () With such a grouping, the voltages of the several generators 
 are added together for the total available difference of potential, and 
 the internal resistances are added together for the total internal resist- 
 ance of the system. With n cells thus grouped, we have 
 
 C= nE 
 nr + R 
 
 It is evident that when R is small, the effect of n upon the value of C 
 must also be small, but that when R is large, the effect of multiplying 
 r is more than counterbalanced by the corresponding multiplication 
 of E. 
 
 (b) Having a given number of similar cells and a certain known 
 external resistance, the maximum current may be obtained by joining 
 the cells in such a way as to make the resistance of the battery as 
 nearly equal as possible to the resistance of the external part of the 
 circuit. 
 
 CLASSROOM EXERCISES. 
 
 1. Determine the current strength of a battery of five cells joined 
 in parallel, each having an E.M.F. of 2 volts and an internal resistance 
 of 0.5 ohms, (a) when the external resistance is 0.1 ohm ; (6) when 
 the external resistance is 500 ohms. Ans. (a) 10 amperes. 
 
 (&) Nearly 0.004 amperes. 
 
 2. Determine the current strength of a battery made up by coupling 
 
ELECTRIC GENERATORS, ETC. 483 
 
 
 
 the same 5 cells in series, (a) when the external resistance is 0.1 
 ohm ; (b) when the external resistance is 500 ohms. 
 
 Ans. (a) 3.846 + amperes. 
 (b) 0.0199+ amperes. 
 
 3. Connect in parallel 8 voltaic cells, each having an E.M.F. of 2 
 volts, and an internal resistance of 8 ohms, the total external resistance 
 being 16 ohms. Determine the current strength. Ans. 0.1176 amperes. 
 
 4. Compute the current strength of the same 8 cells connected in 
 series. Ans. 0.2 amperes. 
 
 5. Compute the current strength of the same 8 cells when joined 
 in two rows, each row being a series of four cells, and the rows being 
 joined in multiple arc. Ans. 0.25 amperes. 
 
 6. Each of ten given cells has an electromotive force of 1 volt and 
 an internal resistance of 5 ohms. What is the current strength of a 
 single cell, the external resistance being 0.001 of an ohm ? 
 
 Ans. 0.19996 + amperes. 
 
 7. The ten cells above mentioned are joined in parallel. The 
 external resistance is 0.001 of an ohm. What is the current strength 
 of the battery? Ans. 1.996 + amperes. 
 
 8. The ten cells above mentioned are joined in series, the external 
 resistance remaining the same. What Is the current strength of the 
 battery? Ans. 0.19999 + amperes. 
 
 9. What is the current strength given by one of the above men- 
 tioned cells when the external circuit has a resistance of 1,000 ohrns? 
 
 Ans. 0.00099502 amperes. 
 
 10. When the ten cells are joined in parallel with an external resist- 
 ance of 1,000 ohms, what is the ampere yield of the battery? 
 
 Ans. 0.0009995 amperes. 
 
 11. When the ten cells are joined in series with an external resist- 
 ance of 1,000 ohms, what is the current strength of the battery? 
 
 12. Six cells, each having an E.M.F. of 2 volts and an internal 
 resistance of 0.8 of an ohm, are joined in series. When the circuit 
 is closed, the wire connections aggregate 6 feet of No. 8 copper wire, 
 (a) What is the total resistance of the circuit? (6) What is Lhe cur- 
 rent strength of the battery? Ans. (a) 4.80386 ohms. 
 
 (6) 2.498 amperes. 
 
 13. Suppose the same six cells to be joined in parallel, the wire 
 resistance being the same as before, (a) What is the total resistance 
 of the circuit? (b) What is the current strength of the battery? 
 
 Ans. (a) 0.1371 ohms. 
 (b) 14.6 amperes. 
 
484 
 
 SCHOOL PHYSICS. 
 
 14. The terms "tandem" and "abreast" are sometimes used to 
 describe the methods of grouping cells that we have studied. Which 
 term refers to grouping in series? 
 
 15. Two voltaic cells give equal currents on "short circuit," i.e., 
 when the external resistance is very small. How can you experimen- 
 tally ascertain whether their electromotive forces are equal? 
 
 16. Review Laboratory Exercises 4 and 7, page 453, and indicate 
 the direction of the magnetic lines of force of the rectangle, of the 
 solenoid and of the magnet, and show how they may be made to 
 account for the observed phenomena. 
 
 Electromagnetic Induction. 
 
 Experiment 364. For a galvanoscope more delicate than any we 
 have yet used, procure two soft pine blocks, 4 cm. square and 2 cm. 
 thick. On the square faces of each, nail or glue a thin piece of wood, 
 6 cm. square. (These pieces may be cut from a cigar box.) The 
 channel around the edges of the blocks will be 2 cm. wide and 1 cm. 
 deep. Through the middle of each block, from face to face, bore a 
 
 hole at least 1.5 cm. in di- 
 ameter. Wind the grooves 
 full of No. 36 insulated cop- 
 per wire, and mount the 
 blocks, A and B, on a base- 
 board with their opposing 
 faces about 1 cm. apart, as 
 shown in Fig. 374. Connect 
 the wires of the two coils 
 so that a current flowing 
 through the wire will circle 
 around the coils in the same 
 FIG. 374. direction; i.e., connect them 
 
 in series. 
 
 Straighten and magnetize four or five pieces of watch spring each 
 1.5 cm. long, and fasten them with thin shellac varnish to the back of 
 a piece of looking glass, 1.5 cm. square and as thin as you can get. 
 See Fig. 375. From a support made of brass wire, suspend the mirror, 
 M, by a strand of silk, the lightest that will carry the load. A single 
 silk fiber may be strong enough. The mirror when suspended should 
 hang midway between the two coils, and directly in line with the holes 
 through the two coils. So adjust the base of the galvanoscope that 
 
ELECTRIC GENERATORS, ETC. 
 
 485 
 
 the coils are parallel to the mirror when the latter is freely suspended 
 between them, and protect the apparatus from air 
 currents by a glass cover. A feeble current pass- 
 ing through the coils will deflect the delicately 
 suspended needles, as was roughly illustrated in 
 Experiment 315. By placing a bar magnet on the 
 table so as partly to neutralize the directive ten- 
 dency of the terrestrial magnetism, the sensitive- 
 ness of the galvanoscope may be increased. 
 
 Stick a pin into the end of the base-board and 
 in line with the centers of the openings in the 
 coils, as appears more plainly in Fig. 376. The 
 eye may be so placed that the pin will cover its 
 image in the mirror. The slightest deflection of F _ 
 
 the mirror will be manifested by the destruction 
 of this coincidence. Indicate the polarity of the suspended magnets 
 by marking the letters N and S near the edges of the base-board 
 
 FIG. 376. 
 
 between the coils .4 and B. Put the galvanoscope into circuit with 
 a single cell, and note the deflection of the mirror. Record on the 
 base-board of the instrument the fact that " This instrument shows 
 a deflection of the J\ T end of the needle toward the east when the zinc 
 plate of a cell is connected with the free terminal of coil B (or of -A, 
 as the case may be). 
 
 Experiment 365. Make a coil of wire with many turns of No. 36 
 insulated copper wire, as shown at H in Fig. 376. The coil should 
 
486 SCHOOL PHYSICS. 
 
 have an internal diameter of about 3 cm., and a cross-section area of 
 at least 1 sq. crn. Connect the terminals of the coil with the ter- 
 minals of the galvanoscope. Level the galvanoscope, and see that 
 its needle-mirror is freely suspended as directed in the preceding- 
 experiment. Thrust the end of a bar magnet at least 1.5 cm. in 
 diameter into the coil, H, thus filling the coil with lines of force. An 
 electric pulse deflects the mirror of the galvanoscope. That the 
 deflecting current was of momentary duration is shown by the fact 
 that the mirror returns to its first position. When it has come to rest, 
 remove the magnet from the coil. The mirror is turned the other 
 way and comes to rest as before, thus showing that the direction of 
 the second current was opposite to that of the 
 first, and that its duration was but momentary. 
 Repeat the experiment, making the motions of 
 the magnet more rapid. Notice that the pulses 
 are more marked than before. Repeat the ex- 
 periment again, using a low resistance solenoid 
 that carries a current of electricity, as shown 
 in Fig. 377, instead of the bar magnet. Then 
 place the solenoid inside the coil, //, and break, 
 and make the battery circuit. Place a soft 
 iron rod inside the solenoid and again break 
 and make the circuit, noticing any increase in the deflections of the 
 needle. 
 
 That the galvanoscope may be free from disturbing magnetic 
 influence, see that all knives, keys, watches and other articles of iron 
 or steel are kept at a considerable distance from it, and that the coil, H, 
 is so far removed that the magnet or the solenoid may not have any 
 perceptible direct influence upon it. It will be well to wind the wire 
 of the coil, H, upon a spool as shown in Fig. 378. 
 
 388. Induced Currents. When the number of mag- 
 netic lines of force that pass through a closed coil of wire 
 is changed, as in Experiment 365, pulses of electricity are 
 generated in the coil. The rapidity with which the coil 
 is filled or emptied has a marked effect upon the intensity 
 of the pulses generated. These momentary currents are 
 said to be induced in the coil; i.e., they are induced currents. 
 
ELECTRIC GENERATORS, ETC. 
 
 487 
 
 Experiment 366. Connect the coil, H (Fig. 376), to the galvano- 
 scope, G. Make another coil of No. 20 insulated copper wire, the 
 same size as H, and call it A. Connect A with the battery, and deter- 
 mine, by the corkscrew rule, which side of it is north, and so mark it. 
 Consider the deflections of G to the right as + , and deflections to 
 the left as . Consider lines of force going through H from its upper 
 side as + , and lines that flow in the opposite direction as . 
 Bring the north end of a magnet to the coil, H. 
 " " south " " " " " " " " 
 " " north side of the coil A to the coil, H. 
 " " south " " " " " " " " " 
 Lay A, north side down upon H, and make the circuit. 
 "A, " " " " " " break " " 
 " A, south " " " " " make " " 
 1 " ' " break " " 
 
 In each of these cases, record the deflection of G, and the direction 
 of the lines of force passing through H. When a magnet is used, the 
 direction of the flux may be determined by the marked polarity of 
 the magnet. When the coil, -4, is used, the direction of the flux may 
 be determined by the corkscrew rule. Remember that there can be 
 no deflection of G without a change in the number of lines of 
 force in H. In each case, record your answer to these two ques- 
 tions : 
 
 (1) Was there an increase or decrease in the flux of force in Hf 
 (*2) What deflection of G results from an increase of that flux in 
 H, and what from a decrease ? 
 
 Experiment 367. Place a soft iron core in the coil H as shown in 
 
 Fig. 378, and repeat Experiment 
 366. Notice that the deflections 
 are now much more marked. 
 
 FIG. 379. 
 
 FIG, 378. 
 
 Experiment 368. Place the 
 coil, H, in circuit with a telephone 
 
488 SCHOOL PHYSICS. 
 
 receiver instead of the galvanoscope. When the circuit of A is made 
 or broken, a distinct click may be heard in the receiver which is a 
 delicate detector of pulses of electricity. One may be bought at a 
 low price, or borrowed. 
 
 389. Laws of Induced Currents. The following laws 
 have been established : - 
 
 (1) An increase in the number of the lines of force pass- 
 ing through a closed coil induces a current in one direction 
 through the wire of the coil; a decrease in the number of 
 the lines of force induces a current in the other direction. 
 
 (2) The electromotive force of the induced currents de- 
 pends upon the rapidity of change in the number of lines 
 of force that pass through th3 coil. 
 
 390. The Magneto. A number of permanent magnets 
 might be fastened to a wheel so that the revolution of the 
 wheel would carry the ends of the magnets in front of a 
 closed coil of wire, corresponding to the coil, H, of our 
 recent experiments. As each magnet approaches the coil, 
 a current would be generated within the coil ; as it recedes 
 from the coil, a current of opposite direction would be 
 generated in the coil. We should thus obtain an alter- 
 nating current of electricity from mechanical power. Such 
 a device for inducing electric currents in wire coils or bob- 
 bins, by variations in the relative positions of the coils and 
 of permanent magnets, is called a magneto-electric machine, 
 or simply a magneto. 
 
 (a) The fundamental process in the generation of electric currents 
 from mechanical power consists in revolving closed conductors in a 
 magnetic field in such a way as to vary the number of lines of force 
 passing through them, i.e., by successively filling and emptying closed 
 coils. The mechanical motion may move the coils, or the source of 
 
ELECTRIC GENERATORS, ETC. 489 
 
 the magnetic flux, or it may simply move a mass of iron that forms a 
 ready path for the lines of force. The magneto made it practicable 
 to obtain electric currents from mechanical power, an advance step 
 because mechanical power is cheaper than the chemicals used in a 
 voltaic battery. The magneto is of great historical interest, but it has 
 been largely displaced by the more efficient dynamo. 
 
 391. The Dynamo, or dynamo-electric machine, differs 
 characteristically from the magneto in that the former 
 employs a field of force due to the influence of electro- 
 magnets, while the latter utilizes permanent magnets. 
 
 392. The Simple Dynamo. Of course, it makes no 
 difference whether the coil or the flux of force moves, 
 provided that the num- 
 ber of lines of force that 
 
 pass through the coil is 
 continually changing. 
 Suppose a single loop of 
 wire to turn upon a hori- 
 zontal axis, and between 
 
 FIG. i>60. 
 
 the opposite poles of two 
 
 magnets, iVand $, as shown in Fig. 380. When the loop 
 stands in a vertical plane, as indicated by the heavy black 
 line, the magnetic lines of force between the pole-pieces 
 thread through the loop in the greatest possible number. 
 When the loop has been turned upon its axis through 
 ninety degrees, until it lies in a horizontal plane, as indi- 
 cated by the dotted lines in the figure, the lines of force 
 run parallel to the plane of the loop, and none thread 
 through it. During this quarter revolution of the loop, 
 the number of lines of force that pass through the loop 
 was decreasing, and an electric current was thereby in- 
 
490 SCHOOL PHYSICS. 
 
 duced in the loop, as indicated by the arrows. During the 
 next quarter revolution of the loop, the number of lines of 
 force threading the loop was increasing, but as they passed 
 through the loop from the other side, the current induced 
 in the loop had^the same direction as before. During the 
 next half revolution, the induced current will flow through 
 the loop in the opposite direction. The current, therefore, 
 reverses twice for each revolution of the loop. 
 
 393. The Direct Current Dynamo, one of the most im- 
 portant of the modern, practical devices for the trans- 
 formation of mechanical into electrical energy, consists 
 essentially of three parts : an armature made of coils of 
 wire, which may be revolved in a magnetic field, and thus 
 successively filled with lines of force and emptied of them ; 
 a commutator for giving a uniform direction to the alter- 
 nating currents induced in the coils by their rotation in 
 the field of force ; and a large electromagnet as a source 
 of flux of force. 
 
 394. The Armature. If the revolving coil is composed 
 of many turns of wire instead of a single loop, the electro- 
 motive force generated by the revolution will be multi- 
 plied by the number of turns. If the loop is filled with 
 soft iron, which has a greater magnetic permeability than 
 air, the number of lines of force gathered into the space 
 traversed by the coil will be increased, and the electric 
 effect thereby augmented. A soft iron cylinder or ring 
 upon which coils of insulated copper wire have been wound 
 and arranged for rapid rotation in a magnetic field is called 
 an armature. 
 
 (a) The Siemens or shuttle armature, represented in Fig. 381, 
 
ELECTRIC GEJsTJRATORS, ETC. 
 
 491 
 
 consists of a coil of wire wound in two broad grooves plowed on op- 
 posite sides of an iron cylinder. Such armatures are largely used in 
 the magnetos used for " calling up " on telephone circuits, but they 
 are not well adapted for large currents, because the " local currents " 
 
 FIG. 381. 
 
 (often called Foucault currents) generated in the iron core absorb 
 energy, and transform it into heat. This heat increases the internal 
 resistance of the coil, and is objectionable in other ways. Moreover, 
 with such an armature, the current falls to zero twice every revolu- 
 tion and, for many purposes, such a current is useless. 
 
 (ft) The drum armature differs from the shuttle armature chiefly in 
 that it employs many coils instead of one. The cylindrical iron core 
 is made of thin disks of soft iron insulated from each other, thus min- 
 imizing the " local currents " and the heating effects thereof. The 
 insulation for this purpose sometimes consists of tissue paper, some- 
 times of varnish, and sometimes only of the oxidation on the surfaces 
 of the metal. On the cylinder thus built up, many separate coils are 
 wound lengthwise, as is shown in Fig. 382. These separate coils are 
 
 FIG. 382. 
 
 joined in series, and the several junctions connected to insulated bars, 
 the extremities of which are grouped around the shaft of the arma- 
 ture as shown at the left of the figure. Brass bands around the out- 
 side of the cylinder hold the coils in place. 
 
 (c) The Brush or ring armature consists of eight or more coils 
 wound in grooves upon an annular core, as shown in Fig. 383. The 
 core is laminated, i.e., built up by winding a thin band or ribbon of 
 
492 
 
 SCHOOL PHYSICS. 
 
 soft iron in successive layers, each layer being insulated from the next. 
 
 The wedge-shaped projections that separate the coils are made by 
 
 thin pieces of iron placed cross- 
 wise between successive layers 
 of the long band as the ring is 
 built up. Coils radially oppo- 
 site are joined in series, and 
 the terminals of each such pair 
 are carried to the commutator 
 on the shaft of the armature. 
 
 (d) Armature coils are some- 
 times wound upon arms or 
 spokes that project radially 
 from a central hub, or are set 
 in succession on the face of a 
 
 disk and near its circumference. 
 FIG. 383. 
 
 395. The Commutator. If the connections of the arma- 
 ture coils are reversed at the moment when the current in 
 the coils is reversed, the induced currents will all flow in 
 the same direction in the external circuit. The special 
 device for thus changing the connections of armature coils 
 is called a commutator. 
 
 (a) The commutator of the Siemens armature consists of the two 
 halves of a metal collar around the armature shaft, and two metal 
 strips or " brushes." The two halves 
 of the collar, i.e., the " commutator 
 segments," m and n, are separated from 
 the shaft, s, that carries them by a bush- 
 ing of insulating material, and are sepa- 
 rated from each other as shown in Fig. 
 384. One end of the armature coil is 
 connected with one segment, and the 
 other end with the other segment. 
 The brushes, bb', are held by fixed 
 supports so that their free ends rest FlG - 384 - 
 
 lightly on the segments. The points of contact are diametrically 
 opposite. 
 
ELECTRIC GENERATORS, ETC. 
 
 493 
 
 Consider b and b' the terminals of the dynamo, and that they are 
 connected by a wire that constitutes the external circuit. Remember 
 that m and n are connected through the armature coil. Assume that 
 the connections of the terminals of the armature coil with the commu- 
 tator segments are such that current flows through the coil and passes 
 out by way of n and b. As the armature is turned a little further, 
 the current in the coil is reversed, and flows out through ?;i instead of n. 
 But the same rotation of the shaft that carries both the armature and 
 the commutator has now brought m into contact with b so that the 
 current continues to flow through b which thus remains the -f ter- 
 minal as long as the shaft is turned in the direction indicated by the 
 arrow. 
 
 (6) There are many different ways of connecting armature coils 
 with their commutators, each one of which may call for careful study. 
 The following may be taken as typical of most of them : in Fig. 385, 
 the numbered loops represent the armature coils joined in series as in 
 the ring armature. The heavy broken circle represents commutator 
 segments on which rest the ends of the brushes, b and b'. The brushes 
 divide the coils into two sec- 
 tions. In the figure, coils 
 numbered 2, 3, 4, 5, 6, and 7 
 constitute the right-hand sec- 
 tion, and coils 8, 9, 10, 11, 
 12, and 1 constitute the left- 
 hand section. The six coils 
 of each section are connected 
 in series, and the two sec- 
 tions are connected in par- 
 allel. As the armature turns 
 between the pole-pieces, N 
 and S, and in the direction 
 indicated by the arrow, the currents induced in the coils of the 
 right-hand section will flow in the direction indicated by the arrow- 
 heads. At the same time, the currents induced in the coils of the 
 left-hand section will flow in the opposite direction, as indicated 
 by the arrow-heads. Imagine a current returning from the external 
 circuit and entering the generator at b', the negative terminal. It 
 will find two paths of equal resistance, one through the right-hand 
 section, and the other through the left-hand section. In either case, 
 the direction of the current freshly induced in those sections coincides 
 
 FIG. 385. 
 
494 
 
 SCHOOL PHYSICS. 
 
 with its own. It, therefore, divides itself equally between the two 
 paths and flows from the generator at b, the positive terminal. 
 
 396. The Field Magnet. The electromagnet that sup- 
 plies the flux of 
 force must have a 
 current to excite 
 it. This current is 
 sometimes supplied from an 
 outside source, as is dia- 
 grammatically shown in Fig. 
 386. Such a dynamo is said 
 to be separately excited. 
 Often all of the current 
 from the armature is carried 
 around the coils of the field 
 magnet, thus forming a 
 series dynamo, as is shown in Fig. 387. Sometimes a 
 part of the current from the 
 armature is carried through a 
 shunt circuit consisting of many 
 turns of. wire that is smaller than 
 the wire of the main circuit, as 
 is shown in Fig. 388. Such a 
 dynamo is said to be shunt wound. 
 Sometimes, for purposes of regu- 
 lation, the field magnet is encir- 
 cled by both series and shunt 
 coils, as is shown in Fig. 389, or 
 by either of those with a separately excited coil. Such 
 a dynamo is said to be compound wound. 
 
 For arc lighting, a current that is constant under vary- 
 
 FIG. 386. 
 
 FIG. 387. 
 
ELECTRIC GENERATORS, ETC. 
 
 495 
 
 ing load is needed ; it is generally secured by a " regu- 
 lator" connected with the dynamo, as shown at R in 
 Fig. 442. The regulator may be automatic in its action. 
 For incandescence lighting, a potential that is constant 
 under varying load is needed ; it is generally secured by 
 compound winding. 
 
 SHUNT CIRCUIT 
 FIG. 388. 
 
 FIG. 389. 
 
 (a) When the armature of a "self exciting" dynamo, i.e., one that 
 has not an exciting current from^an external source, is put in motion, 
 the feeble residual magnetism of .the cores of the field magnets induces 
 feeble currents in the armature coils. These currents flow around the 
 magnets, intensifying their power, and thus increasing the E.M.F. 
 of the machine. The current thus strengthened further energizes 
 the field magnet. Thus, the machine "builds up" its current until 
 the magnets have reached the limit of excitation. Many dynamos, 
 especially those used for the generation of alternating currents, have 
 more than two pole-pieces. 
 
 (6) Lines of force generated by the field magnet, and that do not 
 pass from pole to pole, are termed the stray-field or the leakage lines. 
 The stray-field between the pole-pieces and the bed-plate of a dynamo 
 may become the source of serious loss and annoyance. 
 
 (c) Fig. 390 represents the Brush dynamo complete. A shaft runs 
 through the machine from end to end, carrying a pulley, P, at one 
 end, a commutator, c, at the other end, and a wheel armature, R, at 
 
496 
 
 SCHOOL PHYSICS. 
 
 the middle. The armature carries eight or more helices of insulated 
 wire, H H, connected in pairs as described in 394 (c) . As the shaft 
 is turned by the action of the belt upon the pulley, the armature and 
 the commutator are turned with it. The armature coils are thus 
 carried rapidly across the four poles of the field magnets, MM, 
 
 FIG. 390. 
 
 traversing the intenser parts of the magnetic field, and cutting the 
 lines of force. 
 
 CLASSROOM EXERCISES. 
 
 1. What is an induced electric current? How is it produced? 
 
 2. How are induced currents made continuous? 
 
 3. Give some proof that the condition of a wire when it closes an 
 electric circuit is different from the condition of the same wire when 
 the circuit is open. 
 
 4. Why are the field magnets of dynamos generally provided with 
 iron cores? 
 
 5. What advantage is there in making the field-magnet cores of 
 cast iron instead of pure soft iron ? 
 
 6. Upon what does the E.M.F. of a dynamo depend? 
 
 7. What is the difference between a magneto and a dynamo? 
 
 8. When a dynamo is in operation, its field magnets are likely to 
 become heated. Does this increa >e or diminish the efficiency of the 
 machine, and why ? 
 
 9. How are the field magnets of a shunt-wound dynamo energized? 
 
ELECTRIC GENERATORS, ETC. 497 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. A 1-ohm resistance coil of No. 30 iron 
 wire ; a resistance coil of No. 30 German-silver wire ; two magneto- 
 scopes; voltaic cells; plates of antimony, and of zinc, and of copper; 
 a copper cartridge-shell ; hydrochloric acid ; pieces of electric light 
 carbon; a telephone receiver; German-silver wire; two semicircles 
 of soft iron ; an iron rod 45 cm. long; a brass tube, and one of rubber. 
 
 1. Given the two electrodes of a concealed voltaic battery, deter- 
 mine which of the wires is connected to the zinc plate. 
 
 2. Connect a Leclanche cell and a freshly prepared dichromate cell 
 in parallel, and place a galvanoscope in the circuit, between the 
 carbons, (a) Determine and record the direction of the current. 
 (&) Place the galvanoscope between the zincs, and determine the direc- 
 tion of the current, (c) Why should this current flow? (rf) Is it 
 advisable to connect cells that are dissimilar in parallel, and why? 
 (e) Suppose the E.M.F. of the dichromate cell to be 2 volts, and that 
 of the Leclanche cell, 1.42 volts. Suppose the resistance of the dichro- 
 mate cell to be 0.6 of an ohm, that of the Leclanche cell to be 0.8 
 of an ohm, and that of the wire and galvanometer to be 1 ohm. What 
 is the resultant current in the system? Remember that when two 
 electromotive forces are in opposition, their difference is all that is 
 available. 
 
 3. Prepare a voltaic cell by immersing a strip of amalgamated zinc 
 in a copper cartridge-shell filled with dilute sulphuric acid. Connect 
 this cell in parallel with a large copper and zinc pair and, by means of 
 the galvanoscope, determine whether either cell forces current over 
 into the other. Make several trials, using acid of the same strength 
 in both cells. If carefully done, it will be found that the E.M.F. 's 
 are nearly equal. 
 
 4. Form a cell with antimony and copper plates, and dilute sul- 
 phuric acid. Insert a galvanoscope in the circuit. Note and record 
 the deflection. Prepare a jar of dilute hydrochloric acid. Lift the 
 plates from one jar to the other without otherwise changing the 
 apparatus. Note and record the deflection. Which is attacked more 
 vigorously by sulphuric acid, antimony or copper ? Which by hydro- 
 chloric acid? 
 
 5. Provide a glass tube about 1 cm. internal diameter. Insert a 
 wire in each end, and fill the tube with pieces of pounded electric light 
 carbqn. Pass a current from a cell through the apparatus, interpos- 
 
 32 
 
498 
 
 SCHOOL PHYSICS. 
 
 ing a low resistance galvanoscope. By means of a wooden rod, com- 
 press the powdered carbon. Why is the deflection largely increased ? 
 Why is a low resistance galvanoscope used? 
 
 6. Calculate the length of No. 30 iron wire that has a resistance of 
 1 ohm. Procure the wire, and wind it on a board, being careful that 
 adjacent turns do not touch. With this addition to your apparatus, 
 determine whether the resistance of a telephone receiver is greater or 
 less than an ohm, and whether it differs much or little from an ohm. 
 
 7. Wind 4 ounces or more of No. 30 insulated German-silver wire 
 upon a spool. Connect this bobbin in series with a single cell and 
 a low resistance galvanoscope. Record the deflection of the latter. 
 Change the low resistance block of the galvanoscope for one of high 
 resistance. Again note and record the deflection. Explain the 
 increased deflection of the needle that accompanies the increased 
 resistance of the circuit. 
 
 8. Prepare two semicircles of |-inch soft iron rod, two inches in 
 diameter, and file the faces smooth, so that they will fit together nicely. 
 
 FIG. 391. 
 
 Prepare two bobbins of approximately equal weight, one made of 
 about 20 turns of No. 16 wire, and the other of No. 30 wire, both 
 insulated. Slip the bobbins on one of the iron semicircles. Connect 
 the terminals of the fine wire coil to those of the mirror galvanometer 
 (see Experiment 364). Arrange the galvanometer so that the mirror 
 
ELECTRIC GENERATORS, ETC. 
 
