UNIVERSITY OF CALIFORNIA. 
 
 Received. 
 Accessions 
 
 ON & CO. 
 Stationers 
 
ELEMENTS 
 
 OF 
 
 NATURAL PHILOSOPHY. 
 
 A TEXT-BOOK 
 
 FOR HIGH SCHOOLS AND ACADEMIES. 
 
 BY 
 
 ELROY M. AVERY, PH.D., 
 
 M 
 AUTHOR OF A SERIES OF PHYSICAL SCIENCE TEXT-BOOKS. 
 
 ILLUSTRATED BY MORE. THAN 400 WOOD ENGRAVINGS. 
 
 SHELDON ANDCOMPANY, 
 
 NEW YORK AND CHICAGO. 
 
DR. AVERY'S 
 PHYSICAL SCIENCE SERIES 
 
 'St. 
 
 FIRST PRINCIPLES OF NATURAL PHILOSOPHY, 
 
 9*. 
 
 THE ELEMENTS OF NATURAL PHILOSOPHY. 
 
 THE ELEMENTS OF CHEMISTRY. 
 
 4 th. 
 THE 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^ 1878, 1885, by Sheldon & Company. 
 
 Klectrotyped by SMITH A McDoUGAL, 
 82 Beekman St., New York. 
 
CHAPTEK I. 
 
 THE DOMAIH OF PHYSICS. 
 
 PAGE 
 
 SECTION I. The Domain of Physics 1 
 
 II. The Properties of Matter 6 
 
 " III. The Three Conditions of Matter 21 
 
 CHAPTEE II. 
 
 D Y N A MICS. 
 
 SECTION I. Force and Motion 25 
 
 " II. Gravitation 46 
 
 " III. Falling Bodies 57 
 
 " IV. The Pendulum 69 
 
 " V. Energy 76 
 
 CHAPTER III. 
 
 SIMPLE MACHINES. 
 
 SECTION I. Principles of Machinery ; the Lever 86 
 
 " II. The Wheel and Axle ; Wheel- work 97 
 
 " III. The Pulley ; the Inclined Plane 103 
 
 " IV. The Wedge, Screw, Compound Machines and 
 
 Friction 109 
 
 CHAPTEE IV. 
 
 LIQUIDS. 
 
 SECTION I. Hydrostatics 116 
 
 " II. Liquid Equilibrium ; Capillarity ; Buoyancy 128 
 
 " III. Specific Gravity 135 
 
 " IV. Hydrokinetics . 145 
 
IV CONTENTS. 
 
 CHAPTER V. 
 
 PNEUMATICS. 
 
 PAOH 
 
 SECTION I. The Atmosphere and Atmospheric Pressure 156 
 
 '" II. The Relation of Tension and Volume to Pressure . 163 
 " III. Air, Forcing and Lifting Pumps ; the Siphon 168 
 
 CHAPTER VI. 
 
 ELECTRICITY AND MAGNETISM. 
 
 SECTION I. General View 183 
 
 II. Frictional Electricity 192 
 
 " III. Voltaic and Thermo-Electricity 366 
 
 " IV. Magnetism 301 
 
 V. Induced Electricity 333 
 
 " VI. Electric Currents related to Heat and Mechanical 
 
 Work 353 
 
 CHAPTER VII. 
 
 SOUND. 
 
 SECTION I. Nature, Refraction and Reflection of Sound 367 
 
 " II. The Telephone and Phonograph Composition and 
 
 Analysis of Sounds 384 
 
 CHAPTER VIII. 
 
 H EAT. 
 
 SECTION I. Temperature, Thermometers, Expansion 412 
 
 " II. Liquefaction, Vaporization, Distillation 424 
 
 " III. Latent and Specific Heat 436 
 
 " IV. Modes of Diffusing Heat 450 
 
 V. Thermodynamics 462 
 
 CHAPTER IX. 
 
 LIGHT. 
 
 SECTION I. Nature, Velocity and Intensity of Li^ht 475 
 
 II. Reflection of Light 483 
 
 " III. Refraction of Light , 500 
 
 IV. Chromatics and Spectra 516 
 
 " V. Optical Instruments and Polarization 534 
 
 CONCLUSION ; ENERGY 552 
 
 APPENDICES 561 
 
 INDEX.. 584 
 
TO THE TEACHER. 
 
 IN this book will be found an unusual number of prob 
 lems. It is not intended tbat 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. No 
 author can make a comfortable Procrustean bedstead. 
 
 You would do well to secure, in the fail of the year, a 
 supply of the pith of elder or sunflower stalk, and several 
 full-blown thistle-heads, that they may be well dried and 
 ready for experiments in electricity during the dry, cold 
 weather of winter. 
 
 The author would be glad to receive any suggestions 
 from any of his fellow- teachers who may use this book, or 
 to answer any inquiries concerning the study or apparatus. 
 
 Most of the apparatus mentioned in this book may 
 be obtained from JAMES W. QUEEN & Co., Philadelphia. 
 
 The author has prepared a Teacher's Hand-Book to 
 accompany this volume, with answers to the problems, 
 and much additional matter of interest to teachers of 
 Natural Philosophy. 
 
TO THE PUPIL. 
 
 EECENT easeful and extended examination shov/fc 
 1 that diseases of the eye, such as near-sight, are 
 lamentably frequent among school-children. Your eye- 
 sight is worth more to you than any information you are 
 likely to gain from this book, however valuable that may 
 be. You are therefore earnestly cautioned: 
 
 1. To be sure, in studying this or any other book, that 
 you have sufficient light. 
 
 2. That you do not allow direct rays of light to fall 
 npon your eyes, and that you avoid the angle of reflection. 
 
 3. That you avoid a stooping position and a forward 
 inclination of the head. Do not read with the book in 
 your lap. The distance of the eye from the page should 
 be not less than twelve inches (30 cm.) nor more than 
 eighteen inches (45 cm.) Hold the book up. 
 
 4. That you sit erect when you write. The light 
 should be received over your left shoulder. 
 
 5. Especially, that you avoid, as much as possible, books 
 and papers poorly printed or printed in small type. 
 
 6. That you cleanse the eyes with pure soft watei 
 morning and night, and avoid overtaxing them in any 
 way. 
 

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THE DOMAIN OF PHYSICS. THE PROPERTIES OF 
 
 MATTER. THE THREE CONDITIONS 
 
 OF MATTER. 
 
 I. 
 
 THE DOMAIN OF PHYSICS, OR NATURAL 
 PHILOSOPHY. 
 
 Introductory. On the page opposite, you have an 
 outline map of the wide realm of human knowledge. As 
 from a mountain top, you look upon the plain below, and 
 clearly see the position of each province, and its relation 
 to its neighbors. Through some of these provinces you 
 may have passed, and with them have become more or 
 less familiar. From the whole number we now select one 
 that promises enough of interest and profit to justify the 
 time and effort of careful study. Not satisfied with the 
 cursory glance, we seek more definite information. For 
 this, we must leave the peak and enter the plain; for 
 though distance may lend an enchantment, it also begets a 
 dimness fatal to our purpose. 
 
 1. What is Science ? Science is classified 
 knowledge. 
 
 A person may have lived for years among plants, have 
 acquired a vast store of information concerning them, 
 
2 THE DOMAIN OF PHYSICS. 
 
 know that this one grows only in wet ground, that anothe! 
 is valuable for such and such an end, and that a third 
 has certain form, size, and color. This general informa- 
 tion may be valuable, but it is only when the facts are 
 classified, and the plants grouped into their respective 
 orders, genera and species, that the knowledge becomes 
 entitled to the name of botany, a science. 
 
 2. What is Matter? Matter is anything that 
 occupies space or " takes up roojn." 
 
 There are many realities that are not forms of matter. 
 Mind, truth, and hope do not occupy space ; the earth and 
 the rain-drop do. 
 
 3. Divisions of Matter. Matter may be con- 
 sidered as existing in masses, molecules, and atoms. 
 
 A clear apprehension of the meaning of these terms 
 is essential to a full understanding of the definition of 
 Physics as well as of much else that follows. 
 
 4. What is a Mass? A mass is any quantity 
 of matter that is composed of molecules. 
 
 The word molar is used to describe such a collection of 
 molecules. 
 
 (a.) The term mass also lias reference to real quantity as distin- 
 guished from apparent quantity or size. A sponge may be com- 
 pressed so as to seem much smaller than at first, but all of the 
 sponge is still there. Its density is changed ; its quantity or mass 
 remains the same. This double use of the word is unfortunate, 
 but the meaning in any given case may be easily inferred from the 
 connection. 
 
 (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 eqmally masses of matter. 
 
DOMATN OF PHYSICS. 3 
 
 5. What is a Molecule? A molecule is the 
 smallest quantity of matter that can exist by itself. 
 It is the physical unit of matter and can be divided only 
 by chemical means. 
 
 (a.) We know that a drop of water may be divided into several 
 parts, and each of these into several others, each part still being 
 water. The subdivision may be carried on until we reach a limit 
 fixed by the grossness of our instruments and vision ; each particle 
 still is water. Even now, imagination may carry forward the 
 work of subdivision until at last we reach a limit beyond which we 
 cannot go without destroying the identity of the substance, In 
 other words, we have a quantity of water so small that if we divide 
 it again it will cease to be water ; it will be something else. This 
 smallest quantity of matter that can exist by itself and retain its 
 identity is called a molecule. The word molecule means a little 
 mass. (See A very 's Chemistry, 4.) 
 
 (&.) The smallest interval that can be distinctly seen with the 
 microscope is about 8 Q jyoiy i n ch. It has been calculated that about 
 2000 liquid water molecules might be placed in a row within such 
 an interval. In other words, an aggregation of 8,000,000,000 water 
 molecules is barely visible to the best modern microscopes. 
 
 6. What is an Atom ? An atom is the 
 smallest quantity of matter that can enter into 
 combination. It is the chemical unit of matter and is 
 considered indivisible. 
 
 In nearly every case an atom is a part of a molecule. 
 
 (a.) If a molecule of water be divided, it will cease to be water 
 at all, but will yield two atoms of hydrogen and one of oxygen. 
 The molecule of common salt consists of one atom of sodium and 
 one of chlorine. Some molecules are very complex. The common 
 sugar molecule contains forty-five atoms. 
 
 (&.) Atoms make molecules ; molecules make masses. Of the 
 absolute size and weight of atoms and molecules little is known ; 
 Df their relative size and weight much is known, and forms an im- 
 portant part of the science of chemistry. 
 
 7. Forms of Attraction. Each of these three 
 divisions of matter has its own form of attraction : 
 
4 THE DOMAIN OF PHYSICS. 
 
 Molar attraction is called gravitation. 
 
 Molecular attraction is called cohesion or adhe- 
 sion. 
 
 Atomic attraction is called chemical affinity (chem- 
 ism). "'.-. 
 
 8. Forms of Motion. Each of these three divi- 
 sions of matter has its own form of motion : 
 
 Molar motion, or visible mechanical motion, is called 
 by different names according to the nature of the 
 substance in motion ; e. g., the flow of a river or the 
 vibrations of a pendulum. 
 
 Molecular motion, called heat, light, electricity, or 
 magnetism. 
 
 Atomic motion. (Purely theoretical as far as known.) 
 
 9. Physical Science. Physical science com- 
 prises Physics and Chemistry. 
 
 The first of these deals with masses and molecules; the 
 second with atoms and combinations of atoms. 
 
 1C. What is a Physical Change? A physi- 
 cal change is one that does not change the identity 
 of the molecule. 
 
 (a.) Inasmuch as the nature of a substance depends upon the 
 nature of its molecules, it follows that a physical change is one that 
 does not affect the identity of a substance. A piece of marble may 
 be ground to powder, but each grain is marble still. Ice maj 
 change to water and water to steam, yet the identity of the sub- 
 stance is unchanged. A piece of glass may be electrified and a 
 piece of iron magnetized, but they still remain glass and iron. These 
 changes all leave the composition and nature of the molecule un^ 
 changed ; they are physical changes. 
 
 11. What is a Chemical Change ? ^ chemi* 
 
THE DOMAIN OF PHYSICS. 
 
 cal change is one that does change the identity 
 of the molecule. 
 
 (a.} If the piece of marble be acted upon by sulphuric acid, fi 
 brisk effervescence takes place caused by the escape of carbonic acid 
 gas which was a constituent of the marble; calcium sulphate 
 (gypsum), not marble, will remain. The water may, by the action 
 of electricity, be decomposed into two parts of hydrogen and one of 
 oxygen. The nature of the glass and iron may easily be changed. 
 These change the nature of the molecule ; they are chemical 
 
 2. Definition. Physics, or Natural Philos* 
 ophy, is the branch of science that treats of the 
 laws and physical properties of matter, and of 
 those phenomena that depend upon physical 
 changes. 
 
 Recapitulation. To be reproduced and amplified 
 by the pupil for review. 
 
 Matter. 
 
 PHYSICAL 
 SCIENCE. 
 
 PHYSICS... 
 
 Divisions. 
 
 [MASSES. 
 MOLECULES 
 MULtLULtb> 
 
 Attractions. 
 GRAVITATION. 
 
 Motions. 
 
 COHESION - 
 ADHESION 
 
 ( Heat. 
 
 - \ \ Li & ht * 
 
 . 1 Electricity. 
 
 [ Magnetism 
 
 (CHEMISM 
 OR 
 AFFINITY 
 
THE PROPERTIES OF MATTER. 
 
 ECTfON H. 
 
 THE PROPERTIES OF MATTER. 
 
 13. Properties of Matter. Any quality thai 
 belongs to matter or is characteristic of it is called 
 a property of matter. 
 
 Properties of matter are of two classes, physical and 
 chemical. 
 
 14. What are Physical Properties t Physi- 
 cal properties are such as may be manifested 
 without changing the identity of the molecule ( 10). 
 
 (a.} A piece of coal takes up room, it is hard and heavy, it can- 
 not move itself. These several qualities or properties the coal may 
 exhibit and still remain coal, or still retain its identity. They are, 
 therefore, physical properties of coal. 
 
 15. What are Chemical Properties ? Chem- 
 ical Properties are such as cannot be manifested 
 without changing the identity of the molecule (11). 
 
 (a.) A piece of coal may be burned ; therefore combustibility is 
 a property of the coal. This property has been held by the coal 
 for countless ages, but it never has been shown. Further, this 
 piece of coal never can show this property of combustibility with- 
 out ceasing to exist as coal, without losing its identity. When the 
 coal is burned, the molecules are changed from coal or carbon to 
 carbonic acid gas (C0 2 ). 
 
 16. Experiment. Take a piece of ordinary sul- 
 phur (brimstone) and attempt to pull it in pieces ; the 
 degree of its resistance to this effort, or its tenacity, 
 measures the attraction of the molecules for each other. 
 Strike it with a hammer, and it breaks into many pieces, 
 thus manifesting its br idleness; but each piece is ordinary 
 
THE PROPERTIES OF MATTER. 7 
 
 sulphur. Heat it in a spoon, and it assumes the liquid 
 form, but it is sulphur yet. In none of these changes haa 
 the nature cf the molecule, or the identity of the sub- 
 stance, undergone any change. On the other hand, ii 
 the sulphur be heated sufficiently it will take fire and 
 burn, producing the irritating, suffocating gas familiar to 
 all through the use of common matches. We thus see 
 that the sulphur is combustible. This combustibility is 
 a chemical property, in the manifestation of which the 
 identity of the substance is destroyed. Before the mani- 
 festation we had sulphur; after it we have sulphurous 
 anhydride (SO*). The original molecules were elemen- 
 tary, composed of like atoms ; the resultant molecules 
 are compound, composed of unlike atoms, sulphur and 
 oxygen. 
 
 17. Division of Physical Properties. Physi- 
 cal properties of matter are, in turn, divided into two 
 classes, universal and characteristic. 
 
 18. What are Universal Properties ? Uni- 
 versal properties of matter are such as belong to 
 all matter. 
 
 All substances possess them in common ; no body can 
 exist without them. We cannot even imagine a body 
 that does not require space for its existence. This qual- 
 ity of matter, which will soon be named, is, therefore, 
 universal. 
 
 19. What are Characteristic Properties? 
 
 Characteristic properties of matter are such as 
 belong to matter of certain kinds only. 
 
 They enable us to distinguish one substance from an- 
 
8 THE PROPERTIES OF MATTER. 
 
 other. Glass is brittle, and by this single property may 
 be distinguished from india-rubber. 
 
 20. List of Universal Properties. The prin- 
 cipal universal properties of matter are extension, im- 
 penetrability, weight, indestructibility, inertia, 
 mobility, divisibility, porosity, compressibility, ex- 
 pansibility, and elasticity. 
 
 21. List of Characteristic Properties. The 
 
 characteristic properties of matter (often called specific or 
 accessory properties) are numerous. They depend, for the 
 most part, upon cohesion and adhesion. The most im- 
 portant characteristic properties are hardness, tenacity, 
 brittleness, malleability, ductility. 
 
 22. What is Extension? 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 property of matter, involved 
 in the very definition of matter. 
 
 (.) All matter must have these three dimensions. We say that 
 a line has length, a surface has length and breadth ; but lines and 
 surfaces are mere conceptions of the mind, and can have no material 
 existence. The third dimension, which affords the idea of solidity 
 or volume, is necessary to every form of every kind of matter. No 
 one can imagine a body that has not these three dimensions, that 
 does not occupy space, or " take up room." Figure or shape neces- 
 sarily follows from extension. 
 
 23. English Measures. For the purpose of com. 
 paring volumes, as well as surfaces and lengths, measures 
 are necessary. In the United States and England the 
 yard has been adopted as the unit, and its Divisions, ag 
 
THE PROPERTIES OF MATTER. 9 
 
 feet and inches, together with its multiples, as rods and 
 miles, are in familiar use. This unit is determined by 
 certain bars, carefully preserved by the governments of 
 these two nations. 
 
 24. Metric Measures. The international system 
 iias the merits of a less arbitrary foundation and of far 
 greater convenience. From its unit it is known as the 
 metric system. This system is in familiar use in most of 
 the countries of continental Europe and by scientific 
 writers of all nations, and bids fair to come into genera] 
 use in this country. For these reasons, as well as for its 
 greater convenience, an acquaintance with this system is 
 now desirable, and will soon be necessary. It has been 
 already legalized by act of Congress. 
 
 25. Definition of Meter. The meter was in- 
 tended to be forty -millionth of the earth's meridian 
 which passes through Paris, or as the ten-millionth of a 
 quadrant of such a meridian. It is equal to 39.37 
 inches. Like the Arabic system of notation and the table 
 of U. S. Money, its divisions and multiples vary in a ten- 
 fold ratio. 
 
 26. Metric Measures of Length. Ratio 
 = 1 : 10. 
 
 (Millimeter (mm.) = .001 w. 0.03937 inches 
 DIVISIONS. 1 Centimeter (cm.) = .01 m.= 0.3937 " 
 [ Decimeter (dm.) = .1 m.= 3.937 
 
 ClNiT. Meter (m.) = 1. m.= 39.37 
 
 r Dekameter (Dm.)- 10. m.=393.7 
 
 Hektometer (Hm.)= 100. w. = 328 ft. 1 inch. 
 MULTIPLES. < 
 
 I Kilometer (Km.)= 1000. m.= 0.62137 miles 
 
 I Myriameter (Jfw.)=10000. w.= 6.2137 
 
10 THE PROPERTIES OF MATTER. 
 
 Note. 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, mitti-, centi-, and deci-, signifying respectively 
 TnVrr T^O> an( ^ iV an( ^ already familiar in the mill, cent, 
 
 2 and dime of U. S. Money, are used for the divisions, 
 
 3 while the Greek prefixes deka-, liekto-, Tdlo- t and myria-, 
 '^ signifying respectively 10, 100, 1000, and 10000, are used 
 for the multiples of the unit. Each name is accented on 
 E the first syllable. 
 
 o 
 
 27. Metric Measures of Surface. 
 
 H Ratio = 1 : 1O 2 = 1 : 1OO. 
 
 U 
 
 f Square millimeter (sq. mm.} =0.000001 sq. m. 
 | DIVISIONS.^ Square centimeter (sq.cm.) =0.0001 " 
 [ Square decimeter (sq. dm.) =0.01 " 
 
 
 
 n UNIT. Square meter (sq. m.) =1. 
 
 etc., etc. 
 
 U 
 
 2 Note. The table may be read : 100 sq. mm. = 1 sq. cm. ; 
 S 100 sq. cm. = 1 sq. dm., etc. The reason for tile change 
 8 of ratio from 10 to 100 may be clearly shown by represent- 
 ing 1 sq. dm., and dividing it into sg. cm. by lines, which 
 shall divide each side of the sq. dm. into 10 equal parts or 
 centimeters. 
 
 28. Metric Measures of Volume. 
 FlG z Ratio = 1 : 1O 3 = 1 : 1OOO. 
 
 f Cubic millimeter (cu. mm.) = 0.000000001 cu. m. 
 DIVISIONS. < Cubic centimeter (cu. cm.) = 0.000001 " 
 
 [ Cubic decimeter (cu. dm.) = 0.001 " 
 
 UNIT. Cubic meter (cu.m.) = 1.308 cu. yds. 
 
 etc., etc. 
 
 29. Metric Measures of Capacity. Ratio = 
 
 JO. For many purposes, such as the measurement of 
 articles usuall} r sold by dry and liquid measures, a smaller 
 unit than the cubic meter is desirable. For such purposes 
 
THE PROPERTIES OF MATTER. 11 
 
 the cubic decimeter has been selected as the standard, 
 and when thus used is called a liter (pronounced leeter) 
 
 f Milliliter (ml.) 1 cu. cm.= 0.061022 cu. in. 
 DIVISIONS. \ Centiliter (cl.) = 10 " = 0.338 fid. oz. 
 [ Deciliter (dl.) = 100 " = 0.845 gill. 
 
 UNIT. Liter (1.) =1000 = 1.0567 liquid qts. 
 
 f Dekaliter (Dl.) ~ 10 cu. dm.= 9.08 dry qts. 
 MULTIPLES. -I Hektoliter (HI.) = 100cu.dm.= 2 bu. 3.35 pks. 
 [ Kiloliter (Kl.) - 1 cu. ra. = 26417 gals. 
 
 30. Comparative Helps. It may be noticed that 
 the m. corresponds somewhat closely to the yard, which it 
 will replace. Kilometers will be used instead of miles. 
 The cu. cm. may be represented by the ordinary die used 
 in playing backgammon. The L does not differ very much 
 from the quart, or the Dl. from the peck, which they will 
 respectively replace. In fact, the L is, in capacity, inter- 
 mediate between the dry and liquid quarts. 
 
 31. What is Impenetrability? Impenetra- 
 bility is that property of matter "by virtue of ivhich 
 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. 
 
 32. Experiment. Through one cork of a two- 
 necked bottle pass a small funnel or " thistle-tube," and 
 let it extend nearly to the bottom of the bottle. Through 
 
12 
 
 THE PROPERTIES OF MATTER. 
 
 FIG. a. 
 
 the other cork lead a tube to the water-pan, and let it 
 
 terminate beneath or 
 within the neck of 
 a clear glass bottle 
 filled with water, 
 and inverted in the 
 water-pan. See that 
 the corks are air- 
 tight; if necessary, 
 seal them with wax 
 or plaster of Paris. 
 If a two-necked bot- 
 tle be not convenient, 
 substitute therefor a 
 
 wide-mouthed bottle having two holes through the cork. 
 The delivery tube is best made of glass. It may be easily 
 bent by first heating it red-hot in an alcohol or gas flame, 
 Pour water steadily through the funnel ; as it descends, 
 air is forced out through the delivery tube, and may be 
 seen bubbling through the water in the inverted bottle. 
 At the end of the experiment, the volume of water in the 
 two-necked bottle will be nearly equal to the volume of air 
 in the inverted bottle. This clearly shows the impene- 
 trability of air. 
 
 33. What is Weight? Weight is (as the term 
 is generally used) the measure of gravity or molar at- 
 traction ( 7) of which it is a necessary consequence. 
 
 (a.) As all masses of matter exert tins force, weight necessarily 
 pertains to all matter ; but, in general use, the term weight has 
 reference to bodies upon the earth. If a body be placed near the 
 earth's surface and left unsupported, the mass attraction of the 
 earth for each molecule in the body will dww the two together, and 
 
THE PROPERTIES OF MATTER. 13 
 
 the body is said to fall to the earth. But in this case we have no 
 means of measuring the force that draws the two bodies together. 
 If now the body be supported, the force acts as before and produces 
 pressure upon the supporting substance. This pressure measures 
 the attractive force acting between the earth and the body, and is 
 called weight. If a second body like the first be placed beside it, 
 the mass attraction of the earth is exerted upon twice as many 
 molecules, and, reciprocally, the attraction of twice as many mole- 
 cules is exerted upon the earth; i. e., the attraction has become twice 
 as great, and the measure of that attraction, or the weight, has been 
 doubled. 
 
 (6.) If the same body were upon the moon, its weight would be 
 the measure of the attraction existing between the body and the 
 moon. But as the mass of the moon is less than that of the earth, 
 the attraction between the body and the moon would be less than 
 that between that body and the earth, and the weight would be 
 proportionally diminished. 
 
 34. English Measures of Weight. For the 
 
 comparison of weights, as well as of extension, standards 
 are necessary. In England and the United States the 
 pound is taken as the unit. Unfortunately, we have 
 pounds Troy, Avoirdupois, and Apothecaries', the use vary- 
 ing with the nature of the transaction. As with the yard, 
 these units are arbitrary, determined by certain carefully 
 preserved standards. 
 
 35. Metric Measures of Weight. Ratio 
 = 1 : 10. 
 
 C Milligram (mg.) = 0.0154 grains 
 
 DIVISIONS. \ Centigram (eg.} = 0.1543 " 
 
 [Decigram (dg.) = 1.5433 " 
 
 UNITS. Gram (g) = 15.432 
 
 r Dekagram (Dg.) = 0.3527 oz. avoirdupois, 
 
 I Hektogram (Eg.) = 3.5274 
 
 | Kilogram (Kg.) = 2.2046 Ibs. 
 
 I Myriagram (Mg.) = 22.046 " " 
 
14 THE PROPERTIES OF MATTER. 
 
 36. What is a Gram ? A gram is the weight 
 of one cu. cm. of pure water, at its temperature of 
 greatest density (4 0. or 39.2 F.). A 5-cent nickel coin 
 weighs 5 g. 
 
 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 
 Df the acid will a liter flask contain ? ' J 6 ' Vn~ 
 
 3. If alcohol is 0.8 times as heavy as water, how much will 1250 
 cu. cm. of alcohol weigh ? / u c & ' % r^.-- 
 
 4. What part of a liter of water is 250 g. of water ? '/y 
 
 5. What is the weight of a cu. dm. of water ? 
 
 6. What is the weight of a dl. of water? 
 
 37. What is Indestructibility? Indestructi- 
 bility is that property of matter by virtue of which 
 it cannot be destroyed. 
 
 (a.) Science teaches that the universe, when first hurled into space 
 from the hand of the Creator, contained the same amount of matter, 
 and even the same quantity of each element, that it contains to-day. 
 This matter has doubtless existed in different forms, but during all 
 the ages since, not one atom has been gained or lost. Take carbon 
 for instance. From geology we learn that in the carboniferous age, 
 long before the advent of man upon the earth, the atmosphere was 
 highly charged with carbonic acid gas, which, being absorbed by 
 plants, produced a vegetation rank and luxuriant beyond comparison 
 with any now known. The carbon thus changed from the gaseous 
 to the solid form was. in time, buried deep in the earth, where it 
 has lain for untold centuries, not an atom lost. It is now mined as 
 coal, burned as fuel, and thus transformed again to its original 
 gaseous form. No human being can create or destroy a single atom 
 of carbon or of any other element. Matter is indestructible. 
 Water evaporates and disappears only to be gathered in clouds and 
 condense and fall as rain. Wood burns, but the ashes and smoke 
 contain the identical atoms of which the wood was composed. In a 
 different form, the matter still exists and weighs as much as before 
 the combustion. 
 
 38. What is Inertia? Inertia is that prop- 
 erty of matter by virtue of which it is incapable 
 
THE PROPERTIES OF MATTER. 15 
 
 of changing its condition of rest or motion, or the 
 property by virtue of which it has a tendency when at 
 rest to remain at rest, or when in motion to continue in 
 motion. 
 
 (a.) If a ball be thrown, it requires external force to put it in mo- 
 tion; the ball cannot put itself in motion. When the ball is passing 
 through the air it Las no power to stop, and it will not stop until 
 some external force compels it to do so. This external force may 
 be the bat, the catcher, the resistance of the air, or the force of 
 gravity. It must be something outside the ball or the ball will move 
 en forever. 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 play- 
 ground, the frequent falls which result from jumping from cars in 
 motion, the backward motion of the passengers when a car is sud- 
 denly started and their forward motion when the car is suddenly 
 stopped, the difficulty in starting a wagon and the comparative ease 
 of keeping it in motion, the " balloon" and " banner" feats of the 
 circus-rider, etc., etc., may be used to illustrate this property of 
 matter. 
 
 39. Experiment. Upon the 
 tip of the fore-finger 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 experi- 
 ment 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 
 bottle for the finger-tip. 
 
 40. What is Mobility IMobility is that prop- 
 erty of matter by virtue of which the position of 
 bodies may be changed. 
 
16 THE PROPERTIES OF MATTER. 
 
 (a.) A body is any separate portion of matter, be it large or small, 
 as a book, a table, or a star. The term is nearly synonymous with 
 mass, but has not so distinct a reference to the absolute quantity of 
 matter. Bodies or masses are composed of molecules ; molecules 
 are composed of atoms. 
 
 (6.) On account of inertia, the body cannot change its own posi- 
 tion ; on account of mobility any mass of matter may be moved if 
 sufficient for,ce be 'applied. This changing of position is called 
 motion ; motion presupposes force. (See 64.) 
 
 41. What is Divisibility? Divisibility is that 
 property of matter by virtue of which a body may 
 be separated into parts. 
 
 (a.) Theoretically, the atom is the limit of divisibility of matter. 
 Practically the divisibility of matter is limited before the molecule 
 is reached ; our best instruments are not sufficiently delicate, our 
 best trained senses are not acute enough for the isolation or percep- 
 tion of a molecule. Nevertheless, this divisibility may be carried 
 to such an extent, by natural, mechanical (physical) or chemical 
 means, as to excite our wonder and test the powers of imagination 
 itself. It is said that the spider's web is made of threads so fine 
 that enough of this thread to go around the earth would weigh but 
 half a pound, and that each thread is composed of six thousand fila- 
 ments. A single inch of this thread with all its filaments may be 
 cut into thousands of distinct pieces, and each piece of each fila- 
 ment be yet a mass of matter composed of molecules and atoms. 
 The microscope reveals to us the existence of living creatures so 
 small that it would require thousands of millions of them to aggre- 
 gate the size of a hemp -seed. Yet each animalcule has organs of 
 absorption, etc. ; in some of these organs fluids circulate or exist. 
 How small must be the molecules of which these fluid masses are 
 composed ! What about the size of the atoms which constitute the 
 molecules ? A coin in current use loses, in the course of a score of 
 years, a perceptible quantity of metal by abrasion. What finite 
 mind can form a clear idea of the amount of metal rubbed off at 
 each transfer ? 
 
 42. What is Porosity? Porosity is that prop- 
 erty of matter by virtue of which spaces exist 
 between the molecules. 
 
THE PROPERTIES OF MATTER. 1? 
 
 (a.) When iron is heated, the molecules are pushed further apart, 
 the pores are enlarged, and we say that the iron has expanded. If 
 a piece of iron or lead be hammered, it will be 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 some= 
 times spoken of as ''sensible pores," but these are not properly in- 
 eluded under this head. 
 
 43. What is Compressibility ? Compressibil- 
 ity is that property of matter ~by virtue of which 
 a body may be reduced in size. 
 
 44. What is Expansibility? Expansibility is 
 that property of matter by virtue of which a body 
 may oe increased in size. 
 
 (a.) Compressibility and expansibility are the opposites of each 
 other, resulting alike from porosity. Illustrations have been given 
 under the head of porosity. Let each pupil prove by experiment 
 that air is compressible and expansible. 
 
 45. What is Elasticity? Elasticity is that 
 property of matter by virtue of which bodies resume 
 their original form or size when that form or 
 size has been changed by any external force. 
 
 (a.) 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. The amount of compression mat- 
 ters not except in the case of solids. It was formerly thought that 
 liquids were incompressible ; hence aeriform bodies were called 
 elastic fluids, while liquids were called non-elastic fluids. But the 
 compressibility and perfect elasticity of liquids having been shown, 
 the term "non-elastic fluid" involves a contradiction of terms and 
 would better be dropped. Fluids have no elasticity of form ; on 
 the other hand, all fluids have perfect elasticity of size. What 
 properties of matter are illustrated by the action of the common 
 pop-gun ? 
 
 46. What are Cohesion and Adhesion? 
 
 Cohesion is the force that holds together like mole- 
 
18 THE PROPERTIES OF MATTER. 
 
 cules; adhesion is the force that holds together 
 unlike molecules. 
 
 (a.) Cohesion is the force that holds most substances 
 together and gives them form. Were cohesion suddenly 
 to cease, brick and stone and iron would crumble to finest 
 p IG powder, and all our homes and cities and selves fall to 
 hopeless ruin. In aeriform bodies, cohesion is not ap- 
 parent, being overcome by molecular repulsion (heat). In 
 large masses of liquids the cohesive force is overcome by gravity, 
 which tends to bring all the molecules as low as possible and thus 
 renders their surfaces level. But in small masses of liquids, the 
 cohesive force predominates and draws all the molecules as near 
 each other as possible, and thus gives to each mass the spheroidal 
 form, as in the case of the dew or rain-drop. Globules of mercury 
 upon the hand or table, and drops of water upon a heated stove, are 
 familiar illustrations of this effect of cohesion upon small liquid 
 masses. But in the solid state of matter, cohesion shows most 
 clearly. Cohesion acts only at insensible (molecular) distances. Let 
 the parts of a body be separated by a sensible distance, and cohesion 
 ceases to act ; 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 case of wax or freshly-cut lead ; 
 it may be done by welding or melting, as in the case of iron. Cir- 
 cular plates of glass or metal, about three inches in diameter, often 
 have their faces so accurately fitted to each other that, when pressed 
 together, a considerable force is needed to separate them. (See 
 Fig. 4.) 
 
 (6.) Adhesion is the force that causes the pencil or crayon to leave 
 traces upon the paper or blackboard, and gives efficacy to paste, 
 glue, mortar and cements generally. In a brick wall, cohesion binds 
 together the molecules of the mortar layer into a single, hardening 
 mass, while on either hand adhesion reaches out and grasps the ad- 
 joining bricks and holds them fast a solid wall. Like cohesion, it 
 acts only through distances too small to be measured ; unlike cohe- 
 sion, it acts between unlike molecules. 
 
 47. What is Hardness? Hardness is that 
 property of matter by virtue of which som,e bodies 
 resist any attempt to force a passage between their 
 particles. 
 
THE PROPERTIES OF MATTER. 19 
 
 It is measured by the degree of difficulty with which it 
 is scratched by another substance. Fluids are not said to 
 have hardness. 
 
 (.) Hardness does not imply density. The diamond is much 
 harder than gold, but gold is four times as dense as diamond. 
 
 48. What is Tenacity ? Tenacity is that prop- 
 erty of matter by virtue of which some bodies re- 
 sist a force tending to pull their particles asunder. 
 
 (a.) Like hardness and the other characteristic properties of 
 matter, it is a variety of cohesion which is the general term for the 
 force which holds the molecules together and prevents disintegration. 
 The tenacity of a substance is generally ascertained by shaping it in 
 the form of a rod or wire, the area of whose cross-section may be 
 accurately measured. Held by one end in a vertical position, the 
 greatest weight which the rod will support is the measure of its 
 tenacity. For any given material, it has been found that the tenacity 
 is proportioned to the area of the cross-section ; e. g., a rod with a sec- 
 tional 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 one decimeter in diameter will carry four times as great a load as 
 a similar rod five centimeters 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 the surfaces 
 of twice as many molecules as will the second, and that the third 
 will expose four times as many molecular surfaces as the fourth. 
 But for the same material, each molecule has the same attractive 
 force. Doubling the number of these attractive molecules, which 
 is done by doubling the sectional area, doubles the total attractive 
 or cohesive force, which, in this case, is called tenacity ; quadru- 
 pling the sectional area quadruples the tenacity. Hence the law : 
 Tenacity is proportioned to the sectional area. 
 
 49. What is Brittleness? Brittleness is that 
 property of matter by virtue of which some bodies 
 may be easily broken, as by a blow. 
 
 (a.) Glass furnishes a familiar example of this property. The 
 idea that brittleness is the opposite of hardness, elasticity or tenac- 
 ity, should be guarded against. Glass is harder than wood ? but 
 
THE PROPERTIES OF MATTER. 
 
 very brittle ; it is very elastic, but very brittle also. Steel is fa* 
 more tenacious than lead, and far more brittle. 
 
 50. What is Malleability t 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 282,000 
 sheets, placed one upon the other, would measure but a single inch 
 in height. 
 
 51. What is Ductility ? Ductility is that 
 property of matter by virtue of which some bodies 
 may be drawn into wire. 
 
 (a.) Platinum wire has been made 3^^ of an inch in diameter. 
 Glass, when heated to redness, is very ductile. 
 
 52. Experiment. Heat the middle of a piece of 
 glass tubing, about six 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. 
 
 Recapitulation. To be reproduced and amplified 
 by the pupil from memory. 
 
 f CHEMICAL 
 
 PROPERTIES! 
 OF MATTER. I 
 
 PHYSICAL. 
 
 GENERAL 
 
 ISTIC. 
 
 Extension, Impenetrabil- 
 ity, Weight, Indestruc- 
 tibility, Inertia, Mobil- 
 ity, Divisibility, Po- 
 rosity, Compressibility, 
 Expansibility, Elas- 
 ticity. 
 
 f Hardntss. 
 Tenacity. 
 Brittlentss. 
 Malleability 
 Ductility. 
 
 f ADHESION. 
 ! 
 
 I COHESION. 
 
THE THREE CONDITIONS OF MATTER. 
 
 ECTION HI. 
 
 THE THREE CONDITIONS OF MATTER. 
 
 53. Conditions of Matter. Matter exists in 
 three conditions or forms the solid, the liquid, 
 find the aeriform. 
 
 54. What is a Solid ? A solid is a body whose 
 molecules change their relative positions with 
 difficulty. 
 
 Such bodies have a strong tendency to retain any form 
 that may be given to them. A movement of one part of 
 such a body produces motion in all of its parts. 
 
 55. What is a Liquid? A liquid is a body 
 whose molecules easily change their relative po- 
 sitions, 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. They always so adapt them- 
 selves as to have their free surfaces horizontal. Water 
 is the best type of liquids. 
 
 56. Experiment. Sus- 
 pend a glass or metal plate, 
 of about four inches area, 
 from one end of a scale-beam, 
 and accurately balance the 
 same with weights in the oppo- 
 site scale-pan. The support- 
 ing cords may be fastened to 
 
 the plate with wax. Beneath FIG. 5. 
 
THE THREE CONDITIONS Of 
 
 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. Carefully add small 
 weights to those in the scale-pan. Notice that the water 
 beneath the plate is 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 mole- 
 cules on the plate have been torn from their companions 
 in the saucer. The weights added to the original coun- 
 terpoise were needed to overcome the tendency of the 
 water molecules to cling together. 
 
 Note to the Pupil. After seeing a physical experiment, always asb 
 yourself, " What was the object of that experiment? What does H 
 teach?" Never allow yourself to look upon an experiment as being 
 simply entertaining ; thus reducing the experimenter, so far as you 
 are concerned, to the level of a showman. 
 
 57. What is an Aeriform Body? An aeri- 
 form body is one whose molecules easily change 
 their relative positions, and tend to separate from 
 each other almost indefinitely. 
 
 Atmospheric air is the best type of aeriform bodies. 
 
 58. Gases and Vapors. Aeriform (having the 
 form of air) bodies are of two kinds, gases and vapors. 
 Gases remain aeriform under ordinary conditions, although 
 they may be liquefied by intense cold and pressure. 
 Vapors are aeriform bodies produced by heat from sub- 
 stances that are generally solid or liquid, as iodine or 
 water. They resume the solid or liquid form at ordinary 
 temperatures. 
 
 59. Changes of Condition. The same substance 
 may exist in two or even three of these forms. Most 
 
TffREE CONDITIONS OF MATTE&. 
 
 solids, as lead and iron, may be changed by heat to liquids ; 
 others, as iodine, may be apparently changed directly to 
 vapors ; still others, as ice, may be easily changed first to 
 the liquid, and then to the vapor form. It is probable that 
 any solid might be liquefied and vaporized by the applica- 
 tion of heat, and that the practical infusibility of certain 
 substances is due to our limited abilities in the production 
 of heat. 
 
 (a.) Many vapors and gases, as steam and sulphurous anhydride 
 (SO 2 , the irrespirable gas formed by burning sulphur), may be liquefied 
 by cold, the withdrawal of heat. The process is one of subtraction. 
 A still further diminution of the heat force would, in many cases, 
 lead to a solidifying of the liquid. It is probable that all gasea 
 might be liquefied and all liquids solidified, if we had the power of 
 unlimited withdrawal of heat. In fact, the last of the " permanent 
 gases" has been liquefied already. 
 
 (6.) Recent experiments with electric discharges in high vacuums 
 (Exp. 71, p. 250), have yielded remarkable results wliich are held, by 
 some, to show the existence of a fourth condition of matter. For 
 matter in this " ultra-gaseous " state, the name " Radiant Matter" 
 has been proposed. 
 
 6O. What is a Fluid ? A fluid is a body whose 
 molecules easily change their relative positions. 
 
 The term comprehends liquids, gases, and vapors. 
 
 (a.) In a liquid, cohesion is more powerful than repulsion ; in an 
 aeriform body, repulsion is the more powerful. The change from 
 the liquid to the aeriform condition is caused by an increase of the 
 velocity of the constituent molecules, such increase of velocity being 
 a thermal effect. 
 
 61. Optional Definitions. (1.) A body possessing any 
 degree of elasticity of form ( 45) is a solid ; a body that possesses 
 no elasticity of form is a fluid. 
 
 (2.) A body that can exist in equilibrium under the action of a 
 pressure that is not uniform in all directions is a solid ; a body that 
 cannot exist in equilibrium under such conditions is a fluid. 
 
24 THE THREE CONDITIONS OF MATTER. 
 
 (3.) A fluid that can expand indefinitely so as to fill any vessel, 
 however large, is an aeriform body ; a fluid, a small portion of which, 
 when placed in a large vessel, does not expand at once so as to fill 
 the vessel, but remains collected at the bottom, is a liquid. 
 
 (4.) A body that has a definite volume and form is a solid ; a body 
 that has a definite volume and an indefinite form is a liquid ; a body 
 ihat has an indefinite volume and form is aeriform. 
 
 (5.) A gas is an easily compressible fluid. 
 
 62. Kinetic Theory of Gases. A perfect gas 
 consists of free, elastic molecules in constant motion. 
 Each molecule moves in a straight line and with a uni- 
 form velocity until it strikes another molecule or the ves- 
 sel in which the gas is contained. The blows that the 
 molecules thus strike upon the vessel are so numerous 
 that their total effect is a continuous,, constant force or 
 pressure. 
 