 499 
 
 reflects its beam upon a ground glass scale about a meter away, as 
 shown in Fig. 391. A thin line of black paint drawn vertically across 
 the center of the mirror will aid in exactly locating the spot of light 
 upon the scale. Connect the terminals of the coarser coil to those of 
 a single cell. Open and close the primary circuit, and note the 
 magnitude of the kick of the galvanometer. Repeat with the other 
 half of the ring in place, and notice that the deflection is increased. 
 Explain this increase, remembering the effect of permeability upon 
 the number of lines of force in a magnetic circuit. 
 
 9. Take a rod of iron \ of an inch in diameter and 18 inches long, 
 and wind upon one end a primary, such as was used in the ring of 
 Exercise 8 ; upon the other end of the rod, wind a secondary coil. By 
 means of opening and closing the primary circuit, and noticing the 
 deflection of a galvanoscope properly connected to the secondary, 
 determine at what points along the rod the lines of force are the 
 greatest in number. Why is the maximum deflection found when 
 .the primary and secondary are close together? On paper, map the 
 lines of force as you think they must exist in space. Cover the 
 primary coil with a piece of glass, and pass a current of ten or more 
 amperes through it. Sprinkle the glass with filings, and prove or dis- 
 prove your theory. 
 
 10. Clamp to a vertical board two magnet bobbins (see Exercise 12) 
 joined in series as shown in Fig. 392. Support one end of the arma- 
 ture, bm, by an elastic band, ab. 
 Pass a current through the bob- 
 bins, and notice the pull upon 
 ab. Looking at the upper ends 
 of the bobbins, notice whether 
 the current circles around the 
 two bobbins in the same direc- 
 tion or not, as clockwise or 
 counter-clockwise. Turn one 
 of the bobbins upside down, 
 changing the connections in 
 this respect. Ascertain which 
 connection gives the greater 
 
 pull upon the armature, bm, and, with the bobbins thus joined, bring 
 the movable soft iron yoke, cd, into position as shown in the figure. 
 Explain why this improves the magnetic circuit, so that the upper 
 armature is pulled harder than before, and probably drawn down 
 
 FIG. 392. 
 
500 SCHOOL PHYSICS 
 
 with a sharp click. Remember that all magnetic circuits tend to con- 
 tract themselves, and to make their reluctance as small as possible. 
 
 11. Prepare an exploring coil with several hundred turns of No. 30 
 insulated copper wire and an internal diameter of 5 cm. Place this 
 coil in the field of a strong electromagnet, connect its terminals with 
 those of a telephone receiver, and. make and break the magnet circuit. 
 Determine the points where the flux is the heaviest by moving the 
 coil about and repeating the experiment. Be sure to have the face of 
 the coil at right angles to the supposed direction of the magnetic 
 lines of force. Mount the coil on a stiff wire that passes through the 
 center of the coil, and lies in the plane of the coil. The plane of the 
 coil may be easily changed in the magnetic field by rolling the sup- 
 porting wire between the thumb and forefinger. Place the face of 
 
 the coil in the position that you think is at 
 right angles to the lines of force in the 
 location you have chosen. Make and break 
 the magnet circuit, and notice the strength 
 of the click. Now turn the coil a quarter 
 turn and repeat. If you have estimated 
 FIG 393^ rightly? there should now be no click. Place 
 
 the magnet on a piece of paper, and draw a 
 line under the coil parallel to its face whenever you find a position 
 where no click occurs, and thus map out the field. Sprinkle the paper 
 with filings, and verify your map. 
 
 12. Make two magnetoscopes like that shown in Fig. 373. An 
 ordinary carriage-bolt about 7 cm. long may be used as the core, and 
 a soft iron nut may answer as the armature. With the two magnet- 
 oscopes, a voltaic battery, and a supply of insulated No. 20 copper 
 wire, arrange apparatus so that you can exchange telegraphic signals 
 with another pupil at another table, or in another room. 
 
 397. The Alternator is a dynamo designed for the gen- 
 eration of alternating currents. It has collecting rings 
 instead of a commutator so that the current is delivered 
 just as it is generated ( 395), and a small direct current 
 dynamo for energizing its field magnets, the pole-pieces of 
 which are generally very numerous. Fig. 394 represents 
 one form of the machine. 
 
ELECTRIC GENERATORS, ETC. 
 
 501 
 
 FIG. 31M. 
 
 398. Tesla's Oscillator is a combined prime motor and 
 electric generator, and produces alternating currents with- 
 out rotary motion of 
 the generating coils. 
 The motive force may 
 be that of steam or of 
 compressed air. The 
 machine is represented 
 in section by Fig. 
 395. The powerful 
 field magnets, MM, 
 are excited by a cur- 
 rent from an outside FIQ. 395. 
 
502 SCHOOL PHYSICS. 
 
 source. The generating coils are mounted on the piston- 
 rod, A, and rapidly vibrate back and forth in the direc- 
 tion BB, and in the powerful magnetic fields, at HH. 
 The oscillating piston-rod slides endwise in its supports 
 at BB. The action of the motive power is somewhat 
 peculiar, and depends largely on the inertia of the oscillat- 
 ing parts. The stroke of the piston-rod is from g 1 ^ to f of 
 an inch, according to the pressure used and the nature of 
 the current desired. The output of the machine relative 
 to its weight is exceedingly large, and the machine gives 
 promise of commercial value. 
 
 Experiment 369. Mount a metal clock-wheel upon wooden bear- 
 ings, and solder to its axle a wire crank by which it may be turned. 
 
 Provide two metal springs. The 
 upper end of one should rest upon 
 the toothed edge of the wheel, and 
 " snap " from one tooth to the next 
 as the wheel is turned. The upper 
 end of the other should rest on 
 the axle of the wheel. Consider the 
 fixed ends of these springs as the 
 terminals of this "interrupter." 
 
 FIG 39G " *P\\.i ^is apparatus into the circuit 
 
 with a voltaic battery and the gat 
 
 vanoscope that has a coil of No. 16 wire. Turn the wheel, and no- 
 tice the deflection of the needle. 
 
 399. Alternating Currents have some peculiar properties 
 largely due to the constantly fluctuating field of force 
 that surrounds their conductors. The pulsating current 
 produced by the interrupter has many of the properties 
 of the alternating current, and will facilitate our investi- 
 gations. 
 
 (a) The current does not wholly cease when the spring of the 
 interrupter snaps from tooth to tooth. As the circuit is broken, the 
 
ELECTRIC GENERATORS, ETC. 503 
 
 encircling magnetic lines of force ( 382) are decreased in number, 
 and that very decrease tends to continue the current as explained in 
 400. In brief, the current does not have time wholly to die away 
 before the spring is on the next tooth of the wheel. 
 
 Self-induction. 
 
 Experiment 370. Double a piece of Xo. 24 insulated copper wire 
 about 100 feet long, and wind it upon a wooden rod as shown in 
 Fig. 397. Join the ends of this wire in the series circuit of the 
 apparatus arranged for Experiment 369. Turn the wheel of the inter- 
 rupter rapidly, and note the deflection 
 
 of the galvanoscope. Remove the I J J J J J J J J J J _ I 
 No. 24 wire from the circuit, straighten 
 it, and wind it upon an iron rod so as 
 
 to form an electromagnet. Put this electromagnet into the circuit, 
 and repeat the experiment. Xotice that the deflection of the galvan- 
 oscope is less, and that the sparks at the wheel of the intewupter 
 are greater than before. 
 
 Experiment 371. Place the coil and core of Experiment 367 in the 
 circuit of a voltaic battery, and insert a galvanoscope as shown at G 
 
 in Fig. 398. When the circuit is closed 
 by depressing the key, K, part of the 
 battery current is shunted from m to n 
 through, the galvanoscope, and deflects 
 its needle. Force the needle back to 
 zero, and place some obstacle to prevent 
 its moving again in that direction, but 
 leaving it free to move in the opposite 
 FIG. 398. direction. Break the circuit at K, and 
 
 notice that the needle does swing in 
 
 the opposite direction, showing that a current passed through it from 
 n to m. This current was not the battery current, for the battery 
 circuit was open. 
 
 400. Self-induction. When the number of lines offeree 
 in a coil is increasing, an electromotive force opposite to that 
 of the inducing current is established, thus weakening the di- 
 rect current; when the number is decreasing, an electromotive 
 
504 SCHOOL PHYSICS. 
 
 force that coincides in direction with that of the inducing cur- 
 rent is established, thus strengthening the direct current. In 
 consequence of this, we may have an opposition to the 
 current-How other than the resistance of the circuit, 
 namely, the opposing, self-induced electromotive forces. 
 The coil manifests a conservative tendency, opposing 
 sudden changes. When the doubled wire of Experiment 
 370 was wound upon the wooden rod, every part of it 
 lay adjacent to another part that was carrying current 
 in the opposite direction. The magnetic lines of force 
 generated by one part neutralized the lines of force that 
 circled in the opposite direction around the adjacent part ; 
 i.e. the circuit was non-inductive. In the other case, the 
 lines of force circled in the same direction around adja- 
 cent parts of the wire, and assisted each other in setting 
 up an opposing, self-induced electromotive force that 
 greatly weakened the current that produced them. In 
 Experiment 371, the self-induced electromotive force gen- 
 erated by the action of the several turns of the coil upon 
 one another at the moment of opening the circuit acted 
 through the coil in the same direction that the battery 
 current did, and, consequently, sent an induced current 
 through the galvanoscope in the opposite direction. 
 
 (a) Such a coiled circuit is said to have a reactance. This reactance 
 has much the effect of resistance, but it depends upon other considera- 
 tions, chiefly the frequency of the pulsations, and upon a certain con- 
 stant called the coefficient of self-induction. This coefficient depends 
 upon the shape, coiling, and coring of the circuit and, in practice, is 
 determined only by experiment. Self-induction coefficients are meas- 
 ured by a unit called the henry. 
 
 401. Reactance and Impedance. As alternating cur- 
 rents are fluctuating in value, their measure must be that 
 
UNIVERSITY OF 
 
 DEPARTMENT OF PHYSIOS 
 ELECTRIC GENERATORS, ETC. 505 
 
 of averages. The chosen average is the square root of 
 the arithmetical mean of the squares of all its values. 
 This " square root of a mean square " applies to current 
 and to voltage, and E. For a true alternating current 
 (i.e. one that increases and diminishes by what is called 
 the law of sines), the numerical relations may be repre- 
 sented thus : 
 
 + (2 TrnL)* 
 
 in which R represents the ohmic resistance, n the fre- 
 quency of alternation, and L the coefficient of self-in- 
 duction. The expression 2 irnL represents the reactance. 
 
 The apparent resistance, i.e., V J R 2 + (27rnZ) 2 , is called the 
 impedance, and is measured in ohms. 
 
 (a) The mathematical relations of resistance, reactance and impe- 
 dance may be easily remembered by considering the first and second of 
 these functions as the two sides of a right angled triangle of which 
 the impedance is the hypothenuse, i.e. the " square root of the sum of 
 the squares of the other two sides." 
 
 Experiment 372. Wind about twenty turns of No. 18 insulated 
 copper wire around a |-inch iron rod, or (preferably) around a bundle 
 of iron wires, and put the coil into circuit with a pulsating current. 
 The lines of force inside the coil and in the core fluctuate in value 
 with the current. On the outside of this coil, and carefully insulated 
 from it, wind 300 or 400 feet of No. 28 insulated copper wire. Place 
 one of the terminals of this outer or secondary coil above the tongue, 
 and the other terminal below it. When the pulsating current flows 
 through the inner or primary coil, currents are induced in the second- 
 ary coil, and produce distinct shocks in the tongue. 
 
 402. The Transformer. --By suitably winding and 
 coring primary and secondary coils, an alternate current 
 at one voltage may be received by the primary, and a 
 current at a voltage higher or lower as desired delivered 
 
506 
 
 SCHOOL PHYSICS. 
 
 from the secondary. When the primary is made of a few 
 turns of large wire, and the secondary is made of many 
 turns of small wire, the voltage is increased, and vice 
 versa. Coils so wound and properly cored are called trans- 
 formers. 
 
 (a) Transformers are largely used when currents of high voltage 
 are to be carried great distances, and delivered at a pressure suitable 
 for use. With a given resistance in the line, the loss in watts is less 
 with a small current and high voltage than it is with large current 
 and low voltage. With a given line loss, high voltage currents enable 
 the use of small conductors, and copper wire is expensive. 
 
 (6) When the electric energy is transformed from a current of low 
 voltage and many amperes to one of high voltage and few amperes, 
 the apparatus is called a " step up " transformer. Similarly, when 
 the voltage is decreased, the apparatus is called a " step down " trans- 
 former. 
 
 403. The Induction Coil is a modification of the appa- 
 ratus used in Experiment 372, and is often called the 
 Rhumkorff coil. Receiving a large current of small 
 electromotive force, it delivers a small current at a high 
 pressure, sometimes hundreds of thousands of volts, i.e., 
 it is a " step up " transformer. 
 
 (a) In the diagram shown in Fig. 399, M represents a core of iron 
 
 FIG. 399. 
 
ELECTRIC GENERATORS, ETC. 
 
 507 
 
 wires upon which is wound a primary coil of coarse wire that is in 
 circuit with the voltaic battery. In this primary circuit, are a com- 
 mutator, c, for changing the direction of the current, and an automatic 
 interrupter, b. Wound 
 upon the primary coil, 
 and very carefully in- 
 sulated from it, is a 
 
 M 
 
 V, 
 
 FIG. 400. 
 
 secondary coil made 
 of very many turns of 
 fine wire, the termi- 
 nals of which are 
 marked T T . If the 
 coil is designed to give 
 sparks between T and 
 T', the condenser, CC, 
 is added. This con- 
 sists of sheets of tin-foil separated by sheets of paraffined or shellac- 
 varnished paper. The alternate sheets of tin-foil are joined in 
 parallel; the two groups are connected to the primary circuit on 
 opposite sides of the interrupter. The condenser is generally placed 
 in the base that carries the coil. A simple form of the instrument 
 is shown in Fig. 400. 
 
 (b) The current passes through the commutator, c, up the post, A, 
 through the adjusting screw, d, and across to the spring interrupter, b, 
 which rests against the end of d, and is carried by another post, as 
 shown in Fig. 400. Thence it passes to the primary coil, magnetizing 
 the iron- core, and making its way back to the generator. The iron 
 core thus magnetized attracts the soft iron hammer at the end of the 
 spring, thus breaking the circuit at b. When the current is broken, 
 the core is demagnetized, and the elasticity of the spring throws b 
 against the end of d, again making the circuit. Thus the spring 
 vibrates between the end of the core and the end of the screw, making 
 and breaking the circuit with great rapidity, and inducing currents in 
 the secondary coil. Owing to the permeability of the iron core which 
 intensifies the flux of force through the coils, and to the great number 
 of turns in the wire of the secondary coil, the electromotive force of 
 the induced currents is very high. 
 
 (c) The self-induction of the primary coil when the circuit is made 
 at b develops a counter E.M.F. that opposes the battery current, and 
 thereby lessens the E.M.F. of the induced current. When the circuit 
 
508 SCHOOL PHYSICS. 
 
 is broken, the counter E.M.F. reinforces that of the battery current, so 
 that, for an instant, the latter may be increased by its own interrup- 
 tion. One effect of this is to strengthen the sparks noticeable at b. 
 
 (rf) One effect of the condenser is to make the interruption of the 
 battery current at b more abrupt and, therefore, to increase the E.M.F. 
 of the induced current. Immediately after the interruption of the 
 battery current, the condenser sends a reverse current through the 
 primary coil and battery, thus demagnetizing the core more rapidly, 
 increasing the rate of change in the intensity of the flux through the 
 coils and, in this second way, increasing the E.M.F. of the induced 
 current. Consequently, the E.M.F. of the direct current induced 
 in the secondary coil when the primary circuit is broken is higher 
 than the E.M.F. of the reverse current induced in the secondary coil 
 when the primary circuit is made. 
 
 (e) The length of the spark depends upon the E.M.F. of the induced 
 secondary current. The difference of potential necessary to produce a 
 spark 1 cm. or more in length between parallel plates in air under 
 ordinary barometric conditions is about 30,000 volts per centimeter. 
 For shorter sparks, the difference of potential has a greater value. 
 
 High Potential Phenomena. 
 
 Experiment 373. Connect a voltaic battery with the primary of 
 an induction coil. Bring the terminals of the secondary within a few 
 millimeters of each other, and notice the rapid succession of sparks 
 that strike across the gap filled with air, one of the best of insulators. 
 With a good coil, plates of glass and other non-conductors may be 
 thus perforated. We have not noticed this property of electricity 
 before because we have not had a current of sufficiently high E.M.F. 
 
 Experiment 374. In a shallow tin pan (e.g., a common pie-tin), 
 melt equal quantities of rosin and shellac. Stir the substances to- 
 gether, avoid ignition and the formation of bubbles, and, when the 
 tin is filled, set it aside to cool. Cut a disk of sheet tin a little less in 
 diameter than the resin plate, and fasten a piece of sealing-wax at its 
 center for a handle. Whip the plate briskly with a catskin, or rub it 
 with warm flannel. Place the tin disk upon the resin plate, and touch 
 the former with a finger. Place a number of small bits of paper upon 
 the disk. Lift the disk by its handle ; the charged paper bits are 
 repelled. Bring a knuckle to the edge of the disk ; an electric spark 
 may be seen. Such a discharge in air requires a force of about 130 
 
ELECTRIC GENERATORS, ETC. 
 
 509 
 
 electrostatic units per centimeter of length, although the E.M.F. per 
 unit length is greater for small than for great distances. The disk 
 may be charged many times 
 without repeating the excita- 
 tion of the resinous plate. 
 The apparatus may be im- 
 proved by making the disk 
 of wood, rounding its edge, 
 covering it with tin-foil, and 
 smoothing down the latter 
 with a paper-folder or a finger- 
 nail. 
 
 404. An Electrophorus 
 
 consists of a plate of 
 resinous material or of 
 vulcanite resting on a 
 metallic bed-piece, and 
 a movable metallic cover 
 provided with an insu- 
 lating handle. It is used 
 as illustrated in the preceding experiment. As the sur- 
 face of the resin plate is uneven, the metallic cover touches 
 it at but a few points ; as the material is non-conducting, 
 scarcely any electrification passes from the former to the 
 latter. The two disks and the thin layer of air between 
 them constitute a condenser ( 342). The negatively elec- 
 trified resin plate acts by induction on the disk, holding 
 positive electrification " bound " at its lower surface, and 
 repelling the negative which escapes through the finger. 
 When the plate thus charged is removed from the resin 
 plate, the bound electrification is set free. 
 
 405. Electric Machines for developing statical electrifi- 
 cation in large quantities depend upon either friction or 
 
 FIG. 401. 
 
510 
 
 SCHOOL PHYSICS. 
 
 induction for their operation, and are made in great 
 variety. 
 
 FIG. 402. 
 
 (a) The friction al electric machine usually consists of a plate of 
 glass, A, which is revolved between stationary cushions, Z>, the sur- 
 + faces of which are cov- 
 
 ered with amalgam. 
 The parts of the plate 
 thus positively electri- 
 fied are successively 
 brought between two 
 metallic combs, F, the 
 pointed teeth of which 
 nearly touch the plate. 
 The prime conductor, 
 P, is electrified by in- 
 duction, the negative 
 electrification escaping 
 by air-convection from 
 the pointed teeth to 
 the oppositely electri- 
 fied plate, thus neutral- 
 izing its electrification 
 and leaving the prime 
 conductor positively 
 charged. The negative conductor, N, that carries the cushions is 
 
 FIG. 403. 
 
ELECTRIC GENERATORS, ETC. 
 
 511 
 
 generally connected to earth, as shown in Fig. 402. The potential 
 energy of the electrification thus obtained is the equivalent of the 
 kinetic energy expended in turning the crank, minus that transformed 
 into useless heat. 
 
 (&) The induction machines may almost be described as continuous 
 electrophori. The Wimshurst machine (Fig. 403), which may be taken 
 as a representative of the class, consists for the most part of two equal 
 glass disks that revolve in opposite directions. Sector-shaped strips of 
 tin-foil are fastened to the outer surfaces of the plates, and act as car- 
 riers of electrification and, when opposite each other, as field plates or 
 inductors. Two conductors are placed at right angles to each other, 
 obliquely across the plates, one at the front and the other at the back. 
 The ends of these conductors carry tinsel brushes that lightly touch 
 the sectors as they pass. The discharging circuit is provided with 
 combs that face each plate, and that are connected with small Leyden 
 jars. The distance between the balls of the discharging circuit may 
 be regulated by insulated handles. This machine is almost wholly 
 free from " weather troubles." 
 
 The tin-foil strips or carriers on the rear plate of a Wimshurst 
 machine are represented in Fig. 404 by the outer row of strips ; those 
 on the front plate, by the inner row. The diagonal conductor that 
 faces the rear plate is represented by cd ; the one that faces the front 
 plate, by ab. The strips from 
 which the arrows proceed are 
 charged positively ; the others, 
 negatively. The strips at the 
 top of the rear plate are repre- 
 sented in the diagram as being 
 positively charged; those at 
 the bottom as being nega- 
 tively charged. These condi- 
 tions are reversed for the front 
 plate. The maximum charge 
 upon one of the tin-foil strips 
 or carriers is represented as 
 six units. The opposite mo- 
 tions of the two plates are 
 represented by the two large, 
 
 curved arrows. As the carrier at a moves into the position shown in 
 the diagram, it comes under the inductive influence of the positively 
 
512 SCHOOL PHYSICS. 
 
 charged carrier opposite it on the rear plate. At this instant, it 
 touches the brush of the diagonal conductor, and a transfer of posi- 
 tive electrification from a to b leaves the carrier at a negatively 
 charged. At the same instant and in the same way, the carrier at b 
 is positively charged. Similar effects are also produced in the carriers 
 at c and d. Thus, the carriers of both plates come to m and n, the 
 combs of the discharging circuit, similarly charged, positively at n, 
 and negatively at m. The inductive action of these carriers upon the 
 discharging circuit electrifies its two sides oppositely. 
 
 (c) The phenomena of static electricity that may be exhibited with 
 a machine like that just described are very beautiful, and their study 
 is very enticing. Some of them were known to man before the dawn 
 of authentic history. Static electricity opens a field for deep study 
 that has been of great value in theoretical research, and is now full of 
 promise, but the greater and rapidly growing industrial importance of 
 current electricity, and the necessary limitations of a work like this, 
 compel the author to refer the pupil to other texts for a fuller discus- 
 sion of the subject than he can give here. He does so with a feeling 
 of sadness that utility should thus dominate beauty. 
 
 High Voltage Currents. 
 
 Experiment 375. AVind several turns of wire upon a piece of glass 
 tubing inside of which is an unmagnetized sewing-needle. Discharge 
 a Ley den jar through the wire, and test the needle to see if it has been 
 magnetized. 
 
 Experiment 376. Wind ten or more turns of insulated wire, No. 
 
 22, on the outside of a 
 thin glass tumbler, being 
 careful that the turns 
 do not touch each other. 
 A coating of shellac var- 
 nish will help to hold the 
 wire in place. Wind a 
 smaller coil of ten or 
 twelve turns of similar 
 wire, bringing one end of 
 the wire up through the 
 coil, and being careful 
 FIG. 405. that it does not touch any 
 
ELECTRIC GENERATORS, ETC. 513 
 
 of the convolutions. Tip the two ends of this wire with bullets, and 
 adjust them so that they will be within about 1 cm. of each other. 
 Place the second coil in the tumbler, as shown in Fig 405, and fill the 
 tumbler with high grade kerosene. Connect n, the lower end of the 
 outer wire, with the tin pan of the electrophorus. Charge the disk 
 of the electrophorus, and discharge it through TO, the upper end of the 
 outer coil. Notice the spark between the terminals of the inner coil. 
 Support an iron rod inside the inner coil, being careful that it does 
 not touch the wire. Repeat the experiment, and notice that the 
 " striking distance " between the terminals of the inner coil may be 
 increased. 
 
 Experiment 377. Connect one terminal of the outer coil of the 
 apparatus used in Experiment 376 to a terminal of the secondary of 
 an induction coil. Set the latter in operation, and discharge the other 
 terminal of its secondary into the other terminal of the outer coil of 
 the tumbler. Notice the series of sparks between the terminals of the 
 inner coil of the tumbler, and that the sparks there keep step with 
 those of the induction coil. 
 
 406. Identity. The experiments just given indicate 
 the remarkable similarity between current electricity at 
 high voltage, and static electricity. Each can overcome 
 the enormous resistance of an insulator like the air, and 
 each lends itself to electromagnetic induction in the same 
 way. Many facts tend inevitably to the conclusion that 
 the two kinds of electricity are identical. 
 
 Nature of Electric Discharge. 
 
 Experiment 378. Let another pupil push a pin through a visiting 
 card. Examine the card, and try to tell from which side of the card 
 the perforation was made. Perforate the card by the spark of an 
 induction coil, examine it carefully, and try to tell from which side 
 the perforation was made. Similarly examine the perforations 
 made in a card by the discharges of an electric machine, and of a 
 Ley den jar. What do you infer from your comparison of the per- 
 forations ? 
 
 33 
 
514 
 
 SCHOOL PHYSICS. 
 
 Experiment 379. Wind two or three layers of paper upon MN 
 (Fig. 406), a bar of soft iron, and about fifty turns of No. 22 insulated 
 copper wire upon the paper. Twist loops in the wire at A and B. Tip 
 the ends of the wire with bullets, and bring them very near each other, 
 as at C. Ground the wire at B, i.e., put it into electrical connection 
 
 with the earth, and discharge 
 the electrophorus or a Leyden 
 jar into the loop at A . Notice 
 the sparks at C. 
 
 Experiment 380. Straight- 
 en the wire of Experiment 
 
 ooooooooooooc; c i 
 
 FIG. 407. 
 
 379, and bend it into a long 
 FlG 406 loop returning on itself as in 
 
 Fig. 407. Adjust the knob 
 
 terminals at c for the same distance as in Experiment 379. 
 Ground b, and discharge the electrophorus or Leyden jar into a, as 
 before. You will find great difficulty in getting a spark at c, and may 
 not be able to do so at all. 
 
 407. Oscillatory Discharge. The sparks between the 
 knobs, as observed in Experiment 379, show that, for 
 some reason, the electricity preferred the path through 
 the air at (7, with a resistance of millions of ohms, to the 
 path through the wire coiled upon MN, with a resistance 
 of only a small part of an ohm. If the flow of electricity 
 from a point of high to one of low potential was of the 
 nature of a direct current, it would have followed Ohm's 
 law, and passed in the greatest quantity through the path 
 of least resistance. The formula applicable in such a case, 
 
ELECTRIC GENERATORS, ETC. 515 
 
 offers no possible explanation of the phenomenon ob- 
 served. 
 
 On the other hand, if the flow was like that of an alter- 
 nating current, it would be governed by the law that is 
 expressed thus : - 
 
 0= 
 
 The fact that in Experiment 380, the electricity flowed 
 through the wire of IOAV resistance instead of forcing its 
 way through the enormous resistance of the air as it did 
 in Experiment 379, suggests that the impedance of the 
 circuit coiled around the iron was the cause of the appar- 
 ently paradoxical choice of path, for, when we got rid of 
 that impedance, the choice was what we should have 
 expected. If this hypothesis is correct, the impedance must 
 have been very great. Studying the mathematical expres- 
 sion for impedance, as given above, 
 
 we notice that the value of R (the resistance of the wire) 
 is too small to account for much of the great magnitude. 
 The rest of the expression is the square of the reactance. 
 Studying the values therein involved, we find that n is 
 the only factor that can be great enough to account for 
 the magnitude assumed for the impedance. This factor 
 represents the frequency of -alternation, and its magnitude 
 must be measured by hundreds of thousands in order that 
 the impedance may be sufficiently great to force the flow 
 through the enormous resistance of the insulating air as 
 was done in Experiment 379. 
 
 Recent investigations have done much to sustain con- 
 
516 SCHOOL PHYSICS. 
 
 elusions like those now indicated, and to justify the state- 
 ment that in an electric discharge the flow surges back and 
 forth thousands of times in the brief interval measured by 
 the duration of the spark. This oscillatory movement is a 
 basis of important investigations now in progress, and maps 
 out the line by which static electricity may become a thing 
 of practical utility as well as of phenomenal beauty. 
 
 408. Atmospheric Electricity. The surface of the earth 
 is electrified. The electrification is generally negative but, 
 in time of rain, it may become locally positive. Moreover, 
 the electrical density varies greatly at different times and 
 places. The origin of the earth's electrification is not 
 known with certainty, but it " is influenced very largely, 
 as it would seem, by external matter somewhere ; probably 
 at a distance of not many radii from its surface." 
 
 409. The Electrical Function of Clouds seems to be to 
 collect and to concentrate the diffused electrification of the 
 atmosphere. Suppose a thousand spherical watery parti- 
 cles, each having a unit charge, to coalesce to form a water- 
 drop. The diameter of this drop will be ten times that of 
 a single particle, its capacity will be ten times as great, 
 but its charge will be a thousand times as great; in other 
 words, its potential will be increased a hundred-fold. 
 The condensation and aggregation of charged vapor parti- 
 cles must result in the production of a very high potential. 
 
 410. A Lightning Flash is simply a disruptive discharge 
 between two surfaces oppositely and highly electrified. 
 The discharge may be from cloud to cloud, or from cloud 
 to earth. The charged surfaces and the intervening air 
 are analogous to a huge Ley den jar. Like the discharge 
 
ELECTRIC GENERATORS, ETC. 517 
 
 of the jar, the lightning flash is oscillatory. A lightning 
 flash a kilometer long corresponds to a difference of 
 potential of about thirteen million electrostatic units. 
 
 (a) The sound that follows a lightning flash constitutes thunder. 
 The sudden expansion and compression of the heated air along the 
 line of discharge is followed by a violent rush of air into the partial 
 vacuum produced. When the observer is about equally distant from 
 the two surfaces between which the discharge takes place, a short and 
 sharp thunderclap is heard ; when one end of the path of discharge is 
 considerably further from the observer than the other, so that there 
 is a perceptible difference in the time that the sound requires to reach 
 the ear from the different parts of the path, there is a prolonged roll 
 or rattle. Sometimes near-by hills and clouds reflect the sound so as 
 to produce a continuous or rumbling roar. One-fifth the number of 
 seconds that intervene between seeing the flash and hearing the roar 
 approximately indicates the number of miles that the observer is from 
 the discharge. 
 
 (ft) The induced charge on the earth tends to accumulate on build- 
 ings, trees, and other elevated objects, thus reducing the thickness of 
 the dielectric, intensifying the attraction between the opposite elec- 
 trifications, and increasing the liability of such elevated bodies. Sta- 
 tistical studies seem to show a minimum liability to accident from 
 lightning stroke in thickly settled communities, and that the danger 
 in the country is five times as great as that in the city. Such studies 
 have also shown that there is no foundation for the popular notion 
 that "lightning never strikes twice in the same place" except the 
 fact that lightning often leaves nothing to be struck a second time. 
 At the same time, it is well to remember that "Heaven has more 
 thunders to alarm than thunderbolts to punish," and that one who 
 lives to see the lightning flash need not concern himself much about 
 any personal injury from that flash. 
 
 Experiment 381. Twist together two wires, one of iron and one 
 of German-silver, and attach their free ends to the terminals of a 
 galvanoscope. Heat the junction of the two wires. The deflection 
 of the needle indicates that un electric current was generated. Cool 
 the junction of the dissimilar metals with ice. The opposite deflection 
 of the needle shows that the current now generated flows in a direc- 
 tion that is the reverse of the first. 
 
518 
 
 SCHOOL PHYSICS. 
 
 411. Thermo-electric Pile. Two dissimilar metals joined 
 and used like those of Experiment 
 381, constitute a thermo-electric 
 pair. Antimony and bismuth 
 are the metals generally used for 
 the purpose. Many such pairs 
 connected in series and having 
 their ends exposed constitute a 
 thermo-electric pile. Such a pile 
 with conical reflectors is repre- 
 sented in Fig. 408. When its 
 terminals are connected to the 
 terminals of a delicate galvano- 
 scope, the combination consti- 
 tutes a thermoscope of great sensitiveness. 
 
 CLASSROOM EXERCISES. 
 
 1. (a) How is impedance measured? (6) How is the coefficient of 
 self-induction measured? (c) Upon what does the latter depend? 
 
 2. Show, by the formula for impedance, that the static discharge is 
 of a rapidly alternating nature. 
 
 3. Explain self-induction. How does it interfere with the flow of 
 an alternate current? 
 
 4. (a) Define reluctance, and write the mathematical expression 
 therefor. (b) Show geometrically the relation between reactance, 
 impedance and resistance. 
 
 5. Sketch the connections of the induction coil. Explain the action 
 of the automatic current interrupter. 
 
 6. Describe the electrophorus, and explain its action. 
 
 FIG. 408. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. A gold-leaf electroscope in which the 
 knob shown in Fig. 315 is replaced by a metal disk about 15 or. 20 cm. 
 in diameter; 50 small glass tumblers; sheet zinc; sheet copper; tin 
 plate; Geissler tube ; an incandescence electric lamp ; rosin or pitch. 
 
ELECTRIC GENERATORS, ETC. 519 
 
 1. Place 50 small glass tumblers in a circle. Into each tumbler, 
 put a small strip of clean zinc, and a similar strip of copper. Nearly 
 fill each tumbler with water, and connect the battery in series. Solder 
 a thin copper wire about 50 cm. long to the zinc plate at the end of 
 the series, and a similar wire to the copper plate at the other end of 
 the series. Lay a 'sheet of thin paper that has been well soaked in 
 melted paraffine upon the disk of a gold-leaf electroscope. Place an 
 electrophorus cover upon the paraffined paper, thus making a con- 
 densing electroscope. Bring one of the battery terminals into contact 
 with the disk of the electroscope, and the other terminal into contact 
 with the disk of the electrophorus. Remove the wires, and lift the 
 electrophorus cover and the paper from the disk, thus reducing the 
 capacity of the lower disk and raising its potential. If you notice 
 any evidence of an electric charge on the leaves of the electroscope, 
 determine whether that charge is positive or negative. 
 
 2. Substitute dilute sulphuric acid for the water that was used as 
 the exciting fluid in the "crown of cups " of Exercise 1, and complete 
 the circuit through a resistance of several hundred ohms. By a wire, 
 connect a point in this circuit near the terminal zinc with the disk of 
 the electroscope, arranged as in Exercise 1. Similarly, connect a 
 point in this circuit near the terminal copper with the electrophorus 
 cover. Try to charge the electroscope as in Exercise 1. If you suc- 
 ceed, test the character of the charge, and record your conclusions as 
 to a permanent difference of potential at different points in the'circuit 
 of a voltaic battery. 
 
 3. Attach a Geissler tube to the secondary terminals of an induc- 
 tion coil. Put the coil in operation, and notice the discharge through 
 the tube, and the difference from its discharge through air. Measure 
 the maximum length of the spark obtainable with the coil, and com- 
 pare it with the length of the longest discharge that you can get 
 through a Geissler tube. 
 
 Present a magnet pole to the Geissler tube, and notice the deflection 
 of the discharge. Re- 
 verse the polarity of 
 the primary of the in- 
 duction coil. Xotice 
 
 that the discharge is FlG 409 
 
 now deflected in an 
 
 opposite direction. Does this throw any light on the question 
 whether the alternating pulses of the induction coil are of equal 
 
520 
 
 SCHOOL PHYSICS. 
 
 strength or not? Study the discharge through the tube with refer- 
 ence to the different appearances of the two ends of the tube. Reverse 
 the coil, and notice the corresponding reversal in the positions of the 
 violet tint and the scintillations. On reversing the coil, the lights 
 in the tube reverse. If the tube was excited by a true alternate cur- 
 rent, would such differences be noted ? 
 
 4. Suspend a tin plate about 10 cm. square from each binding post 
 
 of the secondary of a strong 
 induction coil, as shown in 
 Fig. 410. Let the plates 
 hang parallel to each other 
 and about 8 cm. apart. 
 Start the coil. Darken the 
 room, and hold a small Geiss- 
 ler tube in the electrostatic 
 field of force between the 
 plates, with the ends of the 
 tube near but not touching 
 FIG. 410. them. The tube glows 
 
 brightly. Touch the plates 
 
 with the ends of the tube. Notice the increased brightness. Quickly 
 lay the tube in a dark corner, and notice the after-glow. 
 
 5. Grasp a 110-volt incandescence lamp firmly in the hand, keep- 
 ing the fingers away from the brass cap. Let some one else charge the 
 lamp with an electrophorous. Discharge the lamp by touching the 
 brass cap, keeping an eye on the filament. When the discharge takes 
 place, the filament swings around the bulb as if it were sweeping off 
 the charge from the surface of the glass and delivering it to the cap. 
 As there is danger of breaking the filament, it is well to use an old 
 lamp. Repeat the experiment in the dark, and notice the brilliant 
 glow of the lamp when discharging. 
 
 6. Paste strips of tin-foil on a microscope slide as shown in Fig. 
 411. Discharge the induction coil through these strips, and view the 
 spark through the microscope with a 
 
 f-inch or a 1-inch objective. Notice 
 the general resemblance of the dis- 
 charge to the discharge in a vacuum. 
 Note the purple vaporous negative pole, 
 and the scintillating positive pole, as shown in Fig. 412. Bring the 
 pointed ends of the tin-foil strips on the slide as near together as you 
 
 FIG. 411. 
 
ELECTRIC GENERATORS, ETC. 
 
 521 
 
 can without contact. Focus the microscope well, using a i-inch or 
 a i-inch objective. Be careful that the discharge does not enter the 
 end of the objective instead of leaping the gap between the strips, 
 a possible circumstance that would not injure you as much as it 
 
 FIG. 412. 
 
 would your experiment. Watch the points through the microscope, 
 turn on the current, and notice that the negative pole is rapidly eaten 
 away. Quickly reverse the connections of the primary switch, and 
 notice that what was the positive pole is now eaten away. 
 
 7. Connect the outside coating of a Leyden jar by a wire to one of 
 the terminals of an induction coil. Bring the knob of the jar near the 
 other terminal of the coil and allow sparks to pass between them for 
 a minute. Remove the jar, and connect its two coatings with the 
 fingers. A smart shock shows that the jar is charged. Bring the 
 knob of the jar into contact with the free terminal of the coil instead 
 of allowing the discharge to spark across. It will be found impossible 
 thus to charge the jar. Why? 
 
 8. Support two metal balls, a and b (Fig. 413), between the terminals 
 of an induction coil, put the coil in operation, and determine the limit- 
 ing length of the discharge between the balls. Then connect a Leyden 
 
522 SCHOOL PHYSICS. 
 
 jar to the terminals, as shown in Fig. 413. Start the coil again, and 
 
 notice that the spark will 
 not strike across so long a 
 gap, but that it is a much 
 Hotter, " fatter " spark. Open 
 the circuit at x, and insert 
 the oil transformer of Exper- 
 iment 376. It will be found 
 to work in a satisfactory 
 FlG - 413 - manner. 
 
 9. Devise a suitable experiment to determine whether the flame of 
 a carbonaceous substance, e.g., rosin or pitch, or dry air is the better 
 conductor for the high potential discharge between the terminals of 
 the secondary of an induction coil. Describe the experiment in 
 detail. To what conclusion does your experiment lead you? 
 
 10. On a thin hard rubber or glass tube 10 cm. long, wind evenly a 
 layer of No. 16 insulated copper wire. Insulate it thoroughly, and 
 wind on a secondary coil of ten layers of No. 30 insulated copper wire. 
 Place the ends of the secondary wire above and below the tongue, or 
 connect them to the terminals of a telephone receiver. Pass a battery 
 current through the primary coil. On making and breaking the pri- 
 mary circuit, electric pulses are detected in the secondary circuit. 
 Place an iron core in the tube. The pulses are much increased in 
 intensity. Why? Slip a brass tube over the iron core, place it in 
 the rubber tube, and repeat the experiment. The pulses are now of 
 the same intensity that they were before the core was inserted. Slit 
 the brass tube along its length, and repeat the experiment. The 
 pulses are now as strong as they were before the tube was used. 
 Remember that the induced current acts in direct opposition to the 
 lines of force inducing it, and tends to neutralize them. Such an 
 induced current flows through the brass tube which corresponds to 
 a closed secondary coil, absorbing energy, and tending, to neutralize 
 the magnetic effect of the primary current. 
 
ELECTRICAL MEASUREMENTS. 
 
 523 
 
 III. ELECTRICAL MEASUREMENTS. 
 
 412. Electrostatic Units necessarily relate to quantity, 
 potential difference, and capacity ; they have already been 
 denned. Since 
 
 Quantity = capacity x difference of potential, 
 any one may be calculated when the other two are known. 
 
 (a) For practical convenience, certain multiples and submultiples 
 of these absolute C.G.S. units are in common use among electricians. 
 Their names, and their values in absolute electrostatic units are as 
 follows : 
 
 Denomination. 
 
 Quantity 
 
 Potential difference 
 
 Capacity 
 
 Current 
 
 Resistance 
 
 Work (volt-coulomb) 
 
 Activity (volt-ampere) 
 
 Practical Units. 
 
 Name. 
 
 Coulomb 
 
 Volt 
 
 Farad 
 
 Ampere 
 
 Ohm 
 
 Joule 
 
 Watt 
 
 Value. 
 3 x 10 9 
 x 10- 2 
 9 x 1C 11 
 3x 10 9 
 | x ID-" 
 10 7 ergs 
 10 7 ergs per second 
 
 (6) Various methods have been devised for measuring electrostatic 
 quantity, one of the simplest of which is with the Kinnersley electrical 
 air-thermometer, shown in Fig. 414. When a spark passes 
 between the balls within the larger tube, the confined air 
 is expanded, and the liquid column in the smaller com- 
 municating tube rises, and thus approximately indicates 
 the quantity of the charge. 
 
 (c) Instruments for measuring differences of potential by 
 electrostatic action are called electrometers. The gold-leaf 
 electroscope is an electrometer when it is used to indicate 
 equality of potential by equality of divergence of the leaves ; 
 or in that of two bodies dissimilarly electrified by bringing 
 them into contact, and observing zero divergence. One of 
 the best-known instruments of this class is Coulomb's torsion- 
 balance, which consists essentially of a gilt ball, i, carried at the end 
 
 FIG. 414. 
 
524 
 
 SCHOOL PHYSICS. 
 
 of a horizontal shellac needle that is suspended by a fine silver wire 
 from the top of a tube that rises from 
 the cover of the enclosing glass cylinder. 
 A vertical insulating rod passing through 
 the cover carries a handle, a, and a gilt 
 ball, e, at its ends. The tube is turned 
 until i just touches e. When the ball, e, 
 is electrified, it repels i through a certain 
 angle. This angle of deflection is ap- 
 proximately proportional to the force of 
 repulsion, and the force is proportional 
 to the amount of electrification. As the 
 capacity of the ball is constant, the 
 charge that it receives must vary as 
 the potential of the body by which it 
 
 was charged. 
 FIG. 415. 
 
 413. Electromagnetic Units constitute a system based on 
 the electromagnetic actions of the current. The C.G.S. 
 electromagnetic unit of quantity is the quantity which, 
 flowing per second through a circular arc a centimeter in 
 length and a centimeter in radius, exerts a force of a dyne 
 on a unit magnetic pole at the center. The C.G.S. elec- 
 tromagnetic unit of quantity has a value 3 x 10 10 times as 
 great as the corresponding electrostatic unit, a ratio that 
 represents the velocity of light. 
 
 (a) This ratio or its square applies to the other units, so that, for 
 the practical units, we have the following values in absolute electro- 
 magnetic units : 
 
 Coulomb 
 
 Volt 
 
 Farad 
 
 10- 1 
 10 8 
 
 io- 9 
 
 Ampere 
 Ohm 
 
 io- 1 
 
 IO 9 
 
 (6) The wonderful advance made in the last few years by electrical 
 science is largely due to the adoption of' definite electrical units, and 
 the general practice of making exact electrical measurements. 
 
ELECTRICAL MEASUREMENTS. 
 
 525 
 
 414. The Galvanometer is an instrument for determining 
 the strength of an electric current by means of the deflection 
 of a magnetic needle around which the current flows. 
 When a galvanoscope is provided with a scale so that the 
 deflections of its needle may be measured, it becomes a 
 galvanometer. 
 
 (a) The astatic, galvanometer consists of an astatic needle supported 
 by an untwisted liber so that one of its needles 
 is nearly in the center of the coil through 
 which the current passes while the other 
 needle is just above the coil. When the deflec- 
 tions of the needle are less than 10 or 15, they 
 are very nearly proportional to the strengths of the 
 currents that produce them. A current that de- 
 flects the needle 6 is about three times as 
 strong as one that deflects it 2. 
 
 (6) The tangent galvanometer consists of a 
 very short magnetic needle suspended so as 
 to turn in a horizontal plane, and with its 
 point of support at the center of a vertical 
 
 hoop or 
 
 FIG. 416. 
 
 FIG. 417. 
 
 coil of copper wire 
 through which the current is 
 passed. The diameter of the 
 hoop or coil is not less than 
 ten times the length of -the 
 needle. Owing to the short- 
 ness of the needle, pointers of 
 aluminium or of glass fiber are 
 generally cemented across it at 
 right angles, as shown in Fig. 
 417. In use, the hoop is placed 
 in the plane of the magnetic 
 meridian, the current that is 
 to be measured is sent through 
 the hoop, and the deflection of 
 the needle is read from the 
 scale. The strength of the cur- 
 rent is proportional to the tangent 
 
526 SCHOOL PHYSICS. 
 
 of the angle of deflection. For example, suppose that a certain cur- 
 rent gives a deflection of 15, and that another current gives a deflec- 
 tion of 30. The amperes are not in the ratio of 15 : 30 but in the 
 ratio of tan 15 : tan 30. The values of such tangents may be 
 obtained from a table of natural tangents. If a current of known 
 strength, C, gives a deflection of m degrees, and another of unknown 
 strength, x, gives a deflection of n degrees, the value of x may be 
 found from the proportion, 
 
 C : x : : tan m : tan n. 
 
 A table of natural tangents is given in the appendix. 
 
 (c) Any sensitive galvanometer, the needle of which is directed by 
 the earth's magnetism, and in which the frame on which the coils are 
 wound is capable of being turned round a vertical axis, may be used 
 as a sine galvanometer. The coils are set parallel to the needle 
 (i.e., in the magnetic meridian). The current is then sent through 
 the coils, deflecting the needle. The coil is then turned until it over- 
 takes the needle, which once more lies parallel to the coil. Two forces 
 are now acting on the needle and balancing each other, viz., the 
 directive force of the earth's magnetism, and the deflecting force of 
 the current flowing through the coil. At this moment, the strength of 
 the current is proportional to the sine of the angle through which the coil 
 has been turned. The values of the sines may be obtained from a 
 table of natural sines. Such a table is given in the appendix. 
 
 (d) The mirror galvanometer (Fig. 391) has a very short needle 
 rigidly attached to a small concave mirror that is suspended by a 
 delicate fiber in the center of a vertical coil of small diameter. A 
 curved magnet, carried on a vertical support above the coil, serves to 
 counteract the earth's magnetism, and to bring the needle into the 
 plane of the coil when the latter does not coincide with the magnetic 
 meridian, or to direct it within the coil. A beam of light from a 
 lamp passes through a small opening under a millimeter scale about a 
 meter from the mirror, falls upon the mirror, and is reflected back 
 upon the scale. The curved magnet enables the operator to bring the 
 spot of refle6ted light to the zero mark at the middle of the scale. A 
 current passing through the coil turns the needle and its mirror, thus 
 shifting the spot of light to the right or left of the zero point. The 
 current through the galvanometer may be reduced by shunt to any 
 desirable extent, thus extending the serviceable range of the instru- 
 ment. The apparatus was devised by Sir William Thomson, now 
 
ELECTRICAL MEASUREMENTS. 527 
 
 Lord Kelvin, for use in connection with the Atlantic cablo, and is 
 exceedingly sensitive. The current produced by dipping the point of 
 a brass pin and the point of a steel needle into a drop of salt water, 
 and closing the external circuit through this instrument sends the 
 spot of light swinging way across the scale. 
 
 (e) In the Deprez-d'Arsonval dead-beat reflecting galvanometer, a 
 movable coil is suspended between the poles of a strong, permanent 
 U-magnet that is fixed. The coil consists 
 of many turns of fine wire the terminals of 
 which above and below serve as the sup- 
 porting axis. Within the coil is an iron 
 tube that is supported from the back, and 
 that serves to concentrate the magnetic 
 field. The passage of a current turns the 
 coil, and sets it so that its plane encloses 
 a larger number of lines of force. This 
 movement of the coil turns the mirror by 
 means of which the angles of deflection are 
 
 read with a telescope and scale. When the 
 
 , ., , ,, . FIG. 418. 
 
 galvanometer is short circuited, the oscilla- 
 tions of the coil induce currents that quickly bring it to rest. It is 
 simple in construction, and almost wholly independent of the mag- 
 netic field surrounding it. 
 
 (/) In the differential galvanometer, the coil is made of two sepa- 
 rate wires wound side by side. If two equal currents are sent through 
 these wires in opposite directions, the needle will not be deflected. If 
 the currents are unequal, the needle will be deflected by the stronger 
 one with a force corresponding to the difference of the strengths of 
 the two currents. It is much used in null methods of measurement. 
 
 (</) The ballistic galvanometer is provided with a heavy needle that 
 has a slow rate of oscillation, and that k strongly magnetized and 
 placed in a strong directing field. It is used for measuring currents 
 that are variable in the time of measurement, and in measuring 
 condenser capacity. The discharge causes the needle to give a sudden 
 kick. The quantity of electrification discharged and the capacity of the 
 condenser are respectively proportional to the sine of half the angle of 
 deflection of the needle. 
 
 (h) A galvanometer of low resistance, empirically calibrated, i.e., 
 graduated for the direct measurement of electric currents and giving 
 its readings in amperes, is called an ammeter, or ampere-meter. Any 
 
528 
 
 SCHOOL PHYSICS. 
 
 FIG. 419. 
 
 galvanometer that is wound with wire of sufficient size safely to carry 
 
 the current to be measured, 
 and properly calibrated, 
 may be used as an amme- 
 ter. Fig. 419 shows one of 
 the common forms in prac- 
 tical use. 
 
 (i) An electrodynamom- 
 eter is a galvanometer with 
 two coils, at least one of 
 which is movable, and 
 through at least one of 
 which the current to be 
 measured passes. It is very 
 useful in the measurement 
 of alternating currents and voltages. Fig. 420 shows a form of the 
 instrument that is much used in practice. The torque of the movable 
 coil is resisted by a spiral 
 spring. The deflection caused 
 by the current is indicated on 
 a properly graduated dial, and 
 from such indications the cur- 
 rent or voltage is computed. 
 Such an instrument calibrated 
 for direct currents measures 
 the square root of mean square 
 values of alternating currents. 
 (/) If a galvanometer is 
 put in shunt circuit between 
 two points of different poten- 
 tials, current will pass through 
 it, and the current thus pass- 
 ing may be used to measure 
 the difference of potential. A 
 galvanometer of high resist- 
 ance, calibrated so as to indi- 
 cate in volts the difference of p IG 420 
 potential between its termi- 
 nals, is called a volt-meter. The resistance must be high so as to reduce 
 the shunted current, for, if the shunted current is large, the difference 
 
ELECTRICAL MEASUREMENTS. 
 
 529 
 
 of potential between the terminals will be lowered, a change of the 
 very function that is to be measured. In general, a volt-meter is a 
 galvanometer properly calibrated, and wound so as to have a resist- 
 ance of from 5,000 to 50,000 ohms. 
 
 (fc) If the movable coil of an electrodynamometer is made of very 
 fine wire suitable for voltage measurement, and the stationary coil of 
 coarse wire suitable for current measurement, and the high-resistance 
 coil is put in parallel with the main circuit, and the low-resistance 
 coil is put in series, the apparatus may be used to measure, in watts, 
 the rate of working, or the electrical activity of the current. Such a 
 device is called a wattmeter. 
 
 (/) Electric current being a merchantable commodity, it is often 
 desirable to measure both the rate at which the electrical energy is 
 delivered and the time that it 
 is delivered, i.e., the number 
 of watt-hours. This is accom- 
 plished by a modification of 
 the wattmeter. The current 
 swings an armature coil with 
 complete revolutions in the 
 field of a stationary coil. 
 These revolutions are counted 
 by a registering apparatus that 
 gives direct readings in watt- 
 hours. The tendency of the 
 armature to turn is directly 
 proportional to the current. 
 The rotary motion of the ar- 
 mature is retarded by a copper FIG. 421. 
 disk that revolves between 
 
 magnet poles as shown in Fig. 421. The motion of the disk-conductor 
 in the magnetic field develops in the disk eddy or local currents that 
 produce the required drag or brake on the revolving armature. 
 
 (TO) The resistance of a galvanometer should correspond to that 
 of the rest of the circuit ; i.e., a high resistance galvanometer should 
 be used on a high resistance circuit, and vice versa. 
 
 415. Resistance Coils are made of wires of known resist- 
 ance for use with galvanometers in measuring resistances. 
 34 
 
530 
 
 SCHOOL PHYSICS. 
 
 FIG. 422. 
 
 Insulated and doubled wires are wound upon spools, and the 
 
 terminals of each spool con- 
 nected to heavy brass blocks, 
 A) B, C, etc., on the top of the 
 box that carries the spools. 
 This style of winding destroys 
 the magnetic effects, and re- 
 duces the self-induction of the 
 coils. When the brass plugs 
 are inserted, as shown in Fig. 422, the coils are short- 
 circuited, i.e., practically, the whole of a current passing 
 from block to block 
 goes through the 
 plug, but when a 
 plug is withdrawn 
 the current passes 
 through the corre- 
 sponding coil. Such 
 coils with resist- 
 ances of 1, 2, 2, 5, 
 10, 10, 20, 50, 100, 100, 200, 500 ohms, etc., severally are 
 connected to form a resistance-box as shown in Fig. 423. 
 By withdrawing the proper plugs, one may throw into 
 the circuit any resistance desired, from a single ohm up 
 to the full capacity of the box. 
 
 (a) Formerly, German-silver wire was generally used for resistance 
 coils because its resistance is high and little influenced by temperature. 
 "Platinoid" wire, an alloy of German-silver and tungsten, is now 
 generally used for this purpose, as it is much harder, has a much 
 higher specific resistance, and a lower temperature coefficient, and is 
 not expensive. 
 
 FIG. 423. 
 
ELECTRICAL MEASUREMENTS. 
 
 531 
 
 416. The Measurement of Resistance is done in several 
 ways according to the nature and magnitude of the resist- 
 ance. Much use is made of the following important 
 principle : The fall of potential betiveen two points on a 
 conductor is proportional to the resistance of the conductor 
 between those points. 
 
 () In Experiment 305, we observed a certain deflection of the 
 galvanoscope with a wire of unknown resistance in the circuit. By 
 removing such an unknown resistance, and inserting known resist- 
 ances until the same deflection of the same galvanoscope with the 
 same cell is obtained, we may determine the resistance of the wire 
 first used. This method is called resistance measurement by substitu- 
 tion. Its chief defect arises from the variation in the power of the 
 cell. 
 
 (&) The method explained above may be used with any galvanom- 
 eter of sufficient sensitiveness, but 
 with a tangent galvanometer, the proc- 
 ess may be shortened. Suppose the 
 tangent galvanometer and an un- 
 known resistance, R, to be included 
 in the circuit, as in Fig. 424, and that 
 the deflection is a degrees. Substitute 
 for R any known resistance, r, which 
 gives a deflection of b degrees. Since 
 the strengths of the currents are proportional to tan a and tan b 
 respectively, the resistance, R, may be calculated by the inverse pro- 
 portion : 
 
 tan a : tan b : : r: R. 
 
 (c) Another method is to divide the circuit into two branches so 
 that a part of the current flows through the given resistance and round 
 one set of coils of a differential galvanometer, the other part of the 
 current bejng made to flow through known resistances and then round 
 the other set of coils in the opposing direction. When we have 
 matched the unknown resistance by an equal known resistance, the 
 currents in the two branches will be equal, and the needle of the 
 differential galvanometer will show no deflection. With an accurate 
 instrument, this method is very reliable. When the instrument is not 
 
 Fm. 42 
 
532 
 
 SCHOOL PHYSICS. 
 
 known to be accurate, a better way is to balance the given resistance 
 with other resistances, known or unknown. Then substitute known 
 resistances for the given resistance until the deflection of the galva- 
 nometer again is nil. Compare 132 (&), 
 
 (cT) The method that has the most general application is that known 
 as the Wheatstone bridge. In Fig. 425, we have a quadrangle of 
 
 FIG. 425. 
 
 resistances. The four conductors, m, n, p, and x, that form the sides 
 are called the "arms;" the conductor that joins C and D and carries 
 the galvanometer, G, is called the "bridge." The current divides 
 at A y and reunites at B. The fall of potential through n and x is 
 evidently the same as the fall through m and p. The resistances of 
 the arms may be so adjusted that, when the bridge-circuit is closed 
 at K, there will be no deflection of the needle of G. Under such cir- 
 cumstances, C and D are at the same potential, and it may be shown 
 that the resistances of the four arms " balance " by being in propor- 
 tion, thus : 
 
 m : n : : p : x. 
 