 (a.) The mean velocity of a hydrogen molecule has been deter- 
 mined as 184260 cm. (or more than a mile) per second. If its 
 weight were known, the work that it can do might be easily com- 
 puted ( 157). The molecules of other aeriform substances move 
 with smaller velocities. 
 
 Recapitulation. To be reproduced, upon paper or 
 the blackboard, by each pupil. 
 
 MATTER i 
 
 SOLIDS. 
 
 Molecules change 
 their relative po- 
 sitions with diffi- 
 culty. 
 
 FLUIDS. 
 
 Molecules change 
 their relative po- 
 sitions easily. 
 
 LIQUIDS, 
 
 Molecules cling to- 
 gether feebly. 
 
 AERIFORM BODIES. 
 Molecules tend to 
 separate. 
 
 GASES ; ordinarily 
 aeriform. 
 
 KINETIC THEORY. 
 VAPORS; ordinarily 
 liquid or solid. 
 
DYNAMICS. FORCE AND MOTION. GRAVITATION. 
 
 FALLING BODIES. THE PENDULUM. 
 
 ENERGY. 
 
 ECTION I. 
 
 FORCE AND MOTiO N. 
 
 63. Dynamics. Dynamics is that branch of 
 physics which treats of forces and their effects. 
 
 These effects may be of two kinds. 
 
 (a.) The forces employed may be counterbalanced. If they thus 
 act upon a body at rest, that body will remain at rest ; if they act 
 upon a body in motion, the motion will not be changed thereby. 
 The branch of dynamics that treats of forces thus balanced is called 
 Static*. 
 
 (6.) The forces employed may act against the inertia of matter 
 ( 38), and produce motion or change of motion. The branch of 
 dynamics that treats of forces thus used is called Kinetics. If we 
 have a problem relating to the forces that may produce equilibrium 
 in a lever, as in the act of weighing goods, it is a static problem ; 
 if a problem refer to the velocity of a falling body, or the amount 
 of work that may be done by the uncoiling of a watch-spring, it is 
 a kinetic problem. 
 
 Note. No attempt will be made to maintain the distinction be 
 tween the static and kinetic effects of forces. 
 
 64. What is Force ? The word force is difficult 
 of satisfactory definition. As generally used, it signifies 
 
26 FORCE AND MOTION. 
 
 any cause that tends to produce, change or destroy 
 motion. 
 
 It follows from inertia that bodies are incapable of 
 changing their condition of rest or motion. Any cause 
 capable of producing a tendency to change either of these 
 conditions, is called a force. Equal forces will produce 
 equal velocities when applied to the same body for the 
 same time. 
 
 (a.) We say that the tendency of a force acting on a body at rest 
 fs to move it. Motion loill be produced if the body is free to move. 
 This motion may be prevented by the simultaneous action of another 
 force or of other forces. Or the body may be fixed so that a given 
 pull or pressure, {. e., the application of force, will produce no 
 motion. In this case, opposing forces are called into action as soon 
 as the given force begins to act, and thus the new force is neutralized. 
 For instance, a small boy may exert all of his muscular power upon 
 a large stone and not lift it at all. The force employed produces no 
 motion. The attraction between the earth and the stone ( 33) is a 
 force acting in a downward vertical direction. This force is exactly 
 balanced by the upward pressure of the supporting earth or floor 
 ( 93). If the stone weighs two hundred pounds and the boy lifts 
 fifty pounds, the supporting body exerts an upward pressure of only 
 one hundred and fifty pounds. One quarter of the weight of the 
 stone or a downward force of fifty pounds is thus liberated or called 
 into play by the very act of lifting with a force of fifty pounds. 
 Hence no motion is produced, because an opposing force is called 
 into action as soon as the given force begins to act, and thus the 
 new force is neutralized. 
 
 (&.) In this case, the greatest opposing force that can be set free 
 or called into play is a force of two hundred pounds, the full weight 
 of the stone. If, therefore, the stone be lifted with a force of more 
 than two hundred pounds, the new force can not be wholly neutralized 
 and motion will take place. If the body be free to move, the smallest 
 conceivable force will overcome the inertia and produce motion. 
 
 65. Elements of a Force. In treating of forces, 
 we have to consider three things : 
 (1.) The point of application f or the point at which 
 the force acts. 
 
FOKCE AND MOTIOtf. 27 
 
 (.) 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 which it is 
 able to produce motion in a hody free to move. 
 
 66. 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. When this unit has been determined 
 upon, the value of any given force is designated by a nu- 
 merical reference to the unit, just as we refer quantities of 
 weight to the kilogram or pound, or quantities of distance 
 to the meter or yard. The magnitude of any force may be 
 measured by either of two units, which we shall now con* 
 sider. 
 
 67. The Gravity Unit. The given force may be 
 measured by comparing it with the gravity of some known 
 quantity or mass of matter. This is a very simple and 
 convenient way, and often answers every purpose, ^e 
 gravity unit of force is the gravity of any unit of 
 mass. This unit of mass may be a gram, kilogram, 
 pound, or ton, or any other unit that may be more con- 
 venient under the circumstances. (See 102.) 
 
 (a.) A force is said to be a force of 100 kilograms when it may be 
 replaced by the action of a weight of 100 kilograms. The pressure 
 of steam in a boiler is generally measured, at present, in pounds p&r 
 square inch, that is, by determining the number of pounds with 
 which it would be necessary to load down a movable horizontal 
 square inch at the top of the boiler in order to keep it in place 
 against the pressure of the steam. A cord or rope may be pulled 
 with a certain force. This force is measured by finding out 
 
8 FORCE AND MOTTO W. 
 
 many pounds suspended by the cord or rope would give it an equal 
 pull or tension. 
 
 (b.) As we shall see, the force of gravity exerted upon a given 
 mass is variable. A given piece of iron would weigh more at the 
 poles than at the equator. Other variations in the force of gravity 
 are known When, therefore, scientific accuracy is required, it wili 
 not suffice to speak of a force of ten pounds, but we may speak of a 
 force of ten pounds at the sea-level at New York City. The neces- 
 sary corrections may then be made. But for ordinary purposes, 
 &ese details may be disregarded. 
 
 68. The Absolute Unit. The absolute or ki- 
 netic unit of force is the force that, acting for 
 unit of time upon unit of mass, will produce unit 
 9f 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 a velocity of one foot per second. 
 
 (a.) In all kinetic questions the kinetic unit is far more convenient. 
 Gravity units may easily be changed to kinetic units. At the lati- 
 tude of New York, the force of gravity acting upon one pound of 
 matter left free to fall will give it a velocity of 32.16 ft. per second 
 for every second that it acts. Consequently, at such latitudes, the 
 gravity unit is equal to 32.16 kinetic units.. 
 
 69. The Dyne. Instead of using a unit of force 
 based upon the foot and pound, scientific men are coming 
 to use a similar unit based upon the centimeter and gram. 
 This unit has a definite name. The dyne is the force 
 that, acting for one second upon a mass of one 
 gram, produces a velocity of one centimeter per 
 second. 
 
 (a.) If a body weighing 25 grams acquires in one second a velocity 
 of 30 cm., the moving force was 750 dynes. If it acquires the same 
 velocity in 2 seconds, of course the force was only half as great, or 
 375 dynes. As the increment of velocity ( 127) is 980 cm., the 
 weight of a gram equals 980 dynes. 
 
 (b.) The several units based upon the centimeter, gram and second, 
 
FORCE AND MOTION. 29 
 
 constitute a class called (from the initial letters of these words) 
 C. G. S. Units. Thus the dyne is the C. G. S. unit of force. 
 
 Note to the Pupil. We have been speaking of unit of mass, and 
 you have probably had no difficulty in understanding that, by this 
 term, a certain definite quantity of matter is meant. This certain 
 quantity may be any quantity that we agree upon as a unit of 
 measure. In this country we have, as yet, no commonly accepted 
 unit of mass. In countries where the metric system of weights 
 and measures is used, the unit of mass is the quantity of matter 
 contained in one cu. cm. of pure water at its temperature of greatest 
 density. It will be seen that this definition is independent of gravity, 
 and that it holds good for matter anywhere. The quantity of matter 
 in the unit thus defined is invariable, while the gram, which is its 
 weight ( 36), is variable. But notwithstanding this, at any given 
 place, weight is proportional to mass, and we, therefore, conveniently 
 use weight as a means of estimating mass. We speak t without any 
 considerable ambiguity of a pound of matter, because we know that 
 a mass that weighs two pounds at the same place has just twice as 
 much matter as the first, which we may take as a convenient unit of 
 mass. 
 
 70. Momentum. The momentum of cu body is 
 Us quantity of motion. 
 
 Its measure is the product of the numbers representing 
 the mass and the velocity. 
 
 (a.) One tendency of force is to produce motion. In a given 
 time, two units of force will produce twice as much motion as one 
 unit. This doubled momentum or quantity of motion may exist in 
 two units of mass having one unit of velocity, or in one unit of 
 mass with two units of velocity. 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 ft. 
 The momentum of the former is 300 ; that of the latter, 150. Mo- 
 mentum has reference only to force and inertia. Therefore, when 
 acting upon bodies free to move, equal forces will produce equal 
 momenta whether the bodies acted upon be light or heavy. The 
 unit of momentum has no definite name. 
 
 71. Experiment. Figure 6 represents a piece of 
 apparatus, devised by Ritchie of Boston. It consists of 
 
30 
 
 FORCE AND MOTION. 
 
 two ball pendulums, one of which weighs twice as much 
 
 as the other, suspended as 
 represented. The heavier ball 
 contains a spring-hammer, 
 which is held back by a thread. 
 The hammer being thus held 
 back, and the smaller ball 
 resting against its face, the 
 thread is, burned, a blow is 
 struck, and an equal force is 
 exerted upon each ball ( 72 
 [3] and 93). The smaller ball 
 will move twice as fast and 
 twice as far as the larger ball, 
 
 FIG. 6. 
 
 equal forces producing equal momenta. 
 EXERCISES. 
 
 1. Find the momentum of a 500 Ib. ball moving 500 feet a second. 
 
 2. By falling a certain time, a 200 Ib. ball has acquired a velocity 
 of 321.6 ft. What is its momentum? 
 
 8. 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 is meant by a force of 10 pounds ? To how many F. P. S. 
 units is it equal ? 
 
 5. A stone weighing 12 oz. is thrown with a velocity of 1820 ft. 
 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 ft. a second ; what is thn 
 velocity of the other ? 
 
 $. Two balls have equal momenta. The first weighs 100 kilo 
 
FORCE AND MOTION. 31 
 
 grams and moves with a velocity of 20 meters a second. The other 
 moves with a velocity of 500 meters a second. What is its weight \ 
 
 9. A force of 1000 dynes acts on a certain mass for one second and 
 gives it a ve.^city of 20 cm. per second. What is the mass in 
 grams? Ans. 50. 
 
 10. A constant force, acting on a mass of 12 g. for one second Q 
 gives it a velocity of 6 cm. per second. Find the force in dynes. 
 
 11. 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. 
 
 12. Two bodies start from a condition of rest and move towarda L 
 each other under the influence of their mutual attraction ( 7 and 
 
 98). The first has a mass of 1 g. ; the second, a mass of 100 g. The 
 force of attraction is T ^ dyne. What will be the velocity acquired 
 by each during one second ? 
 
 72. 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. 
 
 (2.) Every motion or change of motion is in the 
 direction of the force impressed and is 
 proportionate to it. 
 
 (3.) Action and reaction are equal and opposite 
 in direction. 
 
 73. The First Law. The first law of motion re- 
 sults directly from inertia ( 38). 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. A base-ball when once set in motion has 
 no power to stop itself ( 38, a). If it moved in obe- 
 
32 FORCE AND MOTION. 
 
 dience to the muscular impulse only, its motion would be 
 in a straight line ; but the force of gravity is ever active, 
 and constantly turns it from that line, and forces it to 
 move in a graceful curve instead. 
 
 74. Centrifugal Force. Although it is obviously 
 impossible to give any direct experimental proof of the first 
 
 FIG. 7. 
 
 law of motion, we see many illustrations of the tendency 
 of moving bodies to move in straight lines even when 
 forced to move in curved lines. A curved line may be 
 considered a series of infinitely small straight lines. A 
 body moving in a curve has, by virtue of its inertia, a 
 tendency to follow the prolongation of the small straight 
 line in which it chances to be moving. Such a prolonga- 
 tion becomes a tangent to the curve, to move in which a 
 body must fly further from the centre. This tendency 
 
FORCE AND MOTION. 
 
 of matter to move in a straight line, and, conse- 
 quently, further away from the centre around 
 which it is revolving, is called Centrifugal Force, 
 from the Latin words which mean to fly from the centre. 
 The "laws" of this "centrifugal force" may be studied 
 or illustrated by the whirling-table and accompanying 
 apparatus, represented in Figure 7. (See 77.) 
 
 75. Caution. It is to be noticed that this so-called 
 " Centrifugal Force " is not a force at all. It is 
 simply inertia manifested under special conditions. It is 
 one of the universal properties of matter by virtue of 
 which the body shows a decided determination to obey 
 the first law of motion. The facts of the case are the 
 direct opposite of those implied by this ill-chosen name. 
 Take a common sling, for instance. The implication made 
 by the term, " Centrifugal Force," is that the pebble in the 
 revolving sling has a natural tendency to continue moving 
 in a circle, and that some external force is necessary to 
 overcome that tendency. The truth is that the natural 
 tendency of the pebble is to move in a straight line, and the 
 only reason that it does not thus move is that it is continu- 
 ally forced from its natural path by the pull of the string. 
 As soon as this external force is removed, by intent or 
 accident, away flies the stone in obedience to its own law- 
 abiding tendencies. 
 
 76. Simply Suggestive. Examples and effects of 
 this so-called centrifugal force may be suggested as follows: 
 Wagon turning a corner, railway curves, water flying from 
 a revolving grindstone, broken fly-wheels, spheroidal form 
 of the earth, erosion of river-beds, a pail of water whirled 
 in a vertical circle, the inward leaning of the circus-horse 
 %nd rider, the centrifugal drying apparatus of the laundry 
 
34 FORCE AND MOTION. 
 
 or sugar refinery, difference between polar and equatorial 
 weights of a given mass, etc. 
 
 77. Law of Centrifugal Force. The force neces- 
 sary to overcome this tendency of matter to move away 
 from the centre around which it may be revolving, varies 
 directly as the mass and as the square of the velocity, the 
 radius remaining the same. Doubling the mass doubles 
 the force needed, but doubling the velocity quadruples the 
 needed restraining force. 
 
 78. The Second Law. The second law of motion 
 is sometimes given as follows: A given force will pro- 
 duce 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. 
 
 (a. ) Many attempts have been made to show that these are only 
 two ways of stating the same proposition ; most of them are more 
 perplexing than profitable. In the law as given by Newton ( 72), 
 the word motion is doubtless used in the sense of momentum. If the 
 substitution of " momentum " for " motion " makes the reconciliation 
 any easier, no objection can be made to the substitution. 
 
 79. Resultant Motion. Motion produced by 
 the joint action of two or more forces is called 
 resultant motion. 
 
 The point of application, direction, and magnitude of 
 each of the component forces being given, the direction 
 and magnitude of the resultant force are found by a 
 method known as the composition of forces. 
 
 80. Composition of Forces. Under composi- 
 tion of forces, three cases may arise : 
 
 (1.) When the given forces act in the same direc- 
 tion. The resultant is then the sum of the given 
 forces. Example : Bowing a boat down stream. 
 
FORCE AND MOTION. 35 
 
 When the given forces act in opposite di- 
 rections. The resultant is then the difference 
 between the given forces. Motion will be pro- 
 duced in the direction of the greater force. Ex- 
 ample : Eowing a boat up stream. 
 (3.) When the given forces act at an angle. The re- 
 sultant is then ascertained by the parallelogram of 
 forces. Example : Rowing a boat across a stream. 
 
 81. Graphic Representation of Forces. 
 
 Forces may be represented by lines t the point of 
 application determining one end of the line, the direc- 
 tion 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 ( 65) 
 are the ones that precisely 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 
 problem. Thus the diagram rep- 
 resents two forces applied to the 
 point B. These forces act at right 
 angles to each other. The arrow- 
 heads indicate that the forces rep 
 
 FIG. 8. resented act from B toward A and 
 
 C respectively. The force that 
 
 acts in the direction BA being 20 pounds and the force acting in the 
 direction BC being 40 pounds, 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. 
 
 (6.) The graphic determination or representation of the resultant 
 in the first two cases under the " Composition of Forces " is too 
 simple to need any explanation. 
 
36 FORCE AND MOTION. 
 
 82. Parallelogram of Forces. In the diagram, 
 let AB and AC represent 
 
 A 
 
 two forces acting upon the 
 point A. Draw the two 
 lotted lines to complete the 
 parallelogram. From A, the 
 point of application, draw 
 the diagonal AD. This 
 diagonal will be a complete graphic representa- 
 tion of the resultant. In such cases the two given 
 forces are called components. The resultant of any two 
 components may always be determined in this way. If 
 two forces, such as those represented in the diagram, act 
 simultaneously upon a body at A, that body will move 
 over the path represented by AD, and come to rest at D. 
 
 (a.) Suppose that instead of acting simultaneously, these forces 
 act successively. If AC act first for a given time, it would move the 
 body to C. If then the other force act for an equal time it would 
 move it to the right a distance represented by AB or its equal CD, 
 and the body be left at D as before. If the force represented by AB 
 acted first and the force represented by AC then acted for an equal 
 time, the body would evidently be left at D. Thus we see that these 
 two forces produce the same effect whether they act simultaneously 
 or successively. 
 
 83. Experimental Verification. This prin- 
 ciple of the parallelogram of forces may be verified by 
 the apparatus represented in Fig. 10. ABCD is a very 
 light wooden frame, jointed so as to allow motion at its 
 four corners. The lengths of opposite sides are equal ; the 
 lengths of adjacent sides are in the ratio of two to three. 
 From the corners B and 0, light, flexible silk cords pasa 
 over the pulleys M and N, and carry weights, W and w, 
 of 90 and 60 ounces respectively, the ratio between the 
 
FORCE AND MOTION. 
 
 FIG. 10. 
 
 weights being the same as the ratio between the corres- 
 ponding adjacent sides of the wooden parallelogram. A 
 weight of 120 ounces is hting from the corner A. When 
 the wooden frame comes to rest it will be found that the 
 sides AB and AC lie in the direction of the cords which 
 form their prolongations. These sides AB and AC are 
 accurate graphic representations of the two forces acting 
 upon the point A. It will be further found that the 
 diagonal AD is vertical and twice as long as the side AC. 
 Since the side AC represents a force of 60 ounces, AD will 
 represent a force of twice 60 ounces or 120 ounces. We 
 thus see that AD fairly represents the resultant of the 
 two forces due to the gravity of W and w f for this result- 
 
38 FORCE AND MOTION. 
 
 ant is equal, and opposite to the vertical force which is 
 due to the gravity of V, and this balances the forces repre- 
 sented by AB and AC. Results equally satisfactory will 
 be secured as long as AB : AC :: W : w. 
 
 84. A Substitute. Very satisfactory results may 
 be had by simpler apparatus. Let H 
 
 and K represent two pulleys that work 
 with very little friction. Fix them to a 
 vertical board. The blackboard will 
 answer well if the pulleys can be at- 
 tached without injury. Three silk cords 
 are knotted together at ; two of them 
 pass over the pulleys; the three cords 
 carry weights, P, Q, and R, as shown in FIG. n. 
 
 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. Com- 
 plete the parallelogram AOBD by drawing lines upon the 
 vertical board. Draw the diagonal OD. It will be found 
 by measurement that AO : OD : : P : R; or that BO : OD 
 : : Q : R. Either equality of ratios affords the verification 
 sought. 
 
 85. Determination of the Value of the 
 Resultant. With a carefully-constructed diagram (only 
 half of the parallelogram need be actually drawn) the re- 
 sultant may be directly measured and its value ascertained 
 from the scale adopted. The value and direction of the 
 resultant may be found trigonometrically, without actual 
 construction of the diagram, when the angle between the 
 directions of the components is known. In one or two 
 cases, however, the mathematical solution is easy without 
 
FORCE AND MOTION. 39 
 
 the aid of trigonometrical formulae. When the com- 
 ponents act at right angles to each other, the resultant is 
 the hypothenuse of a right-angled triangle. (See Olney^s 
 Geometry, paragraph 346.) When the components are 
 equal and include an angle of 120, the resultant divides 
 the parallelogram into two equilateral triangles. It is 
 equal to either component, and makes with either an angle 
 of 60. (Let the pupil draw such a diagram.) 
 
 86. Equilibrant. A force whose effect is to 
 balance the effects of the several components is 
 called an equilibrant. It is numerically equal to the 
 resultant, and opposite in direction. Thus in Fig. 10, the 
 gravity of the weight V is the equilibrant of W and w ; 
 it is equal and opposite to the resultant represented by 
 AD. 
 
 87. Triangle of Forces. By reference to Fig. 9, 
 it will be seen that if AC represent the magnitude and 
 direction of one component, and CD the magnitude and 
 direction of the other component, the line AD, which 
 completes the triangle, will represent the direction and 
 intensity of the resultant. Where the point of application 
 need not be represented, this method of finding the rela- 
 tive magnitudes and directions is more expeditious than 
 the one previously given. If the line which completes the 
 triangle be measured from D to A, that is to say, in the 
 order in which the components were taken, it represents 
 the equilibrant ; the arrow-head upon AD should then 
 be turned the other way. If this line be measured from 
 A to D, that is, in the reverse order, it represents the 
 resultant* 
 
40 
 
 FORCE AND MOTION. 
 
 88. Composition of More than Two 
 -Forces. If more than two forces act upon the point of 
 application, the resultant of any two may be combined 
 with a third, their resultant with a fourth, and so on. 
 The last diagonal will represent the resultant of all the 
 given forces. Suppose that four 
 forces act upon the point A, as 
 represented in the diagram. By 
 compounding the two forces AB 
 and AC, we get the partial re- 
 sultant, A/*; by compounding 
 this with AD, we get the second 
 partial resultant, Ar'; by com- 
 pounding this with AE, we get 
 the resultant, AE. 
 
 FIG. 12, 
 
 89. Polygon of Forces. This resultant may be 
 more easily obtained by the polygon of forces. If a num- 
 ber of forces be in equilibrium, 
 they may be graphically repre- 
 sented by the sides of a closed 
 polygon taken in order. If the 
 forces are not in equilibrium, the 
 lines representing them in magni- 
 tude and direction will form a 
 figure which does not close. The line that completes the 
 figure and closes the polygon will, when taken in the same 
 order, indicated by the arrow-head at x, represent the 
 equilibrant ; when taken in the opposite order, indicated 
 by the arrow-head at z, it will represent the resultant. 
 This will be evident from a comparison of the diagram with 
 the one preceding, the forces compounded being the same, 
 
 FIG. 13. 
 
FORCE AND MOTION. 41 
 
 90. Parallelepiped of Forces. The component 
 
 forces may not all act in the 
 same plane, but the method of 
 composition is still the same. 
 \ In the particular case of three 
 such forces it will be readily 
 seen that the resultant of the 
 FlG forces AB, AC, and AD is rep- 
 
 resented by AR, the diagonal 
 
 of the parallelepiped constructed upon the lines represent- 
 ing these forces. 
 
 91. 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. Repre- 
 sent 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. 
 When the problem is to resolve or decompose the given 
 force into two or more components having given directions, 
 it is definite only one construction being possible. The 
 sides that meet at the point of application will represent 
 the component forces. (See 201.) 
 
 92. Example of Resolution of Forces. As 
 
 we proceed we shall find more than one example of the 
 resolution of forces. A single one will answer in this 
 place. It is a familiar fact that a sail-boat may move in a 
 direction widely different from that of the propelling wind, 
 and that, under such circumstances, the velocity of the 
 boat is less than it would be if it were sailing in the direc- 
 tion of the wind,. The force due to the pressure of the 
 
4:2 FORCE AND MOTION. 
 
 wind is twice resolved, and only one of the components 
 is of use in urging the boat forward. In Figure 15, 
 let KL represent the keel of the 
 boat ; BG, the position of the sail ; 
 andAB, the direction and intensity 
 of the wind. In the first place, 
 when the wind strikes the sail thus 
 placed, it is resolved into two com- 
 ponents BG parallel to the sail, and 
 FIG. 15. BD perpendicular to the sail. It is 
 
 evident that the first of tlhese is of 
 no effect. But the boat does not move in the direction of 
 BD, which is, in turn, resolved by the action of the keel 
 and rudder into two forces, BL in the direction of the 
 keel, and BE perpendicular to it. The first of these pro- 
 duces the forward movement of the boat ; the second 
 produces a lateral pressure or tendency to drift, which is 
 more or less resisted by the build of the boat 
 
 93. The Third Law. Examples of the third law 
 of motion are very common. When we strike an egg 
 upon a table, the reaction of the table breaks the egg ; the 
 action of the egg may make a dent in the table. The re- 
 action of the air, when struck by the wings of a bird, 
 supports the bird if the action be 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. 
 
 94. Reaction in Non-elastic Bodies. The 
 
 effects of action and reaction are modified largely by 
 elasticity, but never so as to destroy their equality. Hang 
 
FORVE AND MOTION. 
 
 43 
 
 two clay balls of equal mass by strings of equal lengths 
 
 BO that they will just touch each other. If one be 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 momentum by the 
 
 second is due to the action 
 
 of the first It is equal 
 
 to the loss of momentum 
 
 6y the first, which loss is 
 
 due to the reaction of the 
 
 second. 
 
 95. Reaction in 
 Elastic Bodies. If 
 
 two ivory balls, which are 
 elastic, be similarly placed, 
 and the experiment re- 
 peated, it will be found FIG. 16. 
 that the first ball will give 
 
 the whole of its motion to the second and remain 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. 
 
 96. Reflected Motion. Reflected motion u 
 the motion produced ~by the reaction of a surface 
 when struck by a body, either the surface, or the 
 body, or both being elastic. 
 
 A ball rebounding from the wall of a house, or froni thf 
 
44 FORCE AND MOTION. 
 
 cushion of a billiard-table, is an example of reflected 
 motion. 
 
 97. Law -of Reflected Motion. The angle in- 
 cluded between the direction of the moving body before it 
 strikes the reflecting surface and a perpendicular to thai 
 surface drawn from the point of contact, is called the angle 
 
 FIG. 17. 
 
 of incidence. The angle between the direction of the 
 moving body after striking and the perpendicular, is called 
 the angle of reflection. TJie angle of incidence is 
 equal to the angle of reflection, and lies in the 
 same plane. A ball shot from A will be reflected at B 
 back to C, making the angles ABD and CBD equal. 
 
 EXERCISES. (Answers to le written.) 
 
 t. 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. 
 
 J 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 be made to row a boat at the rate of foul 
 miles an hour directly across a stream flowing at the rate of thre 
 miles an hour. Determine the direction and velocity of the boat. 
 
 4. A flag is drawn downward 64 ft. from the mast-head of a mov- 
 ing ship. During the same time, the ship moved forward 24 ft. 
 Represent the direction and length of the actual path of the flag. 
 
 5. A sailor climbs a mast at the rate of 3 ft. a second ; the ship is 
 
FORCE AND MOTION. 
 
 45 
 
 sailing at the rate of 12 ft. 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 
 a force of- 15 pounds, and one from the south-east having a force 
 of 804 kinetic units. 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 shot? 
 
 8. If tine river mentioned in the third problem be one 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 F. P. S. units of force is the weight of 60 Ib. 
 equal ? 
 
 11. To how many C. GK S. units of force is the weight of 60 Kg. 
 equal ? 
 
 o 
 
 Recapitulation. To be amplified by the pupil for 
 
 revew. 
 
 FORCE. 
 
 STATICS. 
 KINETICS* 
 
 MOTION. 
 
 ELEMENTS. 
 MEASUREMENTS. 
 
 " CENTIFUGAL." 
 
 GRAVITY UNIT. 
 KINETIC UNIT. Dyne. 
 
 Components. 
 Resultant. 
 
 ( COMPOSITION. \ ^uilibrant. 
 
 Parallelogram 
 
 GRAPHIC 
 
 REPRESENTATION. 1 I r . 
 
 [RESOLUTION. ^W^f*' 
 (. Polygon. 
 
 MOMENTUM. 
 NEWTON'S LAWS. 
 RESULTANT MOTION. 
 ACTION AND REACTION. 
 REFLECTED MOTION. 
 
46 QRAVTTATIOK 
 
 XgJECTfON H, 
 
 J\. 
 
 GRAVITATION. 
 
 98, What is Gravitation? Every particle of 
 matter in the universe has an attraction for 
 every other particle. This attractive force is 
 called gravitation. 
 
 99. Three Important Facts. In respect to 
 gravitation, three important facts have been established : 
 
 (1.) It acts instantaneously. Light and electricity 
 require time to traverse space ; not so with this 
 force. If a new star were created in distant 
 space, its light might not reach the earth for 
 hundreds or thousands of years. It might be in- 
 visible for many generations to come, but its pull 
 would be felt by the earth in less than the twink- 
 ling of an eye. 
 
 (2.) It 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. 
 
 (3.) It is independent of the kind of matter, but 
 depends upon the quantity or -mass and 
 the distance. "We must not fall into the error 
 of supposing that mass means size. The planet 
 Jupiter is about 1300 times as large as the earth, 
 but it has only about 300 times as much matter 
 because it is only 0.23 as dense. 
 
GRAVITATION. 4? 
 
 100. Laws of Gravitation. (1.) Gravitation 
 varies directly as the product of the masses. 
 
 (2.) Gravitation varies inversely as the square of 
 the distance (between the centres of gravity, 107). 
 
 For example, doubling the product doubles the attrac- 
 tion ; doubling the distance, quarters the ' attraction ; 
 doubling both the product and the distance will halve the 
 attraction. Trebling the product will multiply the attrac- 
 tion by three ; trebling the distance will divide the attrac- 
 tion by nine ; trebling both the product and the distance 
 
 will divide the attraction by three ( 03 Q ) 
 
 101. Equality of Attraction. The force 
 exerted by one body upon a second is the same as 
 that exerted by the second upon the first. 
 
 The earth draws the falling apple with a force that gives 
 it a certain momentum ; the apple draws the earth with an 
 equal force which gives to it an equal momentum. 
 
 102. Gravity. The most familiar illustration of grav- 
 itation is the attraction between the earth and bodies 
 upon or near its surface. This particular form of grav- 
 itation is commonly called gravity; its measure is weight; 
 its direction is that of the plumb-line, i. e., vertical. 
 
 103. Weight. The weight ofabody varies directly 
 as the mass and inversely as the square of the distance 
 between its centre of gravity and that of the earth. 
 The mass of the earth remaining constant, doubling the 
 mass of the body weighed doubles the product of the masses 
 ( 100) and, consequently, doubles the weight. When we 
 ascend from the surface there is nothing to interfere with the 
 working of this law ; but when we descend from the surface 
 
48 OR A V1TATION. 
 
 we leave behind us particles of matter whose attraction 
 partly counterbalances that of the rest of the earth. 
 
 104. An Example. Consider the earth's radius 
 to be 4,000 miles, and the earth's density to be uniform. 
 At the centre, a body, whose weight at the surface is 
 100 pounds, would be attracted in every direction 
 with equal force. The resultant of these equal and oppo- 
 site forces would be zero, and the body would have no 
 weight. At 1,000 miles from the centre, one fourth of the 
 distance to the surface, it would weigh 25 pounds, one- 
 fourth the surface weight ; at 2,000 miles from the centre, 
 50 pounds ; at 3,000 miles from the centre, 75 pounds ; at 
 4,000 miles from the centre, or the surface distance, it 
 would weigh 100 pounds or the full surface weight. If 
 carried up still further, the weight will decrease according 
 to the square of the distance. At an elevation of 4,000 
 miles above the surface (8,000 miles from the centre) it 
 will weigh 25 pounds, or one-fourth the surface weight. 
 
 105. Law of Weight. Bodies weigh most at 
 the surface of the eaHh. Below the surface, the 
 weight decreases as the distance to the centre de- 
 creases. Above the surface, the weight decreases as 
 the square of the distance from the centre in- 
 creases. 
 
 106. Formulas for Gravity Problems. 
 
 Representing the surface weight by W and the surface dis- 
 tance (4,000 miles) by D, the other weight by w, and the 
 other distance from the earth's centre by d, the above la^v 
 may be algebraically expressed as follows: 
 
 Below the earth's surface : w : W : : d : D. 
 
 Above the earth's surface : w : W : : D 2 : d*. 
 
& RA VITA T1ON. 49 
 
 EXERCISES. 
 
 1. How far below the surface of the earth will a ten-pound ball 
 weigh only four pounds? 
 
 Solution. 
 
 Formula : w : W:: d : D. \ d= 1600, the number of miles 
 
 Substituting : 4 : 10 :: d : 4000 I from the centre. 
 
 4000 1600 2400, the number of miles below the surface. Am. 
 
 2. What would a body weighing 550 Ibs. on the surface of the 
 earth weigh 3,000 miles below the surface ? Ans. 137^ Ibs. 
 
 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 Ibs. and is 25 ft. distant 
 from the third. The second weighs 9 Ibs. and is 50 ft. distant from 
 the third, (a) Which exerts the greater force upon the third? 
 (&) How many times as great ? Ans. |. 
 
 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 avoirdupois 
 weigh only an ounce? Ans. 12,000 miles. / fc,o <0 
 
 , 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 
 Ibs. and of a boy weighing 100 Ibs. ? Ans. 32.65 Ib. 
 
 8. Find the weight of a 180 Ib. ball (a) 2,000 miles above the 
 earth's surface ; (&) 2,000 miles below the surface.^^-^-. J fib* , 
 
 9. (a) Would a 50 Ib. cannon ball weigh more 1,000 miles above 
 the earth's surface, or 1,000 miles below it ? (6) How much ? 
 
 10. If the moon were moved to three times its present distance 
 from the earth, what would be the effect (a) on its attraction for 
 the earth ? (&) On the earth's attraction for it ? 
 
 11. How far below the surface of the earth must an avoirdupois 
 pound weight be placed in order to weigh one ounce ? <3 -7< o -* 
 
 12. How far above the surface of the earth must 2,700 pounds be 
 placed to weigh 1,200 pounds ? Ans. 2,000 miles. 
 
 18. 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 V ^ 
 
 1O7. Centre of Gravity. The centre of grav- 
 ity of a body is the point about which all the 
 matter composing the body may be balanced. 
 
 a 
 
50 
 
 GRAVITATION. 
 
 FlG. 18. 
 
 The force of gravity tends to draw every particle of 
 matter toward the centre 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 paral- 
 lel forces, each of which is acting 
 upon one of the molecules of 
 which that body is composed. 
 We may also consider this sum 
 of forces, or total gravity, as 
 acting upon a single point, just 
 as the force exerted 'by two 
 horses harnessed to a whiffle- 
 
 tree is equivalent to another force (resultant) equal to the 
 sum of the forces exerted by the horses, and applied at a 
 single point at or near the middle of the whiffle-tree. 
 This single point, which may thus be regarded as the 
 
 point of application of the 
 force of gravity acting upon a 
 body, is called the centre of 
 gravity of that body. In other 
 words, the weight of a body 
 may be considered as concen- 
 trated at the centre of gravity. 
 
 1O8. How to find the 
 Centre of Gravity. In 
 
 a freely moving body, the cen- 
 tre of gravity will be broughi 
 as low as possible, and will, 
 therefore, lie in a vertical line 
 FIG. 19. drawn through the point of 
 
GRAVITATION. 5l 
 
 support This fact affords a ready means of determining 
 the centre of gravity experimentally. 
 
 Let any irregularly shaped body, as a stone or chair, be 
 suspended so as to move freely. Drop a plumb-line from 
 "he point of suspension, and make it fast or mark its direc- 
 tion. The centre of gravity will lie in this line. From a 
 second point, not in the line already determined, suspend 
 the body ; let fall a plumb-line as before. The centre of 
 gravity will lie in this line also. But to lie in both lines, the 
 centre of gravity must lie at their intersection. (Fig. 19.) 
 
 1O9. May be Outside of the Body. The cen- 
 tre of gravity may be outside of the matter of which a 
 body consists, as in the case of a ring, hollow sphere, box, 
 or cask. The same fact is illustrated by the " balancer," 
 represented in the figure. The centre 
 of gravity is in 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. In a freely falling body, 
 no matter how irregular its form, or 
 how indescribable the curves made by 
 any of its projecting parts, the line of 
 direction in which the centre of grav- 
 ity or point of application moves will 
 be a vertical line ( 65 [2] ). 
 
 FIG. 20. 11O. Equilibrium. -Inasmuch 
 
 as the centre of gravity is the point at 
 which the weight of a body is concentrated, when the 
 centre of gravity is supported, the whole body will 
 
rest in a state of equilibrium. The centre of gravity 
 will be supported when it coincides with the point of sup- 
 port, or is in the same vertical line with it. 
 
 111. Stable Equilibrium. 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 equili- 
 brium. Such a displacement raises the centre of grav- 
 ity. Examples: a disc supported above the centre; a 
 semi-spherical oil-can ; a right cone placed upon its 
 base ; a pendulum or plumb-line. The cavalry-man 
 represented in Fig. 21, is in stable equilibrium, and 
 may rock up and down, 
 balanced upon his horse's 
 hind -feet, because the 
 heavy ball brings the cen- 
 tre of gravity of the com- 
 bined mass below the 
 points of support. The 
 "balancer" (Fig. 20) af- 
 fords another example of 
 stable equilibrium. 
 
 Unstable Equi- FlG 
 
 librium. A body sup- 
 ported in such a way that, when slightly displaced 
 from its position of equilibrium, it tends to fall 
 further from that position, is said: to be in unstable 
 equilibrium. Such a displacement lowers the centre of 
 gravity. The body will not come to rest until the centre 
 of gravity has reached the lowest possible point, when it 
 will be in stable equilibrium. Examples: A disc sup- 
 
GRAVITATION. 
 
 53 
 
 M 
 
 ported below its centre ; a right cone placed on its apex; 
 an egg standing on its end ; or a stick balanced upright 
 upon the finger. 
 
 113. Neutral Equilibrium. A "body supported 
 in such a way that, when displaced from its 
 position of equilibriuin, 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 centre 
 ol gravity. Examples: A disc supported at its centre ; a 
 sphere resting on a horizontal surface ; a right cone rest- 
 ing on its side. 
 
 (a.) In the accompanying figure M, N and represent three cones 
 
 placed respectively 
 in these three con- 
 ditions of equili- 
 brium. The letter 
 g shows the posi- 
 tion of the centre 
 of gravity in each 
 If a body have 
 two or more points 
 of support lying in 
 
 the same straight line, the body wilt be in neutral, stable or unstable 
 equilibrium according as the centre of gravity lies in this line, is 
 directly below it or above it. 
 
 114. Line of Direction. A vertical line drawn 
 downward f? i om the centre of gravity is called the 
 line of direction. As we have seen, it represents the 
 direction in which the centre of gravity would move if 
 the body were unsupported. It may be considered as a 
 line connecting the centre of gravity of the given body 
 and the centre of the earth. 
 
 115. The Base. The side on ivhich a body 
 rests is called its base. If the body be supported on 
 
GRAVITATION. 
 
 legs, as a chair, the base is the polygon formed by joining 
 the points of support. 
 
 116. Stability. fl^ett the line of direction 
 falls within the base, the body stands ; when with- 
 out the base, the body falls. 
 
 In the case of the tower represented in Fig. 23, if the 
 upper part be removed, the line of direction will be as 
 shown by the left hand dotted line. It falls within the 
 base, and the tower stands. When the upper part is fast- 
 ened to the tower, the line of direction is represented by 
 the right hand dotted line. This falls 
 without the base, and the tower falls. 
 The stability of bodies is measured 
 by the amount of work necessary to 
 overturn them. This depends upon 
 the distance that it is necessary to 
 raise the centre of gravity (equivalent 
 to raising the whole body), that the 
 line of direction may fall without the 
 base. 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 centre of 
 gravity being necessary. The broader the base, and the 
 lower the centre of gravity, the greater the stability. 
 
 117. Illustrations of Stability. Let the figure 
 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 
 centre of gravity, must pass 
 over the edge,c. That is to 
 
 FIG. 23. 
 
 a 
 
 FIG. 34. 
 
GRAVITATION. 55 
 
 Bay, the centre of gravity must be raised a distance equal 
 to the difference between ga and gc, or the distance na 
 But to lift g this distance is the same as to lift the whole 
 brick vertically a distance equal to nc. Now 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 centre of gravity, must be raised 
 before the line of direction can fall without the base, and 
 the body be overturned. To lift the brick, or its centre of 
 gravity, 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 centre 
 of gravity, or both. 
 
 FIG. 25. 
 
 (#.) These facts explain the stability of leaning towers like those 
 of Pisa and Bologna. In some such towers the centre of gravity 
 is lowered by using heavy materials for the lower part and light 
 materials for the upper part of the structure. It is difficult to stand 
 upon one foot or to walk upon a tight rope because of the smallness 
 
56 
 
 GRAVITATION. 
 
 of the base. A porter carrying a pack is obliged to lean forward ; 
 a man carrying a load in one hand is obliged to lean away from the 
 load, to keep the common centre of gravity of man and load over 
 the base formed by joining the extremities of his feet. Why does a 
 person stand less firmly when his feet are parallel and close together 
 than when they are more gracefully placed ? Why can a child walk 
 more easily with a cane than without ? Why will a book placed on 
 i desk-lid stay there while a marble would roll off ? Why is a ton 
 of stone on a wagon less likely to upset than a ton of hay similarly 
 placed? 
 
 EXERCISES. 
 
 Explanatory Note, The first problem in the table below may be 
 read as follows : What will be the weight of a body which weighs 
 1200 pounds at the surface of the earth, when placed 2000 miles 
 below the surface ? When placed 4000 miles above the surface ? 
 (Radius of earth=:4000 miles.) All of the measurements are from 
 the surface. 
 
 NUMBER OP 
 PROBLEM. 
 
 BELOW SURFACE. 
 
 AT SURFACE. 
 
 ABOVE SURFACE. 
 
 Pounds. 
 
 Miles from 
 Surface. 
 
 Pounds. 
 
 Pounds. 
 
 Miles from 
 Surface. 
 
 1 
 
 , 
 
 2000 
 
 1200 
 
 , 
 
 4000 
 
 2 
 
 300 
 
 ? 
 
 1200 
 
 533i 
 
 9 
 
 3 
 
 ? 
 
 3000 
 
 800 
 
 ? 
 
 6000 
 
 4 
 
 ? 
 
 1000 
 
 150 
 
 ? 
 
 1000 
 
 5 
 
 100 
 
 ? 
 
 400 
 
 100 
 
 ? 
 
 6 
 
 250 
 
 3000 
 
 ? 
 
 ? 
 
 4000 
 
 *X. 7 
 
 ? 
 
 1600 
 
 ? 
 
 32 
 
 6000 
 
 8 
 
 12 
 
 ? 
 
 100 
 
 25 
 
 ! 
 
 9 
 
 ? 
 
 8250 
 
 480 
 
 ? 
 
 2000 
 
 10 
 
 90 
 
 f 
 
 450 
 
 50 
 
 ? 
 
 11 
 
 160 
 
 ? 
 
 256 
 
 ? 
 
 12000 
 
 12 
 
 201.6 
 
 2600 
 
 v 
 
 16 
 
 ? 
 
 13 
 
 256 
 
 ? 
 
 ? 
 
 40.96 
 
 16000 
 
 14 
 
 20250 
 
 ? 
 
 324000 
 
 9000 
 
 ? 
 
 15 
 
 ? 
 
 3200 
 
 ? 
 
 1280 
 
 9000 
 
FALLING BODIES. 57 
 
 Recapitulation. In this sectiou we have considered 
 Gravitation ; Facts concerning it ; its Law ; 
 Gravity; Weight; Law of Weight ; Centre 
 of Gravity; Equilibrium and Stability oi 
 
 Bodies. 
 
 y 
 
 ECTJON Hi, 
 
 FALLI NG BODIES. 
 
 118. A Constant Force. The tendency of force 
 is generally to produce motion. Acting on a given mass 
 for a given time, a given force will produce a certain 
 velocity. If the same force acts on the same mass for 
 twice the time it will produce a double velocity. A force 
 which, thus continues to act uniformly upon a 
 body, even after the body has begun to move, is 
 called a constant force. The velocity thus produced 
 is called a uniformly accelerated velocity. If a constant 
 force gives a body a velocity of 10 feet in one second, it 
 will give a velocity of 20 feet in two seconds, of 30 feet in 
 three seconds, and so on. The force of gravity is a con- 
 stant force and the velocity it imparts to the falling body 
 is a uniformly accelerated velocity. 
 
 119. Velocities of Falling Bodies. If a 
 
 feather and a cent be dropped from the same height, the 
 cent will reach the ground first. This is not because the 
 cent is heavier, but because the feather meets with more 
 resistance from the air. If this resistance can be removed, 
 the two bodies will fall ecjiial distances iu ec^ual times, 
 
58 
 
 FALLING BODIES. 
 
 or will fall with the same velocity. This resistance may 
 be avoided by trying the experi- 
 ment 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. Take an iron and 
 a wooden ball of the same size, drop 
 them at the same time from an 
 upper window, and notice that they 
 will strike the ground at sensibly 
 the same time. 
 
 12O. Reason of this Equal- 
 ity. The cent is heavier than the 
 feather and is therefore acted upon 
 by a greater force. The iron ball 
 has the greater weight, which shows 
 that it is acted upon by a greater 
 force than the wooden ball. But 
 this greater force has to move a 
 greater mass, has to do more work 
 For the greater force to do the 
 greater work requires as much time us for the 
 lesser force to do the lesser work. The working force 
 and the work to be done increase in the same ratio. A 
 regiment will march a mile in no less time than a single 
 soldier would do it ; a thousand molecules can fall no fm> 
 ther in a second than a single molecule can. 
 
 121. Galileo's Device. To avoid the necessity 
 for great heights, and the interference of rapid motion 
 with accurate observations, Galileo used an inclined 
 
 FIG. 26. 
 
 than the lesser force. 
 
FALLING BODIES. 59 
 
 plane> consisting of a long ruler having a grooved edge, 
 down which a heavy ball was made to roll. In this way 
 he reduced the velocity, and diminished the interfering 
 resistance of the atmosphere without otherwise changing 
 the nature of the motion. 
 Let AB represent a plane so 
 inclined that the velocity of 
 a body rolling from B toward A 
 A will be readily observable. 
 Let be a heavy ball. The 
 gravity of the ball may be 
 represented by the vertical 
 
 line CD. But CD may be resolved into CF, which repre- 
 sents a force acting perpendicular to the plane and pro- 
 ducing pressure upon it but no motion at all, and CE, 
 which represents a force acting parallel to the plane, the 
 only force of any effect in producing motion. It may be 
 shown geometrically that 
 
 EC : CD :: BG : BA. (Olnetfs Geometry, Art. 341.) 
 
 By reducing, therefore, the inclination of the plane we 
 may reduce the magnitude of the motion -producing com- 
 ponent 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. |fl \\\\ 
 
 122. Attwood's Device. 
 
 For the purpose of lessening 
 the velocity of falling bodies 
 without changing the character 
 of the motion, Mr. Attwood 
 devised a machine which has FIG. 28. 
 
FALLING BODIES. 
 
 taken his name. Att- 
 wood's machine consists 
 essentially of a wheel 
 R, about six inches 
 in diameter, over the 
 grooved edge 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 supported 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 disre- 
 garded, it is evident 
 that the weights will be 
 in equilibrium whatever 
 their position 
 
 This apparatus is sup- 
 ported upon a wooden 
 pillar, seven or eight feet 
 high. The silk cord 
 carrying K, one of the 
 weights, passes in front 
 of a graduated rod 
 which carries a movabk 
 ring B, and a movable 
 platform A. At the top 
 of the pillar is a plate n, 
 
FALLING BODIES. 61 
 
 which may be fastened in a horizontal position for the 
 support of K at the top of the graduated rod. This plate 
 may also be dropped to a vertical position, thus allowing K, 
 when loaded, to fall. A clock, with a pendulum beating 
 seconds, serves for the measurement of time, and the drop 
 ping of the plate at the top of the pillar. A weight ol 
 rider, m, is to be placed upon K, and give it a downward 
 motion. Levelling screws are provided by means of which 
 the graduated rod may be made vertical, and K be made 
 to pass through the middle of B. 
 
 (a.) Suppose that K and K' weigh 315 grams each, and that the 
 rider m weighs 10 grams. When m is placed upon K and the plate 
 dropped by the action of the clock, the gravity of m causes the 
 weights to move. We now have the motion of 640 grams produced 
 by the gravity of only 10 grams. When this force (gravity) moves 
 only 10 grams it will give it a certain velocity. When the same 
 fcrce moves 640 grams it has to do 64 times as much work, and can 
 do it with only \ the velocity. In this way we are able to give to 
 K and m any velocity of fall that we desire. 
 
 123. Experiments. Arrange the apparatus by sup- 
 porting K and m upon the shelf n. As the hand of the 
 clock passes a certain point on the dial, 12 for example, 
 the shelf n is dropped and the weights begin to move. By 
 a few trials, B may be so placed that at the end of one 
 second it will lift m from K, and thus show how far the 
 weights fall in one second. Other experiments will show 
 how many such spaces they will fall in the next second or 
 in two seconds ; in the third second or in three seconds ; 
 in the fourth second or in four seconds, etc. 
 
 Suppose that B lifts off m at the end of the first second. 
 The moving force being no longer at work, inertia will 
 keep K moving with the same velocity that it had at the 
 end. of the first second. By placing A so that K will reach 
 it at the end of the second second, the distance AB wilJ 
 
62 FALLING BODIES. 
 
 indicate the velocity with which K was moving when it 
 passed B at the end of the first second. In a similar way 
 the velocity at the end of the second, third, or fourth 
 second may be found. 
 
 124. Results. Whatever the space passed over in the 
 orst second by the weights or the ball, it will be found 
 that there is an uniform increase of velocity. Galileo found 
 that if the plane was so inclined that the ball would roll 
 one foot during the first second, it would roll three feet 
 during the next second, five feet during the third, and so 
 on, the common difference being two feet, or twice the dis- 
 tance traversed in the first second. 
 
 He found that under the circumstances supposed, the 
 ball would have a velocity of two feet at the end of the 
 first second, of four feet at the end of the next, of six feet 
 at the end of the third, and so on, the increase of velocity 
 during the first second being the same as the increase 
 during any subsequent second. 
 
 He found that, under the circumstances supposed, the 
 ball would pass over one foot during one second, four feet 
 during two seconds, and nine feet during three seconds, 
 and so on. Similar results may be obtained with Att- 
 wood's machine. 
 
 125. Table of Results. These results are gener- 
 alized in the following table, in which t represents any 
 given number of seconds : 
 
 Number of 
 Seconds. 
 I 
 
 Spaces fallen during 
 each Second. 
 1 
 
 Velocities at the End 
 of each Second. 
 2 
 
 Total Number of 
 Spaces fallen, 
 1 
 
 2 
 
 . ..3 
 
 4 
 
 4 
 
 3 
 
 5 
 
 6 
 
 9 
 
 4 
 
 ...7 
 
 8. 
 
 16 
 
 etc. 
 t 
 
 etc. 
 
 etc. 
 
 m-^o.. 
 
 etc. * 
 
FALLING BODIES. 63 
 
 126. Unimpeded Fall. By transferring matter 
 from K' to K, the velocity with which the weights move 
 will be increased. When all of K' has been transferred to 
 K, the weights will fall, in this latitude, 16.08 ft. 
 or 4-9 - during the first second. 
 
 If the plane be given a greater inclination, the ball will, 
 of course, roll more rapidly and our unit of space will in- 
 crease from one foot, as supposed thus far, to two, three, 
 four or five feet, and so on, but the number of such spaces 
 will remain as indicated in the table above. By disre- 
 garding the resistance 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 ft. 
 or 4.9 m. 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. 
 
 127. Increment of Velocity. During the first 
 second the freely falling body will gain a velocity 
 of 32.16 feet. It will make a like gain of velocity 
 during each subsequent second 'of its fall. This distance 
 is therefore called the increment of velocity due to gravity, 
 and is generally represented by g 32.16 ft. or 9.8 m. 
 
 Note This value must not be forgotten. 
 
 128. Formulas for Falling Bodies. If now we 
 
 represent our space by \g, the velocity at the end of any 
 second by v, the number of seconds by t, the spaces fallen 
 each second by s, and the total space fallen through by S, 
 we shall have the following formulas for freely falling 
 
 bodies : 
 
 (1.) v=gt or |f x 2t. 
 
 (2.) * = te(2$-l). 
 (3.) S = ig&. 
 
64 FALLING BODIES. 
 
 129. Laws of Falling Bodies. These formulas 
 may be translated into ordinary language as follows : 
 
 (1.) The velocity of a freely falling body at the end of 
 any second of its descent is equal to 32.16 ft. (9.8 m.) mul- 
 tiplied by the number of the second. 
 
 (2.) The distance traversed by a freely falling body 
 during any second of its descent is equal to 16.08 ft. (4.9 m.) 
 multiplied by one less than twice the number of seconds. 
 
 (3.) The distance traversed by a freely-falling body 
 during any number of seconds is equal to 16.08 ft. (4.9 m.) 
 multiplied by the square of the number of seconds. 
 
 130. For Bodies Rolling Down an Inclined 
 Plane. If the body be rolling down an inclined plane 
 instead of freely falling, of course the increment of velocity 
 will be less than 32.16 ft. The formulas above given may 
 be made applicable by multiplying the value of g by the 
 ratio between the height and length of the plane. 
 
 131. Initial Velocity of Falling Bodies. - 
 
 We have been considering bodies falling from a state of 
 rest, gravity being the only force that produced the motion. 
 But 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. It becomes an illustration of the 
 first case under Composition of Forces ( 80), the resultant 
 being the sum of the components. If a body be thrown 
 downward with an initial velocity of fifty feet per second, 
 the formulas will become v = gt + 50 ; s =>$ (2tl) 
 
 132. Ascending Bodies. In the consideration of 
 ascending bodies we have the direct opposite of the laws of 
 falling bodies. When a body is thrown downward, gravity 
 
FALLING BODIES. 65 
 
 increases its velocity every second by the quantity g. 
 When a body is thrown upward, gravity diminishes its 
 velocity every second by the same quantity. Hence the 
 time of its ascent will be found by dividing its initial 
 velocity by g. TJ^e initial velocity of a body that 
 can rise against the force of gravity for a given 
 number of seconds is the same as the final velocity 
 of a body that has been falling for the same 
 number of seconds. 
 
 (a.) The spaces traversed and the velocities attained during suc- 
 cessive seconds will be the same in the ascent, only reversed in 
 order. If a body be shot upward with a velocity of 321.6 feet, it 
 will rise for ten seconds, when it will fall for ten seconds. The 
 tenth second of its ascent will correspond to the first of its descent, 
 i. e., the space traversed during these two seconds will be the same ; 
 the eighth second of the ascent will correspond to the third of its 
 descent ; the end of the eighth second of its ascent will correspond 
 to the end of the second second of its descent. 
 
 133. Projectiles. Every projectile is acted upon by 
 three forces : 
 
 (1.) The impulsive force, whatever it may be. 
 (2.) The force of gravity. 
 (3.) The resistance of the air. 
 
 134. Random or Range. The horizontal dis- 
 tance from the starting-point of a projectile to 
 ivhere it strikes the ground is called its random 
 or range. In Fig. 30, the line GE represents ^he ran- 
 dom of a projectile starting from F, and striking the 
 ground at E. 
 
 135. Path of a Projectile. The path of a pro- 
 jectile is a curve, the resultant of the three forces above 
 mentioned. Suppose a ball to be thrown horizontally. 
 Its impulsive force will give a uniform velocity, and may 
 
66 
 
 FALLING BODIES. 
 
 be represented by a horizontal line divided into equaJ 
 parts, each part representing a space equal to the velocity. 
 
 The force of gravity may be 
 
 /> fi / J\ yv -^ 
 
 represented by a vertical line 
 divided into unequal parts, 
 representing the spaces 1, 3> 5, 7. 
 etc., over which gravity would 
 move it in successive seconds. 
 Constructing the parallelograms 
 of forces, we find that at the 
 16 end of the first second the ball 
 will be at A, at the end of the 
 next second at B, at the end of 
 the third at C, at the end of the 
 25 fourth at D, etc. The result- 
 ant of these two forces is a curve 
 called a parabola. It will be seen that, in a case like this, 
 the range GE may be found by multiplying the velocity 
 by the number of seconds it will take the body to fall 
 from F to G. The resistance of the air modifies the 
 nature of the curve somewhat. 
 
 136. Time of a Projectile. From the second 
 law of motion, it follows that the ball shot horizontally 
 will reach the level ground in the same time as if it had 
 been dropped ; that the ball shot obliquely upward from a 
 horizontal plain will reach the ground in twice the time 
 required to fall from the highest point reached. These 
 statements may be easily verified by experiment. 
 
 FIG. 30. 
 
FALLING BODIES. 67 
 
 EXERCISES. 
 
 1. What will be the velocity of a body after it has fallen 4 
 seconds ? 
 
 Solution : v = gt. 
 
 v = 32.16x4. 
 
 v = 128.64. Ans. 128.64 ft. 
 
 2. A body falls for several seconds ; during one it passes ovel 
 530.64 feet ; which one is it? 
 
 Solution, :. s = ^g (2t 1). 
 
 530.64 = 16.08 x (2t - 1). 
 
 33 = %t - 1. 
 
 34 = 2*. 
 
 17 = t. Ans. 17th second. 
 
 3. A body was projected vertically upward with a velocity = 96.48 
 feet ; how high did it rise ? 
 
 Solution : v = gt. (See 132.) 
 
 96.48 = 32.16*. 
 3 = *. 
 8= fa*. 
 8 = 16.08 x 9. 
 S = 144.72. Ans. 144.72 ft. 
 
 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. 1608 ft. 
 
 6. How far in | second? Am. 4.02 ft. 
 
 7. How far will a body fall during the first one and a half seconds 
 of its fall ? 
 
 8. How far in 12^ seconds ? 
 
 9. A body passed over 787.93 feet during its fall ; what was the 
 ttme required ? Ans. 7 sec. 
 
 10. What velocity did it finally obtain ? 
 
 11. A body fell during 15i seconds ; give its final velocity. 
 
 12." In an Attwood's machine the weights carried by the thread 
 are G| ounces each. The friction is equivalent to a weight of two 
 ounces. When the "rider," which weighs one ounce, is in position, 
 what will be its gain in velocity per second ? Ans. 2.01 ft. 
 
 13. A stone is thrown horizontally from the top of a tower 
 257.28 ft. high with a velocity of 60 ft. a second. Where will it 
 strike the ground? Ans. 240 ft. from the tower. 
 
68 FALLING BODIES. 
 
 14. A body falls freely for 6 seconds. What is the space trav; 
 ersed during the last 2 seconds of its fall ? 
 
 15. A body is thrown directly upward with a velocity of 80.4 ft. 
 (a) What will be its velocity at the end of 8 seconds, and (&) in what 
 direction will it be moving ? 
 
 16. In Fig. 30, what is represented by the following lines : Fl ! 
 Fa? Aa? Fc? Dd? 
 
 17. A body falls 357.28 ft. in 4 seconds. What was its initial 
 velocity ? Ans. 25 ft. 
 
 18. A ball thrown downward with a velocity of 35 ft. 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 ft. 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 = 257.28 
 feet. What is its random ? Ans. 8000 ft. 
 
 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. 452ft. 
 
 22. Required the final velocity of the same body. Ans. 170.8 ft. 
 
 23. A body was 5 seconds rolling down an inclined plane and 
 passed over 7 feet during the first second, (a) Give the entire 
 space passed over, and (6) the final velocity. 
 
 O 24. A body rolling down an inclined plane has at the end of the 
 first second a velocity of 20 feet ; (a) what space would it pass 
 over in 10 seconds? (6) If the height of the plane was 800 ft., 
 what was its length ? Last Ans. 1286.4ft. 
 
 25. A body was projected vertically upward and rose 1302.48 feet; 
 give (a) the time required for its ascent, (6) also 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 will it have 
 passed over during the first 4 seconds ? Ans. 297.28 ft. 
 
 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. 1608 ft 
 
 Recapitulation, To be amplified by the pupil for 
 review, 
 
PENDULUM. 69 
 
 f ACTED UPON BY A CONSTANT FORCE 
 RELATION OF WEIGHT TO VELOCITY. 
 
 ILLUSTRATIVE ( Galileo's, 
 
 r f) 
 
 w 
 
 APPARATUS | Experiments \ Results tabulated. 
 LAWS. ...,.-{ INCREMENT OP VELOCITY WITH (unimpeded 
 
 ^ ^ FALL. / Impeded. 
 
 EXPRESSED 
 
 EFFECT OF INITIAL VELOCITY. 
 
 Ordinary language. 
 
 RELATIONS TO 
 
 (Ascending bodies 
 
 ?!* 
 
 IV. 
 
 THE PENDU LU M. 
 
 137. The Simple Pendulum. A simple pen- 
 dulum is conceived as a single material particle sup- 
 ported by a line without weight, capable of oscillat- 
 ing about a fixed point. Such a pendulum has a 
 theoretical but not an actual existence, and has been con- 
 ceived for the purpose of arriving at the laws of the com- 
 pound pendulum. 
 
 138. The Compound Pendulum. A com- 
 pound or physical pendulum is a iveight so suspended 
 as to be capable of oscillating about a fixed point. 
 The compound pendulum appears in many forms. The 
 most common form consists of a steel rod, thin and flexible 
 at the top, carrying at the bottom a heavy mass of metal 
 known as the bob. The bob is sometimes spherical but 
 generally lenticular, as this form is less subject to resistance 
 from the air. 
 
70 
 
 THE PENDULUM. 
 
 FIG. 31. 
 
 139. Motion of the Pendulum. When the 
 
 supporting thread or bar is vertical, the centre of gravity 
 is in the lowest possible position, 
 and the pendulum remains at 
 rest, for the force of gravity tends 
 to draw it downward producing 
 pressure at the point of support, 
 but no motion. But when the 
 pendulum is drawn from its ver- 
 tical position, the force of grav- 
 ity, MG, is resolved ( 91) into 
 two components, one of which, 
 MO, produces pressure at the 
 point of support, while the other, 
 MH, acts at right angles to it, 
 producing motion. Gravity there- 
 fore draws it to a vertical position, when inertia carries it 
 beyond until it is stopped and drawn back again by grav- 
 ity. It thus swings to and fro in an arc, MNO. 
 
 140. Definitions. The motion from one extremity 
 of this arc to the other is called a vibration or oscillation. 
 The time occupied in moving over this arc is called the 
 time of vibration or oscillation. The angle measured by 
 this arc is called the amplitude of vibration. The trip 
 from M to is a vibration; the angle MAO is the 
 amplitude of vibration. 
 
 141. Centre of Oscillation. A short pendulum 
 vibrates more rapidly than a long pendulum ; this is a 
 familiar fact. It is evident, then, that in every pendulum 
 (not simple) the parts nearest the centre of suspension tend 
 to move faster than those further away, and force them to 
 
THE PENDULUM. 71 
 
 move more rapidly than they otherwise would. On the 
 other hand, the parts furthest from the centre of suspen- 
 sion tend to move more slowly than those nearer, and force 
 these to retard their individual rates of motion. Between 
 these there will be a particle moving, of its own accord, 
 at the average rate of all. The accelerating tendency of 
 the particles above it is compensated by the retarding ten- 
 dency of the particles below it. This molecule, there- 
 fore, will move as if it were vibrating alone, sup- 
 ported ~by a thread without weight. It fulfills all the 
 conditions of a simple pendulum. This point is called the 
 centre of oscillation. 
 
 142. The Real Length of a Pendulum. The 
 
 laws of the simple pendulum are applicable to the com- 
 pound pendulum if we consider the length of the latter to 
 be the length of the equivalent simple pendulum, i. e., the 
 distance between the centres of suspension and 
 oscillation. We, therefore, may say that the real length 
 of a pendulum is the distance between the centre of sus- 
 pension and the centre of oscillation. The real length is 
 less than the apparent length except in the imaginary case 
 of the simple pendulum. 
 
 143. First Law of the Pendulum. The vi- 
 brations of a given pendulum, at any given place, 
 are isochronous, i. e., are performed in equal times, 
 whether the arc be long or short. Each pupil should 
 satisfy himself of the truth of this proposition, by the only 
 true scientific method, experiment. 
 
 144. The Cycloidal Pendulum. The law 
 
 above given is strictly true only when the pendu- 
 
THE PENfiULUM. 
 
 FIG. 32. 
 
 lum vibrates in a cycloidal arc. A cycloid is the 
 
 curve traced by a point 
 in the circumference 
 of a circle that is rolling 
 along a straight line. 
 The pendulum maybe 
 made to move in such 
 an arc by suspending 
 a small heavy ball by 
 a thread between two 
 cheeks upon which the 
 
 thread winds as the pendulum vibrates. The cheeks must 
 be the two halves of a cycloid ; each cheek must have the 
 same length as the thread. The path of the ball will be 
 a cycloid, identical with that to which the cheeks belong. 
 
 (a.) The cycloidal pendulum is of little practical use. If the 
 amplitude of an ordinary pendulum does not exceed five degrees, 
 the circular arc, thus described, will not vary much from the true 
 cycloidal arc, and the pendulum will be practi- 
 cally isochronous. If from the centre of sus- 
 pension, with radius equal to the length of the 
 string, a circular arc be described, the two 
 curves will sensibly coincide for at least five 
 degrees. This is why the pendulums of " reg- 
 ulator " clocks have a small swing or amplitude. 
 
 145. Second Law of the Pen- 
 dulum. The time of vibration is 
 independent of the weight or mate- 
 rial of the pendulum, depending only 
 upon the length of the pendulum, and 
 the intensity of the force of gravity at 
 any given place. 
 
 (#.) Each pupil should try the experiment, 
 ttt home, with balls of equal size but different FIG. 33. 
 
THE PENDULUM. 
 
 weight. The investment of a little time and ingenuity in simple 
 experiments will pay large dividends. 
 
 146. Third Law of the Pendulum. The vibra- 
 tions of pendulums of different lengths are performed in 
 different times. The lengths are directly proportional 
 to the squares of the times of vibration, or in- 
 versely proportional to the squares of the numbers 
 of vibrations in a given time. 
 
 Note. Be careful to distinguish clearly hetween the expressions 
 "times of vibration" and "numbers of vibration." The greater 
 the time, the less the number. You may easily 
 verify by experiment the three laws already 
 given for the pendulum. 
 
 147. The Second's Pendulum. 
 
 At the equator, the length of a second's 
 pendulum, at the level of the sea, is 
 39 inches ; near the poles, 39.2 ; in this 
 latitude about 39.1 inches or 993.3 
 mm. As such a pendulum would be 
 inconveniently long, use is generally made 
 of one one-fourth as long, which, con- 
 sequently, vibrates half seconds. The 
 length and time of vibration of this 
 pendulum being thus known, the 
 length of any other pendulum may be 
 found when the time of vibration is 
 given ; or the time of vibration may be 
 found when the length is given. The 
 third law is applicable to such a problem. 
 
 148. Use of the Pendulum in 
 Time-pieces. The motion of a clock is due to the 
 force of gravity acting upon the weights, or to the elastic- 
 
 FIG. 
 
PffE PENDULUM. 
 
 ity of the spring. But the weights have a tendency toward 
 accelerated motion (falling bodies), while the spring would 
 give an example of diminishing motion. Either defect 
 would be fatal in a time-piece. Hence the properties of 
 the pendulum set forth in the first and third laws are 
 used to regulate this motion and make it available for the 
 desired end. If the clock gains time, the pendulum is 
 lengthened by lowering the bob; if it loses time, the pen- 
 dulum is shortened by raising the bob. 
 
 149. Compensation Pendulums. The expan- 
 sion of metals by heat is a familiar fact. Hence the ten- 
 dency of a clock to lose time in summer and 
 to gain time in winter. One plan for coun- 
 teracting this tendency is by the use of the 
 " gridiron " pendulum which is made of twc 
 substances in such a manner that the down- 
 ward expansion of one will be exactly com 
 pensated by the upward expansion of tho 
 other. In the figure, the heavy single lines 
 represent steel rods, the effect of whose ex- 
 pansion will be to lower the bob. The light 
 double lines represent brass rods, the effect of 
 whose expansion will be to raise the bob. The 
 steel rod to which the bob is directly attached 
 passes easily through holes in the two hori- 
 zontal bars which carry the brass uprights. 
 
 FIG. 35. 
 
 As brass expands more than steel, for a given increase of 
 temperature, it will be seen that these two expansions may 
 be niiwle to neutralize one another. 
 
PENDULUM. 
 
 EXERCISES. 
 
 No. 
 
 INCHES. 
 
 NUMBER. 
 
 TIME. 
 
 No. 
 
 C*. 
 
 NUMBER. 
 
 TIME. 
 
 1 
 
 9 
 
 20 per min. 
 
 ?- 
 
 11 
 
 99.33 
 
 ? 
 
 ? 
 
 2 
 
 ? 
 
 30 " 
 
 ? 
 
 12 
 
 ? 
 
 ? 
 
 2 sea 
 
 3 
 
 30 
 
 ? 
 
 ? 
 
 13 
 
 ? 
 
 f 
 
 2 min. 
 
 4 
 
 16 
 
 I 
 
 ? 
 
 14 
 
 24.83 
 
 ? 
 
 ? 
 
 5 
 
 f 
 
 ? 
 
 sec. 
 
 15 
 
 ? 
 
 8 per sec. 
 
 ? 
 
 6 
 
 ? 
 
 ? 
 
 min. 
 
 16 
 
 397.32 
 
 ? 
 
 ? 
 
 7 
 
 39.37 
 
 ? per min. 
 
 ? 
 
 17 
 
 11.03 
 
 ? 
 
 ? 
 
 8 
 
 ? 
 
 10 " 
 
 ? 
 
 1& 
 
 1 
 
 ? 
 
 10 sec. 
 
 9 
 
 10 
 
 ? per sec. 
 
 ? 
 
 19 
 
 2483.25 
 
 ? 
 
 ? 
 
 10 
 
 9 
 
 1 per min. 
 
 ? 
 
 20 
 
 ? 
 
 ? 
 
 4 sec. 
 
 21. How will the times of vibration of two pendulums compare, 
 their lengths being 4 feet and 49 feet respectively ? Ans. As 2 to 7. 
 
 22. Of two pendulums, one makes 70 vibrations a minute, the 
 other 80 vibrations during the same time ; how do their lengths 
 compare? Ana. As 49 to 64. 
 
 23. If one pendulum is 4 times as long as another, what will be 
 their relative times of vibration ? 
 
 24. The length of a second's pendulum being 39.1 inches, what 
 must be the length of a pendulum to vibrate in ^ second ? 
 
 25. How long must a pendulum be to vibrate once in 8 seconds ! 
 In | second ? 
 
 26. How long must a pendulum be to vibrate once in 3|^ seconds ? 
 
 27. Find the length of a pendulum that will vibrate 5 times in 4 
 seconds ? Ans. 25.02 + inches. 
 
 28. A pendulum 5 feet long makes 400 vibrations during a certain 
 time ; how many vibrations will it make in the same time after the 
 pendulum rod has expanded half an inch ? 
 
 Recapitulation. In this section we have considered 
 Lhe Simple Pendulum ; the Compound Pen- 
 dulum ; the nature of the Motion of the Pendu~ 
 lum and its Cause ; the meaning of the terms Vi- 
 bration, Time of Vibration, Amplitude of 
 Vibration; Centre of Oscillation; Real Length 
 
ENERGY. 
 
 of a Pendulum ; Laws and Formulas for the Pen- 
 dulum ; the Cyeloidal Pendulum; the Second's 
 Pendulum ; the Use of the Pendulum in Clock- 
 work; Compensation Pendulums. 
 
 ECTION V. 
 
 ENERGY, 
 
 150. Work. In physical science, the word ivork 
 signifies the overcoming of resistance of any kind. 
 Whether this overcoming of resistance is pleasant or not 
 does not enter into consideration here, all play being a 
 species of ivork. The word is here used in this technical 
 sense. When a force causes motion through space, it is 
 said to do work. The product of the force acting and the 
 space through which the body is moved measures the work 
 done on that body. Work implies a change of position 
 and is independent of the time taken to do it. 
 
 151. Energy. Energy is the power of doing 
 work. If one man can do more work than another, he 
 has more energy. If a horse can do more work, in a given 
 time, than a man, the horse has more energy than the man. 
 If a steam-engine can do more work than a horse, it has 
 more energy. If a moving cannon-ball can overcome a 
 greater resistance than a base-ball it has more energy. 
 
 152. Elements of Work Measure. Imagine a 
 flight of stairs, each step having a rise of twelve inches. 
 On the floor at the foot of the stairs are two weights, of 
 
ENERGY. 11 
 
 one and ten pounds respectively. Lift the first weight to 
 the top of the first step. How much work have you per- 
 formed ? Perhaps you will answer, one pound of work, 
 Now place the second weight beside the first. How much 
 work did you perform in so doing ? Perhaps you will say 
 ten times as much as before, or ten pounds. Now lift 
 each of them another step, and then another, until they 
 rest on the top of the tenth step. To lift the heavier 
 weight the second, third, and subsequent times involved 
 each as much work as to lift it the first foot, but you 
 would hardly say that you had lifted a hundred pounds. 
 Still it is sure that to place it on the tenth step required 
 just ten times as much work as it did to place it on the first 
 step, or just one hundred times as much work as it did to 
 place the one pound weight on the first step. Moreover, 
 it is evident that the two elements of weight and 
 height are necessarily to be considered in measuring 
 the work actually performed. 
 
 153. Units of Work; the Foot-pound. It 
 
 is often necessary to represent work numerically; hence 
 the necessity for a unit of measurement. The unit com- 
 monly in use, for the present, in England and this country 
 is the foot-pound. A foot-pound is the amount of work 
 required to raise one pound one foot high against 
 the force of gravity. The work required to raise one kilo- 
 gram one meter high against the same force is called a 
 kilogram-meter. 
 
 (a.) To get a numerical estimate of work, we multiply the numbe* 
 of weight units raised by the number of linear units in the vertical 
 height through which the body is raised. A weight of 2^ pounds, 
 raised 3 feet, or one of 3 pounds raised 25 feet, represents 75 foot* 
 pounds. A weight of 15 Kg. raised 10 m., represents 
 meters. 
 
78 ENERGY. 
 
 154. The Erg. The C. G. S. (or absolute) unit of 
 work is called the erg. It is the work done in moving 
 rt free body one centimeter against a force of one 
 dyne ( 69). The work of lifting one gram one centi- 
 meter against the force of gravity is 980 ergs. A foot- 
 pound is about 13,560,000 ergs. , 
 
 (a.) The definition of erg points out the fact that work equals 
 force multiplied, by distance. 
 
 155. Horse -Power. The rate of doing work is 
 called power. A horse-power represents the ability to 
 perform 550 foot-pounds in a second or 33,000 foot- 
 pounds in a minute. It equals 746 x 10 7 ergs per second. 
 
 (a.) An engine that can do 66,000 foot-pounds in a minute or 
 33,000 foot-pounds in half a minute is called a two horse-power 
 engine. To compute the number of horse-powers represented by an 
 engine at work, multiply the number of pounds raised by the num- 
 ber of feet, and divide the product by 550 times the number of seconds 
 or 33,000 times the number of minutes required to do the work. 
 
 156. 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 the direc- 
 tion 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 be the work actually done, it 
 is clear that the manner of expenditure does not change 
 the amount of energy expended. We may, therefore, 
 find to what vertical height the given velocity 
 would lift the body, and thus easily determine its 
 energy in foot-pounds, kilo^ramTn^t&rs or dynes, 
 
ENERGY. 79 
 
 157. An Easier Method. If we can obtain the 
 
 same result without the trouble of finding how high the 
 given velocity could raise it, it is generally desirable to do 
 so. Our vertical height is the whole space passed over by 
 an ascending body ( 132). We have given v to find 8. 
 
 gt = v. 
 
 t= V -. 
 9 
 
 Substituting the above value of tf 8 , we have, 
 
 Energy = wS (the weight into the height). Substitut- 
 ing our new value for $, we have the following important 
 formula : 
 
 Kinetic Energy = ^. 
 ^g 
 
 Since the weight of a body results from its mass and the 
 force of gravity (w = mg\ 
 
 Kinetic Energy = \ 
 
 (a.} If w be given in pounds ; u, in feet per second and g in feet, 
 the first formula will give the value of K. E. in foot-pounds. 
 
 (6.) If the gram be taken as the unit of mass and the centimeter 
 per second as the unit of velocity, the second formula will give the 
 value of K. E. in ergs. 
 
 158. Two Types of Energy. There are two types 
 of energy .which may be designated as energy of motion 
 and energy of position. With the first of these we are 
 familiar. A falling weight or running stream possesses 
 energy of motion ; it is able to overcome resistance by 
 reason of its weight and velocity. On the other hand, 
 before the weight began to fall, while, as yet, it had no 
 
80 ENERGY. 
 
 motion but was at rest, 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, which was not possessed by the waters of the 
 pond in the valley below. This energy or power results 
 from its peculiar position. Energy of motion is called 
 kinetic energy; energy of position is called potential 
 energy. 
 
 159. Convertibility of Kinetic and Poten- 
 tial Energies. "We may at any moment convert kinetic 
 energy into potential, or potential energy into kinetic. 
 One is as real as the other, and when it exists at all, exists 
 at the expense of a definite amount of the other. Imagine 
 a ball thrown upward with a velocity of 64.32 feet. As it 
 begins to rise it has a certain amount of kinetic energy. 
 At the end of one second it has a velocity of only 32.16 ft 
 Consequently its kinetic energy has diminished. But 
 it has risen 48.24 ft., and has already a considerable poten- 
 tial energy. All of this potential energy results from the 
 kinetic energy which has disappeared. At the end of 
 another second, the ball has no velocity; it has reached the 
 turning-point and is at rest. Consequently, it has no 
 kinetic energy. But the energy with which it began its 
 flight has not been annihilated ; it has been stored up in 
 the ball at a height of 64.32 ft. as potential energy. If at 
 this instant the ball be caught, all of the energy may be 
 kept in store as potential energy. If now the ball be 
 dropped, it begins to lose its potential and to gain kinetic 
 energy. When it reaches the ground at the end of two 
 seconds it has no potential energy, "but just ay much of the 
 
ENERGY. 
 
 kinetic type as was given to it when it began to rise. This 
 illustrates in a simple way the important principle, the 
 transformation or convertibility of energy without 
 any change in its quantity. 
 
 160. Energy a Constant Quantity. In the 
 
 case of the ball thrown upward, 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. In any case, 
 the swin of the two continually varying energies is 
 constant. Just as a man may have a hundred gold dol- 
 lars, now in his hand, now in his pocket, now part in his 
 hand and the rest in his pocket ; changing a dollar at a 
 time from hand to pocket or vice versa, the amount of 
 money in his possession remains constant, viz., one hun- 
 dred dollars. 
 
 161. Pendulum Illustration. The pendulum 
 affords a good and simple illustration of kinetic and poten- 
 tial energy, their equivalence 
 
 and convertibility. When the 
 pendulum hangs at rest in a 
 vertical- position, as P#, it has 
 no energy at all. Considered as 
 a mass of matter, separated from 
 the earth, it certainly has po- 
 tential energy; but considered 
 as a pendulum, it has no energy. 
 If the pendulum be drawn 
 aside to 5, we raise it through 
 the space ah ; that is, we do 
 work, or spend kinetic energy upon it. The energy thus 
 
82 ENERGY. 
 
 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 ha, 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 mi sing it from a to I. This kinetic energy 
 now carries it on to c, lifting it again through the space ah. 
 Its energy is again all potential just as it was at I. 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, or 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 #. 
 
 162. Indestructibility of Energy. From the 
 last paragraph it will be seen 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 imped- 
 iments, but the energy thus withdrawn is not destroyed. 
 What becomes of it will be seen when we come to study 
 heat and other forms of energy, which result from the 
 motions and positions of the molecules of matter. The 
 truth is that energy is as indestructible as matter. 
 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. 
 
 . -Physics may now be defined as the science of matter and 
 energy. 
 
ENERGY. 83 
 
 EXERCISES. 
 
 1. How many horse-powers in an engine that will raise 8,250 Ibe. 
 ITO ft. in 4 minutes ? 
 
 2. A ball weighing 192.96 pounds is rolled with a velocity of IOC 
 feet a second. How much energy has it? Ans. 30000 foot-pounds, 
 
 3. A projectile weighing 50 Kg. is thrown obliquely upward with 
 a velocity of 19.6 in. How much kinetic energy has it ? 
 
 4. A ten-pound weight is thrown directly upward with a velocity 
 of 225. 12 ft. (a.) What will be its kinetic energy at the end of the 
 third second of its ascent? (&.) At the end of the fourth second of 
 its descent ? 
 
 5. A body weighing 40 Kg. moves at the rate of 30 Km. per hour. 
 Find its kinetic energy. 
 
 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 ft. 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 two horse-power engine to raise 5 
 tons 100 feet ? 
 
 11. How far can a two horse-power engine raise 5 tons in 30 sec. ? 
 
 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 rest on a perfect, horizontal plane in a 
 vacuum, there will be no resistance 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. 1250 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 ft. 
 which is 50 foot-pounds x 10 x 8. To this add the work done in 
 giving the car kinetic energy.) 
 
84 ENERGY. 
 
 Recapitulation. In this section we have considered 
 the meaning of Work and Energy; the Ele- 
 ments of Work-measure; the Unit of Work, as 
 Foot-pound or Kilogram-meter ; Horse- 
 power; the relation between Velocity and En- 
 ergy ; a very convenient Formula for Energy ; 
 two Types of Energy, Kinetic a. A! Potential ; 
 the mutual Convertibility of these two Types of 
 Energy ; the Sum of these two as a Constant Quan- 
 tity ; the Pendulum as an Illustration of this Con- 
 vertibility and Constancy; the Indestructibility of 
 Energy. 
 
 REVIEW QUESTIONS AND EXERCISES, 
 
 1. (a.) What is a molecule? (&.) An atom? (c.) Name the attrae 
 tions pertaining to each. 
 
 2. (a.) Give an original illustration of a physical change. (&.) Of 
 a chemical change. 
 
 3. (a.) What is the difference between general and characteristic 
 properties of matter? (&.) Give an illustration of impenetrability, 
 not mentioned in the book. 
 
 4. (a.) Upon what property do most of the characteristic proper- 
 ties of matter depend? (b.) Name five general and three charac- 
 teristic properties of matter, (c.) Define inertia. 
 
 5. (.) How does a solid differ from a liquid? (&.) From a gas? 
 (c.) How does a gas differ from a vapor ? (d.) What is a fluid ? 
 
 6. (a.) Define dynamics. (&.) What is the difference between 
 statics and kinetics? (c.) What is the gravity unit of force? (d.) 
 The kinetic unit ? 
 
 7. (.) Give Newton's Laws of Motion. (&.) Explain the meaning 
 of "parallelogram of forces." (c.) What is an equilibrant ? (d.) 
 Give the law of reflected motion. 
 
 8. (a.) What is the difference between gravity and gravitation ? 
 (&.) Give the law of gravitation, (c.) Of weight, (d.) What in 
 meant by centre of gravity ? 
 
 9. (a.) Describe the several kinds of equilibrium. (&.) Upon 
 what does the stability of a body depend? (c.) Show how. (d.} 
 What is the line of direction ? 
 
ENERGY. 85 
 
 10. (a.) Why is it that a lead ball and a wooden ball will fall 100 
 feet in the same time ? (&.) How did Galileo study the laws of 
 falling bodies ? (c.) Who was Galileo and when did he live? (d.) 
 Define increment of velocity. 
 
 11. (a.) Give the laws of freely falling bodies. (&.) Express the 
 same truths algebraically, (c.) What forces act upon a projectile ? 
 (d.) Define random. 
 
 12. (a.) What is a simple pendulum ? (6.) A compound pen- 
 dulum? (c.) What is the real length of a pendulum? (d.) How 
 long must a pendulum be to vibrate once a minute ? (e.) Once a 
 second ? (/. ) What is the most important property of a pendulum ? 
 
 13. Two forces of 6 and 8 pounds respectively act at right angles 
 to each other. Find the direction and intensity of their equilibrant. 
 
 14. (a.) Define energy. (&.) Foot-pound, (c.) Horse-power, (d.) 
 Give the rule for calculating horse-power. 
 
 15. (a.) What is a kilogram-meter? (&.) Give the formula for 
 the calculation of kinetic energy from weight and velocity, (c.) 
 Deduce the same. 
 
 16. (a.) State fully and clearly the difference between kinetic and 
 potential energy. (&.) Illustrate the same by the pendulum. 
 
 17. (a.) What is the object of experiments in the study of phy- 
 sics? (&.) What is the metric unit of weight? (c.) How is it ob- 
 tained ? 
 
 * 18. Three inelastic balls weighing 5, 7 and 8 pounds, lie in the 
 same straight line. The first strikes the second with a velocity of 
 60 feet per second ; the first and second together strike the third. 
 What will be the velocity of the third ? Ans. 15 ft. 
 
 19. To how many F. P. S. units of force is the weight of 9 Ib. 
 equal ? 
 
 20. To how many C. G. S. units of force is the weight of 9 Kg. 
 equal ? 
 
 21. How many ergs will represent the kinetic energy of a ball 
 weighing 50 grams and moving at the rate of 60 cm. a second ? 
 
 Ans. 90,000. 
 
 22. Determine the amount of work performed in discharging a 
 30 gram bullet with a velocity of 400 m. per second. 
 
 Ans. 24 x 10 8 ergs. 
 
V, 
 
 SIMPLE MACH INES. 
 
 ECTfON I. 
 
 PRINCIPLES OF MACHINERY. THE LEVER. 
 
 163. What is a Machine? </2 machine is a 
 contrivance by means of which the force can be 
 applied to the resistance jnore advantageously. Its 
 general office is to effect a transformation in the inten- 
 sities of energies, so that an energy of small intensity, 
 acting through a considerable distance, may be made to 
 reappear as an energy of considerable intensity, acting 
 through a small distance, or vice versa. 
 