 When three of these resistances are known, the other one may be cal- 
 culated, or if the ratio of m : n, and the value of p are known, the 
 
ELECTRICAL MEASUREMENTS. 
 
 533 
 
 value of x may also be determined. Under the conditions described, 
 it is also true that m : p : : n : x. 
 
 The practical working of this method may be illustrated as fol- 
 lows : Suppose that x is the resistance to be determined. The other 
 three arms are built up from the coils of a standard resistance-box. 
 The arms, m and n, are called the " balance-arms," and are so cut into 
 the circuit by the removal of plugs that the ratio between their resist- 
 ances is decimal, as 10 or 100, thus simplifying the solution of the 
 proportion. To illustrate, suppose that the resistance of m is 10 ohms ; 
 that of n, 100 ohms ; and that of jo, 15 ohms, as represented by Fig. 
 
 FIG. 426. 
 
 426. Then the resistance of a; is 150 ohms. If the resistance of n is 
 10 ohms ; that of /, 100 ohms, and that of p, 464 ohms, the resistance 
 of x is 46.4 ohms. In using the bridge, the battery circuit should 
 always be made by depressing the key, , before K. the key of the 
 galvanometer branch, is depressed. This avoids the sudden "throw" 
 of the galvanometer needle, in consequence of self-induction, when 
 the circuit is closed. 
 
 417. The Measurement of Internal Resistance. The 
 best way of determining the internal resistance of a vol- 
 taic cell is to join two similar cells in opposition to one 
 another, so that they send no current of their own. Then 
 
534 SCHOOL PHYSICS. 
 
 measure their united resistance (as if it were the resist- 
 ance of a wire) as just described. The resistance of one 
 cell will be half that of the two. 
 
 418. The Measurement of E.M.F., or of difference of 
 potential, is generally made with a volt-meter, or by 
 comparison with the E.M.F. of a standard cell. 
 
 (a) Represent the known E.M.F. of a Daniell cell by E, and that 
 of the given cell or battery by x. Connect the given cell to the gal- 
 vanometer, and note the number of degrees of deflection that it pro- 
 duces. Represent this deflection by a. Then add enough resistance, 
 R, to bring the deflection down to b degrees (e.g., 10 degrees less 
 than before). Then substitute the Daniell for the given cell in the 
 circuit, and adjust the resistances of the circuit until the galvanometer 
 shows a deflection of a degrees, as at first. Add enough resistance, r, 
 to bring the deflection down to b degrees as before. E, R and r being 
 known, x may be found from the proportion, 
 
 r:R::E:x, 
 
 because the resistances that produce an equal reduction of current are 
 proportional to the electromotive forces. 
 
 419. The Measurement of the Capacity of a condenser 
 is accomplished by placing the given condenser, K, a stand- 
 ard condenser, K', and known resistances, r and r\ in the 
 arms of a Wheatstone bridge, as shown in Fig. 427. 
 
 (a) By pressing the key on the stop, a, the current flows through 
 the point, B, and charges the condensers, the greater quantity going 
 to the condenser of greater capacity. The resistances, r and r', are 
 adjusted so that there is no deflection of the needle at G. When the 
 key is pressed on the other stop, c, there is a rush of current from the 
 condensers that is retarded by the resistances, r and r'. Any change 
 or inequality of the voltage of the condensers is instantly shown by 
 the galvanoscope. Assuming that the capacity of K is less than that 
 of K', its voltage will fall more rapidly unless the resistance, r, is 
 greater than r'. Since capacity equals quantity divided by potential, 
 
 *->' 
 
ELECTRICAL MEASUREMENTS. 
 
 535 
 
 it follows that if the resistances are adjusted so that the voltages are 
 the same for both (i.e., no deflection at G) K will be directly propor- 
 tional to Q. As the condensers discharge in the same time, their 
 
 FIG. 427. 
 
 capacities are proportional to the currents sent through r and r f . As 
 these currents have the same E.M.F., each is inversely proportional to 
 the resistances through which it flows. Hence 
 
 K : K' : : r' : r. 
 Three of these values being known, K is easily determined. 
 
 420. The Measurement of Magnetic Functions. Mag- 
 netic flux is measured directly in webers by the use of a 
 little exploring coil of many turns of fine wire connected 
 to a ballistic galvanometer. The quantity of the current 
 
536 SCHOOL PHYSICS. 
 
 generated by suddenly jerking the exploring coil from the 
 magnetic field is thus measured, and from this the number 
 of lines of force is calculated. Magnetomotive force is 
 usually calculated directly from the ampere-turns. Mag- 
 netizing force is calculated by dividing the magnetomotive 
 force by the length of the magnetic circuit in centimeters. 
 Permeability is calculated directly from the quotient of the 
 induction and the magnetizing force. Curves of per- 
 meability may be determined for iron at various stages of 
 magnetization, and each kind of iron nas its own curve. 
 Such curves are largely used in dynamo design. 
 
 CLASSROOM EXERCISES. 
 
 / 
 
 1. Draw an illustrative diagram, and deduce the formula for the 
 Wheatstone bridge. 
 
 2. Explain why an ammeter should have a low resistance, and a 
 volt-meter a high resistance. 
 
 3. A volt-meter that has a resistance of 26,000 ohms indicates 37 
 volts, (a) What is the strength of the current ? (ft) What voltage 
 would such an instrument indicate with a current of 3 milliamperes ? 
 
 4. Two volt-meters, one of which has a resistance of 25,000 ohms, 
 and the other a resistance of 15,000 ohms, are connected in series 
 across 110 volts. (a) What current flows through the system? 
 (ft) What voltage does the first instrument indicate? (c) the second 
 instrument ? 
 
 Ans. (a) 0.00275 amperes; (ft) 68.75 volts; (c) 41.25 volts. 
 
 5. I have a volt-meter that measures up to 15 volts and that has a 
 resistance of 3,500 ohms. I want to use it on a 115-volt circuit, and, 
 therefore, put it in series with a resistance of 24,000 ohms. With the 
 two thus connected, and with a voltage of 110, (a) What is the current 
 strength? (ft) What is the indication of the volt-meter? (c) By 
 what must the reading of the volt-meter be multiplied to get the 
 actual voltage ? Suppose the voltage to be increased to 1 17. (d) What 
 is the reading of the volt-meter? (e) Is there any change in the 
 multiplier used to give the correct voltage ? 
 
ELECTRICAL MEASUREMENTS. 537 
 
 6. "What resistance must be put in series with the volt-meter of 
 Exercise 5, so that the multiplier shall be 10? Ans. 31,500 ohms. 
 
 7. How many watts is taken by a station volt-meter that indicates 
 110 volts and uses a 0.002-ampere current? 
 
 8. I have an ammeter that indicates milliamperes up to 100. It has 
 a resistance of 6 ohms. I desire to put it on a circuit that I know to 
 have a current of 6 or 7 amperes. As the instrument will not safely 
 carry more than 0.1 of an ampere, I put it in a shunt, as shown in Fig. 
 432. What must be the resistance of R, the other branch of the cir- 
 cuit, so that the instrument shall have a multiplier of 100 ; i.e., so that 
 a current of 6.5 amperes will produce a reading of 65 milliamperes ? 
 Evidently, with such a current and with the shunts properly adjusted, 
 0.065 of an ampere will pass through the milliammeter, and 6.435 
 amperes through R. 
 
 9. At an electric light station, I am called upon to measure the 
 resistance of one of the field-magnet coils of a dynamo. I have a volt- 
 meter and an ammeter, and a small dynamo (the exciter of an alter- 
 nator) that will furnish a 15-ampere current at any desired voltage 
 from 150 to 225. With this outfit, how shall I measure the resistance 
 of the coil ? 
 
 10. Draw a sketch of the connections of a series dynamo, and show 
 how you would arrange a volt-meter to measure the voltage necessary 
 to force the current through the field magnets. 
 
 LABORATORY EXERCISES. 
 
 Additional Apparatus, etc. Three Danisll cells ; galvanoscopes and 
 galvanometers ; volt-meter ; ammeter ; resistance-box ; rheochord as 
 described below ; current reverser ; 2m. of fine platinum wire ; double 
 connector ; wires of unknown resistance ; Wheatstone slide-bridge as 
 described below. 
 
 1. Solder one end of a piece of No. 20 insulated copper wire, 50 cm. 
 long, to one end of a piece of zinc 10 x 2.5 x 0.5 cm., and amalgamate 
 the zinc. Solder a similar wire to a piece of sheet copper 10 x 10 cm. 
 Put the zinc into a porous cup 4 or 5 cm. in diameter and 10 cm. deep, 
 and fill the cup to the depth of 8 cm. with dilute sulphuric acid. Put 
 the copper plate into a glass vessel 7 or 8 cm. in diameter and 10 cm. 
 deep, bending it slightly to fit the inner surface of the tumbler. Put 
 the porous cup and its contents into the glass vessel, and fill the latter 
 to the depth of 8 cm. with a saturated solution of copper sulphate. 
 
538 
 
 SCHOOL PHYSICS. 
 
 Connect the terminals of this Daniell cell with the terminals of a low 
 resistance galvanoscope, and record, at intervals of 5 minutes for half 
 an hour, the deflections of the needle. Ascertain whether the current 
 strength is practically constant after the porous cup is wet through. 
 
 2. Make a resistance frame (rheochord) as follows: Nail two 
 uprights, each 25 x 3 x 1 cm. to the edge of a plank 100 x 10 x 4 cm., 
 and screw the ends of a meter stick to the upper ends of the uprights, 
 as shown in Fig. 428. Set two small metal binding-posts at a, and 
 another pair at the same level at 6. Set similar binding-posts, in 
 pairs, at c, d, and e. Connect the base of the inner post at a with the 
 base of the inner post at b by No. 30 German-silver wire. It is well 
 to solder the wire to the posts. Lead a similar wire around the outer 
 edges of the uprights, and connect its ends to the outer posts at a and b. 
 
 FIG. 428. 
 
 From one of the posts at c, lead a similar wire around both uprights 
 to the other post at c. In like manner, connect the posts at d by No. 
 28 German-silver wire. In like manner, connect the posts at e by 10 
 turns of insulated No. 30 copper wire, laying the wire on carefully so 
 as to prevent the current from leaking across from one turn to the 
 next (short-circuiting). All of the posts should be firmly fixed, and 
 the wire should be drawn tight. 
 
 Near each corner of a wooden block about 10 cm. square, bore a 
 centimeter hole, about a centimeter 
 deep, and number the holes in succes- 
 sion, 1, 2, 3, and 4. These holes are 
 for mercury cups. Set sharp little spikes 
 at the corners of the opposite face of the 
 block, to fix it to the table wherever it 
 is placed. Set metal binding-posts at 
 FIG. 429. the corners of the block so that the 
 
ELECTRICAL MEASUREMENTS. 539 
 
 screw of each penetrates to one of the cups. Provide two stout copper 
 wires, amalgamated at their ends, and bent so that they may connect 
 any of the holes with either of the two adjoining holes. When mer- 
 cury is placed in the cups, the block constitutes a "current reverser" 
 or mercury commutator. 
 
 Connect diagonally opposite mercury cups (as 1 and 3) of the com- 
 mutator to the terminals of a Daniell cell. From one of the other cups 
 (as 2), lead a wire to one of the terminals of a low resistance galvano- 
 scope, and connect the other terminal of the galvanoscope to one of 
 the binding-posts (at 6) of the rheochord. From the other binding- 
 post at 6, lead a wire to the fourth mercury cup. The galvano- 
 scope should be at least a meter from the other parts of the apparatus 
 so that its needle may be unaffected by them, and the wires leading 
 to and from it should lie close together. Connect the two binding- 
 posts at a by a short, stout copper wire. Complete the circuit by 
 placing the two bent copper wires so that one of them shall connect 
 cups 2 and 3, while the other connects 1 and 4. Trace the direction 
 of the current through the galvanoscope. Change the bent wires of 
 the commutator so that one of them connects 1 and 2, while the other 
 connects 3 and 4. Trace the direction of the current through the 
 commutator. By this time, the porous cup of the cell will probably 
 be wet through, and the current nearly constant. 
 
 While the current is flowing through 200 cm. of No. 30 German- 
 silver wire, record the deflection of the needle of the galvanoscope ; 
 reverse the current and record the deflection ; record the average of 
 the two deflections. With a copper wire or a double connector like 
 that shown in Fig. 430, short circuit the two wires near a, so that the 
 current shall flow through 180 cm. of the German-silver wire. Record 
 the three deflections as before. Make similar successive records for 
 160, 140, 120, 100, 80, and 60 cm. of the 
 German-silver wire, ending with the record 
 for 200 cm., taken again to be sure that 
 the current has not fallen off while the 
 measurements were in progress. Tabulate FIG. 430. 
 
 all of your records, and notice whether they indicate, in a general way, 
 any dependence of electrical resistance upon the length of the 
 conductor. 
 
 3. Using the apparatus arranged for Exercise 2, change the con- 
 nections at the rheochord from b to d, so as to put the 200 cm. of Xo. 
 28 German-silver wire into the circuit. Record the deflection ; reverse 
 
540 SCHOOL PHYSICS. 
 
 the current, and record the deflection ; and record the average of the 
 two deflections. Compare this average with the averages obtained in 
 Exercise 2 for the several lengths of No. 30 wire, and estimate the 
 length of the latter that has a resistance equal to that of the 200 cm. 
 of No. 28 wire. Carefully measure the diameters of the two wires, 
 and compute the ratio between the areas of their cross-sections. De- 
 termine the relation between cross-section and resistance. 
 
 4. Using the apparatus arranged for Exercise 3, change the con- 
 nections from d to c, and connect the two binding-posts at b by 
 copper wires to the two binding-posts at d, so as to provide for the 
 current, two equal parallel branches of No. 30 German-silver wire. 
 Record the deflections before and after reversal, and their average, as 
 before. Estimate the length of No. 30 wire, as used in Exercise 2, 
 that has a resistance equal to that of the two 200-cm. pieces in multi- 
 ple arc as used in this exercise. 
 
 5. Determine the length of No. 30 German-silver wire that has a 
 resistance equal to that of 20 m. of No. 30 copper wire. 
 
 6. Wind into spiral coils two equal lengths (e.g., 1QO cm.) of fine 
 platinum wire, and put them into the arms of a Wheatstone bridge. 
 Balance the bridge. Heat one of the spirals in a Bunsen or alcohol 
 flame, and notice that the deflection of the needle indicates that the 
 balance has been destroyed. While the spiral is still heated, balance 
 (roughly) the bridge again, and determine whether the resistance of 
 the wire was increased or decreased by the rise of temperature. 
 
 7. Place in the circuit of the Daniell cell of Exercise 1, a galvano- 
 meter, a set of resistance coils, and a conductor, X, of unknown resist- 
 ance. Adjust the known resistances so that the needle shows a 
 deflection of about 45, and record the exact reading. Remove X 
 from the circuit. Add known resistances to make the deflection the 
 same as before. Repeat the work twice, adjusting the known resist- 
 ances so as to produce deflections of about 43 and 47, and take the 
 average of the three totals of added resistance as the resistance of X. 
 This is called the method by substitution. 
 
 8. To a table-top or other board, tack two stout metal strips, AC 
 and BD, with a meter-stick between them, as shown in Fig. 431. 
 Tack a similar metal strip, EF, 90 cm. long, in position as shown. 
 Solder metal binding-posts at the ends of these strips, and at the 
 middle of EF. The resistance of the strips is negligible. Tightly 
 stretch a German-silver wire, No. 26, over the face of the meter stick, 
 and solder it to the faces of the metal strips at r and s. One of the 
 
ELECTRICAL MEASUREMENTS. 
 
 541 
 
 terminals of a sensitive galvanoscope is to be connected to EF '; the 
 other galvanoscope wire is to make a sliding contact with the Ger- 
 man-silver wire, dividing it into two variable parts, m and p. Put the 
 apparatus into the circuit of a voltaic cell, as shown in the figure. 
 Interpose a conductor of unknown resistance at x and a known resist- 
 ance of approximately the same value at n (the better this guess at the 
 equality of resistances, the less the liability of error in the results 
 attained). You have a AYheatstone bridge, easily comparable to 
 
 FIG. 431. 
 
 that shown in Fig. 425. Make the sliding contact at a point on rs 
 that causes a deflection to the right, and note its position on the 
 meter-scale ; find a position that causes a deflection to the left. As 
 the point of contact at which the bridge will balance is between these 
 points, it is easy to locate it definitely. When the contact is made at 
 such a point on rs that there is no deflection of the needle, read the 
 values of m and p, directly from the meter-scale, and determine the 
 resistance of x. Repeat the work with two slightly different values 
 for n, and take the average of the three computed values of x. 
 
 Note. In practice, the galvanoscope should be placed at a distance 
 from the rest of the apparatus, the connecting wires being kept near 
 together. 
 
 9. Make a Daniell cell similar to that of Exercise 1, with cups of 
 the same size but with plates of sheet metal and 10 x 0.5 cm. in size. 
 Take care that the liquids are of the same depth in the two cells. 
 Put the large-plate cell in circuit with a galvanoscope, inserting the 
 commutator as in some of the preceding exercises. Set the plates as 
 
542 SCHOOL PHYSICS. 
 
 far apart as possible, and record the deflections before and after 
 reversal, and their average. Repeat the work with the plates as near 
 together as possible. Repeat both tests with the small-plate cell. 
 Put 200 cm. of No. 30 German-silver wire into the circuit, and repeat 
 the work with the two cells in succession. Repeat these latter tests, 
 using a galvanoscope of higher resistance. From your record, deter- 
 mine the effect of the size of the plates, and of the distance between 
 the plates upon the current strength, and whether the addition of an 
 external resistance has any effect upon the sensitiveness of the current 
 to changes in the size and relative positions of the plates. 
 
 10. Replace the small plates of the cell described in Exercise 9 by 
 plates like those of the cell of Exercise 1. Join the two like cells in 
 parallel, and put into the circuit a galvanoscope, and 200 cm. of No. 
 30 German-silver wire. Record the deflections as previously directed. 
 Make the tests with galvanoscopes of high and of low resistances. 
 Repeat the tests with the cells joined in series. Remove the German- 
 silver wire from the circuit, and repeat the tests. From your record, 
 determine under what conditions it is better to join cells in pafallel, 
 and when it is better to join them in series. 
 
 11. Join the two Daniell cells of Exercise 10 in parallel, and sub- 
 stitute the battery for the unknown resistance, x, of Exercise 8. 
 Remove the battery used in that exercise, or leave it open circuited 
 at k (Fig. 426). Compare the resistance of the battery with that of 
 the same cells in series, and with that of one of the cells. 
 
 Note. The accurate measurement of the resistance of a cell on 
 closed circuit is a difficult problem. 
 
 12. Place a volt-meter that indicates tenths of a volt in a shunt 
 circuit around a resistance, R, as shown in Fig. 432. Assume that the 
 
 resistance of the instru- 
 ment is so high that 
 the current shunted 
 through it is negligible. 
 Determine by computa- 
 tion the resistance of R 
 
 ->\A A/VV\/VV\A* when a 2-ampere cur- 
 
 Fl 432 ren * flowing through it 
 
 gives a reading of 0.2 
 
 at the volt-meter. Try to verify your result experimentally. Notice 
 that the readings of the volt-meter multiplied by 10 give the current 
 
SOME APPLICATIONS OF ELECTRICITY. 
 
 strength in amperes. Determine the value that should be given to 
 R so that the volt-meter may be used as an ammeter giving direct 
 readings in amperes. 
 
 Note. Many ammeters are made on this principle of shunning a 
 high resistance galvanometer. 
 
 IV. SOME APPLICATIONS OF ELECTRICITY. 
 
 Incandescence Lighting. 
 
 Experiment 382. Place a few centimeters of No. 36 platinum wire 
 across the terminals of a battery of several bichromate cells in series. 
 The wire will be heated to incandescence, and may be melted. Lift 
 one of the plates partly from the liquid, and notice the diminished 
 brilliancy of the light emitted by the incandescent wire. By gradu- 
 ally lowering the plate into the liquid as the cells weaken, the bril- 
 liancy of the platinum wire may be kept nearly uniform. Notice the 
 progressive oxidation of the wire. Try to continue the experiment 
 until the wire breaks down by oxidation, noting the length of time 
 taken. Repeat the work with No. 36 iron wire, and compare the 
 lasting qualities of the two wires. 
 
 421 . Incandescence Lamps operate essentially on the prin- 
 ciple illustrated in Experiment 382, the current being sent 
 through some substance thaf, because of its 
 high resistance, becomes intensely heated and 
 brilliantly incandescent. The only suitable 
 substance known for such a resistance fila- 
 ment is carbon, which, carefully prepared 
 and bent into a loop, is enclosed in a glass 
 bulb from which the air is exhausted to 
 prevent oxidation, i.e., combustion. At the 
 best, the filament gradually deteriorates and 
 finally breaks, thus ruining the lamp. The 
 ends of the carbon filament are cemented to short plati- 
 
544 
 
 SCHOOL PHYSICS. 
 
 num leading-in wires that are imbedded in the glass by 
 the fusion of the latter. These platinum wires are con- 
 nected to the metallic fittings of the lamp in such a way 
 that, when the bulb is screwed into its supporting socket, 
 the connections are properly made. Some such lamps are 
 provided with turn-offs, for open-circuiting the lamp. 
 
 (a) As incandescence lamps are generally connected in parallel, as 
 shown in Fig. 43-1, they require a heavy current at a comparatively 
 
 1_J 1 
 
 MAIN SWITCH 
 
 FIG. 434. 
 
 low voltage. Such currents require large conductors that are gener- 
 ally made of copper. The "hot" resistance of the carbon filaments 
 Caries from about 25 to 250 ohms, according to the voltage of the cur- 
 rent and the candle-power of the lamp. In what is known as " the 
 Edison" 3-wire system," two dynamos are connected in series, as shown 
 in Fig. 435. The lamps on each side of the middle or neutral wire, 
 
SOME APPLICATIONS OF ELECTRICITY. 
 
 545 
 
 vnr 
 
 N, are made as nearly equal as possible in number and resistance. 
 When they thus balance, N carries no cur- 
 rent, and the voltage of the second dynamo is 
 added to that of the first. Under such con- 
 ditions, the effect is the same as if the lamps 
 of each pair were in series, the doubled re- 
 sistance being met by the doubled potential 
 difference of the two generators. Doubling 
 thus the voltage doubles the current, and 
 quadruples the energy delivered. This en- 
 ables a division of the area of cross-section of 
 the line-wires by 4, and results in a saving 
 of f of the weight and cost of the mains. If 
 lamps are turned out on one side of the mid- 
 dle main, current flows along N to supply 
 the required excess. 
 
 Note. The arches at points where con- 
 ductors cross each other in Fig. 434 indicate, FIG. 435. 
 in the conventional way, that the wires cross 
 
 without contact. Dynamos are often represented by commutator 
 circles and brushes as shown in Fig. 435. 
 
 (ft) With lamps placed in parallel, the greater the number of the 
 lamps in use, the less the resistance of the circuit. The current is 
 usually operated at 110 volts, and each 16-c.p. lamp takes about 0.5 of 
 an ampere. The expenditure is, therefore, nearly 3.5 watts per 
 candle-power. Evidently, an increase of current will increase the 
 number of watts expended in the lamp, and the quantity of light pro- 
 duced. The greater the number of watts expended, the higher the 
 temperature of the filament, and the greater the efficiency of the lamp. 
 But excessive temperatures weaken the filament and shorten its time 
 of service, so that in practice efficiency is sacrificed to some extent for 
 the sake of a greater durability. 
 
 (c) The dynamos designed for direct use with such lamps are gen- 
 erally shunt- or compound-wound. As they must deliver currents that 
 are of constant potential but of strength that varies with the number 
 of lamps in use, some regulating device is necessary for the shunt- 
 wound dynamo ; the compound-wound dynamo is self-regulating. 
 
 (rf) Incandescence lamps are often placed on the secondary circuit 
 of a " step down " transformer, the primary cirquit of which carries 
 36 
 
546 
 
 SCHOOL PHYSICS. 
 
 the high-voltage current of an alternator. The primary coils of 
 several transformers may be put in series, as shown in Fig. 436, or in 
 multiple arc, as shown in Fig. 437. 
 
 MAIN 
 
 TO THE ALTERNATOR 
 
 FIG. 436. 
 
 (e) When electric lamps are supplied by an electric lighting com- 
 pany, the customer sometimes pays a fixed rental per lamp per day. 
 
 MAIN 
 TO THE ALTERNATOR 
 
 MAIN 
 
 FIG. 437. 
 
 and sometimes a certain price per watt-hour for the current actually 
 delivered. For this purpose, a wattmeter, like that described in 
 414 (/), is often used ; the Edison meter depends upon the electro- 
 lytic action of a part of the current that is shunted for that purpose. 
 See 429 (a). 
 
 Caution. In experimenting with an incandescence electric lighting 
 current, remember that a low resistance placed across the mains will 
 
SOME APPLICATIONS OF ELECTRICITY. 547 
 
 receive an enormous current. Many a galvanoscope and other piece of 
 apparatus has been ruined in this way. Never "ground" an electric 
 lighting wire. 
 
 The Electric Arc. 
 
 Experiment 383. Connect one of the terminals of the battery to a 
 small file, and draw the other terminal 
 along the rough surface. A series of 
 minute sparks is produced as the circuit 
 is rapidly made and broken. When 
 such a luminous effect is larger and 
 more lasting, the band of light between 
 the terminals is called an electric arc. 
 
 F IG. 4oO. 
 
 Experiment 384. Connect one end of a 3-pound coil of insulated 
 copper wire, No. 20, to one of the mains of a direct current, incan- 
 descence lighting circuit, and the other end to a short piece of No. 6 
 copper wire. Connect another piece of No. 6 copper wire to the other 
 main. Bring the free ends of the No. 6 wires into contact, and slowly 
 separate them. A flashing arc will follow the wires for a short distance 
 and then break. Bring the wires into contact again, separate them, 
 and try to maintain the arc. Notice that the arc is tinted green by 
 the vapor of the copper. The wires will become hot and their ends 
 will be melted. 
 
 Experiment 385. Tip one of the terminals with a screw or other 
 piece of steel, and connect the other-terminal to a block of commercial 
 zinc. Set up an arc between the steel and the zinc. The pyrotechnic 
 effect is very striking. Replace the steel and zinc with two pieces of 
 electric light carbon. Notice that the terminals are not melted, and 
 that the light is a brilliant white. View the arc through a piece of 
 smoked glass, and try to discover, from their appearance, which of 
 the tips is the hotter. 
 
 422. The Voltaic Arc is the most brilliant luminous 
 effect of an electric current. When carbon rods that form 
 part of the circuit of a strong electric current are sepa- 
 rated, as in Experiment 385, their tips glow with a brilliancy 
 greater than that of any other light under human control. 
 
548 
 
 SCHOOL PHYSICS. 
 
 and the temperature of the intervening arc is unequalled by 
 that of any other source of artificial heat. 
 
 (a) It is necessary to bring the carbons into contact to start the 
 light. The tips of the carbons become intensely heated, and the car- 
 bon begins to volatilize. When the carbons are separated, the current 
 passes through this intervening layer of vapor and the accompanying 
 disintegrated matter which acts as a conductor of very high resistance. 
 The intense heat of the voltaic arc is due to the conversion of the 
 energy of the current and not to combustion ; the arc may be pro- 
 duced in a vacuum where there could be no combustion. 
 
 (6) The constitution of the voltaic arc may be studied by project- 
 ing its image on a screen with a lens. 
 Three parts will be noticed : 
 
 1. The dazzling white, concave 
 extremity of the positive carbon. 
 
 2. The less brilliant and more 
 pointed tip of the negative carbon. 
 
 3. The globe-shaped and beau- 
 tifully colored aureole surrounding 
 the whole. 
 
 (c) There is a transfer of mat- 
 ter across the arc in the direction 
 of the current, the positive carbon 
 wasting away more than twice as 
 rapidly as the negative. Most of 
 the light is radiated from the cra- 
 ter at the end of the positive car- 
 bon. 
 