 164. 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 power 
 which 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. 
 
 165. A Common Error. A clear understanding 
 of this fact is very important. There is a very common 
 
PRINCIPLES OF MACHINERY. 87 
 
 erroneous notion that, in some way or other, a 
 machine performs work of itself that it is a source of 
 power. It were as reasonable to imagine that a bank is a 
 source of real money. The bank can pay out no more 
 than it receives; neither can a machine. A man may go 
 to the bank with a ten-dollar gold piece, and get for 
 it ten one-dollar gold pieces. In like manner, he may gc 
 to a machine with an ability of moving ten pounds one 
 foot in a given time, and get for it the ability of moving 
 one pound ten feet in the same time. He may exchange 
 what he has for what he prefers ; but, in the case of the 
 bank and of the machine alike, the equivalent must be 
 paid, and generally a commission for the transfer. 
 
 166. Of what Use are Machines ? Some of the 
 
 many advantages resulting from the use of machines are : 
 
 (1.) It enables us to exchange intensity for a velocity 
 otherwise unattainable, as in the case of the sewing 
 machine or spinning wheel. 
 
 (2.) It enables us to exchange velocity for* an intensity of 
 power otherwise unattainable, as in the case of lift- 
 ing a large stone with a crow-bar or pulleys. 
 
 (3.) It enables us to change the direction of our force, as 
 in the case of hoisting a flag on a flag-staff. It 
 would be inconvenient to climb the pole and then 
 draw up the flag. 
 
 (4.) It enables us to employ other forces than our own, as 
 the strength of animals, the forces of wind, water, 
 steam, etc. 
 
 167. General Laws of Machines. The work to 
 be done by a machine is generally called the weight or 
 load. The force applied is called the power. The work 
 
88 THE LEVER. 
 
 of the power (e. g., foot-pounds) is always equal to the 
 work of the load, the work expended in the machine itself 
 being disregarded. The following laws are, therefore, 
 applicable to machines of every kind : 
 
 (1.) What is gained in intensity of power is lost 
 in time, velocity, or distance; and what is 
 gained m time, velocity, or distance is lost in inten- 
 sity of power. 
 
 (2.) The power multiplied by the distance through 
 which it moves, equals the weight multiplied 
 by the distance through which it moves. 
 
 (3.) The power multiplied by its velocity, equals the 
 weight multiplied by its velocity. 
 
 168. What is a Lever? A lever is an inflex- 
 ible bar capable of being freely moved about a 
 fixed point or line, called the fulcrum. 
 
 In every lever, three points are to be considered, viz.: 
 the fulcrum and the points of application for the power 
 and the weight. Every lever is said to have two arms. 
 The power-arm is the perpendicular distance from the ful- 
 crum to the line in which the power acts; the weight-arm 
 is the perpendicular distance from the fulcrum 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. 
 
 169. Classes of Levers. There are three classes 
 
 of levers, depending upon the 
 relative positions of the power, 
 weight, and fulcrum. 
 
 FIG. 37. (1.) If the fulcrum is be- 
 
THE LEVER. 
 
 89 
 
 FTG. 38. 
 
 tween the power and weight (P. F. W.), the lever is of 
 the first class (Fig. 37); e. g. 9 crowbar, balance, steelyard, 
 scissors, pincers. 
 
 (2.) If the weight is be- 
 tween the power and the 
 fulcrum (P. W. F.), the 
 lever is of the second class 
 (Fig. 38) ; e. g., cork-squeezer, 
 nut-cracker, wheel-barrow. 
 
 (3.) If the power is be- f 
 
 tween the weight and the ful- _ 
 cram (W. P. P.), the lever is *^ === 
 of the third class (Fig. 39); 
 e. g., fire-tongs, sheep-shears, 
 human fore-arm. FlG ' 39 
 
 17O. Static Laws of the Lever. It will be 
 clearly seen or may be geometrically shown that 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 be twice as long 
 as the weight-arm, the power will move twice as fast and 
 twice as far as the weight does. The general laws of ma' 
 chines may therefore be adapted to the lever as follows : 
 
 P x power-arm = W x weight-arm, or P x PF = W x WP. 
 
 /. P : W : : W. F : PF. 
 
 (I.) In the case of the lever, the power and weight are 
 inversely proportional to the corresponding arms of the 
 lever; or, 
 
90 THE LEVER. 
 
 (2.) The power multiplied by the power-arm equals the 
 weight multiplied by the weight-arm ; or, 
 
 (3.) 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. 
 
 Note. A static law expresses the relation between the power and 
 weight when the machine is in equilibrium. In order that there be 
 motim, one of the products mentioned in the law above must be 
 greater than the other. The lever itself must be in equilibrium 
 before the power and weight are applied. It is 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. 
 
 171. The Moment of a Force. The moment 
 of a force acting about a given point, as the fulcrum of a 
 lever, is the product of the numbers representing 
 respectively the magnitude of the force and the 
 perpendicular distance between the given point 
 and the line of the force. In the case of the 
 lever represented in Fig. 37, the weight-arm is 8 mm. 
 and the power-arm is 30 mm. Suppose that the power is 
 4 grams, and let the weight be represented 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 Sx. 
 
 172. Moments Applied to the Lever. We 
 
 sometimes have sev- 
 
 ii^fc 
 eral forces acting 
 5 F 10 | 80 upon one or both 
 
 20] ijf~~ A 20 . , 
 
 J J e\ / arms of a lever, in 
 
 il i 4 i the same or in 
 
 40. opposite directions. 
 
THE LEVER. 
 
 91 
 
 Cinder such circumstances, the lever will be in equilibrium, 
 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+dzza+e+f 30+30 + 40 = 30 + 25+45. 
 or, c+d a = e + fl 30 + 4030 = 25 + 4530. 
 
 173. Bent Levers. When the lever is not a 
 
 straight bar, or when, for any reason, the power and 
 
 weight do not act parallel to each 
 
 other, it becomes necessary to distinguish 
 
 between the real and apparent arms of the 
 
 lever. This will be easily done, if you are 
 
 familiar with the definition of the arms 
 
 of a lever, given in 168. In Fig. 41, we 
 
 Aave represented a very simple kind of 
 
 bent lever, which is sufficiently explained 
 
 by the engraving. In Fig. 42, we have a 
 
 representation of a curved rod lever, WP', at the ends of 
 
 which two forces, 
 not parallel, are 
 acting. Our def- 
 inition of the 
 arms of the lever, 
 already learned, 
 removes every dif 
 
 ficulty arising from the form of the lever, or the direction 
 
 in which the forces act. The arms are not FP' anci 
 
 but FP and FW, 
 
 FIG. 41. 
 
 FIG. 42. 
 
92 THE LEVER. 
 
 174. Load between Two Supports.// a 
 
 beam rest on two supports, and carry a load be- 
 tween them, the beam may be considered a lever 
 of the second class. The part carried by either support 
 may be found by considering it as the power, and the. 
 other support as the fulcrum. (Fig. 43.) 
 
 FIG. 43. 
 
 175. The Balance. The balance is essentially 
 a lever of the first class, having equal arms. Its 
 use is to determine the relative weights of bodies. Its 
 action depends upon the equality of moments explained in 
 171 and 172. The lever itself is called the beam. 
 From the ends of the beam are suspended two pans, one 
 to carry the weights used, the other to carry the article to 
 be weighed. An index needle, or pointer, is often attached 
 to the beam, and indicates equilibrium, by pointing to the 
 zero of a graduated scale, carried by a fixed support. 
 
 (a.) That the balance may be accurate, the arms must be of the same 
 length. To make these arms exactly equal is far from an easy task. 
 That the balance may be delicate, it must turn upon its axis with 
 
THE LEVEti. 
 
 little friction, the axis of support must be a very little above "the 
 centre of gravity, the arms must be of considerable length, and the 
 beam must be 
 light. Balances are 
 made so delicate 
 that they may be 
 turned by less than 
 a thousandth of a 
 grain. The sup- 
 porting edge of the 
 axis is made very 
 sharp and hard, 
 and rests upon two 
 supports, general- 
 ly made of agate 
 or polished steel. 
 A really good bal- 
 ance is an expen- 
 sive piece of appa- 
 ratus. 
 
 FIG. 44. 
 
 176. False Balances. False balances (Levers of 
 the first kind with unequal arms) are sometimes 
 used ~by dishonest dealers. 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 geometrical 
 mean of the two false weights ; that is, by finding the 
 square-root of the product of the two false weights. 
 
 177. Double Weighing 1 . In another way the true 
 weight of a body may be found with a false balance. The 
 article to be weighed is placed in one pan, and a counter- 
 weight, as "of shot or sand, placed in the other pan until 
 equilibrium is produced. The article is then removed, 
 and known weights placed in the pan until equilibrium is 
 
94 
 
 THE LEVER. 
 
 again produced. The sum of these weights will be the 
 true weight of the given article. 
 
 178. Compound Lever. Sometimes it is not con* 
 
 venient to use a lever sufficiently long to make a giver 
 power support a given weight. A combination of levers 
 called a compound lever may then be used. Hay-scales 
 may be mentioned as a familiar illustration of the com- 
 pound lever. In this case we have the following : 
 
 Statical Law. The contin- 
 ued product of the power and 
 the lengths of the alternate 
 arms, beginning ivith the 
 power-arm, equals the contin- 
 ued product of the weight 
 and the lengths of the alter- 
 nate arms beginning with the 
 weight-arm. 
 
 .A 
 
 xms 
 
 x? 
 
 d 
 
 ) f? 
 
 FIG. 45. 
 
 EXERCISES. 
 
 No. 
 
 !i 
 
 1 
 P 
 
 'k 
 
 I 
 
 No. 
 
 IB 
 
 
 
 Us 
 
 P 
 
 0) 
 
 1 
 
 f 
 
 * 
 
 Lever. 
 
 Length. 
 
 Class. 
 ? 
 
 I 
 
 4ft. 
 
 2ft. 
 
 50 Ibs. 
 
 ? 
 
 11 
 
 5ft. 
 
 ? 
 
 SOlbs. 
 
 25 Ibs. 
 
 10ft. 
 
 2 
 
 3ft. 
 
 9ft. 
 
 ? 
 
 75 Ibs. 
 
 12 
 
 ? 
 
 9 
 
 15 oz. 
 
 45 oz. 
 
 12 in. 
 
 2 
 
 3 
 
 10ft. 
 
 4ft. 
 
 141bs. 
 
 ? 
 
 13 
 
 ? 
 
 50cm. 
 
 IKg. 
 
 4 Kg. 
 
 ? 
 
 2 
 
 4 
 
 60 in. 
 
 ? 
 
 21bs. 
 
 SOlbs. 
 
 14 
 
 16.1cm. 
 
 ? 
 
 12 oz. 
 
 2oz. 
 
 ? 
 
 3 
 
 6 
 
 ? 
 
 18cm. 
 
 27 Kg. 
 
 9 Kg. 
 
 15 
 
 3ft. 
 
 5ft. 
 
 10 Ibs. 
 
 ? 
 
 ? 
 
 1 
 
 6 
 
 14ft. 
 
 ? 
 
 45 oz. 
 
 63 oz. 
 
 16 
 
 39.37 in. 
 
 50cm. 
 
 ? 
 
 20 Kg. 
 
 ? 
 
 1 
 
 7 
 
 40cm. 
 
 56cm. 
 
 21 g. 
 
 ? 
 
 17 
 
 ? 
 
 16ft. 
 
 14 Ibs. 
 
 3i Ibs. 
 
 16ft. 
 
 ? 
 
 8 
 
 18 in. 
 
 21 in. 
 
 ? 
 
 24 oz. 
 
 18 
 
 ? 
 
 2ft. 
 
 30 Ibs. 
 
 ? 
 
 10ft. 
 
 1 
 
 9 
 
 26cm. 
 
 ? 
 
 iii)g. 
 
 13 Dg. 
 
 19 
 
 ? 
 
 2ft. 
 
 SOlbe. 
 
 ? 
 
 10ft. 
 
 2 
 
 10 
 
 ? 
 
 1ft. 
 
 SOlbs. 
 
 2500 Ibs. 
 
 20 
 
 2ft. 
 
 ? 
 
 30 Ibs. 
 
 ? 
 
 10ft. 
 
 3 
 
 Note to the Pupil. If any of these problems be obscure to you. 
 remember that it will pay to draw an accurate figure or diagram of 
 the machine representing the several powers and weights in position. 
 Bee Fig. 40. 
 
TtfE LEVER. 95 
 
 21. If a power of 50 pounds acting upon any kind of machine, 
 move 15 feet, (a) how far can it move a weight of 250 pounds 1 
 (&.) How great a load can it move 75 feet? 
 
 22. 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 125 feet per second ? (&.) With what velocity can it 
 move a load of 200 pounds? 
 
 23. A lever is 10 feet long ; F 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? (&.) How great a load can it lift ? 
 
 Ans. to (&.) : Anything less than 50 Ibs. 
 
 24. 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? (&.) If it 
 is of the second ? (c.) If it is of the third class? 
 
 25. 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 ? (&.) What weight can a power of 10 pounds support 
 in each case? 
 
 26. Length of lever = 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 Ib. 
 
 27. At the opposite ends of a lever 20 feet long, two forces are 
 acting whose sum = 1,200 pounds. The lengths of the lever arms 
 are as 2 to 3 ; what are the two forces when the lever is in equi- 
 librium ? 
 
 28. Length of lever = 8 feet, F in the centre. A force of 10 
 pounds acts at one end, one foot from it another of 100 pounds. 
 Three feet from the other end is a force of 100 pounds. Direction 
 of all forces, downward. Where must a downward force of 80 
 pounds be applied to balance the lever ? Ans. 3 ft. from F. 
 
 29. Length of lever ab = 6 feet ; fulcrum 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 equili- 
 brating force acting at b, the distance between b and c being f feet. 
 
 30. On a lever ab, a downward force of 40 pounds acts at a, 10 
 feet from fulcrum c ; on same side and 6| feet from c, an upward 
 force, d, acts, amounting to 56 pounds ; distance be = 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 (&) what 
 direction must it have ? 
 
 31. 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 cwt. 
 
96 THE LEVER. 
 
 8 feet from the other end. Give the pressure on each point of sup- 
 port. Ans. 2288| Ib. at one end. 
 
 32. Length of lever = 3 feet ; where must the fulcrum be placed 
 so that a weight of 200 Ibs. at one end shall be balanced by 40 Ibs. 
 at the other end ? 
 
 33. In one pan of a false balance, a roll of butter weighs 1 Ib. 
 
 9 oz. ; in the other, 2 Ibs. 4 oz. Find the true weight. 
 
 34. A and B at opposite ends of a bar 6 ft. long carry a weight 
 of 800 Ibs. suspended between them. A's strength being twice as 
 great as B's, where should the weight be hung ? 
 
 35. A and B carry a quarter of beef weighing 450 pounds on a 
 rod between them. A's strength is 1 that of B's ; the rod is 8 
 feet long ; where should the beef be suspended ? 
 
 36. Length of lever = 16 feet ; weight at one end, 100 pounds : 
 what power applied at other end, 3| feet from the fulcrum, is re- 
 quired to move the weight ? 
 
 37. A power of 50 Ibs. 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, (a.) 
 Figure the machine. (&.) Find the weight that may be thus sup- 
 ported, (c.) What power will support a weight of 4,400 kilograms ? 
 
 Recapitulation. To be amplified by the pupil for 
 review. 
 
 DEFINITION. 
 
 RELATION TO ENERGY. 
 
 USE. 
 
 GENERAL LAWS. 
 
 W 
 
 DEFINITION. 
 ARMS. 
 
 STATIC LAWS. 
 
 ( True. 
 , i. BALANCE.-? r>au/>fo 
 
 THE LEVER. . . 1 ' * False * 
 
 CLASSES. T 
 
 2. LOAD BETWEEN TWO SUPPORTS. 
 
 BENT. 
 COMPOUND. 
 
 MOMENTS OF FORCES. 
 
THE WHEEL AND AXLE. 
 
 97 
 
 ECTION H. 
 
 THE WHEEL AND AXLE AND WHEEL-WORK. 
 
 179. The Wheel and Axle. The wheel and 
 axle consists of a wheel united to a cylinder in 
 such a way that they may revolve together about 
 a common axis. It is a modified lever of the first 
 or second class. 
 
 ISO. Advantages of the Wheel and Axle. 
 
 The ordinary range of action of a lever of the first clasc 
 
 is very small. In order to raise the 
 
 load higher than the vertical distance 
 
 through which the weight end of the 
 
 lever passes, it is necessary to support 
 
 the load and re-adjust the fulcrum. 
 
 This occasions an intermittent action 
 
 and loss of time, difficulties which are 
 
 obviated by using the wheel and axle. 
 
 FIG. 46. 
 
 181. A Modified Lever. Considered as a lever 
 of the first class, the fulcrum is at 
 the common axis, while the arms of 
 the lever are the radii of the wheel 
 and of the axle. If a c, the radius 
 of the wheel, be used as the power- 
 arm, velocity or time is exchanged 
 for intensity of power. This is the 
 usual arrangement. If be, the radius 
 FIG. 47. of the axle, be used as the power- 
 
98 T&E WHEEL AND AXLE. 
 
 arm, there will be an exchange of intensity of power for 
 velocity or time. In treating of the wheel and axle, unless 
 otherwise specified, reference is made to the former or usual 
 arrangement. 
 
 182. Formulas for Wheel and Axle. The 
 law and formula for the lever apply here : 
 
 P : W : : WF : PF, or, P : W : : r : R, 
 
 the radii of the wheel and of the axle respectively being 
 represented by R and r. But it is a geometrical truth 
 that in any two circles, the ratio of their radii is the same 
 as the ratio of their diameters or circumferences. Hence 
 =ji these ratios may be substituted for 
 
 Jj-ij mmmr~~\n^ tne ra ^ Between ^ ne ra ^" f the 
 
 wheel and axle ; or, 
 
 P : W :: r : R. 
 P : W :: d: D. 
 
 J 
 
 FIG. 48. P : W : : c : C. 
 
 183. Law of Wheel and Axle. The power 
 multiplied by the radius, diameter or circum- 
 ference of the wheel equals the weight multiplied 
 by the corresponding dimension of the axle. 
 
 Note. If the radius of the axle be made the power-arm, the for- 
 mulas will be as follows : 
 
 P:W::WF:PF, or, P : W :: D : d. 
 
 184. Various Forms of Wheel and Axle. 
 
 The wheel and axle appears in various forms. It is not 
 necessary that an entire wheel be present, a single spoke 
 or radius being sufficient for the application of the power, 
 
WHEEL AND A%LE. 
 
 99 
 
 FIG. 49. 
 
 as in the case of the windlass (Fig. 48) or capstan (Fig. 49), 
 
 In ill such cases, the radius being 
 
 given, the diameter or circumference 
 
 of the wheel may be easily computed. 
 
 In one of the most common forms, 
 
 the power is applied by means of a 
 
 rope wound around the circumference 
 
 of the wheel. When this rope is 
 
 unwound by the action of the power, another rope is wound 
 
 up by the axle, and the weight thus raised. 
 
 185. Wheel-work. Another method of securing 
 
 a great difference in the in- 
 tensities of balancing forces, 
 is to use a combination of 
 wheels and axles of moder- 
 ate size. Such a combination 
 constitutes a train. The wheel 
 that imparts the motion is 
 called the driver ; that which 
 receives it, the follower. An 
 axle with teeth upon it is 
 called a pinion. The teeth or 
 cogs of a pinion are called leaves. 
 
 186. Law of Wheel-work, A train of wheel- 
 work is clearly analogous to a compound lever; the statical 
 law, given in 178, may be adapted to our present pur- 
 poses as follows : The continued product of the power 
 and the radii of the wheels equals the continued 
 product of the weight and the radii of the axles. 
 
 187. Another Law of Wheel-work. By 
 
 examination of Fig. 50, it will be seen that while the axle 
 
 FIG. 50. 
 
100 WHEEL-WORK. 
 
 d revolves once, the wheel and pinion c will revolve as 
 many times as the number of leaves borne by c is con- 
 tained times in the number of teeth borne by /. In like 
 manner, while the wheel c revolves once, the wheel and 
 pinion ft will revolve as many times as the number of leaves 
 borne by I is contained times in the number of teeth 
 borne by c. By combination of these results, we see that 
 while d revolves once, b will have as many revolutions as 
 the product of the number of leaves is contained times in 
 the product of the number of teeth. From this it follows 
 that the ratio between, the continued product of the cir- 
 cumference (diameter or radius) of d into the number of 
 leaves on the several pinions and the continued product of 
 the corresponding dimension of b into the number of teeth 
 on the several wheels will be the ratio between the dis- 
 tances or velocities of W and P, and therefore the ratio 
 between the intensities of balancing weights or forces. 
 
 In short, the continued product of the power, the cir- 
 cumference of a and the number of teeth on c and f 
 equals the continued product of the weight, the circum- 
 ference of d and the number of leaves on the pinions c 
 and I. 
 
 188. Example. Suppose the circumferences of a 
 and d to be 60 mm. and 15 mm. respectively ; that ft has 9 
 leaves ; c has 36 teeth and 13 leaves ; / has 40 teeth. 
 
 Then will 
 
 P x 60 x 36 x 40 = W x 15 x 13 x 9. 
 
 189. Ways of Connecting Wheels. Wheels 
 may be connected in three ways : 
 
 (1.) By the friction of their circumferences. 
 (2.) By bands or belts. 
 
WHEEL- WORK. 
 
 101 
 
 (3.) By teeth or cogs. 
 
 The third of these methods has been already considered, 
 
 190. Uses of the First Two Ways. The first 
 method is used where no great resistance is to be overcome, 
 but where evenness of motion and freedom from noise are 
 chiefly desired. It is illustrated in some sewing-machineSo 
 The second method is used when the follower is to be at 
 some distance from the driver. The friction of the belt 
 upon the wheels must be greater than the resistance to be 
 overcome. It is illustrated in most sewing-machines, and 
 in the spinning-wheel. 
 
 191. Relation of Power to Weight De- 
 termined. The follower will revolve as many times 
 as fast as the driver, as its circumference is contained 
 times in that of the driver. The problem of finding the 
 distances passed over in a given time by the power and 
 weight, and thence the relative intensities of the power 
 and the weight, thus becomes an easy one. 
 
 EXERCISES. The Wheel and Axle. 
 
 Reinark. The circumference of a circle is 3.1416 times greatel 
 than its diameter. 
 
 *t 
 
 ? 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 10 
 11 
 
 Power. 
 
 I 
 
 DIMENSIONS. 
 
 R 
 
 D 
 
 
 
 r 
 
 d 
 
 c 
 
 25 Ibs. 
 ? 
 231bs. 
 9 Kg. 
 1341 Kg. 
 195 Ibs. 
 ? 
 3 Ibs. 
 2 Ibs. 
 49 Ibs. 
 13 oz. 
 
 ? 
 750 Kg. 
 230 Ibs. 
 153 Kg. 
 ? 
 ? 
 80 Kg. 
 48 Ibs. 
 40 Ibs. 
 ? 
 ? 
 
 f 
 
 
 20 <"t. 
 
 
 
 4ft. 
 50cm. 
 ? 
 17cm. 
 
 15 in. 
 
 
 12.50 m. 
 
 
 
 ? 
 ? 
 
 
 
 15ft. 
 
 ? 
 628.32 cm. 
 25 in. 
 
 
 
 
 ...... 
 
 20cm. 
 
 
 
 1m. 
 3dm. 
 
 
 
 
 16 in. 
 
 
 
 ? 
 ? 
 
 ? 
 ? 
 7 in. 
 
 10cm. 
 
 16 in. 
 
 78.74 in. 
 
102 
 
 WHEEL- WORK. 
 
 12. 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? 
 
 13. 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 C feet 8 inches in diameter. How great a pressure 
 must each of the men exert ? 
 
 14. With a capstan, four men are raising a 1000 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 ? 
 
 15. The circumference of a wheel is 8 ft.; that of its axle, 16 
 inches. The weight, including friction, is 85 .pounds ; how great a 
 power will be required to raise it ? 
 
 16. 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. 
 
 17. An axle 10 inches in diameter, fitted with a winch 18 inches 
 long, is used to draw water from a well. (.) How great a power will 
 it require to raise a cubic foot of water which weighs 62 \ Ibs. ? (b.) 
 How much to raise 20 litres of water ? 
 
 18. A capstan whose barrel has a diameter of 14 inches is worked 
 Dy 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. 
 
 19. 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 in diameter, to pull a house through 5 miles of streets, if the 
 horse walk at the rate of 2| miles an hour ? 
 
 Recapitulation. To be amplified by the pupil for 
 
 review. 
 
 WHEEL 
 AND AXLE. 
 
 DEFINITIONS. 
 
 ADVANTAGES. 
 
 RELATION TO THE LEVER. 
 
 FORMULAS AND LAWS. 
 
 FORMS. 
 
 WHEEL WORK. 
 
 DRIVER. 
 FOLLOWER. 
 LAWS. 
 CONNECTIONS. 
 
 MODES 
 USES. 
 RELATION OF P TO W 
 
THE PULLEY. 
 
 103 
 
 ECTfON III, 
 
 
 PULLEY AND THE INCLINED PLANE. 
 
 192. What is a Pulley?^ pulley consists of 
 a wheel turning upon an axis and having a cord 
 passing over its grooved circumference. The frame 
 supporting the axis of the wheel is called the block. 
 
 193. A Fixed Pulley. The advantages arising 
 from the use of a pulley depend upon the uniform tension 
 of the cord. If a cord be passed over a 
 
 pulley fixed to the ceiling, a weight being 
 at one end and the hand applied at the 
 other, the tension of the cord will be uni- 
 form, and the hand will have to exert a 
 force equal to the weight of the load. If 
 the weight be moved, the hand and weight 
 will move equal distances. It is evident, 
 ihen, that the fixed pulley affords no 
 increase of power, but only change 
 of direction. 
 
 194. A Movable Pulley. If one 
 
 end of the cord be fastened to the ceil- 
 mg, the load suspended from the pulley, 
 and the other end of the cord drawn up 
 by the hand, it will be evident, from the 
 equal tension of the cord, that the fixed 
 support carries half the load and the hand 
 the other half. It is also evident that to 
 raise the weight one foot the hand must 
 pull up two feet of the cord ; that is to F IG - 5 2 - 
 
 FIG. 51. 
 
104 
 
 THE PULLET. 
 
 say, each section of the cord carrying the weight must be 
 shortened one foot. Thus the hand, by lifting 50 pounds 
 two feet, is able to raise 100 pounds one foot. It is to be 
 noticed that we have here no creation or increase of 
 energy, working power, but that we do 
 secure an important transformation of 
 velocity into intensity. 
 
 195. A Combination of Pul- 
 leys. By the use of several fixed and 
 movable pulleys in blocks, the number 
 of parts of the cord supporting the mov- 
 able block may be increased at pleasure. 
 In all such cases, the tension of the cord 
 will be uniform, and the part of the cord 
 to which the power is applied, will carry 
 only a part of the load. The value 
 of this part of the load depends upon 
 the number of sections into which the 
 movable pulley divides the cord. 
 
 FIG. 53- 196. Law of the Pulley. 
 
 With a pulley having a contin- 
 uous cord, a given power will support a 
 weight as many times as great as itself as 
 there are parts of the cord supporting the 
 movable block. 
 
 197. Concerning: the Number of 
 Parts of the Corel. By observing the sev- 
 eral figures of pulleys in this section, it will be 
 seen that when the fixed end of the cord is at- 
 tached to the fixed block, the number of parts ol 
 FIG. 54. the cord supporting the weight is twice the num- 
 
THE INCLINED PLANE. 105 
 
 her of movable pulleys used ; that when the fixed end of 
 the cord is attached to tt.a movable block the number of 
 parts of the cord is one more than twice the number of 
 movable pulleys used. 
 
 198. What is an Inclined Plane? The in- 
 clined plane is a smooth, hard, inflexible surface 
 inclined so as to make an oblique angle with the 
 direction of the force to be overcome. In most cases it 
 is a plane surface inclined to the horizon at an acute angle, 
 and is used to aid in the performance of work against the 
 force of gravity. 
 
 199. Resolution of the Force of Gravity. 
 
 When a weight is placed upon an inclined plane, the force 
 of gravity tends to draw it vertically downward. This 
 force may be resolved into two forces ( 91), one acting per- 
 pendicularly to the plane, producing pressure completely 
 resisted by the plane, the other component acting opposite 
 to the direction of the power which it is to counterbalance. 
 The first component shows how much pressure is exerted 
 upon the plane ; the other shows what force must be 
 exerted to maintain equilibrium. The value of the second 
 component will, plainly, vary with the direction of the 
 power. 
 
 200. Three Cases. In the use of an inclined plane, three 
 cases may arise : 
 
 (1.) Where the power acts in a direction parallel to the length of 
 the plane. 
 
 (2.) Where the power acts in a direction parallel to the base of the 
 plane (generally horizontal). 
 
 (3. ) Where the power acts in a direction parallel to neither the 
 length nor the base of the plane. 
 
 20 1. The First Case. In the accompanying figure, let 
 
106 
 
 THE INCLINED PLANE. 
 
 \ 
 
 ]St 
 
 c 
 FIG. 55. 
 
 LM represent a plane inclined to the horizontal line LN. Let A 
 represent a ball weighing 20 Kg. The 
 problem is to find what force acting in the 
 direction LM will hold it in equilibrium. 
 The weight of the body A is a downward 
 force of 20 Kg., which may be graphically 
 represented ( 81) by the vertical line AC, 
 20 mm. in length. Any other convenient 
 unit of length might be used, but the 
 scale of 1 mm. to the Kg. being adopted, 
 it must be maintained throughout the 
 problem. The force represented by AC 
 is resolved into two components repre- 
 sented by AD, perpendicular to LM, and by AB, parallel to it. The 
 former component measures the pressure to be resisted by the plane ; 
 the latter component measures the force with which the ball is 
 drawn towards L. This second component is to be balanced by the 
 equal and opposite force AB', the equilibrant of AB. It may be 
 proved geometrically that 
 
 AB : AC : : MN : ML. (Olney's Geometry, Art. 341.) 
 Careful construction and measurement will give the same result. 
 But AB, or rather its equal AB', represents the power ; AG repre- 
 sents the weight ; MN represents the height ; and ML, the length 
 of the plane. Therefore, 
 
 P : W ::h:l, or, P = the | part of W. 
 
 2O2. Law for the First Case. In the figure 
 above, ML is twice the length of MN, and AC is twice the 
 length of AB or AB'. This indi- 
 cates that a force of 10 Kg. acting in 
 the direction LM would hold the 
 ball in equilibrium. This result may 
 be easily verified by experiment. 
 We may therefore establish the fol- 
 
 20 Kg. 
 
 FIG. 56. 
 
 10 Kg. < 
 
 lowing law : When a given power 
 acts parallel to the plane, it will 
 support a weight as many times as great as itself as 
 the length of the plane is times as great as its verti- 
 cal height. 
 
THE INCLINED PLANE 
 
 107 
 
 203. Law for the Second Case. By resolving 
 the force of gravity, or by experi- 
 ment, the following law may be 
 
 established : When a given power 
 acts parallel to the base, it mill 
 support a weight as many 
 times as great as itself as the 
 horizontal base of the plane is 
 times as great as its vertical 
 height. 
 
 204. The Third Case. For the third case, the power 
 acting in a direction parallel to neither the length nor the base of 
 the plane, no law can be given. The ratio of the power to the 
 weight may be determined by resolving the force of gravity, as 
 above explained, the construction and measurement being carefully 
 done. 
 
 EXERCISES. 
 
 Remark. The first problem may be read : 
 
 (a.) In a system of pulleys, the weight being supported by two 
 sections of the cord, a power of 25 Ibs. will support what weight ? 
 
 (6.) In an inclined plane, the power acting in the direction of the 
 length, the height being 3 ft., what must be the length that a power 
 of 25 Ibs. may support the same weight as determined in (a.)? 
 
 
 
 
 PULLET. 
 
 lN< 
 
 3LINED I 
 
 J LANE. 
 
 
 No. 
 
 POWER. 
 
 WEIGHT. 
 
 Cords. 
 
 Height. 
 
 Length. 
 
 Base. 
 
 Case. 
 
 1 
 
 25 Ibs 
 
 ? 
 
 2 
 
 3 ft 
 
 ? 
 
 
 1 
 
 2 
 
 13 Ke- 
 
 78 Kff 
 
 ? 
 
 ? 
 
 12 m 
 
 
 1 
 
 3 
 
 12 OZ5 
 
 ? 
 
 8 
 
 ? 
 
 
 2 ft. 
 
 2 
 
 4 
 
 250 a- 
 
 2 Kg- 
 
 ? 
 
 1 dm 
 
 ? 
 
 
 1 
 
 5 
 3 
 
 ? 
 15 cwt 
 
 "-& 
 350 Ibs. 
 3 T 
 
 7 
 7 
 
 ? 
 4 rds 
 
 ? 
 
 49ft. 
 
 2 
 I 
 
 7 
 
 20 a- 
 
 1 He;. 
 
 ? 
 
 ? 
 
 
 10m. 
 
 2 
 
 8 
 
 *v g. 
 
 500 Kg. 
 
 ? 
 
 8 
 
 ? 
 
 24m. 
 
 
 1 
 
 9 
 
 7 
 
 540 Ibs 
 
 9 
 
 39 37 in 
 
 ?m 
 
 
 1 
 
 10 
 
 75 Ibs. 
 
 100 Ibs. 
 
 
 3yds. 
 
 ? 
 
 ? 
 
 2 
 
108 THE INCLINED PLANE. 
 
 11. With a fixed pulley, what power will support a weight of 50 
 pounds ? 
 
 12. With a movable pulley, what power will support a weight of 
 50 pounds ? 
 
 13. What is the greatest effect of a system of 3 movable and 4 
 fixed pulleys, the power applied being 75 pounds ? 
 
 14. With a system of 5 movable pulleys, one end of the rope 
 being attached to the fixed block, what power will raise a ton 1 
 
 15. If in the system mentioned in the problem above, the rope be 
 attached to the movable block, what power will raise a ton ? 
 
 16. With a pulley of 6 sheaves in each block, what is the least 
 power that will support a weight of 1,800 pounds, allowing \ for 
 friction ? What will be the relative velocities of P and W ? 
 
 17. Figure a set of pulleys by which a power of 50 pounds will 
 support a weight of 250 pounds. 
 
 18. The height of an inclined plane is one-fifth its horizontal 
 base. A globe weighing 250 Kg. is supported 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 intensity of the supporting force. 
 
 19. With the conditions as given in the last problem, except that 
 Ihe pressure of the globe upon the plane is more than 250 Kg., de- 
 termine the intensity of the supporting force. 
 
 20. 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 
 JJtons? 
 
 21. An incline has its base 10 feet ; its height, 4 feet : how heavy a 
 ball will 50 pounds power roll up f 
 
 22. How great a power will be required to support a ball weighing 
 40 pounds on an inclined plane whose length is 8 times its height ? 
 
 23. A weight of 800 pounds rests npon 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. 
 
 24. A load of 2 tons is to be lifted along an incline. The powej 
 is 75 pounds : give the ratio of the incline which may be used. 
 
 25. A 1500 pound safe is to be raised 5 feet. The greatest powei 
 that can be applied is 250 pounds. Give the dimensions of thf 
 shortest inclined plane that can be used for that purpose. 
 
 Recalculation, To be amplified by the pupil foi 
 review. 
 
THE WEDGE. 
 
 109 
 
 PULLEY. 
 
 INCLINED 
 PLANE. 
 
 DEFINITION. 
 
 r FIXED. 
 
 KINDS. \ MOVABLE. 
 
 [ COMBINATIONS. 
 
 LAW. 
 
 RELATION between the number of pulleys and the 
 number of parts of the cord. 
 
 f DEFINITION. 
 FORCE OF GRAVITY I FIRST CASE - LAW - 
 
 CAVITY I SECOND CA SE.-LAW. 
 RESOLVED. ] THIRD CASK 
 
 ECTION IV, 
 
 J \. 
 
 THE WEDGE, SCREW, COMPOUND MACHINES, AND 
 FRICTION. 
 
 2O5. What is a Wedge? A wedge is a mov- 
 able inclined plane in 
 which the power gener- 
 ally acts parallel to the 
 
 2O6. Its Use. The 
 
 wedge is used for moving 
 great weights short dis- 
 tances. The law is the Fl &- 58. 
 same as for the corresponding inclined plane. A common 
 method of moving bodies is to place two similar wedges, 
 with their thin ends overlapping, nnder the load. 
 Simultaneous blows of equal force are 
 struck upon the heads of the wedges. 
 In this case, the same force must be 
 used upon each wedge as if only one 
 FIG. 59. were used, but the power being doubled 
 
110 
 
 THE SCREW. 
 
 FIG. 60. 
 
 and the weight remaining the same, the distance moved in 
 twice as great as when only one wedge is used. 
 
 207. A More Common Use. A more com- 
 
 mon, kind of wedge is that of two in- 
 clined planes united at their bases. Such 
 wedges are used in splitting timher, stone, etc. 
 The power is given in repeated blows instead 
 of continued pressure. For a wedge thus used, 
 no definite law of any practical value can be 
 given, further than that, with a given thick- 
 ness, the longer the wedge the greater the gain 
 in intensity of power. 
 
 208. What is a Screw? A Screw is a cylin* 
 der, generally of wood F. 
 
 or metal, with a spiral 
 groove or ridge winding 
 ribout its circumference. 
 The spiral ridge is called 
 the thread of the screw. 
 The thread works in a nut, 
 within which there is a 
 corresponding spiral groove 
 to receive the thread. 
 
 (a.) The power is used to turn the screw within a fixed nut, or to 
 turn the nut about a fixed screw. In either case, a lever or wheel 
 Is generally used to aid the power. Every turn of the screw or nut 
 3ither pushes forward the screw or draws back the nut by exactly 
 fiie distance between two turns of tha thread, this distance being 
 measured in the direction of the axis c f the screw. The weight or 
 resistance at W is moved this distance, while the power at P moves 
 over the circumference of a circle whose radius is PF. The differ- 
 ence between these distances is generaU T very great. Hence this 
 machine affords great intensity of power vith a corresponding loss 
 of velocity. 
 
 FIG. 61. 
 
COMPOUND MACHINES. 
 
 Ill 
 
 L 
 
 209. Law of the Screw. The second general 
 law of machines (167, [2]) may be adapted to our present 
 purpose as follows : 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 distance between two adjoining turns 
 of the thread. 
 
 210. The Endless Screw. An endless screw 
 is one whose thread acts on the teeth of a wheel. 
 The screw has a rotary but no 
 
 lengthwise motion. As the han- 
 dle is turned, the thread catches 
 the teeth and turns the wheel. 
 The wheel moves one tooth for 
 every turn of the handle. Suc- 
 cessive teeth are caught as others 
 pass out of reach. A continuous 
 motion is thus produced ; hence 
 the name "endless screw." The 
 figure will aid in the application of the second general law 
 of machines to determine the ratio between the weight and 
 the power. 
 
 211. Compound Machines. We have now con- 
 sidered each of the six traditional simple machines. One 
 of these may be made to act upon another of the same 
 kind, as in the case of the compound lever or wheel-work ; 
 or upon another of a different kind, as in the case of the 
 endless screw. When any two or more of these machines 
 are combined, the effective force may be found by comput- 
 ing the effect of each separately and then compounding 
 them ; or by finding the weight that the given power wil) 
 
 FIG. 62. 
 
112 FRICTION. 
 
 support, using the first machine alone, considering the 
 result as a new power acting upon the second machine, 
 and so on. 
 
 212. What is Friction ? The chief impediment 
 to the motion of machinery arises from friction, which may 
 be defined as the resistance which cu moving body 
 meets with from the surface on which it moves. 
 
 213. The Cause of Friction. It is impossible, 
 by any known means, to produce a perfectly smooth sur- 
 face. Even a polished surface contains minute projec- 
 tions which fit into corresponding depressions on the cor- 
 responding surface. To produce motion of one surface on 
 the other, these projections must be lifted out, bent down, 
 or broken off. 
 
 214. Eight Facts Concerning Friction. 
 The following facts have been determined by experiment, 
 and may be easily illustrated in the same way : 
 
 (1.) Friction is greatest at the beginning of motion. 
 After surfaces have been in contact for some time, 
 so that the projections of one have had opportunity 
 to sink deeper into the depressions of the other, the 
 resistance offered by friction is considerably in- 
 creased. Every teamster and street-car driver is 
 familiar with the fact. 
 
 (2.) Friction increases with the roughness of the 
 surfaces. 
 
 (3.) Friction is greater between soft bodies than 
 hard ones. 
 
 (4.) Friction is nearly proportional to pressure, 
 (a.) Place a brick upon a horizontal board. Around it fasten one 
 
 end of a cord and pass the other end over a pulley so that it may 
 
 hang vertically. Add just weights enough to keep the brick in 
 
FRICTION. 
 
 113 
 
 motion after it is started. The weights measure the friction. Place 
 a second similar brick upon the first ; the moving force must be 
 doubled. Place another similar brick upon the other two ; the 
 original moving force must be tripled. 
 
 (5.) Friction is not affected by extent of surface 
 except within extreme limits. In the case of 
 the brick above mentioned, the moving force will 
 be the same whether the brick he on its broad face 
 or on its side. 
 
 (6.) Friction is greater between surfaces of the 
 same material than between those of differ- 
 ent kinds. 
 
 (a.) Bodies of the same material have the same molecular struc- 
 ture ( 10, a). Hence their little projections and cavities mutually 
 fit each other as would the teeth of similar saws. A very little re- 
 flection will show that the element of similarity in molecular struc- 
 ture (just as with the saws) is very important in determining the 
 amount of friction. For this reason, the axles of railway cars being 
 made of steel, the " boxes " in which they revolve are made of brass 
 or other different metal. Hence the advantages of a watch " full- 
 jewelled," and hence the swiftness of the skillful skater. 
 
 (7.) Rolling friction is less than sliding friction* 
 (8.) Friction is diminished by polishing or lubri- 
 cating the surfaces. An unequalled example of 
 friction reduced to its minimum is in the case of 
 the joints of animals. 
 
 EXERCISES. The Screw. 
 
 No. 
 
 P. 
 
 W. 
 
 c. 
 
 d. 
 
 No. 
 
 P. 
 
 W. 
 
 C. 
 
 (I. 
 
 1 
 
 15 Ibs. 
 
 ? 
 
 JO in. 
 
 iin. 
 
 8 
 
 ? 
 
 2500 Kg. 
 
 2.5m. 
 
 1 cm. 
 
 2 
 
 5 Kg. 
 
 ? 
 
 8m. 
 
 1 cm. 
 
 9 
 
 4 oz. 
 
 6 Ibs. 
 
 ? 
 
 7 in. 
 
 3 
 
 lib. 
 
 ? 
 
 75 in. 
 
 {in. 
 
 10 
 
 ?lbs. 
 
 7874 Ibs. 
 
 1m. 
 
 lin. 
 
 1 
 
 ? 
 
 480 Ibs. 
 
 15 in. 
 
 1-fe 
 
 11 
 
 3 Kg. 
 
 aOOKg.i 20cm. 
 
 ? 
 
 5 
 
 20 Ibs. 
 
 800 Ibs. 
 
 ? 
 
 iin. 
 
 12 
 
 3 oz. 
 
 864 oz. 
 
 ? 
 
 1 in. 
 
 6 
 
 25 Ibs. 
 
 ? 
 
 3ft. 
 
 lin. 
 
 13 
 
 100 Ibs. 
 
 ? 
 
 10ft. 
 
 fin. 
 
 7 
 
 2 Ibs. 
 
 192 Ibs. 
 
 4ft. 
 
 ? 
 
 14 
 
 100 Ibs. 
 
 ? 
 
 10ft. 
 
 I to. 
 
THE SCREW. 
 
 15. A book-binder has a press; the threads of its screw are \ in. apart; 
 the nut is worked by a lever which describes a circumference of 
 8 ft. How great a pressure will a power of 15 Ibs. applied at the end 
 of the lever produce, the loss by friction being equivalent to 240 Ibs. 1 
 
 16. A screw has 11 threads for every inch in length. If the 
 lever is 8 inches long, the power, 50 pounds, and friction is $ of the 
 energy used, what resistance may be overcome by it ? 
 
 17. A screw with threads 1| in. apart is driven by a lever 4| ft. 
 long ; what is the ratio of the power to the weight ? (See Appendix A. ) 
 
 18. How great a pressure will be exerted by a power of 15 Ibs. 
 applied to a screw whose head is one inch in circumference and 
 whose threads are % inch apart ? 
 
 19. At the top of an inclined plane which rises 1 ft. in 20 is a wheel 
 and axle. Radius of wheel = 2 * ft. ; radius of axle 4| in. What load 
 may be lifted by a boy who turns the wheel with a f orco of 25 Ibs. ? 
 
 20. The crank of an endless screw whose threads are an inch 
 apart describes a circuit of 72 inches. The screw acts on the 
 toothed edge of a wheel 60 inches in circumference. On the axle 
 of this wheel, which is 10 inches in circumference, is wound a cord 
 which acts upon a set of pulleys, 3 in each block. The effect of the 
 pulleys is exerted upon the wheel of a wheel and axle. The diam- 
 eters of the wheel and of the axle are 4 ft. and 6 inches respec- 
 tively. What weight on the wheel and axle may be lifted by a 
 force of 25 Ibs. at the crank, allowing for a loss of 1 by friction ? 
 
 21. An endless screw which is turned by a wheel 10 ft. in circum- 
 ference acts upon a wheel having 81 teeth ; this wheel has an axle 
 18 inches in circumference ; the power is 75 Ibs. Find the value of 
 the weight that may be suspended from the axle. 
 
 22. In moving a building the horse is attached to 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 pul- 
 leys. What force will be exerted by 500 pounds power, allowing 
 for loss by friction ? 
 
 Recapitulation. To be amplified by the pupil for 
 review. 
 
 %4/rrnnc J DEFINITION. 
 
 WEDGE. j TWO USES AND THE LAW FOR EACH. 
 
 ( DEFINITION. 
 orpc\*/ J j A.W 
 
 { ENDLESS SCREW ; ITS ADVANTAGES ; RELATION OF P TO W. 
 
 COMPOUND MACHINES; RELATION OF p TO w. 
 
 DEFINITION. 
 
 FRICT.ON. 
 
REVIEW. 115 
 
 REVIEW QUESTIONS AND EXEKCISES. 
 
 1. (.) What is a machine? (6.) What is a machine good forl 
 c.) State the general laws of machines and (d) illustrate by the 
 
 pulley 
 
 2. (.) What are the arms of a lever ? (&.) What is meant by the 
 moment of a force ? (c.) Illustrate the equality of moments in ma- 
 chines by the wheel and axle. 
 
 3. (a.) What are the respective advantages to be gained by the 
 several classes of levers ? (b.) Explain the advantage gained by a 
 claw hammer in drawing a nail, (c.) What is meant by double 
 weighing ? 
 
 4. With a lever of given length, in which class will a given 
 power yield the greatest intensity of effect ? 
 
 5. (a.) To what kind of a lever is ordinary clock-work analogous? 
 (&.) Show why. 
 
 6. (a.) Does it require more 'work to lift a barrel of flour into a 
 wagon four feet high than to place it there by rolling it up a plank 
 12 feet long ? (6.) Show why. 
 
 7. (a.) Give the static law for the inclined plane when the power 
 acts parallel to the plane. (&.) When it acts parallel to the horizon. 
 (c.) Figure a system of pulleys by means of which a weight of 5 
 pounds will support a weight of 25 pounds. 
 
 8. (a.) Figure a system of 4 movable pulleys by means of which 
 a weight of 3 Ibs. will support a weight of 27 Ibs. (&.) Deduce 
 the formula for the screw from one of the general laws of machines. 
 
 9. (a.) In raising a boy from a deep well by means of a common 
 rope and pulley, what disadvantages arise from friction ? (&.) What 
 immense advantage ? 
 
 10. (a.) Explain the cause of friction. (&.) Why is friction between 
 iron and iron greater than that between iron and brass? 
 
 11. (a.) How may the centre of gravity of a ring be determined ? 
 (&,) What is the value in inches of the metric unit of length? 
 
 , 12. A body moving with an energy of 20 foot-pounds, strikes the 
 end of the arm of a lever of the first class, four feet from the 
 fulcrum, (a.) How many foot-pounds will be exerted by the other 
 end of the lever, 6 feet from the fulcrum ? (&.) How far would it 
 raise a weight of 4 pounds ? 
 
 13. Deduce the static law for the inclined plane, first case, by 
 resolution of the force of gravity. 
 
 14. (a.) What force is necessary to overturn a body ? (&.) What 
 difference between the forces producing uniform and accelerated 
 velocities ? (c.) Show that the screw is a modified ipclined plane. 
 
IV. 
 
 LIQUIDS. 
 
 ECTION I, 
 
 HYDROSTATICS. 
 
 215. Incompressibility of Liquids. Liquids 
 are nearly incompressible. A pressure of 15 pounds to 
 the square inch, compresses distilled water only 2 * tf 
 part of its volume ; it compresses 
 mercury only one-tenth as much. 
 This virtual incompressibility of 
 liquids is of the highest practical 
 importance. 
 
 216. Transmission of 
 Pressure. Fluids can trans- 
 mit pressure in every direc- 
 tion, upward, downward, and 
 sidewise at the same time. 
 
 (a.) This property of liquids may be 
 illustrated by the apparatus repre- 
 sented in Fig. 63. The globe and 
 cylinder being filled with water and 
 the several openings in the globe 
 FIG. 63. closed by corks, a piston is pushed 
 
n TD R OSTA TICS. 
 
 117 
 
 FIG. 64. 
 
 Jown the cylinder. The pressure thus received and transmitted by 
 the confined water expels the cork and throws a jet of water from 
 each aperture. (See Appendix D.) 
 
 (&.) The explanation of this property of fluids may be seen by 
 reference to Fig. 64, representing five molecules of any fluid. If a 
 downward pressure be applied to 1, it 
 will force 2 toward the right and 3 tow- 
 ard the left, thus forming lateral pres- 
 sure. When thus moved, 3 will force 4 
 upward and 5 downward. Owing to the 
 freedom with which the molecules move 
 on each other, there is no loss by friction, 
 and the downward pressure of 5, the 
 upward pressure of 4, and the lateral 
 pressure of 2, will each equal the pres- 
 sure exerted by 1. It makes no difference with the fact, whether 
 the pressure exerted by 1 was the result of its own weight only, 
 this weight together with the weight of overlying molecules, o? 
 both of these with still additional forces. 
 
 217. Pascal's Law. Pressure exerted any- 
 where upon a mass of 
 
 liquid is 'transmitted un- 
 diminished in all direc- 
 tions, and acts with the 
 same force upon all equal 
 surfaces and in a direc- 
 tion at right angles to 
 those surfaces. 
 
 218. An Argument from 
 
 Pascal's Law. Fill with water 
 
 a vessel of any shape, having in 
 
 Its sides apertures whose areas are 
 
 respectively as 1, 2 and 3, each 
 
 aperture being closed with a piston. 
 
 without friction and the water to have no weight ; then there will 
 
 be no motion. Suppose that the piston whose area is represented 
 
 by 1 rests upon 1000 molecules of the water ; then will the piston 
 
 at 2 rest upon 2000, and that at 3 upon 3000 molecules of water. 
 
 If now a pressure of one pound be applied to the piston at 1, this 
 
 FIG. 65. 
 Suppose the pistons to move 
 
118 
 
 FIG. 66. 
 
 pressure is distributed among the 1000 molecules upon which it 
 presses. Owing to this freedom of 
 motion, these molecules will transmit 
 this pressure to those adjacent, and 
 these to those beyond, until every 
 molecule of water in the vessel exerts 
 a pressure equal to that exerted upon 
 any one of the molecules upon which 
 the pressure was originally exerted, 
 i. e., every thousand molecules in the 
 vessel will exert a force of one pound. 
 Then will the 2000 molecules at 2 
 exert a force of two pounds and the 
 
 3000 molecules at 3 will exert a force of three pounds. 
 
 219, An Important Principle. The foregoing 
 argument may be summed up as follows: When fluids 
 are subjected to pressure, the pressure sustained bij 
 any part of the restraining surface is proportional 
 to its area. 
 
 220. Experimental Proof. The above principle, 
 which we deduced from Pascal's law, may be verified by ex- 
 periment. Provide two com- 
 municating tubes of unequal 
 
 sectional area. When water is 
 
 poured into these, it will stand 
 
 at the same height in both 
 
 tubes. If by means of a piston 
 
 the water in the smaller tube 
 
 be subjected to pressure, the 
 
 pressure will force the water 
 
 back into the larger tube and 
 
 rai se its level t h ere. To prevent 
 
 this result, a piston must be 
 
 fitted to the larger tube and held there with a force as 
 
 many times greater than the force acting upon the other 
 
 FIG. 67. 
 
STDROSTA TICS. 
 
 119 
 
 piston as the area of the larger piston is times greater than 
 the area of the smaller one. If, for example, the smallei 
 piston have 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. 
 
 221. Pascal's Experiment 
 Pascal firmly fixed a very narrow 
 tube about 30 ft. high into the head 
 of a stout cask. He then filled the 
 cask and tube with water. The 
 weight of the small amount of 
 water in the tube, producing a pres- 
 sure as many times greater than 
 itself as the inner surface of the 
 cask was times greater than the 
 sectional area of the tube, actually 
 burst the cask. 
 
 FIG. 68. 222. The Hydro- 
 
 static Bellows. The hydrostatic bellows 
 consists of two boards fastened together by 
 a broad band of stout leather f and a small 
 vertical tube communicating with the in- 
 terior. If the tube have a sectional area of 1 
 sq. cm., the downward pressure at &, its base, 
 will be one gram for every 
 centimeter of depth of water 
 in the tube. If the upper 
 board, B, have a surfacj of 
 1000 sq. cm. exposed to the 
 water in the bellows, it will 
 be pressed upward with a FIG. 69. 
 
120 
 
 HYDR OSTA TICS. 
 
 force of 1000 g. for every gram of downward pressure at I. 
 If the tube be 2 meters high, the downward pressure at E 
 will be 200 g. and the upward pressure exerted on B will 
 be 200 g. x 1000 = 200,000 g. or 200 Kg. 
 
 FIG. 70. 
 
 223. The Hydrostatic Press. The hydrostatic 
 press, often called the hydraulic, or Bramah's press, acts 
 upon the same principle. It is represented in perspective 
 by Fig. 70 and in section by Fig. 71. Instead of the 
 downward pressure produced by the weight of the water 
 in the tube, pressure is produced by the force-pump. In- 
 stead of the two boards and the leather band, a large, 
 
HYDROSTATICS. 
 
 121 
 
 strong reservoir and a piston, working water-tight, are 
 used. The substance to be pressed is placed between K, 
 the head of the piston, and an immovable plate, MN. The 
 reservoir and the cylinder of the pump are connected 
 by the tube, d. By the action of the pump, the water in 
 the cylinder, A, is subjected to pressure and this pressure 
 is transmitted undiminished to the water in B. According 
 to the law given in 219, the power exerted upon the 
 lower surfaces of the two pistons is proportional to their 
 respective areas. But the force exerted by the water upon 
 the under surface of the piston in the pump is the same as 
 the force exerted upon the water by that piston, (equality 
 of action and reaction). The piston,,is generally worked 
 by a lever of the second class, resulting in a still further 
 gain of intensity of power. If the power arm of the lever 
 be ten times as long as the weight-arm, a power of 50 Kg. 
 at the end of the lever will exert a pressure of 500 Kg. 
 upon the water in A. If the piston in A have a sectional 
 area of 1 sq. cm. and the piston in B have an area of 500 
 6 
 
122 
 
 HYDROSTA TICS. 
 
 sq. cm., then the pressure of 500 Kg. exerted by the small 
 piston will produce a pressure of 500 Kg. x 500 = 250,000 
 Kg. upon the lower surface of the large piston. He::oe 
 the following rule : 
 
 Multiply the pressure exerted by the piston of the 
 pump by the ratio between the sectional areas of 
 the two pistons. 
 
 (a.) The accompanying figure shows a device due to Ritchie of 
 Boston. It consists of a base B ; a sliding platform P guided by two 
 vertical pillars ; a bellows-formed rubber bag 
 connecting the base and platform ; and a bag or 
 flask F, fitted with a cap and cork . The flask is 
 connected with the base by flexible tubing. A 
 weight W is placed upon the platform. Fill 
 the globe with water, and elevate it ; th^ pres- 
 sure of the column will force the water into the 
 bellows, raising the weight ; lower the globe, 
 and the weight will force the water back 
 into it. 
 
 224:. Liquid Pressure Due to 
 Gravity. The pressure exerted by 
 liquids, on account of their weight, may 
 be downward, upward, or lateral. Pres- 
 sure in any other direction may be re- 
 solved into two of these. "We shall now 
 briefly consider these three kinds of 
 liquid pressure. 
 
 FIG. 72. 
 
 225. Downward Pressure. The pressure on 
 the bottom of a vessel containing a liquid, is in- 
 dependent of the quantity of the liquid or the 
 shape of the vessel, but depends upon the depth 
 and density of the fluid and the area of the 
 bottom. 
 
123 
 
 (a. ) Pascal contrived a neat experiment to verify this principle, 
 The apparatus consists of a wooden support carrying a ring into 
 which may be screwed any one of three vessels, one cylindrical, one 
 widening upward and one narrowing upward, straight or bent. On 
 he lower side of the ring is a plate a, supported by a thread from 
 
 FIG. 73. 
 
 one end of an ordinary balance. The other end of the balance 
 carries a scale-pan. Weights in the scale-pan hold the plate a 
 against the ring with a certain force. Water is carefully poured 
 into M until the pressure forces off the plate and allows a little 
 of the water to escape. A rod o marks the level of the liquid 
 when this takes place. Repeating the experiment with the same 
 weights in the scale-pan, and either P or Q in the place of M, 
 the plate will be detached when the water has reached the same 
 height although the quantity of water is much less. 
 
 226. Rule for Downward Pressure. When 
 the cylindrical .vessel, mentioned in the last paragraph, ia 
 filled, it is evident that the downward pressure is equal to 
 the weight of the contained liquid. It is further evident 
 
1*4 
 
 HYDROSTATICS. 
 
 that the weight of the counterpoise in the scale-pan, the 
 weight of the liquid contained in P, and the downward 
 pressure exerted on the plate by the liquid contained in 
 M, P, or Q are equal. We therefore deduce the following 
 rule: 
 
 To find the downward pressure on a horizontal 
 surface, find the weight of an imaginary column 
 of the given liquid, whose base is the same as the 
 given surface, and whose altitude is the same as 
 the depth of the given surface below the surface 
 of the liquid. 
 
 Note. A cubic foot of water weighs about 1000 ounces, 62| 
 pounds (more exactly 62.43 Ibs.). 
 
 22*7. Upward Pressure. Some persons have dif- 
 ficulty in understanding that liquids have upward pres- 
 sure. This upward pressure may 
 be illustrated as follows : Take a 
 glass tube open at both ends, hav- 
 ing at its lower end a glass or mica 
 disc supported from its centre 
 by a thread. If this apparatus 
 be placed in water, the tube 
 being vertical, the upward pres- 
 sure of the water will hold the 
 disc in its place. If the disc does 
 not accurately 6t the end of the 
 tube, water will be forced into the 
 tube, and gradually fill it from 
 below. If the disc does fit accu- 
 rately, as is desirable, pour water 
 carefully into the tube. In either case, the disc will be 
 
 FIG. 74. 
 
HYDROSTATICS. 
 
 125 
 
 held in place against the force of gravity until the level of 
 the water within the tube is very nearly the same as that 
 in the outer vessel. The disc will not fall until the weight 
 of the water in the tube plus the weight of the disc equals 
 the upward pressure. 
 
 Note. A lamp-chimney answers the purpose of this experiment. 
 On the glass disc pour a little fine emery powder, and on this rub 
 the end of the lamp-chimney until they fit accurately. The string 
 may be fastened to the disc with wax. 
 
 228. Rule for Upward Pressure. To find 
 the upward pressure on any horizontal surface, 
 find the weight of an imaginary column of the 
 given liquid whose base is the same as the given 
 surface, and whose altitude is the same as the 
 depth of the given surface below the surface of 
 the liquid. 
 
 229. The Hydrostatic Paradox. It may seem 
 strange at first thought that vessels whose bottoms are 
 subjected to equal pressure, like those represented in Fig. 
 75, do not exert equal pressures upon the stand supporting 
 tli em; in other words, that they do not weigh the same. 
 The difficulty will be removed by remembering that the 
 pressure on the bottom of the vessel is only one of 
 the elements which combine to produce the pres* 
 sure upon the 
 
 stand. By refer- C 
 ence to the figure, 
 which represents 
 three vessels of un- 
 equal capacity but 
 having equal pres- 
 sures upon the bot- 
 
 L H 
 
126 
 
 HYDR OSTA TICS. 
 
 torn, it will be seen that the weight may be the resultant 
 of several forces, compounded according to the first and 
 second cases specified in 80. 
 
 230. Lateral Pressure. We have already seen 
 that downward and upward pressure are proportional to 
 the depth of the liquid. Owing to the principle of equal 
 transmission of pressure in all directions, the same holds 
 
 true for lateral pressure, the 
 effects of which are some- 
 times disastrously shown by 
 the giving way of flood-gates, 
 dams, and reservoirs. 
 
 (a.) These effects of lateral 
 pressure may be safely illus- 
 trated by a tall vessel provided 
 with, a stop-cock near its base, 
 and arranged to float upon the 
 water. When this vessel is filled 
 with water, the lateral pressure 
 at any two points at the same 
 depth and opposite each other 
 will be equal. Being equal and 
 opposite they will neutralize each other and produce no motion. If 
 now the stop-cock be opened, the pressure at that point tending to 
 drive the apparatus in a certain direction, say toward the left, is re- 
 moved ; the pressure at the opposite point tending to drive the 
 vessel toward the right, being no longer opposed by its equal, will 
 now produce motion and the vessel will float in a direction opposite 
 to that of the spouting water. Instead of being floated upon water, 
 the vessel may be supported by a long thread. The same principle 
 is illustrated in Barker's Mill. (Fig. 91.) 
 
 231 . Rule for Lateral Pressure. To find the 
 pressure upon any vertical surface, find the weight 
 of an imaginary column of the liquid whose base 
 is equal to the given surface and whose altitude 
 is the same as the depth of the centre of the given 
 surface below the surface of the liquid. 
 
 FIG. 76. 
 
H YDR OSTA TICS. 127 
 
 EXERCISES. 
 
 1. What will be the pressure on a dam in 30 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 sq. yd. , 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 sq. m. is filled with water 
 to the depth of two 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 ft. of water ? 
 
 8. What will be the upward pressure upon a horizontal plate 30 
 cm. square at the depth of 8 m. of water ? 
 
 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 1728 cubic inches is two- 
 thirds full of sulphuric acid, which is 1.8 times as heavy as water. 
 Find the pressure on one side. 
 
 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. Arts. 8295 g. ' 
 
 12. In the above problem, substitute inches for centimeters, and 
 then find the pressure on the bottom. 
 
 13. What would be the total liquid pressure on a prismatic vessel 
 containing a cubic yard of water, the bottom of the vessel being 2 
 by 3 feet? 
 
 14. The lever of a hydrostatic press is 6 feet long, the piston-rod 
 being 1 foot from the fulcrum. The area of the tube is one-half 
 square inch ; that of the cylinder is 100 square inches. Find the 
 weight that may be raised by a power of 75 Ibs. 
 
 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 ? 
 
128 EQUILIBRIUM. 
 
 Recapitulation. In this section we have considered 
 Ineompressibility; the Transmission of Pres- 
 sure with Explanation and Illustration ; Pas- 
 cal's Law with Argument and Conclusion 
 therefrom; one of Pascal's Experiments ; the 
 Hydrostatic Bellows; the Hydrostatic Press; 
 Downward Pressure with experimental illustra- 
 tions; Rule for computing downward pressure ; Up- 
 ward Pressure with experimental illustrations; 
 Rule for computing upward pressure ; Lateral 
 Pressure with experimental illustrations; Rule for 
 computing lateral pressure. 
 
 ECTfON H, 
 
 V. 
 
 EQUILIBRIUM. CAPILLARITY. BUOYANCY. 
 
 232. Conditions of Liquid Rest. The force 
 of gravity tends to draw all liquid particles as near the 
 earth's centre as possible. The following are necessary 
 conditions, that a liquid may be at rest : 
 
 (1.) The free surface of the liquid must be 
 everywhere perpendicular to the force of gravity, 
 i. e., horizontal. In the case of the ocean, this condition 
 is modified by the so-called centrifugal force, which gives 
 rise to the spheroidal shape of the earth. 
 
 (2.) Every molecule must ~be subjected to equal 
 and contrary pressures in every direction. 
 
 233. Equilibrium of Liquids. A liquid of 
 small surface area is said to be level when all the points of 
 
EQUILIBRIUM. 
 
 129 
 
 its surface are in the same horizontal plane, 
 idea is expressed in the 
 familiar saying, water 
 seeks its level. This 
 is true whether the 
 liquid be placed in a 
 single vessel or in sev- 
 eral vessels that com- 
 municate with each 
 other. 
 
 234:. Communi- 
 cating Vessels. 
 
 When any liquid is 
 placed in one or more 
 
 The central 
 
 FIG. 77. 
 
 of several vessels communicating with each other, it will 
 not come to rest until it stands at the same height 
 in all of the vessels, so that all of the free surfaces lie 
 in the same horizontal plane. This principle is prettily 
 illustrated by the apparatus represented in Fig. 77. It 
 consists of such communicating vessels containing a liquid. 
 
 (a.) This important principle that " water seeks its level" finds a 
 gigantic illustration in the system of water-pipes by which water is 
 distributed in cities and large towns. Brought or pumped into an 
 elevated reservoir near the city, the water flows, in obedience to the 
 force of gravity, through all the turns and windings of all the pipes 
 connected with the reservoir, and is thus brought into thousands of 
 buildings. Into any of the rooms of any of these houses the water 
 may thus be led, provided only that the ends of the pipes be below 
 the level of the water in the reservoir. 
 
 (6.) Among the many other results of this tendency of water to 
 seek its level may be mentioned the action of springs and Artesian 
 wells, the use of locks on canals, the spirit-level, the flow of 
 streams, etc. 
 
130 CAPILLARITY. 
 
 235. Capillary Attraction. The statements 
 made concerning the equilibrium of liquids are subject to 
 one important modification. When the vertical sides of 
 the containing vessel are very near each other, as in the 
 case of small tubes, we have a manifestation of what is 
 called capillary attraction. 
 
 236. Capillary Phenomena. If a clean glass 
 rod be placed vertically in water, the water will rise above 
 its level . at the sides of the glass. If the rod be now 
 plunged into mercury, this liquid will be depressed instead 
 of raised. If the experiments be repeated, it may be noticed 
 that the water wets the glass while the mercury does not. 
 If the glass be smeared with grease and placed in water, 
 the surface of the water will be depressed ; if a clean lead 
 or zinc plate be placed in the mercury the surface of the 
 
 FIG. 78. 
 
 mercury will be raised. In this case the greased glass will 
 come out dry, no water adhering to it, while mercury will 
 adhere to the lead or zinc. This is found to be invariably 
 true: all liquids that will wet the sides of solids 
 placed in thein will be lifted, while those that do 
 not will be pushed down. In the figure, a represents 
 
ARCHIMEDES' PRINCIPLE. 131 
 
 a glass rod in water ; b, a glass tube in water ; and c, a 
 glass tube in mercury. 
 
 (a.) This so-called attraction is said to be " capillary " because 
 its phenomena are best shown in tubes as fine as a hair (Latin, 
 capttlus). If fine glass tubes be placed in water, the liquid will 
 rise, wet the tube, and have a concave surface. If they be placed in 
 mercury, the liquid will be depressed, will not wet the tube, and 
 will have a convex surface. The finer the tube, the greater the 
 capillary ascent or depression. 
 
 237. Displacement of a Fluid by an Im- 
 mersed Solid. A solid immersed in a fluid will 
 displace exactly its own bulk of the fluid. This may 
 be proved, if desirable, by plunging a heavy body of known 
 polume, as a cubic centimeter of iron, into water contained 
 in a glass vessel graduated to cubic centimeters. The 
 water will rise just as if another cubic centimeter of water 
 had been added. Thus, the volume of any irregularly 
 shaped body may be found. 
 
 238. Archimedes' Principle. The loss of 
 weight of a body immersed in a fluid equals the 
 iveijSht of the fluid which it displaces. 
 
 (a.) It is a familiar fact that a person may easily raise to the sur- 
 face of the water a stone which he cannot lift any further. When 
 an arm or leg is lifted out of the water of a bath-tub, there is a 
 sudden and very perceptible increase of weight at the surface. Let 
 us try to find a reason for these familiar truths. Imagine a cube, 
 six centimeters on a side, immersed in water so 
 that four of its surfaces are vertical and its 
 upper horizontal surface twelve centimeters 
 below the surface of the water. The lateral 
 pressures which the water exerts upon any two 
 opposite vertical surfaces are clearly equal and 
 opposite. They will have no tendency to move 
 the body. But the vertical pressures upon the 
 two horizontal surfaces are not equal. The 
 lower face will be pressed upward with a force 
 represented by the weight of (6 x 6 x 18 =) FIG. 79. 
 
132 ARCHIMEDES' PRINCIPLE. 
 
 648 cu. cm. of water (see 228) while the upper face will be pressed 
 downward with a force represented by the weight of (6x6x12 =) 
 432 cu. cm. of water. The resultant of all these forces, therefore, 
 will be a net upward pressure represented by the weight of (648 
 432=) 216 cu. cm. of water. But 216 cu. cm. is the volume of the 
 cube. This net upward pressure or buoyant effort is exerted against 
 the force of gravity, and diminishes the weight of the cube. 
 
 239. An Experimental Demonstration. 
 
 This principle of Archimedes may be experimentally veri- 
 fied as follows : From one end of a scale-beam suspend a 
 
 FIG. 80. 
 
 cylindrical bucket of metal, b, and below that a solid cyl- 
 inder, a, which accurately fits into the bucket. Counter- 
 poise with weights in the opposite scale-pan. Immerse a 
 in water and the counterpoise will descend, showing that a 
 has lost some of its weight. Carefully fill # with water. 
 It will hold exactly the quantity displaced by a. Equili- 
 brium will be restored. 
 
BUOYANCY. 133 
 
 (a.} Insert a short spout in the side of a vessel (as a tin fruit-can) 
 about an inch below the top. Fill the vessel with water and let all 
 above the level of the spout escape. This is to replace the vessel 
 of water in which a (Fig. 80) is immersed. Instead of the bucket, 
 &, use a cup placed on the scale pan. Instead of a, use any con' 
 venient solid heavier than water, as the fragment of a stone. Coun- 
 terpoise the cup and stone in the air. Immerse the stone in the 
 water and catch, in any convenient vessel, every drop of water that 
 overflows. This will be the fluid that the solid displaces. The 
 equilibrium is destroyed, but may be restored by pouring the 
 water just caught into the cup on the scale-pan. 
 
 24O. Floating Bodies. When solids of different 
 densities are thrown into a given liquid, those having den- 
 sities greater than that of the liquid 
 will sink, because the force of gravity 
 overcomes the buoyancy of the liquid ; 
 those having densities equal to that of 
 the liquid will remain at rest in any 
 position in the liquid, because the op- 
 posing forces, gravity and buoyancy, 
 are equal; those having densities less FIG. 81. 
 
 than that of the liquid will float, because the force of 
 gravity will draw them down into the liquid until they 
 displace enough of the liquid to render the buoyant effect 
 equal to the weight. Hence, a floating body displaces 
 its own weight of the fluid. This may be shown ex- 
 perimentally by filling a vase with water. "When a float- 
 ing body is placed on the surface, the water displaced will 
 overflow and may be caught. The water thus caught will 
 weigh the same as the floating body. 
 
 (a) Place the tin vessel with a spout, mentioned in the last 
 article, upon one scale-pan, and fill it with water, some of which 
 will overflow through the spout. 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 
 
134 BUOYANCY. 
 
 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. 
 
 EXERCISES. 
 
 1. How much weight will a cu. dm. of iron lose when placed in 
 
 water ? 
 
 2. How much weight would it lose in a liquid 13.6 times as heavy 
 as water ? 
 
 3. If the cu. dm. of iron weighs only 7780 g., what does your 
 answer to the 3d problem signify ? 
 
 4. How much weight would a cubic foot of stone lose in water ? 
 
 5. If 100 cu. cm. of lead weigh 1135 g. t what will it weigh in 
 water ? 
 
 6. If a brass ball weigh 83.8 g. in air and 73.8 g. in water, what is 
 its volume ? 
 
 7. If a brass ball weigh 83.8 oz. in air and 73.8 oz. in water, what 
 is its volume ? 
 
 Recapitulation. In this section we have considered 
 the Conditions of Liquids at Rest ; the Equi- 
 librium of liquids in Single and Communica- 
 ting Vessels ; the Water Supply of cities ; the 
 Equilibrium of Different Liquids in commu- 
 nicating vessels ; Capillary Attraction and some 
 of its Phenomena ; Capillary Tubes ; the 
 quantity of a Fluid Displaced by an immersed 
 solid; the Buoyancy of Fluids ; Archimedes' 
 Principle ; several Explanations of Archimedes' 
 Principle and its Experimental Verification ; 
 Floating Bodies. 
 
SPECIFIC GRAVITY. 135 
 
 ECTION III, 
 
 SPECIFIC GRAVITY. 
 
 241. What is Specific Gravity tTke specific 
 gravity of a body is the ratio betiveen its weight 
 and the weight of a like volume of some other 
 substance taken as a standard. 
 
 242. Standard of Specific Gravity. The 
 
 standard taken must be invariable. For solids and liquids, 
 the standard adopted is distilled water at a tem- 
 perature of 4 C., or 39.2 F. For aeriform bodies, the 
 standard is air or hydrogen. 
 
 (a.) The water is to be distilled, or freed from all foreign sub 
 ftances, because the weight of a given quantity of water varies with 
 the substances held in solution. It is to be at a fixed temperature 
 because of the expansion by heat. The temperature above men- 
 tioned is that of water at its greatest density. In cases where air or 
 hydrogen is taken as a standard, the additional condition of atmos- 
 pheric pressure must, for obvious reasons, be recognized. The pres- 
 sure to which all observations in this country are reduced is that 
 recorded by 30 inches (760 mm.} of the barometer. 
 
 243. Elements of the Problem. For solids 
 or liquids, the dividend is the weight of the given 
 body ; the divisor is the weight of the same bulk 
 of water ; the quotient, which is an abstract number, is 
 the specific gravity, and signifies that the given body is so 
 many times heavier than the standard. The weight of the 
 same bulk of water is found sometimes in one way and 
 sometimes in another, but in every case it is the divisor. 
 By grasping and keeping this idea, you will avoid much 
 possible confusion. Of course, when any two of these 
 three are given, the third can be found* 
 
136 
 
 SPECIFIC GRAVITY. 
 
 344. To Find the Specific Gravity of Solids* 
 
 The most common method of finding the specific grav- 
 ity of a solid heavier than water, is to find the weight of 
 the body in the air (= W), then suspend the body by a 
 light thread and und its weight in water (= W), and 
 divide the weight of the body in air by the weight of the 
 same bulk of water ( 238, Archimedes' Principle). 
 
 (a.) The method is illustrated by the following example , 
 Weight of substance in air = 58 oz. 
 Weight of substance in water = 51 oz. 
 Weight of equal bulk of water = 7^ oz. 
 Specific gravity = 58 oz. -=- 7 oz. = 7.8, An* 
 
 FIG. 82. 
 
 245. To Find the Specific Gravity of Solids 
 Lighter than Water. If the given body be lighter 
 than water, fasten to it some body heavy enough to sink 
 
SPECIFIC GRAVITY. 137 
 
 it. Find the loss in weight of the combined mass when 
 weighed in water. Do the same for the heavy body. 
 Subtract the loss of the heavy body from the loss of the 
 combined body. Divide the weight of the given body by 
 this difference. (Show that this divisor is as indicated in 
 243.) A modification of this method is to balance the 
 sinker in water. Then attach to it the light substance in 
 question, e. g., a cork, and determine the buoyant effort of the 
 cork, i. e. , the weight of its bulk of water. Divide as before. 
 
 (a.) The first method is illustrated by the following example : 
 (1.) Weight of cork and iron in air 82.4 g. 
 
 (2.) 
 (3.) 
 (4.) 
 (5.) 
 (6.) 
 (7.) 
 (8.) 
 
 " " " water 52.4 g. 
 
 water displaced by cork and iron .... 30. g. 
 
 iron in air 77.8 g 
 
 " water 67.8 g. 
 
 water displaced by iron 10. g. 
 
 cork (3) - (6). . . .20. g 
 cork in air (1) (4). . . 4.6 g 
 
 (9.) Specific gravity of the cork (8) -*- (7) 23 
 
 (10.) " " " iron (4) -s- (6), . . . 7.78 
 
 246. To Find the Specific Gravity of 
 Liquids. The principle is unchanged. A simple 
 method is as follows: 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 
 1000 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. 
 
 247. Another Simple Method. The specific gravity of 
 a liquid may be easily determined as follows : Find the loss of 
 weight of any insoluble solid in water and in the given liquid 
 
138 SPECIFIC GRAVITY. 
 
 From 238, determine what these two losses represent. Divide aa 
 before. The solid used is called a specific gravity bulb. 
 
 Other methods are sometimes used, but as they depend upon the 
 principles already explained, they need not be set forth here. 
 Some of them will be illustrated in the problems. 
 
 24:8. To Find the Specific Gravity of Gases. 
 
 The specific gravity of an aeriform body is always found 
 by comparing the weight of equal volumes of the standard 
 (air or hydrogen) and of the given substance. The method 
 is strictly analogous to the one first given for liquids. The 
 air is removed from the flask with an air-pump an in- 
 strument to be studied soon. The accurate determination 
 of the specific gravity of gases presents many practical dif- 
 ficulties which cannot be considered in this place. 
 
 Note. The weight of any solid or liquid (in grams per cu. cm.) 
 Tepresents its specific gravity. Bodies are commonly weighed in 
 the air. But, in common with all other fluid bodies, the air has 
 weight and therefore ( 238) diminishes the true weight of all bodies 
 thus weighed. This diminution is generally disregarded, but in 
 certain delicate operations it must be carefully considered. 
 
 249. Hydrometers. Instruments, called hydrom- 
 eters or areometers, are made for the more convenient de- 
 termination of specific gravity. They dispense with the 
 use of the balance, an instrument requiring careful hand- 
 ling and preservation. Hydrometers are of two kinds : 
 (1.) Hydrometers of constant volume, as Nicholson's. 
 (2.) Hydrometers of constant weight, as Beaume's. 
 
 250. Nicholson's Hydrometer. Nicholson's 
 hydrometer is a hollow cylinder carrying at its lower end 
 a basket d, heavy enough to keep the apparatus upright 
 when floated on 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 
 
SPECIFIC GRAVITY. 
 
 139 
 
 FIG. 83. 
 
 the apparatus to a fixed point marked on the rod (as c). 
 The given body, which must weigh less than W, is placed 
 m the pan, and enough weights (= w) added to sink the 
 point c to the water line. It is evident that the weight of 
 the given body is W w. It is now taken from the pan 
 and placed in the basket, when additional weights (= x) 
 must be added to sink the point c to the water line. 
 
 W ~ w 
 
 Sp. Gr. = 
 251. Fahrenheit's 
 
 JC 
 
 Hy- 
 
 drometer. Fahrenheit's Hy- 
 drometer is similar in form to 
 Nicholson's, but is made of glass 
 instead of metal, so that it may 
 be used in any liquid. The bas- 
 ket is replaced by a bulb loaded 
 with shot or mercury. The 
 weight of the instrument ( W ) 
 is accurately determined. The 
 instrument is placed in water, 
 
 FIG. 84. 
 
140 
 
 SPECIFIC GRAVITY. 
 
 and a weight (= w\ sufficient to sink the point c to the 
 water line, is placed in the pan. The weight of water dis- 
 placed by the instrument = W + w. The hydrometer is 
 now removed, wiped dry, and placed in the given liquid. 
 A weight (= z), sufficient to sink the hydrometer to c, is 
 placed in the pan. 
 
 Nate. A Nicholson's hydrometer may be used as a Fahrenheit's 
 in any liquid which has no chemical action upon the metal of which 
 it is made. Neither of these hydrometers gives results as accurate 
 as those obtained by the methods previously given. 
 
 252. Constant Weight Hydrometers. A 
 
 hydrometer of constant weight consists of a glass tube neai 
 
 the bottom of which are two bulbs. The lower and smallei 
 
 bulb is loaded with mercury or shot. 
 
 The tube and upper bulb containing air, 
 
 the instrument is lighter than water. 
 
 The point to which it sinks when placed 
 
 in pure water is generally marked zero. 
 
 The tube is graduated above and below 
 
 zero, the graduation bein'g sometimes 
 
 upon a piece of paper placed within the 
 
 tube. As a long stem would be incon- 
 
 venient, it is customary to have two in- 
 
 struments, one having zero near the 
 
 top, for liquids heavier than water ; the 
 
 other having zero near the bulb, for 
 
 liquids lighter than water. The scale of graduation is arbi- 
 
 trary, varying with the purpose for which the instrument is 
 
 intended. These instruments are more frequently used to 
 
 determine the degree of concentration or dilution of certain 
 
 FIG. 85. 
 
SPECIFIC GRAVITY. 
 
 141 
 
 liquids, as acids, alcohols, milk, solutions of sugar, etc., 
 than their specific gravities proper. According to their 
 uses they are known as acidometers, alcoholometers, lac- 
 tometers, saccharometers, etc. They all depend upon the 
 principle that a floating body will displace its own weight 
 of the liquid upon which it floats, and, consequently, a 
 greater volume of light than of heavy liquids. 
 
 253. Tables of Reference. (1.) Specific gravities 
 of some solids : 
 
 Brass... . 8.38 
 
 Iridium 23.00 
 
 Platinum 22.069 
 
 Gold (forged)... 19.36 
 
 Lead (cast) 11.35 
 
 Silver (cast).... 10. 47 
 Copper (cast). .. 8.79 
 
 Iron (bar) 7.78 
 
 Tin (cast) 7.29 
 
 Iron (cast) 7.21 
 
 Zinc (cast) 6.86 
 
 Flint Glass...... 3.33 
 
 Marble (statuary). 2. 83 
 Anthracite Coal. .1.80 
 Bituminous Coal. 1.25 
 
 Ice (melting) 92 
 
 Pine 65 
 
 Cork. . . .24 
 
 (2.) Specific gravities of some liquids: 
 
 Mercury 13.6 
 
 Sulphuric Acid.. 1.84 
 Hydrochloric Acid 1.24 
 
 Nitric Acid 1.22 
 
 Milk 1.03 
 
 Sea Water.. ..1.026 
 
 Turpentine 87 
 
 Alcohol 8 
 
 Ether.. . .72 
 
 (3.) Specific gravities of some gases : (Barometer = 760 
 mm. - 9 Temperature = 32 F. or 0C.) 
 
 Am = STANDARD. 
 
 Hydroiodic Acid 4.41 
 
 Carbon Dioxide 1.52 
 
 Oxygen 1.1 
 
 Air 1.0 
 
 Nitrogen 97 
 
 Hydrogen 06* 
 
 HYDROGEN = STANDARD. 
 
 Hydroiodic Acid 64 
 
 Carbon Dioxide 22 
 
 Oxygen 16 
 
 Air 14.5 
 
 Nitrogen 14 
 
 Hydrogen 1 
 
 Note. The weight of a cubic foot of any solid or liquid is equal 
 to 62.421 Ibs. avoirdupois multiplied by its specific gravity. 
 
 The weight of a cubic centimeter of any solid or liquid is equal 
 to 1 gram multiplied by its specific gravity. 
 
 The weight of a liter (or cu. dm.) of any solid or liquid is equal 
 to 1 Kg. multiplied by its specific gravity. 
 
 The tables above give only average densities. Any given speci 
 men may vary from the figures there given. 
 
142 
 
 SPECIFIC GRAVITY. 
 
 EXERCISES. 
 
 Note. Be on the alert to recognize Archimedes' Principle in 
 disguise. Consider the weight of water 62| Ibs. per cubic foot. 
 
 The numbers obtained for the right hand column may be either 
 "olus or minus ; the former sign denotes weight in the fluid ; the 
 /atter, the load it could support in the fluid. 
 
 
 Weight 
 
 Weight 
 
 Loss of 
 
 Spec. 
 
 
 ANY 
 
 FLUID. 
 
 
 in Air. 
 
 in Water. 
 
 Weight in 
 Water. 
 
 Grav. 
 
 Volume. 
 
 Sp. Qr. of 
 
 Weight in 
 
 1 
 
 1500 Ibs. 
 
 1000 Ibs. 
 
 ? 
 
 ? 
 
 ?cuft. 
 
 1.5 
 
 ? 
 
 2 
 
 5000 oz. 
 
 V 
 
 1500 oz. 
 
 v 
 
 ? 
 
 ? 
 
 2000 oz. 
 
 3 
 
 ? 
 
 1875 g. 
 
 
 2 
 
 ? 
 
 1.8 
 
 9 
 
 4 
 
 ? 
 
 9375 g. 
 
 
 ? 
 
 ? 
 
 1.5 
 
 4687.5 g. 
 
 5 
 
 ? 
 
 ? 
 
 
 7.5 
 
 300 cu. cm. 
 
 2.5 
 
 ! 
 
 6 
 
 ? 
 
 1125 Its. 
 
 
 ? 
 
 ? 
 
 3 
 
 875 Ibs. 
 
 7 
 
 ? 
 
 ? 
 
 
 ? 
 
 8 cu. ft. 
 
 13.6 
 
 2700 Ibe. 
 
 8 
 
 ? 
 
 ? 
 
 
 6.86 
 
 5 cu. dm. 
 
 13.6 
 
 ? 
 
 9 
 
 IKg. 
 
 ? 
 
 ? 
 
 1 
 
 ? 
 
 ? . 
 
 200 g. 
 
 20 
 
 ? 
 
 ? 
 
 ? 
 
 2.83 
 
 ?0 cu. ft. 
 
 .8 
 
 ? 
 