 423. The Arc Lamp is es- 
 sentially a device for auto- 
 matically separating the car- 
 bons when the current is 
 turned on, for " feeding " the carbons together as they are 
 burned away at their tips, and, in some cases, for short- 
 circuiting the lamp in case of irregularity or accident. 
 
 FIG. 439. 
 
SOME APPLICATIONS OF ELECTRICITY. 
 
 549 
 
 Such lamps of from one to two thousand candle-power 
 require an expenditure, at the dynamo, of about three- 
 fifths of a horse-power 
 per lamp. A common 
 form of the arc lamp is 
 shown in Fig. 440. 
 
 I 
 
 (a) In the arc lamp as 
 ordinarily supplied for com- 
 mercial uses, the distance be- 
 tween the carbon tips is about 
 | of an inch. Such lamps re- 
 quire a current of from 9 to 
 10 amperes, and have a poten- 
 tial difference between the 
 carbons of 45 to 50 volts. 
 They are generally operated 
 in series, so that the current 
 passes in succession through 
 all the lamps on the circuit. 
 The resistance of the circuit 
 is thus increased by the suc- 
 cessive addition of lamps. As 
 many as 125 arc lamps have 
 been worked in series. The 
 E-.M.F. of the current re- 
 quired is often 3,000, and 
 occasionally 6,000 volts. Such 
 currents must be handled 
 with care, as dangerous results might follow ignorance or neglect. 
 
 (6) The mechanism for separating and feeding the carbons consists 
 chiefly of a clutch-washer, w, a clutch, c, and a solenoid or " sucking 
 magnet," S, doubly and oppositely wound. One of these windings 
 is of coarse wire in series with the carbons ; the other constitutes a 
 high resistance shunt across the arc. The two cores of the solenoid 
 and their connecting yoke move freely up and down, under the 
 alternating influence of magnetic attraction and gravity. At the 
 start, the carbons are in contact. When the current is turned on, 
 
 FIG. 440. 
 
550 
 
 SCHOOL PHYSICS. 
 
 the series magnet lifts c ; c lifts one edge of to, thus causing it to 
 clutch and to lift the rod that carries the upper carbon. The arc being 
 
 Fia. 441. 
 
 thus established, the greatly increased difference of potential between 
 the arc terminals sends more current through the oppositely wound 
 shunt circuit, thus weakening the lifting power of S. As the carbons 
 wear away and the arc grows longer, the gradually increasing poten- 
 tial difference between the terminals of the arc gradually forces more 
 current through the shunt winding of the solenoid, antagonizing the 
 lifting effect of the series magnet until gravity pulls down the cores 
 and the clutch. When w falls into a horizontal position, it releases 
 its grip on the carbon rod and allows it to slip down, thus reducing 
 the length of the arc, strengthening the current through the series 
 coils, and reducing the current through the shunt coils. Ihc 
 clutch is immediately lifted and the fall of the carbon thus arrested. 
 So delicately have these devices been adjusted that the feeding of the 
 
SOME APPLICATIONS OF ELECTRICITY. 551 
 
 carbons is as imperceptible as the movement of the hour hand of a 
 watch. The current of the shunt circuit may be made to traverse an 
 electromagnet at T, so that when the arc becomes abnormally long, 
 as it will if the carbon does not feed properly, an iron bar pivoted at 
 i is attracted until it closes a short circuit at m. R represents a resist- 
 ance properly adjusted. In some lamps, the carbons are separated at 
 the start, the shunt magnet brings them into contact, and the series 
 magnet separates them, thus establishing the arc. The shunt then 
 feeds the carbons as before. Sometimes the " sucking magnet " has 
 but a single core. Many search lights are made without any auto- 
 matic mechanism, the carbons being fed by hand. 
 
 (c) Since arc lamps are operated in series, any particular lamp 
 that is to be extinguished must be short-circuited. The dynamo is 
 provided with appliances for maintaining a uniform current strength 
 regardless of the number of lamps in use on its circuit. When the 
 number of lamps is increased, the voltage of the dynamo is corre- 
 spondingly increased. The connections of a system of arc lights are 
 
 FIG. 442. 
 
 diagrammatically shown in Fig. 442, in which m and n represent short- 
 circuiting or cut-out switches ; C, the commutator of the dynamo; F, 
 the field-magnet coils ; and R, a regulating resistance. Any lamp may 
 be cut out by closing a switch at m. By closing the switch at n, the 
 current is diverted from the field magnets. This destroys the mag- 
 netic field and, of course, destroys the current. When n is open, the 
 
552 
 
 SCHOOL PHYSICS. 
 
 proportion of the current that is sent through F (and, consequently, 
 the strength of the magnetic field) may be regulated by the resistance 
 that is thrown into the shunt circuit at R. 
 
 (d) Some arc lamps are made to operate on incandescence circuits 
 at constant potential. They are extinguished by open-circuiting 
 them. Incandescence and arc lamps are often operated from central 
 lighting stations. 
 
 Experiment 386. Separate the terminals of a bichromate cell in 
 illuminating gas escaping from an ordinary burner. It will be dim- 
 cult to make the spark light the gas. Interpose a large, low-resistance 
 electromagnet in the circuit, and renew the attempt. Explain the 
 increased magnitude of the spark. Try to light the gas with a spark 
 from the electrophorus ; from an induction coil; and from a static 
 electric machine. 
 
 424. Electric Gas Lighting is often effected by sparks 
 from the interrupted circuit of a 
 voltaic battery, in which circuit 
 is a " kicking coil," as illustrated 
 in Experiment 386, or by sparks 
 from the secondary of an induc- 
 tion coil, or from a machine for 
 the generation of static electric- 
 ity. Burners like that shown in 
 Fig. 443 are connected in series 
 in such a circuit. 
 
 FIG. 443. 
 
 425. Electric Welding has be- 
 come a common application of 
 the electric current. A suitable transformer changes an 
 alternating current of high voltage into a current of 
 many amperes, the small electromotive force of which is 
 adequate for the lo\v resistance of the metals to be welded. 
 It is found that when metals thus heated are welded, the 
 
SOME APPLICATIONS OF ELECTRICITY. 
 
 553 
 
 union is unusually firm and perfect. When a weld so 
 made is finished off with machine-tools, the line of union 
 cannot be detected by the eye. Railway tracks are some- 
 times made continuous by this process. 
 
 Electric Motors. 
 
 Experiment 387. Fasten 4 iron strips to the face of a wooden 
 cylinder 4 cm. long and 6 cm. in diameter, parallel to the axis of the 
 cylinder, and at equal distances from each other. Support the axle so 
 that, as the cylinder turns, the iron strips will pass near the end of an 
 electromagnet, as shown in Fig. 
 444. When the cylinder is ro- 
 tated, a square nut on its axle 
 acts as a cam, forcing the vertical 
 spring to the right, and closing 
 an electric circuit at the tip of 
 the set-screw, s, four times for 
 each revolution. The metal sup- 
 port that carries s is connected 
 to the binding-post, b. The 
 metal support that carries the 
 vertical spring is connected to 
 one terminal of the electromag- 
 net, the other terminal of which 
 is connected to the binding-post, FIG. 444. 
 
 a. The nut is set so that the cir- 
 cuit is broken at s just as one of the iron strips on the face of the cylin- 
 der comes to the end of the core of the magnet. The momentum of the 
 rotating cylinder carries it over the dead point until the next corner 
 of the nut forces the vertical spring into contact at s. The apparatus 
 will be improved by placing a small fly-wheel at the other end of the 
 axle. All of the metal parts, except the core of the magnet, and 
 the 4 strips 011 the cylinder, would better be made of brass. Place 
 this apparatus in the circuit of several cells joined in series, and set 
 the cylinder in rotation ; adjust the position of the nut if necessary 
 to secure a continuous motion. 
 
 Experiment 388. Connect a small battery-motor (one may be 
 bought for a dollar or less) to a number of cells joined in series, and 
 
554 SCHOOL PHYSICS. 
 
 interpose a low-resistance galvanoscope as indicated in Fig. 445. Hold 
 
 the shaft of the motor to prevent its rota- 
 tion, and note the reading of the galvano- 
 scope. Then permit the motor shaft to 
 revolve, and again note the reading of the 
 galvanoscope. The resistance of the cir- 
 cuit seems to be greater when the arma- 
 ture is in motion than when it is at rest. 
 
 426. An Electric Motor is a de- 
 vice for doing mechanical work at 
 
 the expense of electric energy. As made for industrial 
 use, it is generally similar to the dynamo in form and 
 construction, and is often identical with it. The current 
 from a dynamo, perhaps miles distant, is sent through the 
 armature of the motor (the binding-posts of one machine 
 being connected to the binding-posts of the other), and 
 causes the motor armature to revolve in a direction oppo- 
 site to that in which it would revolve if the motor was 
 acting as a dynamo. This assumes that the motor is 
 series wound. It thus appears that the motor is based 
 upon the principle of the reversibility of the dynamo. 
 The pulley on the armature shaft is belted or geared to 
 other machinery. 
 
 (a) When the armature of a dynamo revolves in the magnetic 
 field, the motion develops a magnetic field for the armature coils that 
 acts in opposition to that of the field magnets, thus opposing the 
 motion of the armature and acting as an addition to friction, etc., as 
 a drag or counter torque. Hence, the transformation of mechanical 
 foot-pounds into electrical watts. Conversely, when a current is sent 
 through the armature of a dynamo or motor at rest, the opposition 
 between the magnetic field of the field magnets and the magnetic field 
 of the armature coils produces a repulsion that causes the rotation of 
 the armature. Hence the transformation of watts into foot-pounds. 
 Any direct-current dynamo will act as an efficient motor when it is 
 
SOME APPLICATIONS OF ELECTRICITY. 555 
 
 supplied with a current of the same strength and potential as that 
 which it yields when acting as a dynamo. 
 
 (&) The E.M.F. of the inverse current generated in the armature 
 acts in direct opposition to the E.M.F. of the direct current. Repre- 
 senting the E.M.F. of the inverse current by , Ohm's law, as applica- 
 ble to this case, is as follows : 
 
 ^ _ E e 
 R 
 
 Evidently, it is not well to turn the whole voltage of the actuating 
 current suddenly upon a motor; the full current might; do injury to 
 the motor before its armature could acquire sufficient speed to produce 
 the inverse E.M.F. (e) that is necessary to reduce the current to a safe 
 magnitude. 
 
 (c) Electric motors are made in great variety of form, and for 
 almost countless purposes. In our cities and large villages, they are 
 placed on the circuits of powerful dynamos at central "power houses," 
 that correspond to electric lighting stations, and that are often iden- 
 tical with them. The convenience, cleanliness and economy of the 
 electric motor have led to its common use for the operation of light 
 machinery, such as fly and ventilating fans, sewing machines, lathes, 
 printing presses, etc. On the larger scale, the motor is used for the 
 propulsion of street cars, and is even displacing the locomotive engine 
 on some railways. As a generator and as a motor, the dynamo is 
 revolutionizing more than one department of the industrial world. 
 
 427. An Electric Bell consists mainly of an electromag- 
 net, E (Fig. 446), and a vibrating armature that carries a 
 hammer, H, that strikes a bell. One terminal of the magnet 
 coils is connected to the binding-post, and the other ter- 
 minal to the flexible support of the armature. The arma- 
 ture carries a spring that rests lightly against the tip of 
 an adjustable screw at O. This screw is connected to the 
 other binding-post. The bell is connected to a battery of 
 2 or 3 cells in series, a key, a push-button, P, or some other 
 device for closing the circuit being placed in the line. 
 
 (a) When the circuit is closed by pushing the button at P, the 
 
556 
 
 SCHOOL PHYSICS. 
 
 magnet attracts the armature and causes the hammer to strike the bell. 
 
 This movement of the ar- 
 mature breaks the circuit 
 at C. E, being thus de- 
 magnetized, no longer at- 
 tracts its armature, which 
 is thrown back against the 
 end of the screw by the 
 elasticity of the spring that 
 supports it. It is then 
 again attracted and re- 
 leased, thus vibrating rap- 
 idly and striking a blow 
 upon the bell at H at every 
 vibration (see 403, a). 
 The rapidity of the strokes 
 depends largely upon the 
 
 FIG. 446. 
 
 length of the pendulum-like hammer (see 115). 
 
 428. A Fire Alarm Box contains a crank which the 
 person Avho " turns in " the alarm is to pull down once. 
 This motion of the crank winds up a spr-ing that drives 
 a train of wheel-work that puts in revolution a make-and- 
 break wheel. The circumference of this wheel has a 
 series of notches arranged to correspond to the number 
 of the box ; e.g., if the number of the box is 371, there 
 will be three notches, separated by a longer space from a 
 succession of seven notches, which are followed at a simi- 
 lar distance by one notch. This notched wheel and an 
 arm that. presses upon the circumference of the wheel 
 are in the circuit. When the wheel revolves, the circuit 
 is broken as each notch passes under the arm. When the 
 circuit is broken, an electromagnet at the fire station is 
 demagnetized. The armature of the magnet is then drawn 
 back by a spring, and strikes one blow upon a bell. A 
 
SOME APPLICATIONS OF ELECTRICITY. 557 
 
 single revolution of the inake-aiid-break wheel in the 
 distant alarm box gives a succession of 3 strokes, 7 
 strokes and 1 stroke, thus indicating the number, 371. 
 The wheel- work may turn the make-and-break wheel two 
 or three times, thus repeating the alarm signal. The 
 location of Box 371 being known, valuable time is saved 
 in determining the vicinity of the fire. 
 
 Electrolysis. 
 
 Experiment 389. Put a solution of sodium sulphate, or any other 
 neutral salt, that has been colored with an infusion of purple cabbage 
 into a V-tube about 1.5 cm. in diameter, and supported in any con- 
 venient way. Close the ends of 
 the tube with corks that carry 
 platinum wires terminating in 
 narrow strips of platinum foil 
 that reach nearly to the bend 
 of the tube. Put this apparatus 
 in the circuit of 2 or 3 cells 
 joined in series. In a few min- 
 utes, the liquid at the positive 
 electrode will be colored red, 
 and that at the negative elec- 
 trode, green. If, instead of col- JT IG 447. 
 oring the solution, a strip of 
 
 blue litmus paper is hung near the positive electrode it will be red- 
 dened, while a strip of reddened litmus paper hung near the negative 
 electrode will be colored blue. These changes of color are chemical 
 tests ; the appearance of the green or blue denotes the presence of an 
 alkali (caustic soda in this case), while the appearance of the red 
 denotes the presence of an acid. 
 
 Experiment 390. Arrange apparatus as shown in Fig. 448. The 
 glass vessel may be made from a glass funnel, or by cutting the bottom 
 from a wide mouthed bottle, and may be supported in any convenient^ 
 way. The platinum electrodes should be about 2 cm. apart and cov- 
 ered with water (H 2 O) to which a little sulphuric acid has been added 
 
558 
 
 SCHOOL PHYSICS. 
 
 to increase its conductivity. Fill two test-tubes with acidulated water, 
 and invert them over the electrodes. When the circuit is closed, 
 bubbles of oxygen escape from the positive electrode, and bubbles of 
 hydrogen from the negative. The volume of hydrogen thus collected 
 will be about twice as great as that of the oxygen. When a sufficient 
 quantity of the gases has been collected, they may be tested; the 
 
 FIG. 448. 
 
 hydrogen, by bringing a lighted match to the mouth of the test-tube, 
 whereupon the hydrogen will burn ; the oxygen, by thrusting a splinter 
 with a glowing spark into the test tube, whereupon the spark will 
 kindle into a flame. If the gases thus separated are mixed, and an 
 electric spark produced in the mixture, the ions will recombine with 
 explosive violence. 
 
 Experiment 391. Repeat Experiment 389, placing a solution of 
 copper sulphate instead of sodium sulphate in the V-tube. When the 
 circuit is closed, copper will be deposited upon one of the electrodes, 
 while oxygen will be evolved at the other. Reverse the current, and 
 notice the disappearance of the copper from the electrode where it was 
 first deposited. Copper may be dissolved from the platinum foil with 
 nitric acid if desirable. 
 
 Experiment 392. Melt some tin, and pour the melted metal slowly 
 into water. Dissolve some of this granulated tin in hot hydrochloric 
 acid, and add a little water. Into this hot solution of tin chloride, 
 introduce electrodes made of tinned iron (tin-plate) . Pass the current 
 
SOME APPLICATIONS OF ELECTRICITY. 559 
 
 of the battery joined in series through the liquid, and notice the 
 remarkable tree-like growth of tin crystals. Modify the experiment 
 by successively using solutions of lead acetate, and of silver nitrate. 
 
 429. Electrolysis, etc. The decomposition of a chemi- 
 cal compound, called the electrolyte, into its constituent 
 parts, called ions, by an electric current is called electroly- 
 sis. When, for example, water is electrolyzed, the hydro- 
 gen collects at the negative electrode, called the cathode ; 
 such an ion is called a cation, and is said to be electroposi- 
 tive. The oxygen similarly collects at the positive elec- 
 trode, called the anode ; such an ion is called a anion, 
 and is said to be electronegative. 
 
 (a) In battery or in electrolytic bath, the metallic or electroposi- 
 tive ion is carried with the current through the electrolyte. Simi- 
 larly, when a chemical salt is electrolyzed, the metallic base is carried 
 to the cathode, while the acid constituent appears at the anode. The 
 amount of chemical decomposition effected in a given electrolytic 
 bath in a given time is proportional to the current strength. This 
 principle has been utilized in devices for the commercial measurement 
 of electric energy. 
 
 Experiment 393. Fasten a copper wire to a silver coin, and a 
 similar wire to a piece of sheet copper of about the same size. Sus- 
 pend the two pieces of metal in a tumbler containing a solution of 
 copper sulphate. Connect the wire that carries the silver to the 
 negative terminal of a strong battery of cells joined in parallel, and 
 the other wire to the other terminal. Close the circuit, and notice 
 that a firm, hard copper coating is deposited upon the silver. Reverse 
 the current until the copper is remoyed from the silver. Then con- 
 nect the cells of the battery in series, and notice that copper is depos- 
 ited upon the silver as a spongy mass instead of a firm coating. 
 
 430. Electrometallurgy is the art or process of deposit- 
 ing certain metals, such as gold, silver and copper, from 
 solutions of their compounds by the action of an electric 
 
560 SCHOOL PHYSICS. 
 
 current. Its most important applications are electroplat- 
 ing and electrotyping. In electroplating, an adherent 
 film of metal is thus deposited on some other material 
 (strictly speaking, on metallic substances only). In 
 electrotyping, the metallic film deposited in the bath is 
 not adherent. 
 
 (a) For plating with gold, a solution of the cyanide of gold is 
 generally used ; for plating with silver, a solution of the cyanide of 
 silver is generally used. 
 
 (b) The most common forms of electrotypes are copies of medals, 
 jewelry, silverware, woodcuts, and pages of composed type. The metal 
 most used is copper. The form to be copied is molded in wax ; the 
 face of the mold is dusted with powdered plumbago, in order to make 
 it a conductor; the mold thus prepared is immersed in a solution of 
 copper sulphate, and subjected to the action of a current as illustrated 
 in Experiment 393. When the copper film is thick enough (say as 
 thick as an ordinary visiting card), it is removed from the mold, and 
 strengthened by filling up its back with melted type-metal. The 
 copper film and the type-metal are made to adhere by means of an 
 alloy of equal parts of tin and lead. The copper-faced plate thus 
 produced is an exact reproduction of the form from which the mold 
 was made. When used for printing, it is more durable than the type 
 from which it was copied. 
 
 (c) Current for electrometallurgical processes is generally provided 
 by specially constructed dynamos of low voltage. Such dynamos are 
 called electroplating machines, or simply platers. 
 
 Secondary Cells. 
 
 Experiment 394. Arrange apparatus as in Experiment 390. After 
 the passage of the current for a few minutes, disconnect the battery 
 and put a galvanoscope in its place. The deflection of the needle 
 shows that the " water voltameter " is developing an electric current, 
 and illustrating the reversibility of electrolytic action. 
 
 Experiment 395. Fit neatly to a large tumbler two pieces of sheet 
 lead as large as can be used without contact between them. To each 
 lead plate, solder a copper wire about 50 cm. long. Fill the tumbler 
 
SOME APPLICATIONS OF ELECTRICITY. 561 
 
 with dilute sulphuric acid. Connect the wires to the terminals of a 
 high-resistance galvanoscope, and see if there is any deflection of the 
 needle. Free one of the lead-cell wires from the galvanoscope. Put 
 the lead-cell and the galvanoscope in series in the circuit of a battery 
 of several cells joined in series. Xote the deflections of the galvano- 
 scope needle for several minutes. Quickly throw the battery out of 
 the circuit, and connect the lead-plate cell with the galvanoscope. 
 Note the deflection of the needle, and the direction and permanency 
 of the current now flowing from the^ lead-plate cell. Open and close 
 this circuit to make sure that the deflection of the needle is caused by 
 a current from the lead plates, and not by any sticking of the instru- 
 ment. 
 
 431. A Secondary or Storage Battery is a combination 
 of cells each of which consists essentially of two plates of 
 metallic lead coated with red oxide of lead, and immersed 
 in dilute sulphuric acid. Sometimes the oxide is plas- 
 tered on the roughened surface of the lead, and some- 
 times it is packed in little pockets made in the lead plates 
 for that purpose. When such a cell is "charged" by 
 passing an electric current through it, the electrolysis of 
 the liquid liberates oxygen and hydrogen. One of these 
 ions peroxidizes the coating of one of the plates ; the 
 other ion reduces, i.e., deoxklizes, that of the other plate, 
 thus storing up chemical energy to be given back as an 
 electric current when the poles of the charged cell are con- 
 nected, and the chemical action is reversed. Such a cell 
 or battery is often called an accumulator. 
 
 (a) In a charged secondary battery, the two plates are unlike, and 
 the potential energy of chemical separation is converted into the 
 kinetic energy of an electric current, just as with an ordinary or " pri- 
 mary " battery. When a secondary battery has run down, the passage 
 of a current through it will restore the plates to their former effective 
 condition ; when a primary battery has run down, a current will not 
 thus restore the plates. Thus, the great advantage of the secondary 
 36. 
 
562 SCHOOL PHYSICS. 
 
 cell lies in the fact that no costly materials are consumed, the lead 
 and acid being as useful at the end of the operation as at the begin- 
 ning, and the coal consumed for the operation of the dynamo that 
 delivers the charging current being much less expensive than the 
 zinc that is consumed in the primary battery. Owing largely to the 
 mechanical weakness of the lead plates, the storage battery has not 
 yet proved the commercial success that was expected a few years ago. 
 
 (6) The secondary cell has a low internal resistance, and an E.M.F. 
 of about 2 volts. 
 
 (c) The condition of the plates of a charged secondary cell is 
 closely analogous to that of the polarized plates of a primary cell. 
 The ions have a tendency to reunite by virtue of their chemical affin- 
 ity, and thus to set up an opposing E.M.F. , as was illustrated in 
 Experiment 371. In the electrolysis of water, this E.M.F. is about 
 1.45 volts. Consequently, an E.M.F. of more than 1.45 volts is 
 necessary for the decomposition of water. 
 
 Telegraph. 
 
 Experiment 396. Connect two telephone receivers, two batteries 
 and two keys as shown in Fig. 449. Both batteries are on open 
 circuit. When the key is depressed at 2 or 3, and thus raised at 1 or 
 
 FIG. 449. 
 
 4, clicks will be heard at T and R. Trace the path of the current in 
 each case. It would be easy to devise a code of signals for communi- 
 cation with such apparatus between two distant stations. 
 
 Experiment 397. Support a metal cylinder, C, upon an axle. Pivot 
 a metal bar at a (Fig. 450) so that the style, s, at its other end may 
 rest upon the cylinder. Connect battery wires to the axle of the 
 cylinder, and at a, interposing a key, K. Make a paste by boiling 
 starch in water. Dissolve about 3 g. of potassium iodide in 3 or 4 
 
SOME APPLICATIONS OF ELECTRICITY. 
 
 563 
 
 en. cm. of hot water, aud add a little of the paste. Prepare a long 
 ribbon of white paper, and soak it in the starch and iodide solution. 
 While the paper is moist, fasten one end of it to a spool, S, and turn 
 the handle so as to draw the paper between the style and cylinder. 
 While the paper is moving over the surface of C, make and break the 
 
 Fio. 450. 
 
 circuit at K so as to inscribe a series of blue dots and dashes on the 
 paper at s. With A' at one station and s at another, it would be easy 
 for a person at K to send a dot and dash message to a person at s. 
 Consult the code of signals given on page 564, and, with your appa- 
 ratus, write the word Morse. 
 
 Experiment 398. Arrange a line between two stations as shown 
 in Fig. 451, using galvanoscopes, G and G', instead of the telephone 
 receivers used in Experiment 396. Each of the keys consists of two 
 metal springs (e.g., 1 and 2), which are fastened to a board at one end, 
 
 FIG. 451. 
 
 passing under the metal strip, n, with which they are in contact, and over 
 the metal strip, ro. When any of these keys is depressed, it makes con- 
 tact with m or m', and breaks contact with n or n'. When 1 is de- 
 pressed, the needles at G and G' will be turned in one direction ; when 
 2 is depressed, the needles will be turned in the other direction. Simi- 
 
564 
 
 SCHOOL PHYSICS. 
 
 larly, depressing 3 or 4 will cause opposite deflections of the needles. 
 Trace the course of the current for a depression of each of the four 
 keys. Call a deflection of the needle in one direction a dot, and a 
 deflection in the opposite direction a dash, and signal the word Kelvin. 
 
 432. The Electromagnetic Telegraph is a device for trans- 
 mitting intelligible messages at a distance by means of 
 interrupted electric currents. It consists essentially of a 
 line-wire or main conductor ; a battery or dynamo for the 
 generation of the current ; a transmitter or key ; and an 
 electromagnetic receiving instrument. The use of the tele- 
 graph on a commercial scale is chiefly due to S. F. B. 
 Morse of New York. The system devised by him about 
 1844 is still in general use. 
 
 (a) The Morse code of signals is as follows : 
 
 
 LETTERS, ETC. 
 
 
 FIGURES. 
 
 a 
 
 Tc 
 
 u 
 
 \ . 
 
 b 
 
 1 
 
 i' 
 
 '2 
 
 c - - - 
 
 m 
 
 w 
 
 '4 
 
 d 
 
 n 
 
 X 
 
 4 
 
 e - 
 
 o - - 
 
 y. - .. 
 
 5 
 
 f 
 
 
 
 
 
 J ~ 
 
 P ~ 
 
 & ~ - * 
 
 
 g 
 
 q 
 
 If 
 
 7 
 
 h 
 
 r - 
 
 
 8 
 
 f - - 
 
 s 
 
 f 
 
 9 
 
 j 
 
 / 
 
 . 
 
 
 
 To prevent confusion, a small space is left between successive letters, 
 a longer one between words, and a still longer one between sentences, 
 thus : 
 
 H e w 1 1 1 
 
 m 
 
 a t 
 
 ten 
 
 (>) The line-wire is most commonly made of iron, coated with zinc 
 or copper. It connects the apparatus at the several stations and is 
 carefully insulated. When the stations are far distant from each 
 other, the ends of the line-wire are connected to large metallic plates 
 buried in the earth (see Fig. 457), or otherwise " grounded." Whether 
 
SOME APPLICATIONS OF ELECTRICITY. 
 
 565 
 
 FIG. 452. 
 
 the earth is considered as a conductor, so that the part between the 
 grounded plates constitutes the return part of the circuit, or as a great 
 "reservoir of electricity" from which current is drawn at one end of 
 the line and into which current is discharged at the other, its use 
 greatly reduces the cost and the resistance of the circuit. 
 
 (c) The battery generally consists of many gravity cells joined in 
 series. A dynamo is often used instead. 
 
 (</) The transmitter or key is a current interrupter manipulated by 
 the operator. It consists essentially of a metal lever, Z, pivoted at 
 aa, and connected to the line by the 
 screw at m which is insulated from 
 the base, and the screw at n which is 
 connected to the base and lever. 
 When the handle of the lever is de- 
 pressed, a platinum point on the under 
 side of the lever makes contact with 
 another platinum point at e, and closes 
 the circuit. The motion of the lever is limited by a set-screw at its 
 further end. When the key is not in use, the switch, s, is turned for 
 the purpose of closing the circuit at that point. 
 