 11. A bone weighs 2.6 ounces in water and 6.6 ounces in air; 
 what is its specific gravity ? 
 
 12. A body weighing 453 g. weighs in water 429.6 g.; what is its 
 specific gravity ? 
 
 13. A piece of metal weighing 52.35 g. is placed in a cup filled 
 with water. The overflowing water weighed 5 g. What was the 
 specific gravity of the metal ? 
 
 14. (a.) A solid weighing 695 g. loses in water 83 g. ; what is its 
 specific gravity ; (6) how much would it weigh in alcohol of specific 
 gravity 0.792? 
 
 15. A 1000 grain bottle will hold 708 grains of benzoline. Find 
 the specific gravity of the benzoline. 
 
 16. A solid which weighs 2.4554 oz. in air, weighs only 2.0778 oz. 
 in water. Find its specific gravity. 
 
 17. A specimen of gold which weighs 4.6764 g. in air loses 0.2447 
 g. weight when weighed in water. Find its specific gravity. 
 
 18. A ball weighing 970 grs., weighs in water 895 grs., in alcohol 
 910 grs.; find the specific gravity of the alcohol. 
 
 19. A body loses 25 grs. in water, 23 grs. in oil, and 19 grs. in 
 alcohol. Required the specific gravity of the oil and the alcohol. 
 
SPECIFIC GRAVITY. 143 
 
 30. A body weighing 1536 g. weighs in water 1283 g.; what is its 
 specific gravity ? 
 
 21. Calculate the specific gravity of sea water from the following 
 
 data. 
 
 Weight of bottle empty 8.5305 g. 
 
 " filled with distilled water.... 7.6722 g. 
 
 ' "';, sea " ... 7.7849 g. 
 
 22. Determine the specific gravity of a piece of wood from the 
 following data : Weight of wood in air, 4 g. ; weight of sinker, 
 lOg. ; weight of wood and sinker under water 8.5 g.; specific 
 gravity of sinker, 10.5. 
 
 23. Apiece of a certain metal weighs 3.7395 g. in air ; 1.5780 g. 
 in water ; 2.2896 g. in another liquid. Calculate the specific grav- 
 ities of the metal and of the unknown liquid. 
 
 24. Find the specific gravity of a piece of glass if a fragment of 
 it weigh 2160 grains in air, and 1511^ grains in water. 
 
 25. A lump of ice weighing 8 Ibs. is fastened to 16 Ibs. of lead. 
 In water the lead alone weighs 14.6 Ibs. while the lead and ice weigh 
 13.712 Ibs. Find the specific gravity of the ice. 
 
 26. A piece of lead weighing 600 g., weighs 545 g. in water and 
 557 g. in alcohol. (.) Find the sp. gr. of the lead ; (&) of the 
 alcohol, (c.) Find the bulk of the lead. 
 
 27. A person can just lift a 300 pound stone in the water ; what 
 is his lifting capacity in the air (specific gravity of stone = 2.5) ? 
 
 In the next three examples, the weight of the empty flask is not 
 taken into account. 
 
 28. A liter flask holds 870 g. of turpentine ; required the sp. gr. 
 of the turpentine. 
 
 29. A liter flask, containing 675 g. of water, on having its remain- 
 ing space filled with fragments of a mineral, was found to weigh 
 1487.5 g. ; required the specific gravity of the mineral. 
 
 30. A liter flask was four-fifths filled with water ; the remaining 
 space being filled with sand the weight was found to be 1350 g. j 
 required the specific gravity of the sand. 
 
 31. A weight of 1000 grs. will sink a certain Nicholson's hydrom- 
 eter to a mark on the rod carrying a pan. A piece of brass plus 40 
 grs. will sink it to the same mark. When the brass is taken from 
 the pan and placed in the basket, it requires 160 grs. in the pan to 
 sink the hydrometer to t^e same mark on the rod. Find the specific 
 gravity of the brass. 
 
 32. A Fahrenheit's hydrometer, which weighs 2000 grs., requires 
 1000 grs. in the pan to sink it to a certain depth in water. It requires 
 3400 grs. in the pan to sink it to the same depth in sulphuric acid. 
 Find the specific gravity of the acid. 
 
144 SPECTFIC ORAVTTT. 
 
 33. 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 leturned 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 
 specific gravity of the given body. 
 
 34. The volume of the earth is 1,082,842,000,000,000 cu. Km. 
 Calculate its weight on the supposition that its average density is 
 5.6604. 
 
 35. A bottle holds 2545 mg. of alcohol (sp. gr. = 0,8095) ; 42740 
 mg. of mercury ; 5829 mg. of sulphuric acid. Calculate the specific 
 gravities of the mercury and of the acid. 
 
 86. 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 specific gravity 
 of the cork. 
 
 37. A piece of wood weighing 300 grs. has tied to it a piece of 
 Jead weighing 600 grs.; weighed together in water they weigh 472.5 
 grs. The specific gravity of lead being 11.35, (a) what does the lead 
 weigh in water ; (&) what is the specific gravity of the wood ? 
 
 38. Calculate the specific gravity of a mineral water from the 
 following data : 
 
 Weight of a bottle empty 14.1256 g. 
 
 " " filled with distilled water. .111.1370 g. 
 
 " mineral " .. 111.7050 g. 
 
 89. A Fahrenheit's hydrometer weighs 618 grs. It requires 93 grs. 
 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 grs. to sink it to the 
 same mark. Find the specific gravity of the oil. 
 
 40. A platinum ball weighs 330 g. in air, 315 g. in water and 303 g. 
 in sulphuric acid. Find the specific gravities (a) of the ball ; (ft) of 
 the acid, (c.) What is the volume of the ball ? 
 
 41. A hollow ball of iron weighs 1 Kg. What must be its least 
 volume to float on water ? 
 
 42. A piece of cork weighing 30 g. in air, was attached to 10 cu. 
 cm. of lead. Loss of both in water = 159 g. Required the specific 
 gravity of the cork. 
 
 43. A body whose specific gravity = 2.8, weighs 37 g. Required 
 its weight in water. 
 
Jl TDK KINETICS* 145 
 
 44. What would a cubic foot of coal (sp.gr. = 2.4) ^eigh in a 
 solution of potash (sp. gr. = 1.2)? 
 
 45. A platinum ball (sp. gr. = 22) weighing 300 g. in air will 
 weigh how much in mercury (sp. gr. = 13.6) ? 
 
 46. 500 cu. cm. of iron, specific gravity 7.8, floats on mercury ; 
 with what force is it buoyed up ? 
 
 47. An areometer weighing 600 grs. sinks in water displacing a 
 volume = v ; in a certain acid, displacing a volume = -f$ v ; find 
 the specific gravity of the acid. 
 
 Recapitulation. In this section we have considered 
 the Definition of Specific Gravity ; the Stan- 
 dards agreed upon ; the Two Elements in specific 
 gravity problems; the Rule for finding the sp.gr. ol 
 Solids heavier than Water ; the same for Solids 
 lighter than Water ; the same for Liquids ; the 
 same for Gases ; the construction and method^ of 
 using Hydrometers ; Tables of specific gravities, 
 and some of the uses that may be made of them. 
 
 XgJECTJON IV, 
 
 H.YDROKI NETICS. 
 
 254:. Telocity of Spouting Liquids. li a 
 
 vessel having apertures ir. the side, similar to the one 
 represented in Fig. 86, be filled with water, the liquid will 
 escape from each of the apertures, but with different veloc- 
 ities. Were it not for the resistance of the air, friction, 
 and the effect of the falling particles, the water issuing at 
 V would ascend to the level of the water in the vessel j 
 i. e., the initial velocity of the water at V would carry it 
 through the vertical distance Vli. But when equal verti- 
 7 
 
FIG. 86 
 
 sal distances are passed over the initial velocity of an ascend 
 ing body is the same as the final velocity of a falling body. 
 ( 132.) Hence, the velocity of the water as it issues at Via 
 the same that it would acquire in freely falling the vertical 
 distance h V. This velocity is caused by lateral pressure. 
 This lateral pressure will be the same at P, which is at the 
 same distance below the level of the liquid. Therefore, the 
 velocity at P will equal the velocity at V. Hence the fol- 
 lowing law: The velocity of a stream flowing from 
 an orifice is the same as that acquired by a body 
 freely falling from a- height equal to the head of 
 the liquid. 
 
 (a.) The Tiead is the vertical distance from the centre of the 
 orifice to the surface of the liquid. 
 
 (6.) With what velocity will water issue from an orifice 144.72 ft. 
 Drtow the surface of the liquid ? 
 
 8 = \gt* ( 128 [8].) 
 
 144.72 = 16.08** /. 9 = * 8 . 
 
 8 = r. 
 
 V = fft. ( 128 [1].) 
 
 t? = 82.16 ft. x 3 = 96.48 ft. An*. 
 
BTbROKINETICS. 14? 
 
 (<?.) In the solution above we were obliged to find the number of 
 seconds that would be required for a body to fall a distance equal 
 to the head, before we could use the formula for the velocity. It is 
 desirable, if possible, to shorten this circuitous process from two 
 stages to one. This we may do as follows : 
 
 Substituting this value of t in the formula, v = gt t 
 
 But li (the head) = 8. Substituting this value of 8 in the last 
 equation, we have, for the velocity of streams issuing from orifices, 
 the following formula : 
 
 v = 
 
 The value of g being taken in feet, A and -v must represent feet 
 also. 
 
 (d.) With what velocity will water issue from an orifice under a 
 head of 144.72 feet ? 
 9 = 8.02 fi 
 
 v = 8.02 /14472~= 8.02 x 12.03 = 96.48, the number of feet. 
 
 255. Orifice of Greatest Range. The path of 
 a stream spouting in any other than a vertical direction is 
 the curve called a parabola ( 135). The range of such a 
 stream will be the greatest when it issues from an orifice 
 midway between the surface of the liquid and the level of 
 the place where the stream strikes. Streams flowing from 
 orifices equidistant above and below this orifice of greatest 
 range will have equal ranges (See Fig. 86.) The range, 
 in any such case, may be calculated by the laws of pro 
 jectiles. 
 
 (a.) Given an aperture four feet below the surface and 20 ft, 
 above the point where the water strikes, to find the range of the 
 jet 
 
 v = 8.02 ^/h = 8.02 x 2 = 16.04 ft. per second. 
 8=W 
 
 20 = 16.08* 8 /. t = 1.11 + sec. 
 Range = 16.04 ft. x 1.11 = 17.8044 ft. 
 
148 HYDRO KINETIC '& 
 
 256. Volume Discharged under a Constant 
 Head. To find the volume discharged in a given 
 time under a constant head, multiply the area of 
 the orifice by the velocity, and this product ~by the 
 number of seconds. 
 
 (a.) Suppose that as soon as the water escapes it freezes and re- 
 tains the form and size given it by the aperture. It will then be 
 evident that the water escaping in one second will form a prism 
 whose section will be the area of the orifice and whose length will be 
 the same as the velocity of the jet. The product of these dimensions 
 will give the volume of the imaginary prism, one of which is formed 
 every second. Care must be had that the velocity and the dimen- 
 sions of the orifice are of the same denomination. The theoretical 
 result computed as above directed, will exceed the amount actually 
 discharged. Why ? (See Appendix E.) 
 
 251. The Flow of Liquids through Hori- 
 zontal Pipes. When liquids from a reservoir are 
 made to flow through pipes of considerable length, the 
 discharge is far less than that due to the head. 
 This is chiefly owing to the friction of the liquid particles 
 against the sides of the pipe. A horizontal inch-pipe 200 
 feet long will not discharge much, if any, more than a 
 quarter as much water as a very short pipe of the same 
 size, the head heing the same. Frequent and abrupt 
 bends in the pipe retard the flow, and must be provided for 
 by an increase in the size of the pipe, or an increase of 
 pressure. 
 
 258. The Flow of Rivers. The friction of a 
 stream against its solid bed fortunately retards the velocity 
 of the water. Otherwise the velocity of the current at 
 the mouth of a river, whose head is elevated 1000 feet 
 above its mouth, would be about 170 miles per hour. 
 Such a current would be disastrous beyond description 
 
HYDR OKINETICS. 
 
 The ordinary river current is from three to five miles pel 
 hour. 
 
 259. The Flow of 
 Liquids through Verti- 
 cal Pipes. Liquids flow ing 
 freely through vertical pipes 
 exert no lateral pressure. 
 The liquid will not wholly 
 fill the tube, but will be sur- 
 rounded by a thin film of air. 
 These air particles will be 
 dragged down by the adhe- 
 sion of the falling liquid. 
 
 (a.) If a small tube, t, be inserted 
 near the top of the vertical pipe a 
 current of air will be forced, 
 through it and down the pipe. 
 This air current may be utilized 
 for blow-pipe and other purposes. 
 With a long discharge pipe, the 
 force with which the air is drawn 
 through t may be used to remove 
 the air from a vessel. R. The ap- 
 
 FIG. 87. 
 paratus then becomes a Sprengel's or Bunsen's air-pump. ( 290, 291.) 
 
 26O. Water-Power. Water may be used to turn a 
 wheel and thus move machinery by its weight, the force 
 of the current, or both. The wheels thus turned are of 
 different kinds; the availability of any one being deter- 
 mined by the nature of the water supply and the work to 
 be done. 
 
 (a.} The water supply depends upon rains ; rains depend upon 
 evaporation ; evaporation is produced by solar heat. The energy of 
 water-power is thus traced to the sun as its source, 
 
150 
 
 HYDR OKINETICS. 
 
 261. The Overshot Wheel. In the overshot 
 wheel, the water falls into buckets at the top and, by its 
 
 weight, aided by 
 the force of the 
 current, turns the 
 wheel. As the 
 
 -- 
 
 * ,' .1 buckets are grad- 
 ually in verted, the 
 
 FIG. 
 
 water is emptied 
 ; _ } and the load thus 
 removed from the 
 other side of the 
 wheel. Such 
 wheels require 
 
 only little water but a considerable fall. It is said that they 
 have been made nearly 100 feet in diameter. The water 
 is led to the top of the wheel by a sluice, v s. 
 
 262. The Breast Wheel. In the breast wheel, 
 the water acts upon float boards fixed perpendicular to the 
 circumference. The stream being received at or near the 
 level of the axis, both the weight 
 of the water and the force of 
 the current may 
 be turned to 
 account. 
 
 FIG. 89. 
 
 263. The Undershot Wheel. In the under- 
 shot wheel, the stream strikes, near the bottom of the 
 
H YDR OKINETICS. 
 
 151 
 
 wheel, against a few float boards, which are more or less 
 
 submerged, 
 and thus acts 
 by the force of 
 the current. 
 
 Note. In point 
 of efficiency, these 
 wheels rank inthe 
 order above given , 
 utilizing from 80 
 FlG - 9- to 25 per cent, of 
 
 the total energy (e. g., foot-pounds) of the stream. 
 
 264:. The Reac- 
 tion Wheel. The 
 
 reaction wheel is well 
 illustrated by Barker's 
 Mill, represented in Fig. 
 91. It consists essential- 
 ly of a vertical tube con- 
 necting with horizontal 
 tubular arms at the bot- 
 tom. The ends of these 
 arms are bent in the 
 same direction, and are 
 open at their ends. The 
 apparatus is supported 
 on a pivot so as to move 
 freely. Water is poured 
 into the upper end of the 
 vertical cylinder, and es- 
 capes through the open- 
 ings a and b, at the FIG. 91. 
 bent ends of the arms. The wheel revolves in a direction 
 
152 . RYDR OKINETICS. 
 
 opposite to that of the water jets. The principle involved 
 was explained in 230. (See Appendix F.) 
 
 265. The Turbine Wheel. The turbine wheel, of 
 which there are many varieties, is the most effective water- 
 wheel yet known, utilizing, in some cases, 85 per cent, of 
 the total energy of the stream. 
 
 FIG. 92. 
 
 (a.) Fig. 92 represents one form in perspective and in horizontal 
 section through the centre of the wheel and case complete. The 
 wheel B and the enclosing case D are placed on the floor of a pen- 
 stock wholly submerged in water, under the pressure of a consid- 
 erable 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, best made of boiler-iron. 
 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 communicates 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 D is covered with a 
 top T, which protects the wheel from the vertical pressure of the 
 water. The axis of the wheel passes through the centre of this 
 cover. The openings by which the water passes to the wheel are 
 called chutes. Sometimes a cylindrical collar, (7, is placed betweei? 
 
HYDROKINETICS. 153 
 
 the wheel B and the outer case D. This collar, called a registei 
 gate, may be turned about its axis by the action of a pinion, P, 
 upon teeth placed upon the circumference of (7. By means of the 
 register gate, the size of the chute may be reduced and the amount 
 of water used thus diminished. The water passages, to and from 
 the wheel, should be of such a size that the velocity of the water 
 running through them shall not exceed one and a half feet per 
 ^econd. 
 
 266. Lateral Pressure of Running Water. 
 
 If water could flow through a pipe unimpeded (v = 8.02 
 A/7*), there would be no lateral pressure. But as the 
 velocity is lessened by friction and other causes, this lateral 
 pressure begins to be felt ; when the velocity is destroyed, 
 lateral pressure has its full force again. Thus, a pipe is 
 less likely to burst when carrying running water than when 
 filled with water at rest. 
 
 267. Bursting Pressure. If a current of water 
 flowing in a pipe be suddenly stopped, much of its mo- 
 mentum will be changed to lateral or bursting pressure. 
 This takes place whenever the faucet of a water-pipe is 
 suddenly closed. Plumbers -frequently leave the ends of 
 such pipes in a vertical position so that a quantity of air 
 may be confined between the closed end of the pipe and 
 the water below. This air by its elasticity acts as a pad or 
 cushion, thus lessening the suddenness of the shock and 
 preventing accidents.- 
 
 (a.) This principle is practically applied in the " hydraulic ram," 
 a contrivance by which the impulse of running water when sud- 
 denly checked may be used to raise a part of the water through a 
 vertical distance greater than the head. 
 
 EXERCISES. 
 
 . 1. A stream of water issues from an orifice at the bottom of a 
 vessel containing water 169 feet deep. Give the velocity of the 
 stream ? 
 
154 HTDROKINETICS. 
 
 2. How much water issues in one hour from the orifice in the 
 bottom of a vessel in which the water always stands 12 feet high, 
 the orifice being ^ of a square inch 'I 
 
 3. How much water per hour will be delivered from an orifice of 
 2 inches area, 25 feet below the surface of a tank kept full, no 
 allowance being made for friction, etc. ? 
 
 4. From an orifice, water spouts with a velocity of 96.24 feet. 
 What is the head? Ans. 144ft. 
 
 5. An orifice is 16.08 feet above a horizontal floor. Water spouts 
 to the distance of 80.2 feet. Required the head. 
 
 6. Determine the formula for the velocity of spouting liquids, 
 using meters instead of feet. Ans. v = 4.427 Vh. 
 
 7. A stream of water issues from an orifice under a head of 25 
 \neters. Find the velocity of the stream. 
 
 8. How many liters of water will flow through an opening of 10 
 ^q. cm. in 20 seconds, the head being kept at 86 m. ? Ans. 531.24 1. 
 
 9. How long will it take for 442,700 cu. cm. of water to escape 
 through a hole 1 centimeter square and 100 meters below the surface 
 <>f the liquid Tf 
 
 10. How long will it take to empty a tank having a base 3 m. by 
 4 m. the water being 5 m. deep, by means of a sq. cm. hole in its 
 bottom ? 
 
 Recapitulation. In this section we have considered 
 the Velocity of spouting liquids ; the orifice of Great- 
 est Range ; the method of computing the Volume 
 discharged by an orifice when the Head is con- 
 stant ; the flow of liquids through Pipes and Rivers ; 
 the uses of Water-power ; the five kinds of Water- 
 wheels ; the Lateral Pressure of running water; 
 the Bursting Pressure when the current is suddenly 
 stopped. 
 
 REVIEW QUESTIONS AND EXERCISES. 
 
 1. (a.) Define Physics. (6.) Define and illustrate four universal 
 properties of matter. 
 
 2. (a.) What is the difference between momentum and energy? 
 (&.) Find the momentum and (c.) kinetic energy of a 15 Ib. ball 
 moving fifty feet per second. 
 
REVIEW QUESTIONS. 155 
 
 3. (a.) Give the third law of motion and illustrate it. (6.) Give 
 the law of reflected motion. 
 
 4. (a.) What would a 1470 Ib. ball weigh at 10,000 miles above 
 the earth t (&.) Give the law that you use. 
 
 5. (a.) How far will a body fall during the fourth second? (b.) 
 How far in four seconds ? (c.) What will be its final velocity ? 
 
 6. The crank of an endless screw whose threads are an inch apart 
 describes a circuit of 72 inches. The screw acts on the toothed 
 edge of a wheel whose circumference is 90 inches and that of its axle 
 12 inches. On the axle is wound a cord which acts on a set of pul- 
 leys three in each block, the force of which pulleys is exerted on 
 the wheel of a wheel and axle, the wheel being 4 feet and the axle 
 8 inches in diameter. What weight on the axle will be lifted by a 
 power of 30 Ibs. at the crank, allowing for a loss of one-third by 
 friction ? 
 
 7. (a.) What is the length of a pendulum making 25 vibrations a 
 minute ? (&.) How many vibrations are made per minute by a pen- 
 dulum 25 inches long? 
 
 8. (.) What is a horse-power ? (&.) A unit of work ? (c.) If a two 
 horse-power engine can j ust throw 1056 Ibs. of water to the top of a 
 steeple in 2 minutes, what is the height of the steeple ? 
 
 9. (a.) What are the laws of machines? (&.) The facts concerning 
 friction? (c.) What is a lever? (d.) Figure a lever of each kind. 
 In a lever of the second kind the power is 4 J, the weight is 40|, the 
 distance of the power from the weight is 18 in. (e.) What is the 
 length of the lever ? (/.) What the length of the short arm? 
 
 10. If the diameters of the wheel and of the axle of a wheel and 
 axle are respectively 60 in. and 6 in., and the power is 150 Ibs., what 
 weight will be sustained ? 
 
 11. (a.) Draw a system of 3 fixed and 2 movable pulleys. (&.) If 
 the power be 90 and the friction one- third, what weight can be 
 raised? 
 
 12. (a.) A weight of 12 pounds, hanging from one end of a five 
 foot lever considered as having no weight, balances a weight of 8 
 pounds at the other end. Find how far the fulcrum ought to be 
 moved for the weights to balance when each is increased by two 
 pounds. (&.) Give the law for the screw ? 
 
 13. A capstan, 14 inches in diameter, has four levers each 7 feet 
 long. At the end of each lever a man is pushing with a force of 
 42 pounds. What is the effect produced, one-fourth of the energy 
 expended being lost by friction ? 
 
PNEUMATICS. 
 
 ECTfON 
 
 THE ATMOSPHERE AND ATMOSPHERIC PRESSURE. 
 
 268. What is Pneumatics t Pneumatics is 
 that branch of Physios which treats of aeriform 
 bodies, their mechanical properties, and the ma- 
 chines by which they are used. 
 
 269. Tension of Gases. However small their 
 quantity, gases always fill the vessels in which they 
 
 are held. If a bladder or India rub- 
 ber bag, partly filled with air, and 
 having the opening well closed, be 
 placed under the receiver of an air- 
 pump, the bladder or bag will be fully 
 distended, as shown in the figure, 
 when the air surrounding the bladder 
 is pumped out. The flexible walls 
 are pushed out by the impact of the 
 moving molecules confined within. (See 62.) 
 
 270. The Type. As water was, for obvious reasons, 
 taken as the type of liquids, so atmospheric air will be 
 
 FIG. 93. 
 
ATMOSPHERIC PRESSURE. 157 
 
 taken as the type of aeriform bodies. Whatever 
 mechanical properties are shown as belonging to air may 
 be understood as belonging to all gases. 
 
 271. The Aerial Ocean. Air is chiefly a mixture 
 of two gases, oxygen and nitrogen, in the proportions of 
 one to four by volume. It is believed that the atmosphere 
 at its upper limit presents a definite surface like that of 
 the sea ; that disturbing causes produce waves there just as 
 they do on the sea, but that, by reason of greater mobility 
 and other causes, the waves on the surface of this aerial 
 ocean are much larger than any ever seen on the surface 
 of the liquid ocean. The depth of this aerial ocean has 
 been variously estimated at from fifty to two hundred miles. 
 
 272. Weight of Air. Being a form of matter, air 
 has weight. This may be shown by experiment. A hol- 
 low globe of glass or metal, having a capacity of several 
 liters and provided with a stop-cock, is carefully weighed 
 on a delicate balance. The air is then removed from the 
 globe by an air-pump, the stop-cock closed, and the empty 
 globe weighed carefully. The second weight will be less 
 than the first, the difference between the two being the 
 weight of the air removed. Under ordinary conditions a 
 cubic inch of air weighs about 0.31 grains ; a liter of ail 
 weighs about 1.293 g., being thus about -^ as heavy ai 
 water. (See Appendix G.) 
 
 273. Atmospheric Pressure. Having weight, 
 such a quantity of air must exert a great pressure upon 
 the surface of the earth and all bodies found there. This 
 atmospheric pressure necessarily decreases as we ascend 
 from the earth's surface. For any surface, at any ele- 
 vation, the upward, downward, or lateral pressure may be 
 
158 ATMOSPHERIC PRESSURE. 
 
 computed in the same way as for liquids ( 226, 228 and 
 231). Owing to the great compressibility of aeriform 
 bodies, the lower layers of the atmosphere are much more 
 dense than the upper ones, but density and pressure alike 
 are constant in value throughout any horizontal layer. 
 The weight of a column of air one inch square extending 
 i'rom the sea-level to the upper limit of the atmosphere is 
 about fifteen pounds; a similar column, a cm. square, 
 weighs about 1 Kg. We express this by saying that the 
 atmospheric pressure at the sea-level is fifteen 
 pounds to the square inch, or 1 Kg. to the sq. cm. 
 Several illustrations of atmospheric pressure will be given 
 after we have considered the air-pump. 
 
 274. Torricelli's Experiment. The intensity oi 
 this pressure may be measured as fol- 
 lows: Take a glass tube a yard long, 
 about a quarter of an inch in internal 
 diameter. Close one end and fill the 
 tube with mercury. Cover the other 
 end with the thumb or finger and in- 
 vert the tube, placing the open end 
 in a bath of mercury. Upon removing 
 the thumb, the mercury will sink, 
 oscillate, and finally come to rest at 
 a height of about 30 inches, or 760 
 mm.) above the level of the mercury 
 in the bath. This historical experi- 
 ment was first performed in 1643, 
 by Torricelli, a pupil of Galileo. 
 The apparatus used, when properly 
 graduated, becomes a barometer, FIG. 94. 
 
ATMOSPHERIC PRESSURE. 159 
 
 275. What Supports the Mercury Column ? 
 
 To answer this very important question, consider the 
 horizontal layer of mercury molecules in the tube at the 
 level of the liquid in the bath. Under ordinary circum- 
 stances, they would hold their position by virtue of the 
 tendency of liquids to seek their level. But in this case, 
 they hold it against the downward pressure caused by the 
 weight of the mercury column above, which is equivalent 
 to fifteen pounds to the square inch. Being in a condi- 
 tion of equilibrium, they must be acted upon by an upward 
 pressure of fifteen pounds to the square inch. It is evident 
 that the pressure of the mercury in the bath is not able to 
 do this work, its powers being fully tasked in supporting 
 the mercury in the tube up to the level of the particular 
 molecules now under consideration. This upward pres- 
 sure then must be due to some force acting upon the sur- 
 face of tho mercury, and transmitted undiminished by that 
 liquid. The only force, thus acting, is atmospheric 
 pressure, which is thus measured. The original column 
 of thirty-six inches fell because its weight was greater 
 than the opposing force. As it fell, its weight diminished, 
 continuing to do so until an equality of opposing forces 
 produced equilibrium. (See Appendix H.) 
 
 276. Pascal's Experiments. Pascal confirmed 
 Torricelli's conclusions by varying the conditions. He 
 had the experiment repeated on the top of a mountain and 
 found that the mercury column was three inches shorter, 
 showing that as the weight of the atmospheric column 
 diminish es, the supported column of mercury also dimin- 
 ishes. He then took a tube forty feet long, closed at one 
 end. Having filled it with water, he inverted it over a 
 
160 
 
 A TMO SPHERIC PRESS URE. 
 
 water bath. The ivater in the tube came to rest at 
 a height of 34 feet. The water column was 13.6 times 
 as high as the mercury column, but as the specific gravity 
 of mercury is 13.6, the weights of the two columns were 
 equal. Experiments with still other liquids gave corres- 
 ponding results, all of which strengthened the theory that 
 the supporting force is due to the weight of the atmos- 
 phere, and left no doubt as to its correctness. 
 
 277. Pressure Measured in Atmospheres. 
 
 A gas or liquid which exerts a force of fifteen pounds upon 
 a square inch of the restraining surface is said to exert a 
 pressure of one atmosphere. A pressure of 60 pounds to 
 the square inch, or 4 Kg. to the sq. cm., would 
 be called a pressure of four atmospheres. 
 
 278. The Accuracy of a Barom- 
 eter. The accompanying figure represents 
 the simplest form of the barometer. The in- 
 strument's accuracy depends upon the purity 
 of the mercury, the accuracy of measuring the 
 vertical distance from the level of the liquid 
 in the cistern to that in the tube, and the 
 freedom of the space at the top of the tube 
 from air and moisture. In delicate observa- 
 tions allowance must be made for differences 
 of temperature. In technical language, 
 u The barometric reading is corrected for 
 temperature." 
 
 279. The Utility of a Barometer. 
 
 This instrument's efficiency depends upon 
 
 the fact that variations in atmospheric pres- FIG. 95. 
 
ATMOSPHERIC PRESSURE. 
 
 161 
 
 sure produce corresponding variations in the height of the 
 barometer column. It is used to determine the height of 
 places above the sea-level, foretell storms, etc. When, at a 
 given place, the " barometer falls," a storm is generally 
 looked for. Sometimes the storm does not come, and 
 faith in the accuracy of the instrument is shaken. But, in 
 Fact, the barometer did not, announce a coming storm ; it* 
 did proclaim a diminution of atmospheric pres- 
 sure from some cause or other. Its declarations are 
 perfectly reliable ; inferences from those declarations are 
 subject to possible error. 
 
 280. The Aneroid Barometer. This instrument consists 
 
 of a cylindrical box of metal with a top 
 of thin, elastic, corrugated metal. The 
 air is removed from the box. The top 
 is pressed inward by an increased 
 atmospheric pressure ; whenever the 
 atmospheric pressure diminishes, it is 
 pressed outward by its own elasticity 
 aided by a spring beneath. These 
 movements of the cover are transmitted 
 and multiplied by a combination of 
 delicate levers. These levers act upon 
 an index which is thus made to move 
 over a graduated scale. Such barome- 
 ters are much more easily portable 
 than the mercurial instruments. They 
 are made so delicate that they show 
 a difference in atmospheric pressure 
 when transferred from an ordinary 
 
 to the floor. Their very delicacy involves the necessity for care- 
 ful usage or frequent repairs. 
 
 281. The Baroscope. Air, having weight, has 
 buoyant power. The Principle of Archimedes ( 238) 
 applies to gases as well as to liquids. Prom this it follows 
 that the weight of a body in air is not its true weight, but 
 that it is less than its true weight by exactly the weight of 
 
 FIG. 96. 
 
162 
 
 ATMOSPHERIC PRESSURE. 
 
 the air it displaces. This principle is illustrated by the 
 baroscope, which consists of 
 a scale-beam supporting two 
 bodies of very unequal size (as 
 a hollow globe and a lead 
 ball), which balance one an- 
 other in the air. If the appa- 
 ratus thus balanced in the air 
 be placed under the receiver 
 of an air-pump, and the air 
 exhausted, the globe will de- 
 scend, thus seeming to be 
 heavier than the lead ball 
 which previously balanced it. 
 Is the globe actually heavier 
 than the lead, or not ? 
 
 FIG. 97 
 
 EXERCISES. 
 
 1. Give the pressure of the air upon a man the surface of whose 
 body is 14 square feet. 
 
 2. A soap-bubble has a diameter of 4 inches ; give the pressure 
 of the air upon it. (See Appendix A). 
 
 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 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 2i by 3^ feet? (6.) How happens it that the owner can open 
 the trunk ? 
 
 7. When the barometer stands at 760 mm. what is the atmos- 
 pheric pressure per sq. cm. of surface? Ans. 1033.6 g. 
 
 Note. In round numbers, atmospheric pressure at the sea-level 
 U called 15 Ibs. to the sq. in., or 1 kilogram to the sq. cm. 
 
TENSION OF GASES. 163 
 
 8. A certain room is 10 m. long, 8 m. wide and 4 m. high. (a.\ 
 What weight of air does it contain ? (&.) What is the pressure upon 
 its floor? (<?.) Upon its ceiling? (d.) Upon each end? (e.) Upon 
 ?-ach side? (/.) What is the total pressure upon the six surfaces? 
 (ff-) Why is not the room torn to pieces ? 
 
 9. An empty toy balloon weighs 5 g. When filled with 10 I. of 
 hydrogen, what load can it lift ? (See Appendix, G.) 
 
 Recapitulation. In this section we have considered 
 the definitions of Pneumatics and Tension ; the 
 Aerial Ocean in which we live ; the mechanical 
 Properties of Air ; the weight of air giving rise to 
 Atmospheric Pressure; a famous experiment by 
 TorricelH,and the explanation thereof; Pascal's ex- 
 periments and the conclusion they confirmed ; the Ba- 
 rometer ; the Aneroid barometer ; the Baro- 
 scope. 
 
 ECTfON II. 
 
 THE RELATION OF TENSION AND VOLUME TO 
 PRESSURE. 
 
 282. Tension of Gases. If a glass flask, provided 
 with a stop-cock, be closed under an atmospheric pressure 
 which supports a mercury column of 30 inches, the atmos- 
 pheric pressure from without is exactly balanced by the 
 tension ( 269) of the air within. If it be closed under a 
 barometric pressure of 28 inches, this equality of the two 
 pressures will continue. If the flask be closed when the 
 surrounding air is subjected to a pressure of two or three 
 atmospheres, the equality will still continue. In none of 
 these cases will the glass be subjected to any strain because 
 
164 
 
 TENSION OF OASES. 
 
 of the air within or without. The tension of aeriform 
 bodies supports the pressure exerted upon them* 
 afid is equal to it. 
 
 283. Experimental Illustrations of Tension. (1.) The 
 
 tension of confined air is well illustrated by the common pop-gun 
 It is also well illustrated by the common experiment 
 with bursting squares. These "squares" are made 
 of thin glass, are about two or three inches on each 
 edge, and are hermetically sealed under the ordinary 
 atmospheric pressure. The tension of the air within, 
 acting with equal intensity against the atmospheric 
 pressure from without, the frail walls remain unin- 
 jured. When, however, the "square" is placed 
 under the receiver of an air-pump and the external 
 pressure removed, the tension of 15 pounds to the 
 siuare inch is sufficient to burst the walls outward. 
 (2.) Half fill a small bottle with water, 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 smaller size. Apply 
 the lips to the upper end of the tube, and force air 
 into the bottle. Notice, describe, and explain what 
 takes place. 
 
 (3.) 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. Explain. 
 
 FIG. 98. 
 
 FIG. 99. 
 
 284. Mariotte's Law. The tempera- 
 ture remaining the same, the volume of 
 a given quantity of gas is inversely as the pres- 
 sure it supports, 
 
 285. Experimental Verification of Mari- 
 otte's Law. This law may be experimentally verified 
 with Mariotte's tube. It consists of a long glass tube bent 
 as shown in Fig. 100, the long arm being open and the 
 short arm closed. A small quantity of mercury is poured 
 into the tube, so that the two mercurial surfaces are in the 
 
TENSION OF GASES. 
 
 165 
 
 FIG. 100. 
 
 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 an ordinary atmospheric pressure. 
 As more mercury is poured into the long arm the confined 
 air will be compressed. 
 
 (a.) When the vertical distance between the levels of the mercury 
 in the two arms is one-third the height of the barometric column 
 at the time and place of the experiment, the pressure upon the 
 confined ah will be f atmospheres ; the tension of the confined air 
 
166 
 
 TENSION OF 
 
 just supports this pressure and must therefore be f atmospheres. 
 The volume of the confined air is only f what it was under a pres- 
 sure of one atmosphere. If more mercury be poured into the long 
 arm until the vertical distance between the two mercurial surfaces 
 is one-half the height of the barometric column, the pressure and 
 tension will be f atmospheres ; the volume of the confined air will 
 be | what it was under a pressure of one atmosphere. When mer- 
 cury has been poured into the long arm until the vertical distance 
 CA is equal to the height of the barometric column, the pressure 
 and tension will be two atmospheres, and the volume of the confined 
 air will be one-half what it was under a pressure of one atmos- 
 phere. The law has been thus " verified " up to 27 atmospheres, 
 notwithstanding which it is not considered rigorously exact. The 
 deviation from exactness, however, can be detected only by meas- 
 urement of great precision. 
 
 286. The Rule Works both Ways. The law 
 holds good for pressures of less than one atmosphere, for 
 rarefied air as well as for compressed 
 air. To show that this is true, nearly 
 fill a barometer tube with mercury and 
 invert it over a mercury bath held in a 
 glass tank as shown in the figure. 
 Lower the tube into the tank until the 
 mercury levels within the tube and 
 without it are the same. The air in the 
 tube is confined under a pressure of one 
 atmosphere. Note the volume of air in 
 the barometer tube. Raise the tube 
 until this volume is doubled. The 
 vertical distance between the two mer- 
 curial surfaces will be found to be half 
 the height of the barometric column. 
 The confined portion of air, which is 
 now subjected to the pressure of half an 
 FIG. 101. atmosphere, occupies twice the space it 
 
TENSION OF GASES. 16? 
 
 did under a pressure of one atmosphere. And so on. It 
 may be more convenient to have the barometer tube open 
 at both ends, the upper end being closed with the thumb 
 or finger before lifting. 
 
 287. A Summing Up. From the foregoing experi- 
 ments we have a right to conclude that the density and 
 tension of a given quantity of gas are directly, and 
 that its volume is inversely, as the pressure ex- 
 erted upon it. Representing the volumes of the same 
 quantity of gas by V and v, and the corresponding pres- 
 sures and densities by P and p, D and d, our conclusion 
 may be algebraically expressed as follows : 
 
 Z- P. ^L 
 v ~~ P == D' 
 
 EXERCISES. 
 
 1. Under ordinary conditions, a certain quantity of air measures 
 one liter. Under what conditions can it be made to occupy (.) 500 
 cu. cm. ? (6.) 2000 cu. cm. ? 
 
 2. Under what circumstances would 10 cu. inches of air at the 
 ordinary temperature weigh 31 grains ? 
 
 3. Into what space must we compress (a.) a liter of air to double 
 its tension ? (&.) A liter 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 mer- 
 cury may fall to 15 inches ? 
 
 5. A vertical tube, closed at the lower end, has at its upper end 
 a frictionless piston which has an area of one sq. inch. The weight 
 of this piston is five pounds, (a.) What is the tension of the air 
 in the tube? (&.) If the piston be loaded with a weight of ten 
 pounds, what will be the tension ? 
 
 6. When the barometer stands at 28| inches, the mercury is at 
 the same level in both arms of a Mariotte's tube. The barometer 
 rises and the difference in the two mercurial surfaces of the Ma- 
 riotte's tube is half an inch, (a.) In which arm is it the higher t 
 (&.) Why? 
 
168 AIR-PUMP. 
 
 7. Eight grains of air are enclosed in a rigid vessel of such size 
 that the tension is 16 pounds per square inch. What will be the 
 tension if three more grains of air be introduced ? 
 
 Recapitulation. Iii this section we have ^considered 
 the Equality of tension and pressure, with several Ex- 
 perimental Illustrations; Mariotte's L,aw; 
 the Verification of that law for Compressed 
 and for Rarefied Gases; a brief Conclusion from 
 the teachings of these experiments. 
 
 ECTION 111, 
 
 AIR-PUMPS. LIFTING AND FORCE-PUMPS. 
 SIPHON. 
 
 288. The Air-Pump. The air-pump is an 
 instrument for removing air from a closed vessel. 
 The essential parts are shown in section by Fig. 102; 
 one form of the complete instrument is represented by 
 Fig. 103. 
 
 The closed vessel R is called a receiver. It fits accu- 
 rately upon a horizontal plate, through the centre of which 
 is an opening communicating, by means of a bent tube, /, 
 with a cylinder, C. An accurately fitting piston moves in 
 this cylinder. At the junction of the bent tube with the 
 cylinder, and in the piston, are two valves, v and v', open- 
 ing from the receiver but not toward it. The tension of 
 the air in R, and the pressure of the air upon* the valves, 
 are equal. When the piston is raised, v' closes and the 
 atmospheric pressure is removed from v. The tension of 
 the air in R opens v. By virtue of its power of indefinite 
 
AIR-PUMP, 
 
 169 
 
 FIG. 102. 
 
 FIG. 103. 
 
iWO AIR-PVMP. 
 
 expansion, the air which, at first, was in R and t, now fills 
 R, t, and G. When the piston is pushed down, v closes, v 
 opens, and the air in escapes from the apparatus. 
 
 (a.) The lower valve is sometimes supported, as shown *in Fig 
 102, by a metal rod which passes through the piston. This rod 
 works tightly in the piston, and is thus raised when the piston is 
 raised, and lowered when the piston is lowered. A button near the 
 upper end of this rod confines its motion within very narrow liniitr, 
 allows v to be raised only a little, and compels the piston, during 
 most of the journeys to and fro, to slide upon the rod instead of 
 carrying the rod with it. 
 
 289. Degrees and Limits of Exhaustion. 
 
 Suppose that the capacity of R is four times as great as 
 that of C. (The capacity of t may be disregarded.) Sup- 
 pose that R contains 200 parts of air (e. g., 200 grains), 
 and (7, 50 parts. After lifting the piston the first time, 
 there will be 160 grains (= 200 x f) of air in R, and 40 
 grains (200 x \) in C. After the second stroke there will 
 be 128 grains [= 160 x f = 200 x f x | = 200 x (|) 2 ] 
 of air in R, and 32 grains in C. After n upward strokes, 
 200 x (f )" grains of air will remain in the receiver. Evi- 
 dently, therefore, we never can, by this means, re- 
 move all the air which R contains, although we 
 might continually approach a perfect vacuum, if this were 
 the only obstacle. It requires an exceedingly good air- 
 pump to reduce the tension of the residual air to -^ inch 
 oi. mercury. This limit is due to several causes, among 
 which may be mentioned the leakage at different parts of 
 the apparatus, the air given out by the oil used for lubri- 
 cating the piston, and the fact that there is a space at the 
 bottom of the cylinder untraversed by the piston. 
 
 290. Sprengel's Air-Piimp. This instrument is 
 used to apply the principles set forth in 259 to the ex- 
 
AIR-PUMP. 171 
 
 haustion of small receivers. The liquid used is mercury. 
 The vertical pipe, below the arm t (Pig. 87), must be 
 longer than the barometer column (six feet is a common 
 length), and have a diameter of not more than -fa inch. 
 The mercury is admitted by large drops, which, filling 
 the pipe, act as valves and in their fall force out succes- 
 sive quantities of air before them. 
 
 (a.) With such an instrument, it requires about half an hour to 
 exhaust a half liter receiver, but the average result attainable is a 
 tension of about one-millionth atmosphere or 0.00003 inch of mer- 
 cury. By this means a tension of only 7-3^0^ atmosphere has 
 been secured. The mercury acts as a dry, frictionless, perfectly 
 fitting, self-adj listing piston. Special precautions must be taken to 
 make the connection air-tight. The only work of the operator is to 
 carry the mercury from the cistern at the foot of the fall tube to 
 the funnel at the top. 
 
 291. Bunseii's Air-Pump. In Bunsen's air- 
 pump the principle is the same, but the liquid used is 
 water, and the length of the vertical pipe at least thirty- 
 four feet. Such an air-pump may be easily provided in a 
 laboratory where the waste-pipe of the sink has the neces- 
 sary vertical height. The tube t (see Fig. 87) being con- 
 nected with the receiver, has its free eiid inserted in the 
 waste-pipe a little way below the sink. A stream of water 
 properly regulated, flowing into the sink, completes the 
 apparatus. 
 
 292. The Condenser. The condenser is an 
 instrument for compressing a large amount of air 
 into a closed vessel. It differs from the air-pump, 
 p-hiefly, in that its valves open toward the receiver. 
 The cylinder is generally attached directly to the stop- 
 cock of the receiver. Its operation will be readily un- 
 derstood. Sometimes the upper valve, v', instead of 
 
172 
 
 AtR-PUMP. 
 
 being placed in the piston, is placed in 
 a tube opening from the side of the cylin- 
 der below the piston. By connecting 
 this lateral tube with a reservoir contain- 
 ing any gas, the gas may be drawn from 
 the reservoir and forced into the receiver. 
 When thus made and used, the instru- 
 ment is called a tramferrer (Fig. 104). 
 
 Note. The pupil will notice that in the case 
 of the air-pump, the condenser, the transferrer, 
 and the lifting and force pumps to be subse- 
 quently considered, the valves open in the di- 
 rection in which the fluid is to move. 
 
 FIG. 104. 293. Experiments. A person 
 
 having an air-pump has the means of 
 performing almost numberless experiments, some amusing 
 and all instructive. Other experiments, which may be per- 
 formed without such apparatus, have been purposely de- 
 ferred until now. The pupil should explain each experiment. 
 
 (1.) The pressure of the atmosphere, which is transmitted in all 
 directions, may be illustrated by filling a tumbler with water, plac- 
 ing a slip of thick paper over its mouth and holding it there while 
 the tumbler is inverted ; the water will be supported when the 
 hand is removed from the card. 
 
 (2.) Plunge a small tube, or a tube having a small opening at the 
 lower end, into water, cover the upper end with the finger and lift 
 It from its bath. The water is kept in the tube by atmospheric 
 pressure. Remove the finger, and the downward pressure of the 
 atmosphere, which was previously cut off, will counterbalance the 
 upward pressure and the water will fall by its own weight. Such 
 a tube, called a pipette, is much used for transferring small quanti- 
 ties of liquids from one vessel to another. The pipette is often 
 graduated. 
 
 (3.) 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 the stone. When the string is pulled 
 
AIR-PUMP. 
 
 173 
 
 FIG. 105. 
 
 gently there is a tendency toward the formation of a vacuum be- 
 tween the leather and the stone. The stone is 
 now pushed upward with a force of 15 Ibs. foi 
 every square inch of its lower surface ( 273.) It 
 is pressed downward with a force of 15 Ibs. upon 
 each square inch of its upper surface not covered by 
 the "sucker." The downward atmospheric pres 
 sure upon the leather is sustained by the string. 
 This difference between the upward and down- 
 ward atmospheric pressures upon the stone may be 
 greater than the gravity of the stone. Then we 
 say that the stone is pulled up by the "sucker;" 
 in reality the stone is pushed up by the air. 
 
 (4.) The hand-glass is a receiver open at both 
 ends. The lower end fits ac- 
 curately upon the plate of the air-pump. (It is 
 well to smear the plate with tallow in this and 
 similar experiments.) The hand is to be 
 placed over the other end. When the pump is 
 worked, the pressure of the atmosphere is felt, 
 and the hand can be removed only by a con- 
 siderable effort. The appearance of the palm 
 of the hand at the end of this experiment is due to the tension ol 
 the air within the tissues of the hand. 
 (5.) Repeat the experiment described in 269. 
 (6.) Over the upper end of a cylindrical receiver, tie tightly a wet 
 bladder, and allow it to dry. Then ex- 
 haust the air. The bladder will be forced 
 inward, bursting with a loud noise. 
 
 (7.) Replace the bladder with a piece of 
 thin india-rubber cloth. Exhaust the air. 
 The cloth will be pressed inward and nearly 
 cover the inner surface of the receiver. 
 The hand-glass, used in experiment (4), 
 will answer for the two experiments last 
 given, by placing the small end upon the 
 pump-plate. 
 
 (8.) Review the experiments mentioned 
 in 283. 
 
 (9.) The "fountain in vacua" consists of 
 
 a glass vessel through the base of which passes a tube terminating 
 in a jet within, and provided with a stop-cock and screw without. 
 By means of the screw it may be attached to the air-pump and the 
 
 FIG. 107. 
 
174 
 
 AIR-PUMP. 
 
 FIG. 108. 
 
 FIG. 109. 
 
 air exhausted. Remove the air, close the 
 
 stop-cock, place the lower end of the tube 
 
 in water, open the stop -cock ; a beautiful 
 
 fountain will be produced (Fig. 109). 
 (10.) The mercury shower apparatus 
 
 consists of a cup through the bottom of 
 
 which passes a plug of oak or other porous 
 wood. Place the cup upon 
 the hand-glass with a tum- 
 bler below ; pour some 
 mercury into the cup ; ex- 
 haust the air, and the at- 
 mospheric pressure will 
 force the mercury through 
 the pores of the wood. 
 
 (11.) The weight-lifter 
 (Fig. 110) is an apparatus 
 
 by means of which the pressure of the atmosphere may be made to 
 
 lift quite a heavy weight. It consists of a stout glass cylinder, C, 
 
 supported by a frame and tripod. Within the lower part of the 
 
 cylinder is a closely fitting pis- 
 ton from which the weight is 
 
 hung. A brass plate is ground 
 
 to fit accurately upon the top 
 
 of the cylinder. This plate is 
 
 perforated and a flexible tube, 
 
 B, connects the cylinder with 
 
 an air-pump. When the air 
 
 is exhausted from the cylin- 
 der, the atmospheric pressure 
 
 on the lower surface of the 
 
 piston raises the piston and 
 
 supported weight the length 
 
 of the cylinder. 
 
 (12.) The Magdeburg hemi- 
 spheres are made of metal. 
 
 They are hollow, and generally 
 
 three or four inches in diam- 
 
 dter. Their edges are provided 
 
 with projecting lips which fit 
 
 one over the other. These 
 
 edges fit one another air-tight ; 
 
 the lips prevent them from FIG. no. 
 
LIFTING- PUMP, 
 
 175 
 
 FIG. in. 
 
 moving sidewise. The edges being greased and placed together, the 
 air is exhausted from the hollow globe through a tube provided 
 with a stop-cock and screw. When the air has been 
 pumped out, close the stop-cock, remove the hemi- 
 spheres from the pump, and screw a convenient 
 handle upon the lower hemisphere, the upper one 
 being provided with a permanent handle. It will 
 be found that a considerable force is necessary to 
 pull the hemispheres asunder. This force is equal 
 to the atmospheric pressure upon the circular area 
 inclosed by the edges of the hemispheres. If this 
 area be ten square inches it will require a pull of 
 150 pounds to separate the hemispheres. 
 
 (13.) Partly fill two bottles with water. Connect 
 them by a bent tube which fits 
 closely into the mouth of one and 
 loosely into the mouth of the other. Place the bot- 
 tles und^r the receiver and exhaust the air. Water 
 will be driven from the closely stoppered bottle 
 into tb other. Readmit air to the receiver and the 
 water thus driven over will be forced back. 
 
 294. The Lifting FlG II2 
 Pump. The lifting- 
 pump consists of a cylinder or bar- 
 rel, piston, two valves, and a suc- 
 tion pipe, the lower end of which. 
 i^ dips below the surface of the liquid 
 to be raised. The arrangement is 
 essentially the same as in the air- 
 pump. As the piston is worked, 
 tho air below it is gradually re- 
 moved. The downward pressure on 
 the liquid in the pipe being thus 
 removed, the transmitted pres- 
 sure of the atmosphere, exerted 
 upon the surface of the liquid, 
 pushes the liquid up through 
 
 FIG. 113. 
 
176 
 
 FORCE-PUMP. 
 
 the suction pipe and the lower valve into the 
 barrel. When the piston is again pressed down, the lower 
 valve closes, the reaction of the water opens the piston 
 valve, the piston sinking below the surface of the liquid in 
 the barrel. When next the piston is raised, it lifts the 
 water above it toward the spout of the pump. At the same 
 time, atmospheric pressure forces more liquid through the 
 suction pipe into the barrel. 
 
 295. Notes and Queries. The cistern or well containing 
 the liquid must not be cut off from atmospheric pressure, i. e., must 
 not be made air-tight. Why ? For water pumps, the suction pipe 
 must not be more than 34 feet high. Why ? Owing to mechanical 
 imperfections chiefly, the practical limit of the water pump is 28 
 vertical feet. As the lifting of the liquid above the piston does not 
 depend upon atmospheric pressure, water may be raised from a very 
 deep well by placing the barrel, with its piston and valves, within 
 28 feet of the surface of the water, and providing a vertical dis- 
 charge pipe to the surface of the ground. The -piston-rod may 
 work through this discharge pipe. Deep mines are frequently 
 drained by using a series of pumps, one 
 above the other, the handles (levers) of 
 which are worked by a single vertical rod. 
 The lowest pump empties the water into a 
 reservoir, from which the second pump lifts 
 it to a second reservoir, and so on. 
 
 296. The Force-Pump. In 
 
 the force-pump, the piston is generally 
 made solid, i. e. 9 without any valve. 
 The upper valve is placed in a dis- 
 charge pipe which opens from the bar- 
 rel at or near its bottom. When the 
 piston is raised, water is forced into 
 1 the barrel by atmospheric pressure. 
 
 FIG. 114. 
 
 - ;-- When the piston is forced down, the 
 suction pipe valve is closed, the water 
 
SIPHON. 
 
 177 
 
 being forced through the other valve into the discharge 
 pipe. When next the piston is raised, the discharge pipe 
 valve is closed, preventing the return of the water above 
 it, while atmospheric pressure forces more water from 
 below into the barrel. 
 
 FIG. 115. 
 
 297. The Air-Chamber of a Force-Pump. 
 
 Water will be thrown from such a 
 pump in spurts, corresponding to 
 the depressions of the piston. A 
 continuous flow is secured by 
 connecting the discharge pipe 
 with an air-chamber. This air- 
 chamber is provided with a delivery 
 pipe, #, the inner end of which termi- 
 nates below the surface of the water 
 in the air-chamber. When water is 
 forced into the air-chamber, it covers 
 the mouth of the delivery pipe and 
 compresses the air confined in the 
 chamber. This diminution of volume of the air is 
 attended by a corresponding increase of tension ( 284), 
 which soon becomes sufficient to force the water through 
 the nozzle of the delivery pipe in a continuous stream. 
 
 298. The Siphon. The siphon consists of a bent 
 tube, open at both ends, having one arm longer than the 
 other. It is used to transfer liquids from a higher to a 
 lower level, especially in cases where they are to be removed 
 without disturbing any sediment they may contain. It 
 may be first filled with the liquid, and then placed with 
 the shorter arm in ! t)ie higher vessel, care being had that 
 the liquid does not escape from the tube until the opening 
 
178 SIPHON. 
 
 O is lower than mn, the surface of the liquid ; or 
 it may be first placed in position, 
 and the air removed by suction 
 at the lower end ; whereupon, by 
 the pressure of the atmosphere, 
 the fluid will be forced up the 
 shorter arm and fill the tube. In 
 either case a constant stream of 
 the liquid will flow from the upper 
 P IG XI 6 vessel until the surface line mn is 
 
 brought as low as the opening in 
 
 the shorter arm, or, if the liquid be received in another 
 vessel, until the level is the same in the two vessels. 
 
 299. Explanation of the Siphon. This action 
 of the siphon may be thus explained : For convenience, 
 suppose that the sectional area of the tube is one inch, 
 that the downward pressure of the water in the arm AB 
 is one pound, and that the downward pressure of the water 
 in the arm BCis three pounds. The upward pressure in 
 the tube at A will equal the atmospheric pressure on each 
 inch of the surface mn outside the tube minus the down- 
 ward pressure of one pound, i. e., (15 1 =) 14 pounds, 
 On the other side, there is at the upward atmospheric 
 pressure of 15 pounds, from which must be taken the 
 downward pressure of the water in BC, leaving a resultant 
 upward pressure of 12 pounds at 0. The upward pressure 
 at A being two pounds greater than that at (7, determines 
 the flow of the water A BC. The greater the difference 
 between la and be, the greater the velocity of the stream. 
 
 300. Limitations. If the downward pressure at A 
 be equal to the atmospheric pressure, the liquid will not 
 
SIPHON. 
 
 179 
 
 flow. Therefore, if the liquid be water t the height, 
 ab, must be less than 34 feet; if it be mercury, db 
 must be less than the mercury column of the barometer. 
 
 3O1. Intermittent Springs. Occasionally a 
 spring is found which flows freely for a time, and then 
 oeases to flow for a time. Fig. 117 represents an under- 
 ground reservoir, fed with water through fissures in the 
 earth. The channel through which the water escapes 
 
 FIG. 117. 
 
 FIG. 118. 
 
 from this reservoir forms a siphon. The water escaping at 
 the surface constitutes a spring. When the water in the 
 reservoir reaches the level of the highest point in the 
 channel, the siphon begins to act, and continues to do so 
 until the water level in the reservoir falls to the mouth of 
 the siphon. The spring then ceases to flow until the 
 water has regained the level of the highest point of the 
 siphon-like channel. This action is well illustrated by 
 "Tantalus' Cup," represented in Fig. 118. 
 
 EXERCISES. 
 
 I. How high can water be raised by a perfect lifting-pump, Trhen 
 the barometer stands at 30 inches ? (See 253, [2].) 
 
180 SIPHON. 
 
 2. If a lifting-pump can just raise water 28 ft., how high can it 
 raise alcohol having a specific gravity of 0.8 ? 
 
 3. Water is to be taken over a ridge 12.5 m. higher than the sur- 
 face of the water, (a.) Can it be done with a siphon ? Why ? (6.) 
 With a lifting-pump ? Why V (c.) With a force-pump ? Why ? 
 
 4. How high will bromine stand in an exhausted tube, when mer 
 cury stands 755 mm.1 (Sp. gr. of bromine = 2.06.) 
 
 5. If water rises 34 feet in an exhausted tube, how high will 
 sulphuric acid rise under the same circumstances ? 
 
 6. The sectional area of the piston of a " weight-lifter*' being 1? 
 sq. inches, what weight could the instrument raise ? 
 
 7. If the capacity of the barrel of an air-pump is | that of the re- 
 ceiver, (a.) what part of the air will remain in the receiver at the 
 end of the fourth stroke of the piston, and (&.) how will its tension 
 compare with that of the external air ? 
 
 8. How high could a liquid with a sp. gr. of 1.35 be raised by a 
 lifting-pump when the barometer stands 29.5 inches V 
 
 9. Over how high a ridge can water be continuously carried in a 
 iphon, the minimum standing of the barometer being 69 cm. ? 
 
 10. What is the greatest pull that may be resisted by Magdeburg 
 hemispheres (a.) 4 inches in diameter? (&.) 8 cm. in diameter? (See 
 Appendix A.) 
 
 Recapitulation. In this section we have considered 
 the Air-pump ; the Limits of Exhaustion at- 
 tainable by the ordinary air-pump ; Sprengel's and 
 Bunsen's air-pumps ; the Condenser and Trans- 
 ferrer; numerous Experiments pertaining to aeri- 
 form pressure and tension; the Lifting-pump; the 
 Force-pump; the Siphon and Intermittent 
 Springs. 
 
 REVIEW QUESTIONS AND EXERCISES. 
 
 1. Define (a.} Physics, (&.) Chemistry, (c.) Atom, (d.) Molecule, (<;.) 
 Solids, (/.) Liquids and (0.) Aeriform Bodies. 
 
 2. Define (a.) Inertia, (6.) Impenetrability and (c.) Hardness, illua 
 trating each by examples. 
 
 3. (a.) Define Momentum and (5.) Energy. A body weighs 500 
 Ibs., and has a velocity of 60 ft. per second ; (c.) what is its momen 
 turn and (d.) what its energy ? (e.) How would each be affected bj 
 doubling the weight ? (/.) By doubling the velocity I 
 
REVIEW. 181 
 
 4. Give (a.) the facts and (6.) the laws of gravity. A body weighs 
 1440 Ibs. at the surface of the earth ; (c.) how far above the surface 
 will its weight be 90 Ibs. 1 (d.) What will it weigh 2200 miles 
 below the surface ? 
 
 5. (a.) What is a machine? (ft.) What is a foot pound? (c.) Tell 
 how the advantage gained by a simple mechanical power is found ; 
 md (d.) show this by an illustration of your own. (e~ ) Explain the 
 jause of friction. 
 
 6. (a.) What is a simple pendulum ? (6.) What is an oscillation? 
 (c.) How does a change of latitude change the number of vibrations ? 
 (d.) Why? 
 
 7. (a.) What is the length of a second's pendulum ? (ft.) What 
 is the length of one vibrating seconds ? 
 
 8. (a.) State the general law of machines, and (ft.) illustrate it by 
 means of the pulley. 
 
 9. (a.) What is the centre of gravity ? (ft.) How found? 
 
 10. (a.) Draw figures illustrating the position of parts in the dif 
 ferent kinds of levers ; (6.) make and solve a simple problem in 
 each. 
 
 11. (a.) What is the relation which the length of a pendulum 
 bears to its time of oscillation ? (6.) Give the length of a pendulum 
 beating once in 2 seconds. 
 
 12o (a.) Give the second and third laws of motion, and (6.) illus- 
 trate them. 
 
 13. A and B, at opposite ends of a bar 6 ft. long, carry a weight 
 of 600 pounds suspended between them. A's strength being twice 
 as great as B's, how far from A must the weight be suspended ? 
 
 14. (a.) Give the formulas for falling bodies, (&.) translating them 
 into common language. (c.) Give the same for bodies rolling 
 freely down inclined planes. A body fell from a balloon one mile 
 above the surface of the earth ; (d.) in what time, and (e.) with what 
 velocity would it reach the earth ? 
 
 15. 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 
 (6.) what is its final velocity ? 
 
 16. (a.) A bricklayer's laborer with his hod weighs 170 pounds ; 
 he puts into the hod 20 bricks weighing 7 pounds each ; he then 
 climbs a ladder to a vertical height of 30 feet. How many units of 
 work does he ? (6.) If he can do 158,100 units of work in a day, 
 how many bricks will he take up the ladder in a day ? 
 
 17. Define three accessory properties of matter. 
 
 18. How much weight will a cubic meter of any solid lose when 
 weighed (a.) in hydrogen? (6.) in air? (c.) in carbonic acid gas? 
 
182 REVIEW. 
 
 19. Can you devise a plan by which an ordinary mercurial barom 
 eter may be used to measure the rarefaction secured by an air-pump 1 
 
 20. (a.) Give the laws of liquid pressure, and (b. ) find the pressure 
 on one side of a cistern filled with water, 5 feet square and 12 feet 
 high ? 
 
 21. (a.) What is specific gravity? (&.) What the standard for 
 ,'iquids and solids? (e.) How is the sp. gr. of solids found? 
 
 22. Calculate the atmospheric pressure upon a man having a body 
 surface of 16,000 sq. cm. 
 
 23. What is the upward pull of a balloon of l,000ew. m. t when 
 filled with gas half as heavy as air, its own weight being 25 Kg. '! 
 
 24. (a.) State Archimedes' principle. (&.) How may it be experi- 
 mentally verified ? (c.) In finding specific gravity, what is always 
 the dividend and what is always the divisor ? (d.) A specific gravity 
 bulb weighs 88 g. in air, 28 g. in water, and 20 g. in an acid. Find 
 the sp. gr. of the acid. 
 
 25. (a.) Describe an overshot water-wheel , and (6.) give a drawing. 
 
 26. (a.) Define the three kinds of equilibrium. (&.) Where is the 
 centre of gravity in a ring ? (c.) Why are lamps, clocks, etc., pro- 
 vided with heavy bases ? 
 
 27. Find the weight in sulphuric acid (sp. gr. 1.75) of a piece of 
 Jead weighing 150 ^., and having a sp. gi. of 11. 
 
 28. A pendulum 1 meter long makes 40 oscillations in a given 
 time ; how long must a pendulum be to make 60 oscillations in the 
 same time and at the same place ? 
 
 29. (a.) Give Mariotte's law. (&.) How high could a fluid having 
 a sp. gr. of 1.35 be raised in a common pump when the barometer 
 stands at 29.5 inches ? 
 
 30. Represent, by drawings in section, the essential parts of (a.) 
 an air-pump, (&.) a lifting-pump, and (c.) a force-pump, (d.) Why 
 does the water rise in the suction pipe of a lifting-pump? (e.) 
 What is the immediate force that throws water in a steady stream 
 from a force-pump ? 
 
 31. Water flows from an orifice 25 feet below the surface of the 
 water, and 144.72 feet above the level ground. Find the range of 
 the jet. 
 
 32. State briefly, by diagram or otherwise, the distinguishing 
 features of solid, liquid and aeriform bodies. 
 
 33. The specific gravity of 1 cu. ft. of wood is 0.9. What is the 
 specific gravity of 1 cu, cm. ? 
 
YI. 
 
 V, 
 
 ELECTRICITY AND MAGNETISM. 
 
 f. 
 
 GENERAL VIEW. 
 
 9. A desire to secure favorable atmospheric conditions for 
 experiments in Motional electricity has determined the order in 
 which the following branches of physics are taken up. In most 
 places in this country, the school-year begins with September. In 
 such cases, this chapter would probably be reached by January, 
 during which month the atmosphere is generally dry. Under 
 other circumstances, the consideration of these subjects would better 
 be omitted until sound, heat and light have been studied. The 
 experiments in this chapter are numbered consecutively. 
 
 3O2. Simple Apparatus. Provide two stout 
 sticks of sealing-wax and one or two pieces of flannel folded 
 into pads about 20 centimeters (8 inches) square; two 
 glass rods or stout tubes closed at one end, 30 or 40 centi- 
 meters in length and about 2 centimeters in diameter (long 
 "ignition tubes" will answer) and one or two silk pads 
 about 20 centimeters square, the pads being three or four 
 layers thick ; a few pith balls about 1 centimeter in diam- 
 eter (whittle them nearly round and finish by rolling 
 them between the palms of the hands) ; a silk ribbon 
 about an inch wide and a foot long; a balanced straw 
 
184 
 
 GENERAL VIEW. 
 
 _ 
 
 FIG. 119. 
 
 about a foot long, represented in Fig. 119. The ends 
 of the straw carry two small discs of paper (bright colors 
 
 ry ^ preferable) fastened on by sealing-wax. 
 
 ^* ~ """^" \j 
 
 The cap at the middle of the straw is 
 a short piece of straw fastened by seal- 
 ing-wax. This is supported upon the point of a sewing- 
 needle, the other end of which is stuck upright into the 
 cork of a small glass vial. From the ceiling or other con- 
 venient support, suspend one of the pith balls by a fine 
 silk thread. 
 
 (a.) The efficiency of the silk pad above mentioned may be in- 
 creased by smearing one side with lard and applying an amalgam 
 made of one weight of tin, two of zinc and six of mercury. The 
 amalgam that may be scraped from bits of a broken looking-glass 
 answers the purpose admirably. 
 
 Experiment I. Draw the silk ribbon between two layers of the 
 warm flannel pad with considerable friction. Hold it near the wall 
 of the room. The ribbon will be drawn to the wall and held there for 
 some time. 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. 
 
 Experiment 2. Briskly rub the sealing-wax with the flannel 
 and bring the wax near 
 the suspended pith ball. 
 The ball will be drawn 
 to the wax. Bring the 
 wax near one end of the 
 balanced straw ; it may 
 be made to follow the 
 wax round and round. 
 Bring it near small 
 scraps of paper, shreds 
 of cotton and silk, 
 feathers and gold leaf, 
 bran and sawdust and 
 other light bodies ; they FIG. 120. 
 
 are attracted to tlie wax. 
 
 Experiment 3. Repeat all of these experiments with a glass rod 
 that has been rubbed with the silk pad. 
 
GENERAL VIEW. 
 
 185 
 
 Experiment 4. Make a light paper hoop or an empty egg-shell 
 roll after your rod. (See 332 6.) 
 
 Experiment 5. Place an egg in a wine-glass or an egg-cup. 
 Upon the egg, balance a yard-stick or a common lath. 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 loop (Fig. 121) or stiff paper stir- 
 rup suspended by a stout silk thread 
 or narrow silk ribbon. It may be made 
 to imitate the actions of the balanced 
 straw or lath.. 
 
 Experiment 6. Suspend the rubbed 
 sealing-wax or glass rod as you did 
 the blackboard pointer in the last ex- 
 periment. Hold your hand near the 
 end of the rod. It will turn round and approach your hand. 
 
 FIG. 121. 
 
 Note. The pupil may be in- 
 genious enough to invent new 
 experiments for himself and 
 the class. The ability to in- 
 vent is often very valuable 
 and may be acquired early in 
 life. Most of the great in- 
 ventors began making experi- 
 ments when mere children. 
 
 3O3. Electric At- 
 traction. TJie at- 
 tractions manifested 
 in the experiments 
 just described were 
 due to electricity that 
 was developed l>y fric- 
 tion. Such electmcity 
 is called frictional or static electricity. 
 
 FIG. 122. 
 
186 
 
 GENERAL VIEW. 
 
 Experiment 7. Bring the rubbed sealing-wax or glass rod near 
 the pith ball again. It will attract the ball as before. Allow the 
 ball to touch the rod and notice that, in a moment, the ball is 
 thrown off. If the ball be pursued with the rod, it will be found 
 that the rod which attracted it a moment ago now repels it. Evidently, 
 the ball has acquired a new property. (Fig. 123. ) 
 
 Experiment 8. Touch the ball with the finger. It seeks the 
 rubbed rod, touches the rod, flies from the rod. Repeat the experi- 
 ments with the sealing-wax after it has been rubbed with flannel. 
 
 Experiment 9. Rub the glass rod with silk and bring it over 
 the small scraps of paper as before. Notice that, after the attrac- 
 tion, the paper bits do not merely fall down, they are thrown down. 
 
 3O4. Electric 
 
 Repulsion. The repulsions 
 manifested in the experi- 
 ments just described were 
 due to static electricity. 
 The glass or wax is said to be 
 electrified by friction. The ball, 
 
 after obtaining its new property 
 of repulsion by coming in con- 
 tact with the glass or wax, is said 
 to be electrified by conduction. 
 The suspended pith ball is 
 called an electric pendulum. 
 
 Experiment 10. Prepare a battery 
 solution according to the recipe given 
 in 392, using only half the quantity 
 of each substance as therein directed. 
 While the solution is cooling, provide a 
 piece of sheet copper and one of sheet zinc, each about 10 centimeters 
 (4 inches) long and 4 centimeters (H inches) wide. To one end of 
 each strip, solder (see Appendix B) or otherwise fasten a piece of 
 No. 18 copper wire (See Appendix I) about 15 centimeters (6 inches) 
 long. Place the zinc strip in a common tumbler about three-fourths 
 full of the battery solution. Notice the minute bubbles that break 
 away from the surface of the zinc and rise to the surface of tlie 
 
 FIG. 123. 
 
GENERAL VIEW. 
 
 187 
 
 liquid. These are bubbles of hydrogen, a combustible gas. The 
 formation of the gas is due to chemical action between the zinc and 
 the liquid. 
 
 Experiment II. Take the zinc from the tumbler and, while it is 
 yet wet, rub a few drops of mercury (quicksilver) over its surface 
 until it has a brilliant, silver-like appearance. Keplace the zinc, 
 thus amalgamated, in the solution and notice that no bubbles are 
 given off. 
 
 Experiment 12. Place the copper strip in the liquid, taking care 
 that it or its wire does not touch the zinc or its 
 wire. No bubbles appear either on the zinc or the 
 copper. It may be convenient to place a narrow 
 glass strip between the ends of the metal strips 
 in the tumbler to keep them apart. 
 
 Experiment 13. Bring the upper ends of the 
 strips together, as shown in Fig. 124, or, still 
 better, join the two wires, as shown in Fig. 179, 
 being sure that the wires are clean and bright 
 where they are united. Notice the formation of 
 bubbles on the surface of the copper, where none 
 
 3O5. Suspicion. It seems that the connecting 
 wire is an important part of the apparatus as now ar- 
 ranged and we are led to suspect that something unusual 
 is taking place in the wire itself. It is evident that we 
 have a complete "circuit" through the liquid, the metal 
 strip and the wire. 
 
 Experiment 14. Untwist the wires or, in other words, " break 
 the circuit." Connect the copper wires with a short piece of very 
 fine iron wire. The connections should be made so that the circuit 
 
 shall include about 2 centimeters 
 (| inch) of iron wire. The iron 
 idll become hot enough to burn the 
 fingers or to ignite a small quantity 
 of gun cotton twisted around it. 
 
 FIG. 125. 
 
 Experiment 15. If one of the 
 copper wires be twisted around one 
 end of a small file and. the free end 
 
188 GENERAL VIEW. 
 
 of the other wire be drawn along its rough surface, a series of 
 minute sparks will be produced as the circuit is rapidly made and 
 broken. 
 
 Experiment 16. Place the cell so that the joined wires shall run 
 north and south, passing directly over the needle of a small com- 
 pass (Experiment 98) and near to it. The needle wttl instantly turn as 
 though it were trying to place itself at right angles to the wire. 
 Break the circuit and the needle will swing back to its north and 
 south position. 
 
 FIG. 126. 
 
 3O6. Certainty. We now feel sure that something 
 unusual is taking place in the wire of our complete circuit, 
 for we have seen the wire become hot, explode gun-cotton, 
 yield sparks and exert a very mysterious influence upon 
 the magnetic needle. As a matter of fact, we now have 
 a current of electricity flowing through a voltaic cell and 
 wire. Electricity thus produced by chemical action 
 is called voltaic or galvanic electricity. It is one 
 form of current electricity. 
 
 Experiment 17. 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 spiral do not touch each other or the iron. 
 It is well to use cotton covered or "insulated" wire. Connect the 
 two ends of the wire spiral with the two wires of the voltaic eel] 
 
GENERAL VIEW. 189 
 
 or, in other words, put the spiral into the circuit. Dip the end of 
 the nail into iron filings. Some of the filings will cling to the naU in 
 a remarkable manner. Upon breaking the circuit, the nail instantly 
 loses its newly acquired power and drops the iron filings. 
 
 If the experiment does not work satisfactorily, look carefully to 
 all the connections of the circuit, see that the ends of the wires are 
 clean and bright and that they are twisted together firmly. It may 
 be necessary to wash the plates, rub more mercury on the zinc and 
 provide a fresh battery solution. 
 
 307. Temporary Magnets. The nail has the 
 power of attracting iron filings while the electric cur- 
 rent is flowing through the surrounding wire coil. 
 You have made an electro-magnet. Its power of 
 attracting iron is called magnetism. Satisfy your- 
 self, by trial, that the nail loses its magnetism as soon as 
 the circuit is broken or the current ceases to flow around 
 it. Remember that your electro-magnet is a temporary 
 magnet. 
 
 Experiment 18. While the nail is magnetized, draw a sewing- 
 needle four or five times from eye to point across one end of the 
 electro-magnet. Dip the needle into iron filings ; some of them mil 
 cling to each end of it. 
 
 308. Permanent Magnets. When steel is 
 treated as in the last experiment, it becomes permanently 
 magnetized. 
 
 Experiment 19. Cut a thin slice from the end of a vial cork and, 
 with its aid, float your magnetized needle upon the surface of a 
 bowl or saucer 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. 
 
 309. A Simple Compass.^ small magnet- 
 ized steel bar freely suspended, is called a com- 
 
190 GENERAL VIEW. 
 
 pass. The one that you have made may be less conven- 
 ient than is the compass of the mariner or the surveyor, 
 but it is as reliable. 
 
 310. Artificial Magnets. The electro-magnet 
 and the permanent magnet that you make are, of course, 
 artificial magnets. There is a natural magnet 
 known as lodestone. 
 
 311. Other Forms of Current Electricity. 
 
 Electric currents may be generated by the action of other 
 currents of electricity or by the action of magnets. Elec- 
 tricity thus developed is called induced electricity. A 
 current of thermo-electricity may be generated by heating 
 the junction of two metals that form part or all of a cir- 
 cuit. 
 
 312. The Different Forms of Electricity 
 are Identical. So far as experiment can show, one 
 form of electricity may have a particular property in 
 greater degree than some other form, but all are identical, 
 each having all the properties of any of the others. 
 
GENERAL VIEW. 
 
 191 
 
 Recapitulation. To be amplified by the pupil foi 
 review. 
 
 H 
 
 r 1 
 
 8 
 s 
 
 n 
 
 m 
 
 c 
 
 q w 
 
 H 
 
II. 
 
 FRICTIONAL ELECTRICITY OR ELECTRIC CHARGES. 
 
 313. The Nature of Electricity. But little is 
 known concerning the real nature of electricity. It is 
 easier to tell what electricity can do than to tell what it 
 is. The majority of modern physicists consider that elec- 
 tricity is a form of energy producing peculiar 
 phenomena ; that it may be converted into other 
 forms of energy and that all other forms of 
 energy may be converted into it. It is believed that 
 electricity is a form of molecular motion, but this belief 
 still rests upon analogy rather than demonstration. Sev- 
 eral theories have been advanced to account for electrical 
 phenomena, but none of them is satisfactory. 
 
 314. Electric Manifestations. Electricity 
 may reveal itself as a charge residing on the sur- 
 face of a body or as a current flowing through its 
 substance. By means of friction, the glass rod or the 
 sealing-wax ( 303, 304) acquired an electrical charge 
 and, consequently, the power of attracting and repelling 
 light bodies ; by means of chemical action, the voltaic dell 
 ( 306) generated electricity that manifested itself as a 
 current. In this section, we shall consider electricity that 
 appears as a charge, i.e., static electricity. 
 
FRICTION 'AL ELECTRICITY. 
 
 193 
 
 (a.) The electrified body is said to be charged. When the electric- 
 ity is removed, the body is said to be discharged. Good conductors 
 ( 324) are instantly discharged when touched by the hand, or by any 
 good conductor connected with the earth. A poor conductor may 
 be readily discharged by passing it rapidly through a flame, as of a 
 lamp or candle. 
 
 Experiment 20. Prepare two electric pendulums. Bring the 
 electrified glass rod near the pith ball of one ; after contact, the ball 
 will be repelled by the glass. Bring the electrified sealing-wax 
 near the second pith ball ; after contact, it will be repelled by the 
 wax. Satisfy yourself that the electrified glass will repel the first ; 
 that the electrified sealing-wax will repel the second. Let the glass 
 rod and the sealing-wax change hands. The first ball was repelled 
 by the glass ; it will be attracted by the sealing-wax. The second ball 
 was repelled by the sealing-wax ; it will be attracted by the glass. 
 
 Experiment 21. Suspend two pith balls as shown in Fig. 127, 
 and touch them with a rubbed 
 rod. Instead of 
 
 con- 
 tinuing to hang side by side, 
 they repel each other and fly 
 apart. If the electrified glass 
 rod be held near them, they 
 separate still further. If 
 the electrified sealing-wax, 
 instead of the glass, be held 
 near them, they will fall 
 nearer together. If the 
 rubbed glass rod be sus- 
 pended as shown in Fig. 121, 
 it will be repelled by another 
 rubbed glass rod, but at- 
 tracted by rubbed sealing- 
 wax. 
 
 FIG. 127. 
 
 315. Two Kinds of Electricity. The 
 
 tricity developed on glass is different in kind from 
 that developed on sealing-wax. They exhibited op- 
 posite forces to a third electrified body, each attracting 
 what the other repels. 
 
194 FRICTION AL ELECTRICITY. 
 
 Experiment 22. Hold the silk pad in a piece of sheet-rubbet 
 and, with it, rub the glass rod. Suspend the glass rod and bring 
 the silk pad near it. The electrified 
 pad will attract the glass, but will 
 repel a suspended stick of sealing-wax 
 that has been rubbed with flannel. 
 
 316. Electric Separa- 
 tion. All electrified bodies 
 net like either tine glass or the 
 sealing-wax. When the glass 
 rod was positively electrified, an 
 F 8 equal amount of negative elec- 
 
 tricity was simultaneously devel- 
 oped in the silk with which it was rubbed. When the seal- 
 ing-wax was negatively electrified, an equal amount of 
 positive electricity was developed at the same time in the 
 flannel. It is as though the two electricities were united 
 in these several substances in their ordinary condition and 
 were torn asunder by the friction, thus producing actual 
 " electric separation." 
 
 (#.) If it be desired to show that the rubber has been electrified, 
 care must be taken not to handle it too much. For example, if seal- 
 ing-wax is to be rubbed with a piece of fur, do not take the fur in 
 the hand, but fasten it to the end of a glass rod as a handle. 
 
 (6.) That the electricities thus simultaneously developed are op- 
 posite in kind and equal in amount may be shown by imparting 
 the electricity of the rubber and the electricity of the thing rubbed 
 to a third body, which will then show no electrification at all. The 
 equal and opposite electricities exactly neutralize each other. 
 
 317. The Two Electricities Named. As the 
 
 two kinds of electricity are opposite in character, they 
 have received names that indicate opposition. The elec- 
 tricity developed on glass by rubbing it with silk 
 
ELECTRICITY. 195 
 
 is called positive or +. The electricity developed 
 on sealing-wax by rubbing it with flannel is called 
 negative or . The terms vitreous and resinous 
 respectively were formerly used. 
 
 318. Electric Series. In the following list, the substances 
 are named in such an order that, if any two be rubbed together, the 
 one that stands earlier in the series becomes positively electrified 
 and the one that is mentioned later becomes negatively electrified : 
 fur, wool, resin, glass, silk, metals, sulphur, india-rubber, gutta percha, 
 collodion. 
 
 319. The Laws of Electrostatics. The most 
 important electrostatic laws may be stated thus : 
 
 (1.) Electric charges of like signs repel each other ; 
 electric charges of opposite signs attract 
 each other. 
 
 (2. ) The force exerted between two electric charges 
 is directly proportional to their product 
 and inversely proportional to the square 
 of the distance between them. This is known 
 as Coulomb's law. The two charges are sup- 
 posed to be collected at two points, or on two 
 
 very small spheres. / = & - 
 
 (a.) Suppose that a and 6 are two small balls, each charged with 
 a quantity of electricity, that we shall call unity. Then the product 
 of the charges will be 1 xl=l. Next, suppose that A and B are 
 two similar balls, that A is charged with twice as much electricity as 
 a and that, similarly, B has a charge represented by 3. The prod- 
 uct of the charges of A and B will be 2 x 3=6. In other words, at 
 equal distances, the repulsion between A and B will be six times as 
 great as the repulsion between a and b. 
 
 (b.) Suppose that two electric charges or two small electrified 
 bodies one inch apart repel each other with a certain force ; at a dis- 
 tance of two inches, they will repel each other with a force one quarter 
 as great ; at a distance of ten inches, they will repel each other with 
 only one per cent, of the original force at the distance of one inch. 
 
190 FRICT10NAL ELECTRICITY. 
 
 320. Electrical Units. There are two systems of 
 electrical units derived from the fundamental "C.G-.S." 
 units, one set being based upon the attraction or repulsion 
 exerted between two quantities of electricity and the 
 other upon the force exerted between two magnefc poles. 
 The former are termed electrostatic units ; the latter, elec- 
 tromagnetic units. 
 
 321. Electrostatic Unit of Quantity. One 
 
 unit of electricity is that quantity ivhich, when 
 placed, at a distance of one centimeter from a 
 similar and equal quantity, repels it with a force 
 of one dyne. It is a C.G.S. unit ( 69) and has no 
 special name. 
 
 (a.) Two small spheres, charged respectively with 6 units and 8 
 units of + electricity, are placed 4 cm. aoart ; find what force they 
 exert on one another. 
 
 By the formula, / = Sli, we find / = ll = * = 3. 
 
 Ans. 3 dynes. 
 
 The force in the above example would clearly be a force of repul- 
 sion. Had one of these charges been negative, the product, Q x g, 
 would have had a value (algebraic) and the answer would have 
 been minus 3 dynes. The algebraic sign, therefore, prefixed to 
 a force, indicates that it is a force of attraction, while the + sign 
 signifies a force of repulsion. 
 
 322. The Test for Either Kind of Elec- 
 tricity. When the pith ball was attracted by the rubbed 
 glass it became, during the time of contact, charged with 
 the + electricity of the glass; hence it was repelled. 
 When it was attracted by the rubbed sealing-wax it be- 
 came, during the time of contact, charged with the 
 electricity of the wax ; then it was repelled. But either 
 
FRICTIONAL ELECTRICITY, 
 
 197 
 
 the wax or the glass attracted the uncharged pith ball. 
 We must, therefore, remember that attraction affords 
 no safe test for the kind of electricity, while re- 
 pulsion does. If glass rubbed with silk repels a body, 
 that body is charged with -f- electricity. If sealing-wax 
 rubbed with flannel repels a body, that body is charged 
 with electricity. 
 
 323. Electroscopes. An instrument used to 
 detect the presence of electricity, or to determine 
 its kind, is called an electroscope. The electric pen- 
 dulum ( 304) is a common form of the electroscope. 
 Two strips of the thinnest tissue paper hanging side by 
 side constitute a simple electroscope. It is well to prepare 
 the paper beforehand by soaking in a strong solution of 
 salt in water and drying. 
 The balanced straw (Fig. 
 119) or, better yet, two 
 gilded pith balls connected 
 by a light needle of glass 
 or sealing-wax balanced 
 horizontally on a vertical 
 pivot, or a goose-quill 
 balanced on the point of 
 a sewing-needle, makes i? 
 convenient electroscope. 
 
 The gold leaf electro- 
 scope is represented in 
 Fig. 129. A metallic rod, which passes through the cork 
 of a glass vessel, terminates below in two narrow strips of 
 gold leaf and above in a metallic knob or plate. The 
 object of the vessel is to protect the leaves from disturb- 
 ance by air currents. The upper part of the glass is often 
 
 FIG. 129. 
 
193 FRICTION AL ELECTRICITY. 
 
 coated with a solution of sealing-wax or shellac in alcohol, 
 to lessen the deposition of moisture from the atmosphere. 
 This instrument may be made by the pupil and, when 
 well made, is very delicate. 
 
 (a.) The electric pendulum is used as an electroscope as follows 
 If an uncharged pith ball be attracted by a body brought near it, 
 the body is electrified. To determine the sign of the electricity of 
 the body thus shown to be electrified, the pith ball is allowed to 
 touch it and be repelled. If the ball then be repelled by a glass rod 
 rubbed with silk (or by any other body known to be positively 
 charged), the pith ball and the body in question manifest -f elec 
 tricity. If the pith ball, after repulsion by the body whose elec- 
 tricity is under examination, be repelled by sealing-wax rubbed with 
 flannel (or by any other body known to be negatively charged), the 
 pith ball and the body in question manifest electricity. Remem- 
 ber that the repulsion and not the attraction constitutes the test. 
 