 (e) The Morse register is represented in Fig. 453. The armature, 
 A y is supported at the end of a lever, and over the cores of the magnet 
 
 bobbins, M. A spring, S, 
 lifts the armature when the 
 cores are demagnetized on the 
 breaking of the circuit by 
 the operator at the key. When 
 A is pulled down by M, a style 
 or pencil at P is pressed against 
 7?, a paper ribbon that is drawn 
 along by clock work. This 
 style may be made to record 
 upon the paper a dot-and-dash 
 communication sent by the 
 operator at a key, perhaps hundreds of miles away. Such registers 
 are little used nowadays, most operators reading by sound, i.e., de- 
 termining the message from the clicks of the magnet armature. 
 
 (/) In the Morse system, just described, a given wire can trans- 
 mit only one message at a time. By what is known as the duplex 
 system, a wire may be made to convey two messages, one each way, 
 
 FIG. 453. 
 
566 
 
 SCHOOL PHYSICS. 
 
 at the same time, without conflict. By what is known as the quad- 
 ruplex system, a wire may be made to carry four messages, two each 
 way, at the same time. The multiplex system enables the sending of 
 six or more messages in the same direction at one time. 
 
 (g) Experiment 398 illustrates the action of a receiver often used 
 with long submarine cables. The minute motions of the needle are 
 rendered visible by the use of a mirror galvanoscope. (See Fig. 391.) 
 There are several telegraphic-printing systems, the object of which is 
 to print the message directly upon paper as it is received. Fac-simile- 
 telegraphy has also been accomplished. In the so-called rapid system, 
 the message is first prepared by punching a series of holes in a strip 
 of paper, each perforation or group of perforations representing a 
 letter. This strip of paper is rapidly passed under metal points con- 
 nected with the line-wire. At each perforation, a point passes through 
 the paper and closes the circuit. At the other end of the line, a band 
 of chemically prepared paper is drawn rapidly under a style connected 
 with the line-wire. The current that is interrupted at the sending 
 station makes a series of stains on the prepared paper at the receiving 
 station, as is illustrated in Experiment 397. As the transmission 
 and recording are automatic, the messages may be sent in rapid 
 succession. 
 
 Experiment 399. Put a key and the apparatus shown in Fig. 392 
 in series in the circuit of a voltaic cell. Keeping the Morse alphabet 
 in mind, try to signal one of the words similarly used in Experiments 
 397 and 398. Consider a short interval between two clicks to be a 
 
 dot, and a longer in- 
 terval to be a dash. 
 
 433. The Sounder 
 is a telegraphic re- 
 ceiver consisting of 
 an electromagnet, 
 and a pivoted ar- 
 mature that plays 
 up and down be- 
 tween its stops as 
 the circuit is alter- 
 
 FIG. 454, 
 
SOME APPLICATIONS OF ELECTRICITY. 
 
 567 
 
 nately made and broken. The message is " read by sound, " 
 i.e., from the clicks made by the armature, substantially as 
 indicated in- Experiment 399. A sounder generally has a 
 resistance of from 3 to 5 ohms. 
 
 Experiment 400. Fasten a wire to the apparatus used in Experi- 
 ment 399, so that when the armature descends, the free end of the 
 wire will be dipped into mercury in the cup at c. Arrange the 
 
 FIG. 455. 
 
 apparatus as shown in Fig. 455, placing a sounder or a telephone 
 receiver at T. As the key is worked at K, the secondary or " local " 
 circuit is made and broken ate, and clicks are produced by the instru- 
 ment at T. 
 
 434. The Relay. With a long main-line and many 
 instruments i n 
 circuit, the re- 
 sistance may be 
 so great as to 
 render the main- 
 battery current _ 
 so feeble that it FlG - 456 - 
 cannot operate the sounder with sufficient energy to render 
 
568 
 
 SCHOOL PHYSICS. 
 
 FIG. 457. 
 
 the signals distinctly audible. 
 This difficulty is met by intro- 
 ducing a "local battery," and 
 a " relay" at each station on 
 the line. The relay (Fig. 456) 
 is an electromagnet made of 
 many turns of fine wire of 
 which the terminals, a and 6, 
 are connected with the main 
 line. This magnet operates an 
 armature lever, e^ the end of 
 which strikes against a metal 
 contact-piece and thus closes the 
 local circuit through the termi- 
 nals, c and d. The resistance 
 of relays varies from 50 to 500 
 ohms. The "Western Union" 
 standard relay has a resistance 
 of 150 ohms. 
 
 (a) -The arrangement of instru- 
 ments is best studied at a telegraph 
 station, one or more of which may 
 be found at almost any town or rail- 
 way station. The general features of 
 the " plant " are represented by the 
 diagram shown in Fig. 457. The pupil 
 will probably find the key, sounder and 
 relay on a table, and the local battery, 
 &, under the table. The keys being 
 habitually" closed, the current passes 
 through all relays on the line, the 
 current being continuous except when 
 a message is being sent from some 
 office. When an operator, in sending 
 
MHIVERSITY OF CAUFORN,. 
 
 DEPARTMENT OF PHV SI <W * 
 
 SOME APPLICATIONS OF ELECTRICITY. J 569 
 
 a message, opens his key, the breaking of the circuit demagnetizes the 
 relays, and allows their springs to draw back the armature levers, e. 
 This breaks each local circuit, and demagnetizes each sounder, the 
 spring of which raises its armature. Things are now as shown in the 
 diagram, which also represents the condition of affairs at every other 
 station on the line. When a message is sent from any station, each 
 relay lever, e, acts as a key to its local circuit, it and the sounder 
 armature working in correspondence with the motions of the key at 
 the sending station. Of course, the message may be read from any 
 sounder on the line. 
 
 (&) If the local circuit at New York (see Fig. 457) is lengthened 
 so as to reach thence to Boston, and the local battery, b, is increased 
 to the size of a main battery, B (ground connections being made, of 
 course), the relay at Xew York will transmit to Boston the message 
 received from Cleveland. In such cases, the relay at Xew York 
 becomes a repeater. 
 
 Experiment 401. Put a telephone receiver in circuit with a bat- 
 tery and two electric-light carbon pencils 
 as shown in Fig. 458. Vary the resist- 
 ance of the circuit by pressing the points 
 of the pencils together, and notice the 
 harsh, grating sound heard in the tele- 
 phone. 
 
 435. The Microphone itr an in- 
 strument for augmenting small 
 sounds. Its action is based 011 
 the fact that when substances of 
 low conductivity are placed in an 
 electric circuit, the resistance of 
 the circuit is diminished by even a very small pressure. 
 
 (a) In one of the simplest forms of the microphone, a piece of char- 
 coal, 6 (Fig. 459), is held between two other pieces of carbon, a and c, 
 in such a way as to be affected by the slightest vibrations carried to it 
 by the air or any other medium. The external pieces being put into 
 
 FIG. 458. 
 
570 SCHOOL PHYSICS. 
 
 circuit with a battery, and a telephone receiver held at the ear, " the 
 
 sounds caused by a fly walking on the 
 wooden support of the microphone ap- 
 pear as loud as the tramp of a horse." 
 
 Experiment 402. Wind 4 oz. of 
 No. 22 insulated copper wire into a 
 coil, A, that has an internal diameter 
 lil'!iil !l!ill|li ^ of 1 cm., and connect its terminals to 
 
 FIG 459 ~ those of a telephone receiver (Fig. 
 
 379). Put a similar coil, J5, in the cir- 
 cuit of a series battery of three or four voltaic cells. Lay B on 
 a block of iron (e.g., a stove cover or a flat-iron), place A upon 
 it, and insert a soft iron core vertically in the openings of the two 
 coils. Place a similar iron bar on end, close to the coils and par- 
 allel with the iron core. Holding the telephone receiver to the 
 ear, quickly lay a soft iron strip upon the upper ends of the two 
 iron rods. A click will be distinctly heard in the telephone receiver. 
 Modify the experiment by replacing the second iron rod by a piece 
 of gas pipe of the same length, and with an internal diameter a little 
 greater than the external diameter of the coils. Put the iron core 
 and the two coils that it carries into the gas pipe, and stand the com- 
 bination on end, close the magnetic circuit with a soft iron strip, and 
 listen at the telephone as before. 
 
 436. The Telephone is an instrument for the transmission 
 of articulate speech to a distant point by the agency of elec- 
 tric currents. The process consists essentially in the trans- 
 mission of electric pulses that agree in period and phase 
 with sound waves in air. These pulses, by means of an 
 electromagnet, cause a plate to vibrate in such a way as to 
 agitate the air in a manner similar to the original disturb- 
 ance, and thus to reproduce the sound. 
 
 (a) The Bell telephone receiver (see Fig. 379) is a magneto-electric 
 device, and is represented in section by Fig. 460. A is a permanent 
 bar magnet around one end of which is wound a coil, , of carefully 
 insulated fine copper wire. The terminals of B are connected to 
 
SOME APPLICATIONS OF ELECTRICITY. 
 
 571 
 
 the binding-posts at D. A soft, flexible sheet-iron disk or diaphragm, 
 
 E, is held by a conical 
 
 mouth-piece or ear 
 
 trumpet across the 
 
 face of -B, near to but 
 
 not quite touching the 
 
 end of A . The outer 
 
 case is made of wood, 
 
 or of hard rubber. 
 (6) When a person 
 
 speaks into the mouth- FIG. 460. 
 
 piece, the sound waves 
 
 beat upon the diaphragm and cause it to vibrate. The nature of these 
 
 vibrations depends upon the loudness, pitch and timbre of the sounds 
 
 uttered. Each vibration of the dia- 
 phragm modifies the magnetic cir- 
 cuit of the receiver, varying the lines 
 of force that pass through B, and 
 thus generating electric pulses in 
 the wire when the circuit is closed. 
 When E approaches B, a current 
 flow r s in one direction ; when E moves 
 the other way, the current flows in 
 the opposite direction. "It is as 
 
 if the close approach and quick oscillation of the piece of soft iron 
 
 fretted or tantalized the magnet, and sent a series of electrical shud- 
 ders through the iron nerve." 
 
 (c) The currents generated in a Bell telephone as just described 
 may be sent through a similar instrument, at a distance of several 
 
 LINE WIRE 
 
 FIG. 461. 
 
 
 
 - 
 
 FIG. 462. 
 
572 
 
 SCHOOL PHYSICS. 
 
 miles, perhaps. The earth may form part of the circuit, as shown in 
 Fig. 462, but a return wire or complete metallic circuit is preferable. 
 When the current generated at E flows in such a direction as to 
 reinforce the magnet at A', the latter attracts E' more strongly than 
 it did before. When the current flows in the opposite direction, it 
 weakens the magnetism of A', which then attracts E' less. The disk, 
 therefore, flies back. Thus, the vibrations of E' keep step with those 
 of E, and produce sound waves that are very faithful counterparts of 
 those that fell upon E. The sound thus produced at E' is feeble, 
 but, when the receiving instrument is held close to the ear of the 
 listener, the sound is clear, and the articulation remarkably distinct. 
 Conversation may be carried on between moderately distant stations 
 with this apparatus, no battery being necessary. 
 
 437. The Transmitter is a microphone adapted for the 
 transmission of telephonic messages and, in general prac- 
 tice, is so used, better results being thus secured than is 
 possible when the transmitter and receiver are identical 
 in form. 
 
 (a) In the Blake transmitter, a diaphragm is supported back of 
 a mouthpiece, as in the Bell telephone. Back of the center of the 
 diaphragm is the point of a spring, m, that carries a small platinum 
 
 LINE WIRE. 
 
 1 
 
 ARTH EARTH- 
 
 FIG. 463. 
 
 ball that makes gentle contact with the diaphragm. Back of this 
 is a spring, n, that is insulated from ra, and that carries a carbon 
 button, B, that rests lightly against the platinum ball. The ball, the 
 button, and the primary of an induction coil are put in series in 
 the circuit of a voltaic battery, D, as shown in Fig. 463. The varia- 
 
SOME APPLICATIONS OF ELECTRICITY. 
 
 573 
 
 tions in the resistance of this circuit, caused by the varying pressure 
 and surface contact between the platinum and the carbon, cause 
 variations in the current that flows through the primary of the induc- 
 tion coil, and thus induce currents in the secondary of the coil. One 
 of the terminals of the secondary is connected through a receiving 
 instrument, R, to the earth, and the other terminal to the line-wire 
 leading to another station, as diagrammatically indicated in Fig. 463. 
 As previously suggested, a complete metallic circuit is preferable to 
 the earth connections. The induced currents correspond closely to 
 the pulsations produced in the primary current by the vibrations 
 of the diaphragm of the transmitter, and in turn set up vibrations in 
 the diaphragm of the receiver at the other station which, accordingly, 
 sends off sound waves similar to those 
 that disturbed the diaphragm of the 
 transmitter. An electric bell, shown 
 at E in Fig. 464, is placed at each 
 station. It is rung by a small mag- 
 neto at the sending station for the 
 purpose of attracting the attention 
 of the person at the receiving station. 
 When the speaker or the listener lifts 
 the receiver, B, from the hook that 
 carries it, as shown in Fig. 464, the 
 upward motion of the hook cuts the 
 magneto and the bells from the circuit, 
 and completes the connections sub- 
 stantially as shown in Fig. 463. - 
 
 (6) The long distance transmitter, 
 represented at C in Fig. 464, differs 
 from the Blake transmitter chiefly in 
 the use of a carbon that is granular 
 instead of hard, and in the use of two 
 or three cells instead of one. 
 
 (c) In most cities and villages, the 
 telephones are connected by wires 
 with a central station, called a tele- 
 phone exchange. The exchange may 
 thus be connected with hundreds of 
 houses in all parts of the city, or even 
 in different cities. Upon request by FIG. 464. 
 
574 SCHOOL PHYSICS. 
 
 telephone, the attendant at the central station connects the lino from 
 any instrument with that running to any other instrument. Long 
 distance telephony has been so nearly perfected that it is common to 
 carry on conversation between places as far distant as Boston or 
 New York and Chicago. 
 
 438. The Bolometer is an instrument designed for meas- 
 uring very small variations in the intensity of radiant 
 energy by the alteration of electrical resistance produced 
 in a metallic conductor by changes of temperature. 
 
 (a) Two narrow and very thin strips of platinum or of iron are 
 made two adjacent arms of a Wheatstone bridge, the other two arms 
 being any convenient adjustable resistance. A delicate galvanometer 
 is placed in the " bridge." The radiation to be measured is allowed to 
 fall upon one of these strips, while the other strip is shielded from it 
 by a screen. The absorption of the radiant energy by the strip 
 increases the resistance of the strip, and thus destroys the balance 
 and deflects the galvanometer needle. With such an instrument, 
 changes of temperature as minute as a hundred-thousandth of a 
 degree centigrade have been measured, and still smaller variations 
 may be detected. 
 
 439. A Lightning Rod is a metallic conductor placed 
 on a building as a protection from lightning. When an 
 electrified cloud floats over a building, the latter is oppo- 
 sitely electrified by induction. The electrification of the 
 building escapes from the pointed conductor, and tends to 
 neutralize the electrification of the cloud. Its action may 
 proceed too slowly to keep down the rapidly rising poten- 
 tial of the cloud and to prevent the disruptive discharge, 
 but even then the rod tends to protect the building by 
 offering a path of less resistance. The discharge does not 
 always follow the path of least resistance, but the protec- 
 tion is probable. The discovery of the oscillatory char- 
 
SOME APPLICATIONS OF ELECTRICITY. 575 
 
 acter of the discharge has largely modified the character of 
 the protection recommended. 
 
 (a) In lightning protection, the following facts should be kept in 
 mind : the surface of the rod is of more importance than sectional 
 area ; iron is, at least, as good as copper ; the upper end should have 
 several branches terminating in sharp points that are plated, or other- 
 wise protected from rust or corrosion; very little reliance should be 
 placed on the so-called " area of protection " ; a rod towering high 
 above the roof is not as good as many smaller ones along the ridge of 
 the roof ; the conductor should be continuous and run to earth by the 
 most direct path, avoiding sharp bends, and going deep enough to be 
 sure of a good connection with a stratum that is always moist ; owing 
 to the high potential involved and the brief duration of the discharge, 
 all possible paths should be provided, and metallic surfaces should be 
 independently connected to earth ; bury terminal earth-plates in 
 damp earth or running water, and do not imagine that you can overdo 
 the matter of making a good ground connection ; insulators should 
 not be used to hold the rod in position. Next to a poor " ground," 
 the chief defects likely to occur are blunted points, and breaks in the 
 continuity of the rod. For ordinary dwellings in city blocks (not 
 unusually exposed) lightning rods are hardly necessary, but scattered 
 houses, especially those built on hillsides, should be thus protected. 
 
 (6) According to Professor Barker, the cheapest way to protect an 
 ordinary house "is to run common galvanized-iron telegraph-wire up 
 all the corners, along all the ridges and eaves, and over all the chim- 
 neys, taking these wires down to -the earth in several places and, at 
 each place, burying a load of coke around the wire in order to estab- 
 lish at each point an efficient connection with the ground." 
 
 CLASSROOM EXERCISES. 
 
 1. A dynamo is feeding 16 arc lamps that have an average resistance 
 of 4.56 oHms. The internal resistance of the dynamo is 10.55 ohms. 
 What current does the dynamo yield with an E.M.F. of 838.44 volts ? 
 
 Ans. 10.04 amperes. 
 
 2. If a wire about 18 inches long is attached to one electrode of a 
 cell, and the other electrode is momentarily touched with the other end 
 of the wire, a minute spark may be noticed at the instant of breaking 
 the circuit. If the wire is bent into a scalariform or ladder-like shape 
 
576 SCHOOL PHYSICS. 
 
 and the experiment repeated, the spark will be greater than before. 
 If the form of the external circuit is again 
 changed by winding the wire into a spiral 
 (as shown in Fig. 465), the spark will be 
 still greater. Explain the increase in the 
 spark. 
 
 3. A dynamo is run at 450 revolutions, 
 
 developing a current of 9.925 amperes. 
 This current deflects the needle of a tangent galvanometer, 60. 
 When the speed of the dynamo is sufficiently increased, the galvanom- 
 eter shows a deflection of 74. What is the current developed at 
 the higher speed ? Ans. 20 amperes. 
 
 4. The current running through the carbon filament of an incan- 
 descence lamp was found to be 1 ampere. The difference of potential 
 between the two terminals of the lamp was found to be 30 volts. What 
 was the resistance of the lamp ? 
 
 5. The hot resistance of a 16-c.p. incandescence lamp is 240 ohms. 
 The lamp is placed in a 110-volt circuit. () What current flows 
 through the lamp ? (ft) How many watts are expended in the lamp? 
 (c) What is the consumption of energy per candle power? 
 
 Ans. () 0.46 ampere; (&) 50.6 watts; (c) 3.16 watts. 
 
 6. I want to place, in series, 10 incandescence lamps, each of 25 
 ohms resistance ; the line- wire is to be 200 feet long and its resistance 
 must be not more than 2 per cent, of the resistance of the lamps. 
 Determine the size of wire that should be used. Ans. No. 23. 
 
 7. I want to place the same lamps abreast. The line-wire is to be 
 200 feet long and have a resistance of not more than 2 per cent, of 
 that of the lamps. Determine the size of wire that should be used. 
 
 Ans. No. 4. 
 
 8. The resistance of the normal arc of an electric lamp is 3.8 ohms. 
 The current strength is 10 amperes. What is the difference of poten- 
 tial between the carbon tips? Ans. 38 volts. 
 
 9. The resistance of the arc lamp above mentioned, when the car- 
 bons are held together, is 0.62 ohm. When it is burning with normal 
 arc and a 10-ampere current, what is the difference of potential between 
 the terminals of the lamp ? Ans. 44.2 volts. 
 
 10. A dynamo has an E.M.F. of 206 volts, and an internal resistance 
 of 1.6 ohms. Find the current strength when the external resistance 
 is 25.4 ohms. Ans. 7.6 amperes. 
 
 11. A dynamo has an internal resistance of 2.8 ohms. The line- 
 
SOME APPLICATIONS OF ELECTRICITY. 577 
 
 wire has a resistance of 1.1 ohms and joins the dynamo to 3 arc lamps 
 in series, each lamp having a resistance of 3.12 ohms. Under such 
 conditions, the dynamo develops a current of 14.8 amperes. What is 
 the E.M.F. ? Ans. 196 .25 vo i ts . 
 
 12. A dynamo, run at a certain speed, gives an E.M.F. of 200 volts. 
 It has an internal resistance of 0.5 of an ohm. In the external circuit 
 
 ,are 3 arc lamps in series, each -having a resistance of 2.5 ohms. The 
 line wire has a resistance of 0.5 of an ohm. I want a current of just 
 25 amperes. Must I increase or lessen the speed of the dynamo ? 
 
 13. With an external resistance of 1.14 ohms, a dynamo develops a 
 current of 81.58 volts and 29.67 amperes. What is the internal resist 
 ance of the dynamo ? A ns. 1.61 ohms. 
 
 14. Upon trial, it was found that a dynamo that was known to have 
 an internal resistance of 4.58 ohms developed a current of 157.5 volts 
 and 17.5 amperes. What was the resistance of the external circuit ? 
 
 Ans. 4.42 ohms. 
 
 15. Three incandescence lamps having a resistance of 39.3 ohms 
 each (when hot) were placed in series. The total resistance of the 
 circuit outside of the lamps was 11.2 ohms. The current measured 
 1.2 amperes. What was the E.M.F.? Ans. 154.92 volts. 
 
 16. A dynamo supplies current for two incandescence lamps in 
 series, each having a hot resistance of 97 ohms. The other resistances 
 of the circuit amounted to 12 ohms. The current in the first lamp was 
 1 ampere. What was the current carried by the carbon filament of 
 the second lamp ? What was the E.M.F. ? 
 
 17. A dynamo is required to f urnish a 9.6-ampere current for 60 arc 
 lamps. Assuming that a copper wire 1 square inch in cross-section 
 will safely carry 2,000 amperes, determine the proper size of wire for 
 the Gramme ring armature of the dynamo. In such an armature, each 
 wire carries half the current. Ans. No. 15. 
 
 18. W 7 hat E.M.F. must be generated by the dynamo mentioned in 
 Exercise 17 if the resistance of the line-wire is 5 ohms, the internal 
 resistance of the machine is 16 ohms, and the difference of potential 
 between the terminals of each lamp is 45 ohms ? 
 
 19. Assume that the E.M.F. of a bipolar dynamo may be deter- 
 mined by the formula, 
 
 F-. nks 
 
 " 100,000,000 ' 
 
 In which E represents the E.M.F.; n the number of lines of force 
 passing effectively through the armature ; k the number of conductors 
 37 
 
578 
 
 SCHOOL PHYSICS. 
 
 in series on the armature ; and s the number of revolutions that the 
 armature makes per second. Determine the E.M.F. of a dynamo the 
 armature of which makes 780 revolutions per minute, has 120 conduc- 
 tors in series, and is threaded by 7,200,000 lines of force. 
 
 Ans. 112.32 volts. 
 
 20. What effect would a slowing of the speed of a dynamo have 
 upon its E.M.F. ? 
 
 21. Suppose that the armatures of two dynamos rotate at the same 
 speed in fields of like intensity. The armatures differ only in that one 
 has twice as many bobbins in series as the other. How will the 
 dynamos compare in E.M.F.? 
 
 22. Suppose that the armature of a dynamo is wound with No. 8 
 copper wire, that it revolves at a uniform speed, and that the potential 
 difference at the terminals of the dynamo is constant. What is to 
 prevent our drawing from the machine a current that is almost 
 unlimited as to strength? 
 
 23. Suppose an adjustable resistance, jR, to be cut into the magiietiz- 
 
 4. _ ing circuit of a shunt-wound 
 
 dynamo as shown in Fig. 
 466. How would an in- 
 creased resistance affect the 
 number of lines of force that 
 pass through the armature, 
 A ? Could the E.M.F. of the 
 dynamo be thus controlled? 
 24. A certain dynamo 
 yields a current of 9.6 am- 
 peres at almost any voltage 
 desired. I want to send a 
 2-ampere current through 
 a coil that has a resistance 
 of 2 ohms. What resistance must be put in parallel with the coil 
 between the terminals of the dynamo? Ans. 0.526 -f ohms. 
 
 25. A system of 127 incandescence lamps, each fed at a potential 
 difference of 110 volts, and with a current of 0.5 of an ampere, is 620 
 feet from the dynamo. Allowing for an absorption of four per cent, 
 of the energy of the current by the line-wire, (a) what must be the 
 voltage of the dynamo? The difference between the voltage of 
 the dynamo and that of the lamps is the fall of potential due to the 
 resistance of the wire. Applying Ohm's law, divide this fall of poten- 
 
 FIG. 466. 
 
ELECTROMAGNETIC CHARACTER OF RADIATION. 579 
 
 tial by the current required, and thus (ft) determine the total resist- 
 ance of the line-wire, (c) Determine the resistance of the line-wire 
 per foot. (Y/) Consult the table in the appendix, and ascertain the 
 proper size of the line-wire. Ans. (a) 114.58 + volts. 
 
 26. The field magnet of a shunt-wound dynamo is to be made of 
 Xo. 14 copper wire. Such a wire cannot carry a current of more than 
 15 amperes without danger of becoming so hot as to injure its insula- 
 tion. Assume that the dynamo delivers current at 110 volts, and 
 determine the length of wire that must be used in the field magnets 
 to keep them from over-heating. 
 
 27. Fire insurance rules allow Xo. 0000 (" four-naught") copper 
 wire to carry a current of 175 amperes, which is sufficient for 350 
 lamps at 110 volts. Suppose that one hundred such lamps are to be 
 placed a mile from a central station, () What will be the resistance 
 of the line if it is made of the wire above mentioned? (ft) What 
 must the voltage at the station be ? 
 
 Ans. (a) 0.53856 ohms; (ft) 136.928 volts. 
 
 28. I have two telegraph sounders. One of them is made with a 
 few turns of coarse wire ; the other of many turns of fine wire. Try- 
 ing them on a long line of great resistance, I find that one works 
 satisfactorily while the other will not work at all. Which sounder 
 works ? Explain the difference in the results secured with the two 
 instruments. 
 
 29. A telegraph line is to be operated between Boston and Chicago. 
 The high resistance of so long a line requires a current of such high 
 potential that there is great difficulty in maintaining the insulation. 
 How may this difficulty be removed ? 
 
 30. I find that I can hear readily through a telephone receiver that 
 is in circuit with several miles of uncoiled wire, but that when the 
 wire is wound upon an iron core, thus making an electromagnet, I 
 cannot hear through the telephone at all. Explain. 
 
 V. ELECTROMAGNETIC CHARACTER OF 
 RADIATION. 
 
 V 
 
 440. Electromagnetic Rotation, etc. When a beam of 
 polarized light is passed through a magnetic field, the 
 plane of polarization is rotated in the direction in which 
 
580 SCHOOL PHYSICS. 
 
 an electric current would have to circulate around the 
 beam to produce the existing magnetism. If the beam is 
 reflected back so as to traverse the magnetic field twice in 
 opposite directions, the magnetic rotation is doubled. 
 When a beam of polarized light is reflected from the 
 polished pole of an electromagnet, the plane of polariza- 
 tion is rotated in a direction contrary to that of the mag- 
 netizing current. A dielectric under electrostatic stress 
 becomes doubly refracting. These and other facts sug- 
 gest that there is some definite relation between elec- 
 tricity and light. 
 
 441. Electrical Oscillations. If an elastic cord is 
 stretched between two supports and its middle pulled to 
 one side, it may be allowed to return to its normal posi- 
 tion so gently as to cause no vibrations in the cord, or it 
 may be released so as to set up vibrations, the frequency 
 of which will depend largely upon the tension of the cord. 
 Similarly, when a Leyden jar is discharged through a dry 
 linen thread, there is a gentle floAV of electrification from 
 one coat to the other, and equilibrium is quietly restored. 
 On the other hand, when the charged jar is discharged 
 through a short metal conductor, the charge rushes sud- 
 denly from one coat to 
 the other, overdoes its 
 work, and surges back 
 ONC5 and forth with gradu- 
 
 100,000 . 
 
 ally weakening energy 
 until the two coats are 
 FlG - 467 - at the same potential. 
 
 (a) Fig. 467 is a graphic representation of such electrical oscilla- 
 tion, the heights of the waves being proportional to the magnitudes of 
 
ELECTROMAGNETIC CHARACTER OF RADIATION. 581 
 
 the flow, and the lengths being proportional to the times required for 
 the successive oscillations. Fig. 468 shows a similar curve for an 
 ordinary alternating current. Comparing the time axes (abscissae) of 
 the two curves, it is seen that the curve of the Leyden jar may be 
 completed in 0.00001 of a second, while the alternate current requires 
 0.004 of a second for a single pulse. Further comparison of the 
 curves shows a marked difference in the rate of change, the time inter- 
 
 t -1 SECONDS 
 
 Fia.468. 
 
 val required, in the first case, for a drop from a maximum value in 
 one direction to a maximum in the other direction being almost 
 infinitesimal. It also appears that the alternating current curve is 
 strictly periodic and repeats itself, while the Leyden jar oscillations 
 gradually die away. It has been shown that when the resistance of 
 the circuit is negligible, the number and periods of these oscillations 
 per second may be represented thus : 
 
 , or t = 2 IT 
 
 In this formula, n represents the frequency, and t the period of oscilla- 
 tion ; K, the capacity ; and L, the coefficient of self-induction. An 
 increase in the values of K and L diminishes the value of n. By dis- 
 charging a large condenser through a high inductive resistance, the 
 frequency of the electrical oscillations has been reduced to 400 per 
 second, under which conditions the electric spark emitted a musical 
 tone. 
 
 442. Electromagnetic Waves. With currents of slowly 
 varying strength, magnetic lines of force surround the 
 
582 SCHOOL PHYSICS. 
 
 conductors that carry the currents. When the direction 
 of the current is changed, the direction of the lines of 
 force is changed. These lines of force spread out from a 
 wire carrying an increasing current much like the ripples 
 on a pond moving outward from the center of disturbance. 
 As the current dies away, these magnetic lines of force 
 are called in again. As the current reverses its direction, 
 other lines of force opposite in direction from the former 
 ones are sent out. This alternating action sets up a series 
 of waves that travels outward. So, when the rapidly 
 oscillating motions of the Ley den jar discharge are applied 
 to a conductor, the magnetic ripples that are propagated 
 never return to the conductor that generates them, but 
 continue on through space like the waves of radiant energy. 
 Just as a vibrating tuning-fork expends its energy in 
 producing air waves, so a discharging condenser sets up 
 vibrations in the medium of electrical action, whatever 
 that medium may be. 
 
 (a) In recent years, Hertz and Nikola Tesla have experimented 
 with these electromagnetic waves, and have shown that they may be 
 reflected, refracted, and polarized, and that they possess all the trans- 
 mittive properties of radiant energy. They have also shown that 
 their velocity is identical with that of light, and that indices of refrac- 
 tion are the same for electromagnetic waves as they are for the shorter 
 waves that are familiarly recognized as radiant energy. 
 
 Experiment 403. Provide two Leyden jars that are alike. Paste 
 a strip of tin-foil so that it touches the inner coat of one of the jars, 
 passes over the edge, and nearly touches the outer coat as shown at 
 a in Fig. 469. From the knob and the outer coat of this jar, /, lead 
 two wires. Tie these wires with silk thread to the edges of a plate 
 of glass that is 6 or 7 cm. wide and supported in a vertical plane. 
 Connect a wire to the outer coat of the other jar, L, bend the wire 
 into a loop, and provide a terminal ball, B, as shown in the figure. 
 Bend the wire so that B is brought very near to the knob, A, without 
 
ELECTROMAGNETIC CHARACTER OF RADIATION. 583 
 
 quite touching it. Place L near /, with its wire loop in a plane that 
 is parallel to that of the suspended glass plate. Charge L by an 
 induction coil or an electrical machine so that a stream of sparks snaps 
 across AB. Connect the two wires carried by /, by a spring clip, C. 
 
 FIG. 4fi9. 
 
 Move the clip back and forth along the wires until you find for it a 
 position such that as sparks pass between A and B, other sparks will 
 snap across the gap at a. The _two jars will then be in " electrical 
 resonance." 
 
 443. Electrical Resonance. When certain relations of 
 capacity and reactance exist between two electric circuits, 
 electrical vibrations of high frequency in one of the cir- 
 cuits will set up electrical vibrations in the other circuit. 
 The best results are obtained when the receiving circuit is 
 so adjusted that its oscillations are synchronous with those 
 of the generating circuit. A receiving circuit so adjusted 
 is called an electrical resonator. Electrical resonance is 
 analogous to acoustic resonance, and has been of great 
 
584 SCHOOL PHYSICS. 
 
 value in recent researches on the electromagnetic theory 
 of light. The adjustment of capacity and self-induction 
 so as to harmonize the vibration-frequency of the two cir- 
 cuits, i.e., to establish resonance, is often a matter of great 
 delicacy and difficulty. In very exact adjustments, minute 
 changes completely destroy the balance, just as they do in 
 acoustic resonance. 
 
 444. The Hertz Experiments. In his study of electric 
 waves, Hertz, the first successful investigator in this field, 
 used an " oscillator " that consisted of an induction coil, 
 the terminals of which carried two metal rods, t and t 1 , 
 that ended in small metal balls, and that were provided 
 
 with large movable 
 t t ' 1Y | R metal plates or 
 
 spheres, A and B. 
 
 The capacity, K, of 
 
 the system was deter- 
 FIG - 470 ' mined from the size 
 
 of the plates or the spheres, A and B, and the coefficient 
 of self-induction, L, from the dimensions of the rods, 
 t and t 1 . Within certain limits, the value of L could 
 be adjusted by varying the position of A and B upon 
 the rods. The values of K and L being known, the pe- 
 riod of a complete oscillation could be determined (see 
 441, a). To reduce the wave-length to convenient val- 
 ues (say a meter or two), the oscillations were made 
 rapid; i.e., K and L were made small. 
 
 (a) The action of this apparatus generates two sets of waves of the 
 same period ; one set being electrostatic, and the other, electromag- 
 netic. The effects produced by these two sets of waves may be 
 separately studied. The electrostatic lines of force extend between A 
 
ELECTROMAGNETIC CHARACTER OF RADIATION. 585 
 
 and B. The electromagnetic lines of force are concentric about the 
 rods, t and i! '. Hertz's resonator was an open 
 wire ring terminally provided with small 
 balls, micrometrically adjustable so that the 
 distance between them could be accurately 
 measured. When this simple resonator is 
 made to enclose the electromagnetic lines of 
 force set up by the oscillator, induction sparks 
 pass between the terminals m and n. Adjust- 
 ment for synchronous effect, and placing the 
 resonator so that its plane passes through the 
 axis of the oscillator, raise the sparks to their FIG. 471. 
 
 maximum value. 
 
 (6) Anywhere in the field, sparks may be obtained between any two 
 metallic objects. Hertz placed two rods in the same line and with 
 their ends near together, and used them as a receiver. He attached 
 sheets of tin-foil to the rods, and thus increased their capacity, so that 
 sparks were obtained at a distance of 20 or 30 m. from the oscillator. 
 He found that non-conductors are transparent to the electric radia- 
 tions, and that conductors act as reflectors. With waves reflected from 
 a zinc-covered wall, and by moving the resonator about, he found 
 points of maximum and minimum disturbance corresponding to the 
 loops and nodes of a vibrating string. The wave-lengths thus deter- 
 mined, multiplied by the frequency of vibration as calculated from K 
 and L, the constants of the oscillator, gave a velocity for electric wave 
 propagation that is practically the same as the velocity of light. He 
 also demonstrated the rectilinear_.propagation of the waves, and focused 
 them with a metallic parabolic mirror. He refracted them with a 
 prism of pitch, and established the index of refraction for radiations 
 of certain wave-lengths. 
 
 (c) Using more delicate apparatus, Lodge has detected electro- 
 magnetic waves that had passed through floors and walls, and at a 
 distance of hundreds of feet. 
 
 445. The Tesla Experiments. By means of his oscil- 
 lator ( 398), in which the armature coils are shot, very 
 rapidly and shuttle-fashion, in and out of the magnetic 
 field, Nikola Tesla has generated alternating currents of 
 
586 SCHOOL PHYSICS. 
 
 higher frequency, potential, and regularity than any pre- 
 viously employed, and has greatly augmented the Hertzan 
 effects and added to them. 
 
 (a) He has shown that such currents flow mostly on the outer sur- 
 face of the conductor, as though ether vortices were rolled along the 
 wire as a rubber band may be rolled along a 
 pencil, and that the impedance of a stout copper 
 rod may be hundreds of times as great as that of 
 an incandescent lamp filament, although the ratio 
 of their resistances is the reverse. For instance, 
 he short-circuited a lamp by a copper rod as shown 
 in Fig. 472. Any ordinary current, direct or 
 alternating, would melt the rod before the lamp 
 began to glow, but Tesla's current brilliantly il- 
 luminated the lamp and left the rod cool. In fact, 
 with Teslaic currents, the resistance of the lamp 
 FIG 472 filaments counts for little or nothing, and the fila- 
 
 ment may as well be short and thick as long and 
 thin. More than even this, the filament and conducting wires 
 may be wholly omitted. Vacuum tubes of ordinary glass held in 
 the hand near the terminal of a high frequency coil became 
 luminous, as shown in Fig. 473, clearly showing that, as the current- 
 frequency rises, electrodynamic conditions are left for those that 
 are electrostatic, and that space itself "is all circuit if we prop- 
 erly direct the right kind of impulses through it." Tesla led a 
 small cable around the walls of a room 40 x 80 feet in size, and con- 
 nected its ends to the terminals of an oscillator. In the middle of the 
 room, he placed a coil-wound resonator three or four feet high and 
 provided with two adjustable condenser plates. These plates stood on 
 edge above the end of the coil and facing each other, much as if they 
 w T ere cymbals resting upon the head of a bass drum. By adjusting 
 the condenser plates, the resonator was so attuned that the periodicity 
 of the induced current kept step with that of the cable current. When 
 current from the oscillator was sent along the cable around the room, 
 powerful sparks poured in dense streams across the space between the 
 cymbal-like plates of the attuned condenser in the middle of the room. 
 A potential difference of 200,000 or 300,000 volts is easily developed 
 in this way, and the high-tension currents pass through the human 
 body without injury. With a similar resonator similarly placed and 
 
ELECTROMAGNETIC CHARACTER OF RADIATION. 587 
 
 properly attuned, an ordinary 16-c.p. lamp was well illuminated. 
 When an 110-volt lamp was attached by one terminal to a wire circle, 
 and the circle held above the resonator coil, the lamp immediately 
 lighted up. Such an illumination of such a lamp calls for the expen- 
 diture of more than a tenth of a horse-power, so that at least that 
 
 FIG. 473. 
 
 amount of energy was transmitted through free space, i. e., without any 
 wire. By connecting to earth one terminal of a coil in which rapidly 
 vibrating currents are thus produced, and leaving the other terminal 
 free in space, Tesla produces striking effects, purple fiery streams and 
 lightning discharges pouring into the air from the tip of the wire "with 
 the roar of a gas well." 
 
 Mr. Tesla has secured his results chiefly because he has "learned the 
 knack of loading electrically on the good-natured ether a little of the 
 protean energy of which no amount has yet sufficed to break it down 
 or put it out of temper." His experiments point toward the possibility 
 of telephony without any wire, i.e., by induction through the air and, 
 in fact, some such transmission of intelligence has been seriously pro- 
 pounded, not as a mere theoretical possibility but as a problem in 
 practical electrical engineering. 
 
588 SCHOOL PHYSICS. 
 
 446. The Electromagnetic Theory of Light. Optical 
 and electrical phenomena seem to call for media that have 
 identical properties; i.e., they indicate that the medium 
 of the one is identical with the medium of the other. The 
 experimental proof that 3 x 10 10 centimeters represent 
 alike the velocity of light and the velocity of electric 
 waves, indicates that the ether is the common medium. 
 This, taken in connection with the close relation estab- 
 lished between specific inductive capacity and index of 
 refraction, and that between electric conductivity and 
 optical opacity, and the experiments of Hertz and of Tesla, 
 " appear to prove beyond a question that light is itself an 
 electrical phenomenon and that optics is a department of 
 electrics. To produce radiation, it is only necessary to 
 produce electric oscillations of sufficiently short period." 
 This theory of light as an electromagnetic disturbance was 
 propounded in 1865 by Maxwell ; if recent investigations 
 do not wholly establish it, they certainly give it very 
 strong support. 
 
 (a) It has been calculated that a condenser of one microfarad 
 capacity might generate electric waves 1,900 Km. long ; a pint Leyden 
 jar, waves 15 or 20 m. long; and a tiny thimble-like jar, waves 1 m. 
 long. Continuing this process to ascertain the size of a circuit that 
 will give wave-lengths comparable to those of light, physicists come 
 to the suggestion that the ether waves that affect the retina of the 
 human eye may be produced by the electric oscillations of circuits of 
 atomic dimensions. An atom of sodium vibrates five hundred 
 million times in one millionth of a second. If we could produce 
 electric oscillations and maintain them at this rate, we could produce 
 light. 
 
 (fc) Light is ordinarily produced by combustion, less than one per 
 cent of the emitted energy being visible. "The problem of the age 
 is to convert some other form of energy entirely into the energy of 
 light. That this is possible in theory, Rayleigh long ago showed. 
 
ELECTROMAGNETIC CHARACTER OF RADIATION. 589 
 
 That it is actually accomplished in Nature, Langley's remarkable 
 measurements upon the glowworm abundantly confirm. Now that 
 the mechanism of the process is before us, it would seem not impos- 
 sible eventually to create and to maintain electric oscillations of the 
 frequency required for . light alone. When this is done, the problem 
 of the economical production of artificial light will have been solved." 
 
 447. Yesterday, To-day, To-morrow. In the light of 
 what has lately been accomplished by the blending of 
 theory and practice, and of the promise that comes from 
 the state of unrest in which electrical science now exists, 
 it seems a fitting final word to suggest that constant 
 study is the price of a clear understanding of conditions 
 that prevail in the domain of electricity. " Its theoretical 
 problems assume novel phases daily. Its old appliances 
 ceaselessly give way to successors. Its methods of pro- 
 duction, distribution, and utilization vary from year to 
 year. Its influence on the times is ever deeper, yet one 
 can never be quite sure into what part of the social or 
 industrial system it is next to thrust a revolutionary force. 
 Its fanciful dreams of yesterday are the magnificent 
 triumphs of to-morrow, and its advance toward domination 
 in the twentieth century is as irresistible as that of steam 
 in the nineteenth." 
 
APPENDIX. 
 
 1. Mensurative, etc. 
 
 TT = 3.14159. 
 
 Circumference of a circle = irD. 
 
 Area of a circle = TrR' 2 . 
 
 Surface of a sphere = 4irR 2 = 7rZ> 2 . 
 
 Volume of a sphere = |7r/t 3 = \irLP. 
 
 Meters x 3.2809 = feet. 
 
 Feet x 0.3048 ^ meters. 
 
 Inches x 2.54 = centimeters. 
 
 Cubic inches x 16.386 = cubic centimeters. 
 
 Cubic centimeters x 0.06103 = cubic inches. 
 
 Kilogrammeters x 7.2331 = foot-pounds. 
 
 2. Table of Materials in Electromotive Order. 
 
 (Electrochemical Series.) 
 
 DILUTE 
 SULPHUEIC ACID. 
 
 DILUTE 
 HYDROCHLORIC 
 ACID. 
 
 SOLUTION 
 OF SULPHIDE OF 
 POTASSIUM. 
 
 SOLUTION OF 
 CAUSTIC POTASH. 
 
 1. Zinc. 
 
 1. Zinc. 
 
 1. Zinc. 
 
 1. Zinc. 
 
 2. Cadmium. 
 
 2. Cadmium. 
 
 2. Copper. 
 
 2. Tin. i 
 
 3. Tin. 
 
 3. Tin. 
 
 3. Cadmium. 
 
 3. Cadmium, i 
 
 4. Lead. 
 
 4. Lead. 
 
 4. Tin. 
 
 4. Antimony. 
 
 .H 5. Iron. 
 
 5. Iron. 
 
 5. Silver. 
 
 5. Lead. 
 
 J 6. Nickel. 
 
 6. Copper. 
 
 6. Antimony. 
 
 6. Bismuth. ^ 
 
 5 7. Bismuth. 
 
 7. Bismuth. 
 
 7. Lead. 
 
 7. Iron. = 
 
 
 
 5 8. Antimony. 
 
 8. Nickel. 
 
 8. Bismuth. 
 
 8. Copper. 5 
 
 9. Copper. 
 
 9. Silver. 
 
 9. Nickel. 
 
 9. Nickel. 
 
 ' 10. Silver. 
 
 10. Antimony. 
 
 10. Iron. 
 
 10. Silver. 
 
 I 11. Gold. 
 
 11. ... 
 
 11. . . 
 
 11. ... 
 
 12. Platinum. 
 
 12. ... 
 
 12. . . 
 
 12. ... 
 
 13. Carbon. 
 
 13. ... 
 
 13. . . . 
 
 13. . . . 
 
 591 
 
592 SCHOOL PHYSICS. 
 
 For any given solution, the farther apart any two materials are 
 in the electromotive table, the stronger will be the electrical effect of 
 a cell with plates made of such materials. 
 
 3. Table of Resistivities. Represent the length of a conducting 
 wire measured in feet by /, its diameter measured in thousandths of 
 an inch (mils) by d, and its resistance measured in ohins by r. In the 
 formula 
 
 K represents a constant that depends upon the material of the wire 
 and, for the substances considered, is as given in the following table 
 of resistivities: 
 
 Silver 9.84 
 
 Copper 10.45 
 
 Zinc . . 36.69 
 
 Mercury 58.24 
 
 Platinum 59.02 
 
 Iron . . 63.35 
 
 German-silver .... 128.29 
 
 These values of K are computed for the temperature of 20. Thus 
 the resistance of 1,000 feet of No. 0000 copper wire at 20, is 
 10.45 x 1,000 -4- 460 2 = 0.049 + ohms. 
 
 4. Dimensions and Functions of Copper Wires. In the table given 
 on the next two pages, the second column gives the diameters in mils, 
 i.e., thousandths of an inch ; the third column in millimeters. The 
 fourth column gives the equivalent number of wires each one mil in 
 diameter. By multiplying the numbers in the sixth column by 5.28, 
 the resistances per mile may be found. The resistance for any other 
 metal than copper may be found by multiplying the resistance given 
 in the table by the ratio between the resistivity of copper and that 
 of the given metal. The resistances given in the table are for pure 
 copper wire. Ordinary commercial copper wire has a lower conduc- 
 tivity than that of pure copper. Consequently, the resistances of 
 such wires will be greater than those given in the table. 
 
APPENDIX. 
 
 593 
 
 Ml 
 
 AXIOVdVQ 
 
 i i ?b CM co 10 cc i i ci i^ 
 
 CC <M ?1 l-l T-I r-l ,-1 
 
 TJH -O CC Ol Ol i-l 1-1 1-1 ri 
 
 CC CC 
 O GO GO 
 
 o o o d H 
 
 CO <3l CO K3 1Q CO r4 fc IQ CO fc> b H 00 OO 
 
 CC CJ ^ ^-, rt 
 
 I 
 
 O 
 
 1 
 
 I 
 
 T3 
 
 
 s 
 
 .2 
 
 * 
 
 S ' 
 
 I 
 
 p 
 
 
 
 CC <M CM 1-1 1-1 i-l 
 
 o<oooooc>ccooocoooocc> 
 
 Si 
 
 o 
 
 ut c c cc o c^ tc c: -f 
 
 Ct-CtClt^CC^Oi^^^Ci 
 
 8O P <5 O O O O Q O O O Q O <N 00 i-l -^ GO ^_ __ 
 9 o K3 o eo 04 *-i 9 cj co S eo a TP o D oo QD c*i^b o 
 o QD OD o eo 00 TH eo Cb o 09 < ^r OD t^~ao c% o O ao ci eo 
 
 Oi "^t 4 ^* O^ t^* OS "^f^ iH Ol ^^ GO ^^ *"H <O O^ T-^ ^^ t^ ^^ lO ! O 
 OOC s JCOOOlOCOCO-^OJr-tOO5GOl>.CDlOlC-^tTtl 
 
 38 
 
594 
 
 SCHOOL PHYSICS. 
 
 "*OOO<MlOt>-iOi Ib- 
 GOl^COiO^OtKMfMCM I 
 
 T-Hi IrH 
 
 I 
 
 I 
 a 
 
 M GO 
 
 < <*OOOfcCO^*O<b- 
 
 CM a: T lOacooaooGOcofM' ( 
 
 i((MCOOGO>O<M>O 
 T-I <M CO 
 
 T-HO51>.COThCOCO<Mr- I i I i I 
 
 I UO Ol rH i-l r-l O 10 O O O O O O 
 iOCOfMQOrH 
 
 r-lrHi ICN(MCOTtHiOOc6ocOOi lOCOQICOt>.CM 
 
 TH TH 
 
 a 
 
 H 
 
 1^05 
 
 20 
 
 H 
 
 fMOi iT^i ( 
 
 TH rH (M Ol CO 
 
 
 
 o o o o o 
 
 -T- 
 
 IOO1 !^OOCMOOiO(MO 
 (MOQOOiOiOCOCMGMt I rH T- I 
 
 rHiOiOi It lCDOt>-(MOOCOl>-CO I O 
 THiOOO<NGOlQ<NOOOQD^TQlMOQ& 
 
 GOt^?DlOlOT^^COCO(M(MCM(MT-H^HTH^-lr-lrHOO 
 
 QJ (^ ?O TtH 1>- O 
 COOST^CO kOrH 
 
 CO CO CM (M (M CM 
 
 O5OTH(MCO'^iOOl>.OOO5OrHCMCO-<^>OCOl.^GOO5O 
 r-<CM<MCM(MCMCM<MCMCM(MCOCOCOCOCOCOCOCOCOCOr^ 
 
APPENDIX. 
 
 595 
 
 5. Table of Natural Tangents. 
 
 ARC. 
 
 TAXGEXT. 
 
 ARC. 
 
 TAXGEXT. 
 
 ARC. 
 
 TAXGEXT. 
 
 ARC. 
 
 TAXGEXT. 
 
 
 
 .000 
 
 23 
 
 .424 
 
 46 
 
 1.036 
 
 69 
 
 2.61 
 
 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 
 
 30 
 
 .577 
 
 53 
 
 1.33 
 
 76 
 
 4.01 
 
 8 
 
 .141 
 
 31 
 
 .601 
 
 54 
 
 1.38 
 
 77 
 
 4.33 
 
 9 
 
 .158 
 
 32 
 
 .625 
 
 55 
 
 1.43 
 
 78 
 
 4.70 
 
 10 
 
 .176 
 
 33 
 
 .649 
 
 56 
 
 1.48 
 
 79 
 
 5.14 
 
 11 
 
 .194 
 
 34 
 
 .675 
 
 57 
 
 1.54 
 
 80 
 
 5.67 
 
 12 
 
 .213 
 
 35 
 
 .700 
 
 58 
 
 1.60 
 
 81 
 
 6.31 
 
 13 
 
 .231 
 
 36 
 
 .727 
 
 59 
 
 1.66 
 
 82 
 
 7.12 
 
 14 
 
 .249 
 
 37 
 
 .754 
 
 60 
 
 1.73 
 
 83 
 
 8.14 
 
 15 
 
 .268 
 
 38 
 
 .781 
 
 61 
 
 1.80 
 
 84 
 
 9.51 
 
 16 
 
 .287 
 
 39 
 
 .810 
 
 62 
 
 1.88 
 
 85 
 
 11.43 
 
 17 
 
 .306 
 
 40 
 
 .839 
 
 63 
 
 1.96 
 
 86 
 
 14.30 
 
 18 
 
 .325 
 
 41 
 
 .869 
 
 64 
 
 2.05 
 
 87 
 
 19.08 
 
 19 
 
 .344 
 
 42 
 
 .900 
 
 65 
 
 2.14 
 
 88 
 
 28.64 
 
 20 
 
 .364 
 
 43 
 
 .933 
 
 66" 
 
 2.25 
 
 89 
 
 57.29 
 
 21 
 
 .384 
 
 44 
 
 .966 
 
 67 
 
 2.36 
 
 90 
 
 Infinite. 
 
 22 
 
 .404 
 
 45 
 
 1.000 
 
 68 
 
 2.48 
 
 
 
596 
 
 SCHOOL PHYSICS. 
 
 6. Table of Natural Sines. 
 
 ARC. 
 
 SINE. 
 
 ARC. 
 
 SINE. 
 
 ARC. 
 
 SINE. 
 
 ARC. 
 
 SINE. 
 
 
 
 0.000 
 
 23 
 
 0.391 
 
 46 
 
 0.719 
 
 69 
 
 0.934 
 
 1 
 
 0.017 
 
 24 
 
 0.407 
 
 47 
 
 0.731 
 
 70 
 
 0.940 
 
 2 
 
 0.035 
 
 25 
 
 0.423 
 
 48 
 
 0.743 
 
 71 
 
 0.946 
 
 3 
 
 0.052 
 
 26 
 
 0.438 
 
 49 
 
 0.755 
 
 72 
 
 0.951 
 
 4 
 
 0.070 
 
 27 
 
 0.454 
 
 50 
 
 0.766 
 
 73 
 
 0.956 
 
 , 5 
 
 0.087 
 
 28 
 
 0.469 
 
 51 
 
 0.777 
 
 74 
 
 0.961 
 
 ' 6 
 
 0.105 - 
 
 20 
 
 0.485 
 
 52 
 
 0.788 
 
 75 
 
 0.966 
 
 7 
 
 0.122 
 
 30 
 
 0.500 
 
 53 
 
 0.799 
 
 76 
 
 0.970 
 
 8 
 
 0.139 
 
 31 
 
 0.515 
 
 54 
 
 0.809 
 
 77 
 
 0.974 
 
 9 
 
 0.156 
 
 32 
 
 0.530 
 
 55 
 
 0.819 
 
 78 
 
 0.978 
 
 10 
 
 0.174 
 
 33 
 
 0.545 
 
 56 
 
 0.829 
 
 79 
 
 0.982 
 
 11 
 
 0.191 
 
 34 
 
 0.559 
 
 57 
 
 0.839 
 
 80 
 
 0.985 
 
 12 
 
 0.208 
 
 35 
 
 0.574 
 
 58 
 
 0.848 
 
 81 
 
 0.988 
 
 13 
 
 0.225 
 
 36 
 
 0.588 
 
 59 
 
 0.857 
 
 82 
 
 0.990 
 
 14 
 
 0.242 
 
 37 
 
 0.602 
 
 60 
 
 0.866 
 
 83 
 
 0.993 
 
 15 
 
 0.259 
 
 38 
 
 0.616 
 
 61 
 
 0.875 
 
 84 
 
 0.995 
 
 16 
 
 0.276 
 
 39 
 
 0.629 
 
 62 
 
 0.883 
 
 85 
 
 0.996 
 
 17 
 
 0.292 
 
 40 
 
 0.643 
 
 63 
 
 0.891 
 
 86 
 
 0.998 
 
 18 
 
 0.309 
 
 41 
 
 0.656 
 
 64 
 
 0.899 
 
 87 
 
 0.999 
 
 19 
 
 0.326 
 
 42 
 
 0.669 
 
 65 
 
 0.906 
 
 88 
 
 0.999 
 
 20 
 
 0.342 
 
 43 
 
 0.682 
 
 66 
 
 0.914 
 
 89 
 
 0.999 
 
 21 
 
 0.358 
 
 44 
 
 0.695 
 
 67 
 
 0.921 
 
 90 
 
 1.000 
 
 22 
 
 0.375 
 
 45 
 
 0.707 
 
 68 
 
 0.927 
 
 
 
INDEX. 
 
 NUMBERS REFER TO PAGES UNLESS OTHERWISE INDICATED. 
 
 Aberration, Chromatic, 371. 
 
 Spherical, 339, 363. 
 Abscissas, Axis of, 95. 
 Absolute temperature, 274. 
 
 unit of force, 67. 
 
 zero, 273. 
 Absorption of gases, 50. 
 
 of radiation, 386. 
 Acceleration, 58. 
 
 due to gravity, 110, 123. 
 Accordion, 261. 
 Accumulator, Electric, 561. 
 Achromatic lens, 371. 
 Acoustics, 201. 
 Activity, 85. 
 Adhesion, 29. 
 Aeriform body, 39. 
 ^Esculin, see esculin. 
 Agonic lines, 476. 
 Air, 182. 
 
 Air columns, Vibratory, 260. 
 Air pump, 194. 
 Air thermometer, 272. 
 Alternating currents, 502, 515. 
 Alternator, 500. 
 Amalgamating zinc, 433. 
 Ammeter, 527, 543. 
 Ampere, 445, 523, 524. 
 
 Ampere's theory of magnetism, 473. 
 Ampere-turns, 469. 
 Amplitude of oscillation, 119. 
 
 of vibration, 208. 
 Analysis of light, 368. 
 
 Spectrum, 381. 
 Analyzer, 399. 
 Aneroid barometer, 185. 
 Angle of polarization, 398. 
 Anion, 559. 
 Annealing, 30. 
 Anode, 559. 
 Anti-nodes, 236. 
 Aperture of mirror, 333. 
 Aqueous humor, 402. 
 Archimedes, 162. 
 Arc lamps, 548. 
 
 lighting, 547. 
 Armature of dynamo, 490. 
 
 of magnet, 456. 
 Astatic galvanometer, 525. 
 
 needle, 458. 
 Athermancy, 385. 
 Atmospheric electricity, 516. 
 
 pressure, 182. 
 Atom, 10. 
 Atomic forces, 15. 
 Atwood machine, 109, 117. 
 Axis of lens, 357. 
 
 of mirror, 333. 
 
 597 
 
598 
 
 SCHOOL PHYSICS. 
 
 Nwmbers refer to Pages unless otherwise indicated. 
 
 Balance, 133. 
 
 Ballistic galvanometer, 527. 
 
 Barometer, 184. 
 
 Base, 101. 
 
 Battery, Electric, 429. 
 
 Voltaic, 438, 481, 482. 
 Beam of rays, 313. 
 Beams, Rigidity of, 36. 
 Beats, Acoustic, 252. 
 Bells, Electric, 555. 
 
 Vibrations of, 265. 
 Bell telephone, 570. 
 Blake transmitter, 572. 
 Blind spot, 403. 
 Block and tackle, 142. 
 Body, 9. 
 
 Boiling-point, 272, 291. 
 Bolometer, 575. 
 
 "Bound" electric charges, 427. 
 Boyle's law, 189. 
 Breaking strength, 35, 37. 
 Bright-line spectra, 382. 
 Brush arc lamp, 549. 
 
 dynamo, 495. 
 Bunsen cell, 480. 
 
 photometer, 323. 
 Burning glass, 347. 
 
 C. 
 
 Calipers, 34. 
 Calorescence, 389. 
 Calorimetry, 299. 
 Calory, 300, 447. 
 Candle, Standard, 323. 
 Capacity, Electrical, 426, 534. 
 
 Thermal, 303. 
 Capillary attraction, 47. 
 
 tubes, 48.- 
 Capstan, 140. 
 
 Carhart-Clark cell, 443. 
 
 Cathode, 559. 
 
 Cation, 559. 
 
 Celsius thermometer, 273. 
 
 Center of mass, 99, 100. 
 
 Centigrade thermometer, 273. 
 
 Centrifugal force, 78. 
 
 C.G.S. units, 68. 
 
 Charge, Electric, 415, 419. 
 
 Residual, 429. 
 Chemical changes, 12. 
 
 effects of electric current, 557 
 
 effects of radiation, 387. 
 Chemism, 15. 
 Chladni's plates, 265. 
 Chords, Musical, 232. 
 Choroid coat, 401. 
 Chromatic aberration, 371. 
 
 scale, 233. 
 Chromatics, 368. 
 Chromic acid cell, 480. 
 Circuit, Electric, 437. 
 Clarinet, 261. 
 Clocks, 123, 126. 
 Clouds, 516. 
 Coefficient of elasticity, 29. 
 
 of expansion, 285, 299. 
 
 of friction, 130, 137, 138. 
 
 of self-induction, 504. 
 Coercive force, 471. 
 Cohesion, 29. 
 Coincident waves, 245. 
 Colloids, 53. 
 Color, 372. 
 Color blindness, 403. 
 Commutator, 492, 507, 539. 
 Complementary colors, 374. 
 Condensation, 290. 
 Condenser, Electric, 427, 507. 
 Condensing pump, 196. 
 Conduction, Electric, 414, 416. 
 
IXDEX. 
 
 599 
 
 Numbers refer to Pages unless otherwise indicated. 
 
 Conduction, Thermal, 278, 279. 
 Conductivity, Electric, 441. 
 Conjugate foci, 220, 335, 359. 
 Convection, 278, 282. 
 
 Electric, 420. 
 Co-ordinates, Axes of, 95. 
 Cork-screw rule, 468. 
 Cornea, 401. 
 Coulomb, 445, 523, 524. 
 Coulomb's torsion balance, 523. 
 Couple, 71. 
 Co-vibration, 244. 
 Critical angle, 353. 
 Crova disk, 216. 
 Crown of cups, 519. 
 Crystalline lens, 401. 
 Crystallization, 41. 
 Crystalloids, 53. 
 
 Current electricity, 422, 433, 437. 
 Curvilinear motion, 77. 
 
 D. 
 
 Daniell cell, 443, 480, 538. 
 Dark-line spectra, 382. 
 Dead-beat galvanometer, 527. 
 Declination, Magnetic, 475. 
 Density of matter, 167. 
 
 Electric, 419. 
 Deprez d'Arsonval galvanometer, 
 
 527. 
 
 Deviation of rays, 356. 
 Dew-point, 290, 299. 
 Dialysis, 53. 
 Diamagnetic, 456. 
 Diathermancy, 385. 
 Diatonic scale, 232. 
 Dielectric, 415, 430. 
 
 constant, 426. 
 Differential galvanometer, 527. 
 
 thermometer, 272. 
 
 Diffraction, 394. 
 
 grating, 396. 
 Diffusion of gases, 52. 
 
 of heat, 278. 
 
 of radiant energy, 328. , 
 
 Dip, Magnetic, 475. 
 Dipping needle, 458. 
 Discharge, Electric, 513. 
 Discharger, 429. 
 Disgregation, 300. 
 Dispersion, Irrationality of, 396. 
 
 of light, 368. 
 
 Distance, Estimation of, 403. 
 Distillation, 293. 
 Divisions of matter, 10. 
 Double refraction, 397, 399. 
 Ductility, 32. 
 Duplex telegraph, 565. 
 Dynamo, 489. 
 Dynamometer, 68. 
 Dyne, 67. 
 
 E. 
 
 Ebullition, 290, 292. 
 Echoes, 220. 
 
 Edison 3- wire system, 544. 
 Efficiency of machines, 129. 
 Elastic force of gases, 186. 
 Elasticity, 28. 
 
 and reaction, 76. 
 Electric accumulator, 561. 
 
 action, Laws of, 418. 
 
 arc, 547. 
 
 battery, 429. 
 
 bells, 555. 
 
 capacity, 426. 
 
 circuit, 437. 
 
 condenser, 427. 
 
 current, 422, 433, 437, 465, 486. 
 
 density, 419. 
 
600 
 
 SCHOOL PHYSICS. 
 
 Numbers refer to Pages unless otherwise indicated. 
 
 Electric discharge, 513. 
 
 field, 421. 
 
 fire alarm, 556. 
 
 gas lighting, 552. 
 ? generators, 478. 
 
 induction, 425. 
 
 lighting, 543, 547. 
 
 lines of force, 421. 
 
 machines, 509. 
 
 measurements, 523. 
 
 motors, 553. 
 
 oscillations, 580. 
 
 pendulum, 413. 
 
 resonance, 583. 
 
 units, 418, 426. 
 
 waves, 581. 
 
 welding, 552. 
 Electricity, 412. 
 
 Atmospheric, 516. 
 
 Nature of, 429. 
 Electrification, 414, 416, 420, 423, 
 
 431. 
 
 Electrochemical series, 591. 
 Electrodes, 437. 
 Electrodynamics, 453. 
 Electrodynamometer, 528. 
 Electrolysis, 557. 
 Electrolyte, 559. 
 Electromagnet, 472. 
 Electromagnetic induction, 484. 
 
 radiation, 579. 
 
 telegraph, 564. 
 
 theory of light, 588. 
 
 units, 418, 524. 
 
 waves, 581. 
 
 Electrometallurgy, 559. 
 Electrometer, 523. 
 Electromotive force, 424, 443, 534, 
 577. 
 
 table, 591. 
 Electrophorus, 509. 
 
 Electroplating, 560. 
 Electroscope, 417. 
 
 Condensing, 519. 
 Electrostatic units, 418, 623. 
 Electrotyping, 560. 
 Element, 12. 
 Endosmosis, 53. 
 Energy, 12, 85. 
 
 Conservation of, 90. 
 
 Measurement of, 88, 89, 90. 
 
 Kadiant, 312. 
 
 Relation to velocity, 88. 
 
 Types of, 86. 
 
 Units of, 88, 89. 
 Engine, Steam, 308. 
 Equilibrant, 69. 
 Equilibrium, 101. 
 Equipotential surfaces, 422. 
 Erg, 84. 
 Esculin, 388. 
 Ether, 312, 429. 
 Evaporation, 289, 290. 
 Exosmosis, 53. 
 Expansion, 27, 271, 283, 297. 
 Experiment, 16. 
 Extension, 16. 
 
 Measurement of, 17. 
 Eye, the human, 401. 
 
 F. 
 
 Fahrenheit hydrometer, 170. 
 
 thermometer, 273. 
 Falling bodies, 106, 111. 
 Farad, 426, 523, 524. 
 Far-sight, 402. 
 Field, Electric, 421. 
 
 magnet, 494. 
 
 Magnetic, 458. 
 
 of force, 421. 
 Fife, 261. 
 Films, Superficial, 44. 
 
INDEX. 
 
 601 
 
 Numbers refer to Pages unless otherwise indicated. 
 
 Fire alarm, Electric, 556. 
 Flats and sharps, 234. 
 Flotation, 165. 
 Fluid, 38. 
 Fluorescence, 388. 
 Flute, 261. 
 
 Flux of force, 461, 535. 
 Focal length, 335, 365. 
 Focus, 333, 334, 358, 360. 
 Foot-pound, 84. 
 Foot-poundal, 84. 
 Force, 15. 
 
 Centrifugal, 78. 
 
 Coercive, 471. 
 
 Composition of, 70, 73, 81, 82. 
 
 Electromotive, 424. 
 
 Elements of, 66. 
 
 Flux of, 461, 535. 
 
 Graphic representation of, 69. 
 
 Magnetomotive, 468, 536. 
 
 Measurement of, 67. 
 
 Moment of, 132. 
 
 Parallelogram of, 71. 
 
 pump, 194. 
 
 Kesolution of, 74. 
 
 Units of, 67. 
 Foucault currents, 491. 
 F.P.S. units, 68. 
 Fraunhofer lines, 383. 
 Freezing-point, 272. 
 Friction, 129, 137, 138. 
 Frictional electric machine, 509. 
 
 electricity, 412. 
 Fundamental tones, 236. 
 Fusing-point pressure, 293. 
 Fusion, 288. 
 
 Latent heat of, 300. 
 
 G. 
 
 Galilean telescope, 408. 
 Galileo, 109. 
 
 Galvanometer, 525. 
 Galvanoscope, 439, 484. 
 Gamut, 230. 
 Gas, 39. 
 
 lighting, Electric, 552. 
 Gases, Kinetic theory of, 52. 
 
 Mechanics of, 179. 
 Gauss, 461, 476. 
 Geissler tube, 519, 520. 
 Gilbert, 469. 
 Glass working, 21. 
 Graduate, 20. 
 Gram, 22. 
 
 Graphic study of sound, 238. 
 Gravitation, 95. 
 
 Law of, 96. 
 Gravity, 96. 
 
 cell, 480. 
 
 Center of, 99. 
 
 unit of force, 67. 
 Grenet cell, 479. 
 Grove cell, 480. 
 
 H. 
 
 Halo, 395. 
 Hanchett cell, 435. 
 Hardness, 30. 
 Harmonic motion, 208. 
 Harmonics, 236. 
 Hearing, 230. 
 Heat, 12, 270. 
 
 Diffusion of, 278. 
 
 Latent, 300. 
 
 Mechanical equivalent of, 307. 
 
 Production of, 277. 
 
 Sensible, 300. 
 
 units, 299. 
 Henry, The, 504. 
 Hertz experiments, 584. 
 Homogeneous light, 372. 
 Horse-power, 85. 
 
602 
 
 SCHOOL PHYSICS. 
 
 Numbers refer to Pages unless otherwise indicated. 
 
 Humidity, 291. 
 Hyaloid membrane, 402. 
 Hydraulic press, 153. 
 Hydrometer, 168. 
 Hygrometer, 291. 
 Hypermetropia, 402. 
 Hypothesis, 13. 
 Hypsometer, 293. 
 
 Iceland spar, 397. 
 Identity, Electrical, 513. 
 Image, 318, 332, 336, 361. 
 Impedance, 504, 505, 586. 
 Impenetrability. 21. 
 Incandescence lighting, 543. 
 Inclination, Magnetic, 475. 
 Inclined plane, 143. 
 Indestructibility, 25. 
 Index of refraction, 350. 
 Induced electric currents, 486, 488. 
 Induction coil, 506. 
 
 Electric, 425. 
 
 Electromagnetic, 484. 
 
 Self, 503. 
 
 Inductive capacity, 426. 
 Inertia, 26. 
 
 Center of, 99. 
 Insulators, 414. 
 Intensity of sound, 225, 226. 
 Interference of radiation, 393. 
 ' of sound, 251, 257. 
 Intermolecular spaces, 11. 
 Interrupter, 502. 
 Intervals, Musical, 230. 
 Ions, 559. 
 Iris, 402. 
 Irradiation, 396. 
 Irrationality of dispersion, 396. 
 Isoclinic lines, 475. 
 
 Isodynamic lines, 475. 
 Isogonic lines, 475. 
 
 J. 
 
 Jolly balance, 178. 
 Joule, 446, 523. 
 Joule's law, 447. 
 Joule's principle, 307. 
 
 Kathode, see Cathode. 
 Ration, see Cation. 
 Key-note, 230. 
 Key, Telegraph, 565. 
 Kicking coil, 552. 
 Kilogram, 22. 
 Kilogram meter, 84. 
 Kinetic energy, 86. 
 
 theory of gases, 52. 
 Kinnersley thermometer, 523. 
 
 L. 
 
 Law, 14. 
 
 Leclanchc* cell, 443, 480. 
 
 Lens, 371. 
 
 Lever, 130. 
 
 Ley den jar, 428. 
 
 Lift pump, 193. 
 
 Light, 314. 
 
 Electromagnetic theory of, 588. 
 
 Intensity of, 321. 
 
 Velocity of, 320. 
 Lightning, 516. 
 
 rod, 574. 
 
 Lines of force, 421, 460. 
 Liquefaction, 287. 
 Liquid, 39. 
 Liquids, mechanics of, 150. 
 
INDEX. 
 
 603 
 
 Numbers refer to Pages unless otherwise indicated. 
 
 Liter, 19. 
 
 Local action, 479. 
 currents, 491. 
 Lodestone, 456. 
 Longitudinal waves, 211. 
 Loudness of sound, 225, 226. 
 
 M. 
 
 Mach apparatus, 212. 
 Machines, 127. 
 
 Efficiency of, 129. 
 
 Laws of, 128. 
 
 Magdeburg hemispheres, 181. 
 Magic lantern, 410. 
 Magnet, 455. 
 
 Field, 494. 
 Magnetic field, 458, 535. 
 
 lines of force, 460. 
 
 mass, 461. 
 
 needles, 457. 
 
 p*hantom, 459, 478. 
 
 potential, 463. 
 
 resistance, 470. 
 
 substances, 456. 
 
 transparency, 462. 
 Magnetism, 454, 473. 
 
 Residual, 473. 
 Magnetite, 456., 
 
 Magnetization, 456, 463, 465, 536. 
 Magneto, 488. 
 
 Magnetomotive force, 468, 536. 
 Magnetoscope, 481. 
 Magnifying glass, 406. 
 
 power, 367, 406, 409. 
 Malleability, 32. 
 Manometric flames, 239. 
 Mariotte's law, 190. 
 Mass, 11, 12. 
 
 Center of, 99, 100. 
 
 Measurement of, 22. 
 
 Matter, 9, 15. 
 
 Conditions of, 38. 
 
 Divisions of, 10. 
 
 Properties of, 16. 
 
 Radiant, 40. 
 
 Structure of, 9. 
 Measurements, Delicacy of, 24. 
 
 Electrical, 523. 
 
 Mechanical equivalent of heat, 307. 
 Mechanics, 57. 
 Medium of radiation, 312, 429. 
 
 of sound, 206. 
 Megohm, 440. 
 Melodeon, 261. 
 Meter, 17. 
 
 Metric measures, 18, 19, 23. 
 Mho, 441. 
 Microfarad, 426. 
 Microhm, 440. 
 Microphone, 569. 
 Microscope, 406. 
 Milliampere, 445. 
 Mirror, Concave, 333, 346. 
 
 Convex, 340, 346. 
 
 galvanometer, 526. 
 
 galvauoscope, 484, 498. 
 
 Plane, 331, 342. 
 Molar forces, 15. 
 
 motion, 12. 
 Molecular attraction, 29. 
 
 forces, 15. 
 
 motion, 12. 
 Molecules, 11. 
 
 Superficial, 43. 
 Moment of force, 132. 
 Momentum, 62. 
 Monochromatic light, 372. 
 Morse alphabet, 564. 
 Motion, 57. 
 
 Accelerated, Laws of, 60. 
 
 Composition of, 61. 
 
604 
 
 SCHOOL PHYSICS. 
 
 Numbers refer to Pages unless otherwise indicated. 
 
 Motion, Curvilinear, 77. 
 
 Forms of, 12, 206, 207, 208. 
 
 Graphic representation of, 60. 
 
 Laws of, 65, 74. 
 
 Parallelogram of, 61. 
 
 Reflected, 76, 77. 
 
 Resolution of, 62. 
 
 Resultant, 69. 
 Motors, Electric, 563. 
 Multiple arc, 438, 481. 
 Multiplex telegraph, 566. 
 Music and noise, 253. 
 Musical intervals, 230. 
 
 scale, 230. 
 Myopia, 402. 
 
 N. 
 
 Near-sight, 402. 
 Needle, Magnetic, 457. 
 Newton's disk, 370. 
 
 laws of motion, 65. 
 
 rings, 393. 
 
 Nicholson hydrometer, 168. 
 Nicol prism, 399. 
 Nodes, 234. 
 Noise and music, 253. 
 Normal spectrum, 396. 
 
 O. 
 
 Obscure heat, 385. 
 Octave, 230, 231. 
 Oersted, 470. 
 Ohm, 440, 523, 524. 
 Ohm's law, 446. 
 
 law, Analogue of, 470. 
 Old-sight, 402. 
 Opacity, 316. 
 Opera glass, 408. 
 Optical angle, 403. 
 
 Optical center, 357. 
 
 lantern, 409. 
 
 study of sound, 241. 
 Ordinates, Axis of, 95. 
 Organ-pipe, 261. 
 Oscillation, Center of, 122. 
 
 of pendulum, 119. 
 Oscillations, Electric, 580. 
 Oscillator, Tesla's, 501. 
 Oscillatory electric discharge, 514. 
 Osmose, 53. 
 Overtones, 234. 
 
 P. 
 
 Parallel grouping of voltaic cells, 
 
 438, 481. 
 
 Paramagnetic, 456. 
 Partial tones, 236. 
 Pascal, 152, 184. 
 Pencil of rays, 313. 
 Pendular motion, 207. 
 Pendulum, 118. 
 
 Electric, 413. 
 
 Torsional, 28. 
 Penumbra, 318. 
 Period of oscillation, 119. 
 
 of vibration, 208, 210. 
 Permeability, 469, 536. 
 Persistence of vision, 403. 
 Phantom curves, 459, 478. 
 Phenomenon, 13. 
 Phosphorescence, 388. 
 Photographer's camera, 405. 
 Photometry, 322. 
 Physical changes, 13. 
 Physics, 16. 
 Piano scale, 234. 
 Pigments, Mixing, 377. 
 Pipe instruments, 261. 
 Pitch of sounds, 225, 228, 231. 
 
INDEX. 
 
 605 
 
 Numbers refer to Pages 
 
 Plater, 560. 
 
 Plates, Vibrations of, 264. 
 
 of voltaic cell, 437. 
 Pliicker tube, 392. 
 Pneumatics, 179. 
 Polariscope, 399. 
 Polarization of cell, 435, 479. 
 
 of light, 397, 579. 
 Polarizer, 399. 
 Poles, Magnetic, 456, 462. 
 
 of voltaic cell, 437. 
 Porosity, 27. 
 
 Potassium dichromate cell, 479. 
 Potential, Electric, 422, 444, 534. 
 
 energy, 86. 
 
 Magnetic, 463. 
 Poundal, 67. 
 Power, 128. 
 Presbyopia, 402. 
 Pressure, Fluid, 151, 182. 
 
 -gauge, 160. 
 Prevost's theory of exchanges, 
 
 385. 
 
 Primary battery, 561. 
 Prism, 355. 
 
 Prismatic spectrum, 369. 
 Projectiles, 112. 
 Proof-plane, 417. 
 Properties of matter, 16. 
 Pulley, 141, 149. 
 Pumps, 193. 
 Pupil of eye, 402. 
 
 Q 
 
 Quadruplex telegraph, 566. 
 Qualitative experiment, 16. 
 Quality of sound, 225, 236. 
 Quantitative experiment, 16. 
 Quantity, Electric, 418. 
 
 unless otherwise indicated. 
 R. 
 
 Radiant energy, 312, 385, 387. 
 
 heat, 385. 
 
 matter, 40. 
 Radiation, 312. 
 
 Intensity of, 321. 
 Rainbow, 377. 
 Range of projectile, 113. 
 Rarefaction, Waves of, 210. 
 Ray, 313. 
 Reactance, 504. 
 Reaction, 66, 74, 75, 76. 
 Reaumur thermometer, 273. 
 Reed instruments, 261. 
 Reflection of electrical waves, 585. 
 
 of motion, 76, 77. 
 
 of radiation, 326. 
 
 of sound, 219. 
 
 Total, 351. 
 Refraction of electrical waves, 685. 
 
 Double, 397, 399. 
 
 Index of, 350. 
 
 of radiation, 346. 
 
 of sound, 221. 
 Refractor, 407. 
 Regelation, 295.^ 
 Register, Telegraph, 565. 
 Relay, Telegraph, 567. 
 Reluctance, 470. 
 Reluctivity, 470. 
 Remanance, 471. 
 Repeater, Telegraph, 569. 
 Residual charge, 429. 
 
 magnetism, 473. 
 Resistance coils, 529. 
 
 Electric, 439, 441, 442, 447, 480, 
 531, 533. 
 
 Magnetic, 470. 
 Resistivity, 441, 592. 
 Resonance, Acoustic, 249, 254. 
 
606 
 
 SCHOOL PHYSICS. 
 
 Numbers refer to Pages unless otherwise indicated. 
 
 Resonance, Electric, 583. 
 Resultant, 69. 
 motion, 69. 
 Retina, 401. 
 Rheocord, 538. 
 Rhumkorff coil, 506. 
 Rigidity of beams, 36. 
 Rods, Vibrations of, 263. 
 Rumford photometer, 322, 325. 
 
 S. 
 
 Scales, Musical, 230, 232, 233. 
 
 Science, 9. 
 
 Sclerotic coat, 401. 
 
 Screw, 147. 
 
 Secondary cells, 560. 
 
 Self-induction, 503. 
 
 Series grouping of voltaic cells, 438, 
 
 482. 
 
 Shadows, 316. 
 Sharps and flats, 234. 
 Shunt, 448. 
 
 Sine galvanometer, 526. 
 Sines, Natural, 596. 
 Sinusoidal curve, 209, 211. 
 Siphon, 190, 199. 
 Siren, 228. 
 
 Size, Estimation of, 403. 
 Sky, The color of, 374. 
 Smee cell, 479. 
 Soap bubbles, 56. 
 Sodium dichromate cell, 479. 
 Solar spectrum, 369. 
 Solenoid, 467. 
 Solid, 38. 
 Solidification, 288. 
 Solution, 40, 287. 
 Sonometer, 235, 246, 258. 
 Sound, 201. 
 
 Cause of, 202. 
 
 Sound, Characteristics of, 225. 
 
 media, 206. 
 
 Reflection of, 219. 
 
 Refraction of, 221. 
 
 Velocity of, 218, 223. 
 
 waves, 209, 210. 
 Sounder, Telegraph, 566. 
 Sound-mill, 247. 
 Specific gravity, 167. 
 
 gravity bulb, 170. 
 
 gravity flask, 170. 
 
 heat, 302. , . 
 
 inductive capacity, 426. 
 
 magnetic resistance, 470. 
 
 resistance, 441. 
 Spectroscope, 379. 
 Spectrum, 368, 369, 372, 379, 382, 
 383, 396. 
 
 analysis, 381. 
 Speculum, 408. 
 Spherical aberration, 363. 
 Spheroidal state, 293. 
 Spy-glass, 407. 
 
 Square root of mean square, 505. 
 Stability, 102. 
 Static electricity, 412, 512. 
 Steam-engine, 308. 
 Stereopticon, 410. 
 Stereoscope, 404. 
 Still, 294. 
 
 Storage battery, 561. 
 Strain, 27. 
 Stress, 27. 
 
 Stretching weight, 37. 
 Structure of matter, 9, 10. 
 Sublimation, 293. 
 Substance, 9. 
 Sucker, 196. 
 Sucking magnet, 551. 
 Suction pump, 93. 
 Surface density, 419. 
 
OF 
 
 Numbers refer to Page* unless otherwise indicated. 
 
 Surface tension, 45. 
 
 viscosity, 44. 
 
 Sympathetic vibrations, 245, 247. 
 Synthesis of light, 369. 
 
 T. 
 
 Tangent galvanometer, 525. 
 Tangents, Natural, 595. 
 Telegraph, 562. 
 Telephone, 487, 570. 
 Telescope, 407. 
 Temperament, 234. 
 Temperature, 270. 
 
 Absolute, 274. 
 
 Absolute zero of, 273. 
 Tempering, 30. 
 Tenacity, 31. 
 
 Terrestrial magnetism, 474. 
 Tesla, Nikola, 388, 501, 585. 
 Theory, 13. 
 Therm, 300. 
 Thermal effects of radiation, 385. 
 
 unit, 299. 
 
 Thermo-dynamics, 306. 
 Thermo-electricity, 518. 
 Thermometer, 271, 275, 523. 
 Thermoscope, 271, 518. 
 Thunder, 517. 
 Timbre, 225, 236. 
 Torpedo, 454. 
 Torricelli, 183. 
 Torsion, 37. 
 
 balance, 523. 
 
 pendulum, 28. 
 Total reflection, 352. 
 Touch paper, 204. 
 Tourmaline tongs, 397. 
 Transformer, 505, 546. 
 Transparency, Optical, 316. 
 
 Magnetic, 462. 
 
 Turbine wheel, 172. 
 
 U. 
 
 Umbra, 318. 
 
 Units, Electric, 418, 426, 523. 
 
 Metric, 18, 19, 23. 
 
 Thermal, 299. 
 
 V. 
 
 Vapor, 39. 
 Vaporization, 289. 
 
 Latent heat of, 302. 
 Variation, Magnetic, 475. 
 Velocity, 57. 
 
 Relation to energy, 88 
 
 of sound, 218, 223. 
 Vibgyor, 369. 
 Vibration, Laws of, 258. 
 Vibratory motion, 206. 
 Vibroscope, 238. 
 Visual angle, 403. 
 Vitreous humor, 402. 
 Volt, 443, 523, 524. 
 Voltaic arc, 547. 
 
 battery, 438, 481, 482. 
 
 cell, 437, 443, 478. 
 Voltameter, 560. 
 Voltmeter, 528. 
 Vortex-ring, 473. 
 
 W. 
 
 Water power, 171. 
 
 wheels, 172. 
 Watt, 85, 446, 447, 523. 
 Wattmeter, 529. 
 Wave forms, 208. 
 
 length, 210, 211. 
 
 motion, 206, 209, 210. 
 
608 
 
 SCHOOL PHYSICS. 
 
 Numbers refer to Pages unless otherwise indicated. 
 
 Weber, 461, 476. 
 Wedge, 146. 
 Weighing, 133. 
 Weight, 21, 97, 128. 
 
 Law of, 97. 
 
 Measurement of, 22. 
 Welding, Electric, 552. 
 Wheatstone bridge, 532, 535, 541. 
 Wheel and axle, 139. 
 Whirling table, 78. 
 Whistle, 261. 
 
 Wimshurst electric machine, 510. 
 Windlass, 140. 
 Wire, Breaking strength of, 35. 
 
 Wire gauge, 34. 
 
 Table of dimensions, etc., 592. 
 Wiring for electric lights, 544. 
 Work, 83. 
 
 units, 84. 
 
 Y. 
 
 Yard, 17. 
 Yellow spot, 403. 
 
 Zinc, Amalgamation of, 433. 
 
14 DAY USE 
 
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 UNIVERSITY OF CALIFORNIA LIBRARY