 (&.) One way of testing with the gold leaf electroscope is to bring 
 the electrified body near the knob ; the leaves will diverge. Touch 
 the knob with the finger ; the leaves will fall together. Remove first 
 the finger and then the electrified body ; the leaves will diverge 
 again. If now the divergence of the leaves be increased by bring- 
 ing a positively charged body near the knob, the original charge 
 was ; if the divergence be thus diminished, the original charge 
 was +. 
 
 (c.) The knob and rod of the gold leaf electroscope may be made 
 by soldering a wire to a smooth metal button. The vessel may be 
 any clear glass bottle with a wide mouth. Thrust the wire down- 
 ward through the cork of the bottle and bend the wire at right 
 angles, so that when the cork is in place the horizontal part of the 
 wire shall be about f inch long and come just below the shoulder of 
 the bottle. Cut a strip of gold or Dutch leaf, 4 inches long and ^ 
 inch wide and paste it at its middle line to the horizontal part of the 
 wire, so that the two halves of the strip shall hang downward facing 
 each other. See that the cork is perfectly dry ; heat the bottle until 
 it is perfectly dry ; insert the cork firmly in its place, and pour 
 melted sealing-wax over the cork and around the mouth of the 
 bottle so that no moisture can get into your electroscope. If you 
 cannot get the gold or Dutch leaf (try at some good-natured dentist's 
 or sign painter's), use two discs of gilt paper as large as the mouth 
 of your bottle will admit and tie them to the wire by very short 
 cottoo or linen threads.. 
 
FRICTIONAL ELECTRICITY. 
 
 199 
 
 Experiment 23. From a horizontal glass rod or tightly-stretched 
 ilk cord, suspend a fine copper wire, a linen thread and two silk 
 threads, each at least a meter long. To the lower end of each, at- 
 tach a metal weight of any kind. Place the weight supported by 
 the wire upon the plate of the gold leaf electroscope. Bring the 
 electrified glass rod near the upper end of the wire ; the gold leaves 
 instantly diverge. Repeat the experiment with the linen thread ; in 
 a little while the leaves diverge. 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 yet appears. Wet 
 the second silk cord thoroughly and, with it, repeat the experiment ; 
 the leaves then diverge instantly. 
 
 Experiment 24. Support a yard stick or common lath upon a 
 glass tumbler. Bring the glass rod, electrified by rubbing it with 
 silk, to one end of the stick and hold some small pieces of gold leaf 
 or paper 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 electricity passed along the stick from end to end. 
 
 324:. Conductors. Such experiments clearly show 
 that some substances transmit electricity readily and 
 that others do not. Those that offer little resistance 
 to the passage of electricity are called conductors ; 
 those that offer great resistance are called non- 
 conductors or insulators. A conductor supported by a 
 non-conductor is said to be insulated. 
 
 (a.) In the following table, the substances named are arranged in 
 the order of their conductivity-: 
 
 Conductors. 
 t. Metals. 
 2. Charcoal. 
 3. Graphite. 
 4. Acids. 
 
 5. Salt water. 
 6. Fresh water. 
 7. Vegetables. 
 8. Animals. 
 9. Linen. 
 
 10. Cotton. 
 11. Dry wood. 
 12. Paper. 
 13. Silk. 
 14. India rubber. 
 
 15. Porcelain. 
 16. Glass. 
 17. Sealing-wax. 
 18. Vulcanite. 
 Insulators. 
 
 (&.) The fact that a conductor in the air may be insulated, show?; 
 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 for electricity of high potential. All experiments in fric- 
 tional electricity should, therefore, be performed in clear, cold weather 
 
200 FRICTIONAL ELECTRICITY. 
 
 when the atmosphere is dry, for a moist atmosphere renders insula 
 tion for a considerable length of time impossible. 
 
 (c.) A simple way of determining experimentally whether a body is 
 a good conductor or not is, to hold it in the hand and touch the knob 
 of a charged gold leaf electroscope with it. If the substance be a 
 good conductor, the electroscope will be quickly discharged. 
 
 Experiment 25. Suspend a copper globe or other metal body by 
 a silk thread and strike it two or three times with a cat's skin or 
 fox's brush. Bring the gold leaf electroscope near the globe. The 
 leaves will diverge. 
 
 325. Electrics. Any substance, when insulated, 
 inay be sensibly electrified ; but when an uninsulated 
 conductor is rubbed, the electricity escapes as fast 
 as it is developed. The old division of bodies into elec- 
 trics and non-electrics, or bodies that can be electrified 
 and those that cannot be electrified, is nothing more than 
 a division into conductors and non-conductors. 
 
 326. Tension. Electricity exists under widely dif- 
 ferent conditions with respect to its ability to force its 
 way through a poor conductor or to leap across a gap. 
 The electricity developed Tn a voltaic cell will not pass 
 through even a very thin piece of dry wood ; the elec- 
 tricity developed by rubbing the glass rod will pass through 
 several feet of dry wood. It would require a battery of 
 many cells to force a current across an air-filled gap of 
 y^fl- of an inch. It is not difficult to force friction al 
 electricity across a gap of several inches, while we all know 
 that, in the case of lightning, electricity leaps across a 
 gap of many hundred feet. In the one case, the electricity 
 is said to be of low potential ; in the other case, it is said 
 to be of high potential. The terms "low tension" and 
 " high tension " are often used in the same sense. 
 
FRICTIONAL ELECTRICITY. 201 
 
 327. Potential. The term, electrical potential (or 
 simply potential), has reference to the electrical condition 
 of a body, or to its degree of electrification. If the poten- 
 tial of A be higher than that of B and the two bodies be 
 connected by a good conductor, an electric current 
 will flow from A to B until the potentials are 
 alike. Difference of potential is somewhat analogous to 
 difference of liquid level and gives rise to electromotive 
 force. 
 
 (.) The electric condition of the earth is sometimes taken as the 
 zero of potential. The electric condition of other bodies is then 
 described as being a certain number of units above or below zero ; 
 i.e., as being + or . In determining the flow of liquids, it is not 
 necessary to know the height of either reservoir above the earth's 
 centre or above the sea level, but only the head or difference of 
 liquid level. Similarly, the difference of potential is what determines 
 the direction and strength of an electric current flowing through a 
 given conductor. 
 
 328. Difference of Potential. The difference 
 of potential between two points represents the work 
 that must be done in carrying a + unit of electricity 
 (321) from one point to the other. The work done 
 will be the same, whatever the path along which the unit 
 is moved from one point to the other. Similarly, the 
 work done in lifting a weight from one point to another 
 at a higher level will be the same whatever the path along 
 which the weight is lifted. 
 
 329. Electrostatic Unit of Difference of 
 Potential. The unit of difference of potential is 
 that which exists between two points, when it re- 
 quires the expenditure of one erg to bring a unit 
 of -f- electricity from one point to another against 
 
202 FRICTIONAL ELECTRICITY. 
 
 the electric force. Let A be a small sphere positively 
 
 electri6ed and P and , two points at different distances 
 
 from A. If Q is just so far 
 
 ,---" from P that it requires one erg 
 
 ^ \ of work to push a unit of -f 
 
 electricity from Q to P, there 
 ? t will be unit difference of poten- 
 tial between P and Q. This 
 unit has no special name. 
 
 (a.) Let P and Q be in the outer 
 
 FIG. 130. surfaces of concentric, spherical, shells 
 
 at the centre of which is A. To move 
 
 the + unit from one point in either of these surfaces to any other 
 point in the same surface requires no further overcoming of elec- 
 tric forces and, therefore, no expenditure of work. Such a surface 
 is called an equipotential surface. 
 
 330. Electric Capacity. Bodies vary in respect 
 to their capacity for holding or accumulating electricity. 
 The electrostatic unit of capacity is the capacity 
 of a conductor that requires a charge of one unit 
 of electricity to raise its potential from zero to 
 unity. It has no special name. A sphere of one centi- 
 meter radius has unit capacity. The capacities of spheres 
 are proportional to their radii. (See 359.) 
 
 (a.) A small conductor (e.g., a sphere the size of a pea) will require 
 less than one unit to raise its potential from to 1 ; it is of small 
 capacity. A sphere five meters in diameter will require many units 
 to raise its potential from to 1 ; it is of preat capacity. In other 
 words, the electrostatic capacity of a conductor or condenser is 
 measured by the quantity of electricity which must be imparted to 
 it in order to raise its potential from to 1. 
 
 331. Charging- by Contact. If an insulated, un- 
 electrified conductor be brought into contact with a simi- 
 
FRICTIONAL ELECTRICITY. 
 
 203 
 
 lar conductor that is electrified, or near enough to it for 
 the easy passage of an electric spark, electricity will pass 
 from the latter to the former until the two conductors are 
 equally charged with the same kind of electricity, i.e., un- 
 til they are of the same potential. The former is said 
 to be charged ~by conduction. 
 
 332. Electrostatic Induction. From several of 
 the preceding experiments, we see that actual contact with 
 an electrified body is 
 not necessary for the 
 manifestation of electric 
 action in an unelectri- 
 fied body. When an 
 electrified body, (7, is 
 brought near an insu- 
 lated, unelectrified con- 
 ductor, B, provided 
 with electric pendu- 
 lums, as shown in Fig. 131, the latter shows electric ac- 
 tion. The electricity of C repels one kind of electricity 
 in B and attracts the other, thus separating them. The 
 second body, B, is then said to be polarized. 
 
 The two kinds of electricity in B, each of which a mo- 
 ment ago rendered the other powerless, are still there, but 
 they have been separated and each olothed with its proper 
 power. This effect is due to the action of the electrified 
 body, C, which is said to produce electric separation by 
 induction. This action will take place across a consider- 
 able distance, even if a large sheet of glass be held be- 
 tween B and C. When C is removed, the separated elec- 
 tricities of B again mingle and neutralize each other. 
 
 FIG. 131. 
 
204 
 
 FRICTIONAL ELECTRICITY. 
 
 (a.) Conductors for the purposes of this and similar experiments 
 may be made of wood, covered with tin-foil, gold leaf or Dutch 
 leaf. They may be insulated by fastening them on top of long- 
 necked bottles or sticks of sealing-wax, or by suspending them by 
 silk threads. 
 
 (&.) Prick a pin-hole in each end of a hen's egg and blow out the 
 contents of the shell. Paste tin-foil or Dutch leaf smoothly over 
 the whole surface of the egg. Fasten one end of a white silk thread 
 
 to the egg with a drop 
 of melted sealing-wax, 
 so that the egg may 
 hang suspended with its 
 greater diameter hori- 
 zontal. Three or four 
 such insulated conduc- 
 tors will be found con- 
 venient. Sometimes, it 
 is better for each egg to 
 have two thread sup- 
 FIG. 132. ports. Place a loop or 
 
 ring at the free end of 
 
 each thread. When the loops are placed on a horizontal rod (e.g., a 
 piece of glass tubing), the greater diameters of the suspended eggs 
 should lie in the same straight line. An elongated conductor like 
 AB of Fig. 133 may be made by hanging two or three egg con- 
 ductors, so that they are in contact, as shown in Fig. 132. 
 
 Experiment 26. While the charged glass rod is held near the 
 egg conductors, shown in Fig. 132, bring a pith ball electroscope 
 near. The attraction will be evident at the free ends of the two 
 eggs, but very little, if any, will be found at or near the point 
 where the eggs are in contact. 
 
 333. A Neutral Line. If an insulated conductor, 
 bearing a number of pith ball (or paper) electroscopes, be 
 brought near an electrified body, (7, (Fig. 133), but not 
 near enough for a spark to pass between them, the pith 
 balls near the ends of the conductor will diverge, showing 
 the presence of separated or un combined electricity. The 
 pith balls at the middle of the polarized conductor will not 
 diverge, marking thus a neutral line. If has a positive 
 
FRICTION AL ELECTRICITY. 205 
 
 charge, the charge at A will be negative and that at B 
 will be positive, as may be shown by charging an electric 
 pendulum and testing at A and B. 
 
 FIG. 133. 
 
 If be removed or " discharged " by touching it with 
 the hand, all traces of electrical separation in A B will 
 disappear. The charged pith ball will be attracted at 
 every point of A B. 
 
 Experiment 27. While the charged glass rod is held near the 
 egg conductors shown in Fig. 133, slide the loop, carrying A about 
 4 inches (10 cm.} to the left and then hold the rod between the two 
 eggs. The rod will repel one egg and attract the other. 
 
 334. Charging a Body by Induction. If the 
 
 polarized conductor be touched with the hand, or other- 
 wise placed in electric communication with the earth, the 
 electricity repelled by C (Fig. 133) will escape, and the 
 pith balls at B will fall together. The electricity at the 
 other end will be held by the mutual attraction between 
 it and its opposite kind at G. The line of communica- 
 tion with the ground being broken and the conductor 
 
206 FR1CTIONAL ELECTRICITY. 
 
 being removed from the vicinity of O, it will be found 
 charged with electricity opposite in kind to that of C. 
 
 A body may be thus charged by induction with 
 no loss to the inducing body. If the conductor, A B, 
 be made in two parts and the parts separated, while 
 under the inductive action of the electrified body, C 9 the 
 two electricities can no longer return to neutralize each 
 other, but must remain, each on its own portion of the 
 conductor. The two parts will thus be oppositely charged. 
 
 335. Successive Induction. If a series of insu- 
 lated conductors, like the egg shells of Fig. 132, be placed 
 in line as shown in Fig. 134, and a positively electrified 
 
 FIG. 134. 
 
 body be brought near, each conductor will be polarized. 
 The first will be polarized by the influence of the + of 
 (7; the second by the influence of the + of M, and so on. 
 
 (a.) Either kind of electricity may be carried from M or N by a 
 small insulated body, called a proof-plane (Fig. 139), to the elec- 
 troscope, there tested and found to be as represented in the figure. 
 If the conductors, M and N, be now placed in actual contact, the + 
 of both will be repelled by G to the furthest extremity of N and 
 the of both will be attracted to the opposite end of M, near to Cl 
 
FRICTIONAL ELECTRICITY. 207 
 
 '&.) It is very plain that any body may be looked upon as a collet- 
 lion of many parallel series of such conductors, each molecule rep- 
 resenting a conductor. Thus, each molecule may be polarized, + 
 at one end and at the other. If the body in question be a good 
 conductor of electricity, this polarization of the molecules is only for 
 an instant. The two electricities pass from molecule to molecule 
 and accumulate at opposite ends of the body. The body is then 
 polarized, bat not the molecules of the body. On the other hand, 
 good insulators resist this tendency to transmit the electricities from 
 molecule to molecule and are able to maintain a high degree of 
 molecular polarization for a great length of time. In brief, the 
 molecules of conductors easily discharge their electricities into each 
 other ; those of non-conductors do not. 
 
 336. Polarization Precedes Attraction. 
 
 When an electrified glass rod is brought near an electric 
 pendulum, the pith ball is polarized 
 as shown in the figure. As the 
 electricity of the ball is nearer the + 
 of the glass than is the + of the ball, 
 
 the attraction is greater than the re- 
 
 FIG. 135. 
 
 pulsion. If the pith ball be sus- 
 pended, not by a silk thread but by some good conductor, 
 the attraction will be more marked, for the -f- of the ball 
 will escape to the earth through the support and, thus, the 
 repelling component will be removed. 
 
 Note. Polarization and electrification by induction explain a great 
 many electrical phenomena. 
 
 337. Provisional Theory of Electricity. 
 
 While the real nature of electricity remains unknown, the 
 following theory will be found convenient for classifying 
 results already attained and suggesting directions for fur- 
 ther inquiry. But we must not let it influence our judg- 
 ment as to what is the true and full explanation of elec- 
 
208 FRICTIONAL ELECTRICITY. 
 
 trical phenomena, which explanation may be found here- 
 after : 
 
 (1.) We may assume that a neutral or unelectri- 
 fied body contains equal and equally dis- 
 tributed quantities of positive and of nega- 
 tive electricity. 
 
 (2.) We may assume these electricities to be un- 
 limited in amount. 
 
 (3.) We shall then conceive that a positively elec- 
 trified body has an excess of -f electricity 
 and that a negatively electrified body has 
 an excess of electricity. 
 
 (4.) In this light, we shall see that communi- 
 cating 4- electricity to a body is equiva- 
 lent to removing an equal amount of 
 electricity from it, and conversely. 
 
 338. The Electrophorus. This simple instru- 
 ment consists generally of a shallow tinned pan filled with 
 resin, on which rests a movable metallic cover with a glass 
 or other insulating handle. The resinous plate may be 
 replaced by a piece of vulcanized india-rubber. The metal 
 surface and the resinous surface touch at only a few 
 points ; they are practically separated by a thin layer of 
 insulating air. 
 
 (a.) The resinous plate may be prepared by melting together 
 equal quantities of resin and Venice turpentine and then adding a 
 like quantity of shellac. The substances should be heated gradually 
 and stirred together so as to prevent the forming of bubbles. Be 
 careful that the mixture does not take fire in course of preparation. 
 The Venice turpentine is desirable, but not necessary. For a handle, 
 a stout wire may be soldered to the centre of the disc and covered 
 with rubber tubing, or a piece of sealing wax, of convenient size, 
 
FRICTIONAL ELECTRICITY. 
 
 209 
 
 m 
 
 FIG. 136. 
 
 may be fastened to the disc for the purpose. A still better plan is 
 to make the cover of wood, a little less in diameter than the resinous 
 plate. Its edges should be carefully rounded off. For a handle, a 
 glass rod or tube may be tightly 
 thrust or cemented into a hole in 
 the middle of the cover. Place tin- 
 foil all over the cover and smooth 
 down all rough ed^es of the foil 
 with the finger-nail or paper-folder. 
 The wire support for a pith ball or 
 paper electroscope may be thrust 
 into the wood of the cover, care be- 
 ing taken that it touches the tin- 
 foil. 
 
 (&.) For an electroscope for the 
 electro phorus, provide a bit of wire 
 about 8 cm. long and bend it at 
 right angles about 1 cm. from, each 
 end. Solder one of the bent arms 
 of the wire (see Appendix B) to 
 the upper side of the metal cover, near its edge, in such a way that 
 the central part of the wire shall be vertical. Cut a strip of gold 
 leaf (or Dutch metal) about 8 cm. long and 8 mm. wide. Moisten 
 the sides of the free horizontal wire-arm with a little mucilage, 
 place the middle of the gold-leaf strip over the top of the arm and 
 bring the ends of the leaf down to a vertical position, touching each 
 other. The mucilage will hold the leaf to the wire. When the 
 wire support and gold leaves are electrified, the latter will diverge. 
 When the apparatus is not in use, this electroscope may be protected 
 by inverting a tumbler or beaker glass over it. 
 
 (c.) The plate is rubbed or struck with flannel or catskin and 
 thus negatively electrified. The cover is then placed upon the resin 
 and thus polarized by induction. If the cover be provided with a 
 gold-leaf electroscope, the free negative electricity of the cover will 
 cause the leaves to diverge ; the positive electricity of the cover 
 will be " bound " on the under side of the cover by the attraction 
 of the negative electricity of the resin. Remove the cover and the 
 separated electricities reunite, as is shown by the falling together of 
 the lately divergent gold leaves. Place the cover again upon the 
 resin. Polarization is manifested by the divergence of the leaves. 
 Touch the cover with the finger as shown in the figure ; the 
 electricity escapes and the leaves fall. The cover is now charged 
 positively, but its electricity is all "bound" at Us under surface 
 
210 
 
 FR1CTIONAL ELECTRICITY. 
 
 and cannot cause the leaves to separate. Remove the cover by its 
 insulating handle and the electricity, lately "bound" but now 
 " free," diffuses itself and the leaves are divergent with + elec- 
 tricity. The charged cover will give a spark to the knuckle or other 
 unelectrified body presented to it. (Fig. 137.) 
 
 339. The Electrophorus Charged by Induc- 
 tion. The cover may 
 be thus charged and 
 discharged an indefi- 
 nite number of times, 
 in favorable weather, 
 without a second elec- 
 trifying of the resinous 
 plate. This could not 
 happen if the electricity 
 of the cover were drawn 
 from the plate. More- 
 over, if the charge of 
 the cover were drawn 
 from the plate, it would 
 be , and not + . 
 There is no escape from 
 the conclusion that the 
 
 FIG. 137. 
 cover is charged by induction and not by conduction. 
 
 (a.) If the resin were a good conductor like the metal cover, its 
 molecules would all receive + electricity from the cover and give 
 electricity to it. But as the resin is a poor conductor, only the 
 very few molecules that come in actual contact with the cover at 
 each charging Lave their electrical equilibrium restored. The + 
 of the cover cannot readily pass through them to their electrified 
 neighbors. Hence, it requires a great many placings of the cover 
 upon the plate to discharge the resin by reconveying to it the + 
 electricity removed at its electrification. When the cover is charged, 
 it gives up part of its electricity ; when it is discharged, it re- 
 
FRACTIONAL ELECTRICITY. 
 
 211 
 
 ceives this electricity back again from the body that discharges 
 it. As this giving and taking is neither to nor from the resin, it 
 may be continued almost indefinitely. A Leyden jar ( 353) may be 
 charged with an electrophorus. 
 
 34O. Whence this Energy ? At every discharge 
 of the electrophorus, it gives a definite amount of elec- 
 tricity, capable of doing a definite amount of work. As 
 this is obtained not by the expenditure of any part of the 
 original charge,, we are led to seek for the source of this 
 apparently unlimited supply of energy. 
 
 " As a matter of fact, it is a little harder work to lift 
 the cover when it is charged with the + electricity than 
 if it were not charged, for, when charged, there is the 
 
 FIG. 138. 
 
 ;orce of electric attraction to be overcome as well as the 
 force of gravity. Slightly harder work is done at the ex- 
 pense of the muscular energies of the operator and this is 
 
212 
 
 FRICTIONAL ELECTRICITY. 
 
 the real origin of the energy stored up in the separate 
 charges." 
 
 Experiment 28. Insulate a metal globe and provide it with two 
 closely fitting hemispherical shells that have insulating handles. 
 Electrify the globe ; bring it near the electroscope to be sure that it is 
 electrified. Place the hemispheres upon the globe. Remove them 
 quickly, being careful that their edges do not touch the sphere 
 after the first separation. (Fig. 138.) Bring first one shell and then 
 the other near the electroscope ; they are electrified. Bring the globe 
 itself near the electroscope. It is no longer electrified. Delicate 
 manipulation is needed to make the experiment successful. You 
 will fail, perhaps, more times than you succeed. But when the 
 experiment is successful, it is instructive. The apparatus is called 
 Biot's hemispheres. 
 
 FIG. 139. 
 
 Experiment 29. By means of a few sparks rroir tne elect:* 
 phorus, charge an insulated hollow sphere, li&vai% an orifice in tlae 
 
FRICTION AL ELECTRICITY. 
 
 213 
 
 top. Bring a proof plane (made by fastening a disc of gilt paper to 
 a long, thin insulating handle) into contact with the outer surface 
 of the sphere. The proof-plane is charged by the sphere, as may be 
 shown by bringing it near -an electroscope. Discharge the proof 
 plane and bring it into contact with the inner surface of the sphere. 
 Remove it carefully without allowing it to touch the sides of the 
 orifice. Bring it to the electroscope. It is not charged. (Fig. 139.) 
 An empty tin fruit can supported on a clean, dry, glass tumbler will 
 answer for the experiment. 
 
 Experiment 30. Make a conical bag 
 of linen, supported, as shown in Fig. 
 140, by an insulated metal hoop five or 
 six inches in diameter. Charge the bag 
 with the electrophorus. 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 described 
 above. Turn the bag and repeat the 
 test. Whichever surface of the linen is 
 external, no electricity can be found upon 
 the inside of the bag. Nothing can be 
 more conclusive than this. 
 
 FIG. 140. 
 
 Experiment 31. Vary the experiment by the use of a hat sus- 
 pended by silk threads. Notice that the greatest charge can be 
 obtained from the edges ; less from the curved or flat surface ; none 
 from the inside. 
 
 341. A Charge Resides on the Surface. 
 
 Many experiments have been made showing that when a 
 conductor is electrified, the electricity passes to the 
 surface and escapes if the body be not insulated. 
 A bomb-shell and a cannon ball of equal diameter will 
 receive equal quantities of electricity from the same source. 
 The hollow conductors commonly used in experiments with 
 static electricity are as serviceable as if they were solid. 
 A wooden prime conductor coated with gold-leaf is as 
 
214 FRICTIONAL ELECTRICITY. 
 
 efficient as if it were made of solid gold. Experiment is 
 unable to find any difference in this respect between a 
 solid sphere of metal and the thinnest soap-bubble of the 
 same diameter. 
 
 (.) This does not apply to an electric current. A hollow wm 
 will not conduct electricity as well as a solid wire of the same 
 diameter. Electricity may be drawn to the inside of a hollow con- 
 ductor by placing there an electrified, insulated body. 
 
 (6.) The linen bag of Experiment 30 was devised by Michael 
 Faraday, but his most striking experiment was made with a wooden 
 cage, measuring 12 feet each way, covered with tin-foil, insulated 
 and charged by a powerful electric machine. He carried his most 
 delicate electroscopes into this cage. Large sparks and brushes 
 were darting off from every part of the outer surface, but the phil- 
 osopher and his sensitive instruments within the cage failed to 
 detect the least electric influence. 
 
 Experiment 32. Place a carrot horizontally upon an insulating 
 support. Into one end of the carrot, stick a sewing-needle. Bring 
 tne electrified glass rod near the point of the needle without touching 
 it. The electricity of the carrot quietly escapes from the point 
 to the rod and the carrot is charged with the + electricity that 
 remains. 
 
 342. Density. Experiments show that when a spher 
 ical conductor is charged, the electricity is evenly dia 
 tributed over the surface, provided no other electrified 
 body be near to affect the distribution by induction. The 
 electric density (or number of electrical units per unit ot 
 area) is the same at every point. Experiments on an 
 elongated cylinder, like the prime conductor of the elec- 
 tric machine, show that the density is greater at the ends. 
 On an egg-shaped conductor, like that shown in Fig. 141, 
 the density is greatest at the smaller end. In general, 
 the electric density is very great at any pointed 
 part of a charged conductor. 
 
FRICTION AL ELECTRICITY. 215 
 
 This density at a point may become so great that the 
 electricity will escape rapidly and quietly, the air particles 
 
 FIG. 141. 
 
 quickly carrying off the charge by convection. This 
 explains the effect of pointed conductors, which plays so 
 important a part in the action of electric machines. This 
 property will be illustrated in several of the experiments 
 of 371. It is fundamental to the quiet action of light- 
 ning rods. 
 
 343. Electric Machines. Machines have been 
 made for developing larger supplies of electricity more 
 easily than can be done with a rod of glass or sealing-wax 
 or with the electrophorus. Each of them consists of one 
 part for producing the electricity and another part for 
 collecting it. 
 
 344. The Plate Electric Machine. This in- 
 strument is represented in Fig. 142. It consists of an in- 
 sulator (or electric), a rubber, a negative and a positive or 
 prime conductor. The electric is a glass (or ebonite) plate, 
 A, generally one, two or three feet in diameter. This plate 
 has an axis, B, and handle, C, and is supported upon two 
 upright columns. The rubber, Z>, is made of two cush- 
 
216 FRlCTlONAL ELECTRICITY. 
 
 ions of silk or leather, covered with amalgam (see 302, a). 
 They press upon the sides of the plate and are supported 
 
 FIG. 142. 
 
 from the negative conductor, with which they are in 
 electric connection. The negative conductor, JV, is sup- 
 ported upon an insulating column and, when only posi- 
 tive electricity is desired, is placed in electrical connection 
 with the earth hy means of a chain or wire, W. The 
 prime conductor, P, is insulated. One end of the prime 
 conductor terminates in two arms, P, which extend one 
 on either side of the plate. These arms, being studded 
 with points projecting toward the plate, are called combs. 
 The teeth of the combs do not quite touch the plate. A 
 silk bag, S, is often supported so as to enclose the lower 
 part of the plate. All parts of the instrument except the 
 teeth of the combs are carefully rounded and polished, 
 sharp points and edges being avoided to prevent the es- 
 cape of electricity as already explained. This avoiding of 
 points and edges is to be regarded in all apparatus for use 
 with electricity of high potential. 
 
FRICTION AL ELECTRICITY. 
 
 (a.} The pupil may make a plate machine without much expense. 
 A glazier will cut for him a disc of place glass, possibly from a 
 fragment on hand. The edges of this disc may be rounded on a wet 
 grindstone. A hole may be bored in the middle with a round file 
 kept moistened with a solution of camphor in turpentine. The con- 
 ductors, AT and P, may be made of wood covered with gold-foil or 
 Dutch leaf and supported on pieces of stout glass tubing. The 
 prime conductor may well have two such supports. The arms may 
 consist of two stout wires thrust into the end of a prime conductor, 
 their free ends being provided with knobs of lead or other metal. 
 The combs may be made by soldering pin points to one side of each 
 arm. See that the gold-foil makes actual contact with the metal 
 arms. See that all metal parts except the pin points are polished 
 smooth. The columns that support the plate may be made of sea- 
 soned wood. The part of the handle to which the hand is app^ed 
 may be made of glass or insulated by covering it with rubbe;- 
 tubing. 
 
 345. Operation of the Plate Machine. The 
 
 plate is turned by the handle. Electric separation is pro- 
 duced by the friction of the rubbers. The -j- electricity of 
 the rubber and negative conductor passes to the plate; the 
 electricity of the plate passes to the rubber and negative 
 conductor. The part of the plate thus positively charged 
 passes to the combs of the prime conductor. The + of 
 the plate acts inductively upon the prime conductor, polar- 
 izes it, repels the -f and attracts the electricities. Some 
 of the electricity thus attracted streams from the points 
 of the combs against the glass, while some of the -f elec- 
 tricity of the glass escapes to the prime conductor. This 
 neutralizes that part of the plate, or restores its electric 
 equilibrium, and leaves the prime conductor positively 
 charged. As each successive part of the plate passes the 
 rubber, it gives off electricity and takes an equal 
 amount of -f ; as it passes between the combs it gives off 
 its + electricity and takes an equal amount of . The 
 
218 FRICTIONAL ELECTRICITY. 
 
 rubber and negative conductor are kept in equilibrium by 
 means of their connection with the earth, " the common 
 reservoir." As the plate revolves, the lower part, passing 
 from N to P, is positively charged ; the upper part, pass- 
 ing from P to JV, is neutralized. If negative electricity 
 be desired, the ground connection is changed from N to 
 P and the charge taken from N. 
 
 346. The Dielectric Machine. This instru- 
 ment is represented in Fig. 143. Two plates of vulcanite 
 (ebonite), A and B, overlap each other without touching 
 and revolve in opposite directions. The upper plate is 
 made to revolve much more rapidly than the lower by 
 means of the pulleys shown at the right of the figure. 
 The prime conductor and the axes of the two plates are 
 carried by two insulating pillars. From the prime con- 
 ductor, a comb is presented to the upper part of the upper 
 plate. Another comb is presented to that part of A which 
 is overlapped by the upper part of B. This comb is con- 
 nected by a universal joint at e with a discharging rod and 
 ball, which may be brought near the end of the prime 
 conductor or turned away from it. The rubbers and the 
 lower comb are to be in electrical communication with 
 the earth. The general arrangement is clearly set forth 
 in the figure. 
 
 347. Operation of the Dielectric Machine. 
 
 The plate, B, is turned directly by the handle and the 
 plate, A, indirectly by the aid of the pulley. The plate, 
 J9, is negatively electrified by friction with the rubber 
 and thus acts by induction upon the lower part of A, 
 which is thus polarized. The -f of this part of A is 
 
FRICTION AL ELECTRICITY. 
 
 219 
 
 bound by the attraction of the - - of B, while the of 
 A is repelled, escapes by the lower comb and is replaced 
 by + from the earth 
 through the lower 
 comb and its ground 
 connection. This part 
 of A, thus positively 
 charged, is soon re- 
 moved from the induc- 
 ing body and the -f 
 charge, bound by B, is 
 set free. It then 
 comes to the upper 
 comb, polarizes it and 
 the prime conductor 
 and exchanges some of 
 its own + for an equal 
 amount of from the 
 prime conductor. This 
 neutralizes that part of the upper plate and leaves the 
 prime conductor positively charged. As each successive 
 part of A passes the lower comb, it gives off electricity 
 and takes an equal amount of -f- ; as it passes the upper 
 comb, it gives off -f- electricity and receives an equal 
 amount of . The charge of B is continually main- 
 tained by friction with the rubber. When the discharging 
 rod and ball are brought near the prime conductor, as 
 shown in the figure, a rapid succession of spark's is pro- 
 duced, owing to the recombination of the separated elec- 
 tricities. If another body is to be charged from the prime 
 conductor, the ball and rod may be turned aside. The 
 efficiency of this machine is greater than that of the plate 
 
 FIG. 143. 
 
220 
 
 FRICTIONAL ELECTRICITY. 
 
 or cylinder machine. It is less affected by atmospheric 
 moisture and is more compact, but the vulcanite plates 
 seem to deteriorate with use. They should be washed 
 occasionally with ammonia water and rubbed with paraf- 
 fin oil. Machines of similar construction, but having 
 glass plates, are made. 
 
 348. The Holtz Electric Machine. This in- 
 strument is represented in Fig. 144. It contains two thin, 
 
 circular plates of 
 glass, the larger 
 of which is held 
 fast by two fixed 
 pillars. The 
 smaller plate re- 
 volves rapidly 
 very near it. 
 There are two 
 holes in the fixed 
 FlG - X 44- plate near the 
 
 extremities of its horizontal diameter. To the sides of 
 these openings are fastened paper bands called armatures. 
 The armatures point in a direction opposite to that in 
 which the revolving plate moves. Opposite these armatures 
 and separated from them by the revolving plate, are two 
 metallic combs, connected respectively with the two knobs 
 and Leyden jars shown in the front of the picture. One of 
 these knobs is carried by a sliding rod so that their distance 
 apart is easily adjusted. When this machine works well, it 
 gives results superior to either of those previously mentioned. 
 It is, however, peculiarly subject to atmospheric conditions 
 and is generally considered extremely capricious. 
 
FRICTIONAL ELECTRICITY. 221 
 
 349. Action of the Holtz Machine. To un- 
 derstand the action of this machine requires careful atten- 
 tion. The knobs are placed in contact and a small initial 
 charge is given to one of the armatures by some charged 
 body, as a piece of vulcanite or a glass rod. The handle 
 is then turned, the effort necessary to keep up the motion 
 increasing rapidly. The knobs are then separated and a 
 series of discharges takes place between them. 
 
 (a.) Suppose a small + charge to be imparted at the outset to the 
 right armature. This charge acts inductively across the revolving 
 plate upon the metallic comb, repels + electricity through it and 
 leaves the points negatively electrified. They discharge negatively 
 electrified air upon the front surface of the movable plate ; the re- 
 pelled + charge passes through the brass rods and balls and is dis- 
 charged through the left comb upon the front side of the movable 
 disc. Here it acts inductively upon the paper armature, causing 
 that part of it which is opposite itself to be negatively charged and 
 repelling a + charge into its farthest part, viz., into the armature. 
 This, being bluntly pointed, slowly discharges a + charge upon 
 the back of the movable plate. When the plate is turned round, 
 this + charge on the back conies over from the left to the right side 
 and, when it gets opposite the comb, increases the inductive effect 
 of the already existing + charge on the armature and, therefore, 
 repels more electricity through the brass rods and knobs into the 
 left comb. Meantime the charge, which we saw had been in- 
 duced in the left armature, has in turn acted on the left comb, caus- 
 ing a + charge to be discharged by the points upon the front of the 
 plate and, drawing electricity through the brass rods and knobs, 
 has made the right comb still more highly , increasing the dis- 
 charge of negatively electrified air upon the front of the plate, 
 neutralizing the + charge which is being conveyed over from the 
 left. These actions result in causing the top half of the moving 
 disc to be positively electrified on both sides and the bottom half of 
 the disc to be negatively electrified. The charges on the front 
 serve, as they are carried round, to neutralize the electricities let off 
 by the points of the combs while the charges on the back, induced 
 respectively in the neighborhood of each of the armatures, serve, 
 when the rotation of the plate conveys them round, to increase the 
 inductive influence of the charge on the other armature, Hence, a 
 
FRL 
 
 
 very small initial chai 
 
 being reached when tLt LJctJ j ___ LJ ___ ____ 
 
 that the loss of electricity at their surface equals the gain by con- 
 vection and induction. 
 
 Note. Other forms of electric machines are made. One of the 
 latest of these, known as the Toepler-Holtz, is very compact and 
 efficient and remarkably free from the limitations of atmospheric 
 conditions. It may be described as a continuously acting electro- 
 phorus ( 227). A very good one may be bought for $25 or more. 
 One should be provided for the school in some way if possible. Any 
 electrical machine should be free from dust and perfectly dry when 
 used. It should be warmer than the atmosphere of the room, that 
 it may not condense moisture from the surrounding air. The drier 
 the atmosphere, the better will be the action of the machine. 
 
 EXERCISES. 
 
 1. How can you show that there are two opposite kinds of elec- 
 tricity ? 
 
 2. How would you test the kind of electricity of an electrified 
 body? 
 
 3. Quickly pass a rubber comb through the hair and determine 
 whether the electricity of the comb is positive or negative. 
 
 4. Why do we regard the two electric charges produced simul- 
 taneously by rubbing 1 together two bodies as being of opposite 
 kinds? 
 
 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. Electrify one insulated egg-she] 1 conductor ( 332, 6). Bring it 
 near a second conductor but not in contact with it. Touch the 
 second egg-shell with the finger, (a.) Experimentally, determine 
 whether the second egg-shell is electrified or not. (b.) If you find 
 that it is, what word explains the method of charging? (c.) If the 
 second egg-shell is charged, will its potential and the potential of the 
 first be of the same or of opposite signs ? 
 
 7. (a.} In 323, b, it is directed that an electrified body be brought 
 " near" the knob of the gold-leaf electroscope. Why not touch the 
 knob with the charged body? (6.) Why do not the gold leaves 
 diverge immediately after touching the knob with the finger as there 
 directed? (c ) If the electrified body being tested had a + charge, 
 is the charge of the gold leaves + or ? Explain. 
 
 8. (a.) What is a proof-plane ? (6.) An electroscope? (c.) Describe 
 one kind, of electroscope, (d.) Another kind. 
 
FRICTIONAL ELECTRICITY. 
 
 9. (a.) Define electrics, conductors and insulators. (&.) Explain 
 electric induction. 
 
 10. (a.) If a metal globe suspended by a silk cord be brought near 
 the prime conductor of an electric machine in action, feeble sparks 
 will be produced. Explain. (6.) If the globe be held in the hand, 
 stronger sparks will be produced. Explain. 
 
 11. 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 an axis. Give this piece of scientific 
 apparatus an appropriate name. 
 
 12. (a.) Prepare two wire stirrups, A and B, like those shown in 
 Fig. 121 and suspend them by threads. Electrify two glass rods 
 by rubbing them with silk and place them in the stirrups. Bring 
 A near B. Notice the repulsion, (b.) Repeat the experiment with 
 two sticks of sealing-wax that have been electrified by rubbing with 
 flannel. Notice the repulsion, (c.) Place an electrified glass rod in A 
 and an electrified stick of sealing-wax in B. Notice the attraction. 
 Give the law illustrated by these experiments. 
 
 13. Two small balls are charged respectively with + 24 and 8 
 units of electricity. With what force will they attract one another 
 when placed at a distance of 4 centimeters from one another ? 
 
 Ans. 12 dynes. 
 
 14. 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. 
 
224 
 
 FRICTIONAL ELECTRICITY. 
 
 Experiment 33. Hang a negatively charged pith ball inside a 
 dry glass bottle. Bring an electrified glass rod to the outer side of 
 the bottle. The pith ball will rush to the side of the bottle nearest 
 the rod because of the attraction between the opposite electricities. 
 
 Experiment 34. Paste a piece of tin-foil, two or three inches 
 square, on the middle of each face of a pane of glass. Hold a finger 
 on one of the metallic coats while the other coat is held, for a short 
 time, in contact with the prime conductor of an electric machine in 
 operation. Remove the pane and place it on edge without touching 
 both coats at the same time. Although both coats are oppositely 
 charged ( 384), they may be touched in succession without any 
 shock. When both are touched at the same time, the shock is 
 greater than would have been received from the prime conductor by 
 which this condenser was charged. 
 
 35O. Condensation of Electricity. Two 
 
 suspended pith balls oppositely charged attract one 
 another across the intervening air. They attract mu- 
 tually even when a plate of glass is held between them 
 
 although neither the balls 
 c nor their electric charges can 
 
 pass through the glass. In 
 the case of the pane of 
 glass with its two tin-foil 
 coats, or in the similar case 
 of two metallic plates, A 
 and B, separated by a layer 
 of dry air or other non- 
 conductor, (7, as shown in 
 Fig. 145, the two charges 
 are "bound," each by the 
 attraction of its opposite 
 on the other side of the 
 pane. It is found that two such coats may be charged 
 much more strongly than either one could be if the oppo- 
 site coat were wanting. If a third plate like JB, but hav~ 
 
 \\ 
 
 FIG. 145. 
 
FRICTIONAL ELECTRICITY. 225 
 
 ing no opposite plate like A, be connected with B by a 
 copper wire and the middle of the wire brought into con- 
 tact with the prime conductor, nearly the whole charge 
 will go to B and very little to the third plate. The ca- 
 pacity of a charged conductor is greatly increased 
 by bringing it near a second charged conductor 
 oppositely charged. Its capacity being thus increased, 
 a greater quantity of electricity must be put into it to 
 raise it to as high a potential. Such a method of increas- 
 ing the quantity of electricity that a conductor may re- 
 ceive without raising its potential is called the condensa- 
 tion or accumulation of electricity. 
 
 351. Electric Condensers. An apparatus for 
 collecting a large quantity of electricity at a moderate po- 
 tential, as just described, is called an electric condenser. 
 
 (a.) Let A and B, Fig. 146, 
 represent two insulated metallic 
 plates about six inches in diam- 
 eter, separated by C, a plate of 
 glass somewhat larger. Let each 
 metallic plate have an electric 
 pendulum, a and b. Remove A 
 and connect B with the conductor 
 of the electric machine, by means 
 of the wire, x. The divergence of 
 b shows the presence of free electricity. Connect A with the 
 ground by the wire, y, and place it in position as represented. By 
 the inductive influence of B, the - electricity of A is drawn to the 
 surface, n, while the + escapes by y. But this - electricity at n 
 attracts the + of B largely to the surface m and holds it there as 
 bound electricity, thus increasing the electrical density at that sur- 
 face. This change is shown by less divergence of b. Consequently, 
 B can receive more electricity from the machine, which will, in 
 turn, attract more - electricity to n. This further supply will, in 
 
226 
 
 FRICTIONAL ELECTRICITY. 
 
 FIG. 147. 
 
 turn, bind more of the + electricity of B at m. In this way, a large 
 quantity of + electricity may be accumulated at m and a large 
 
 quantity of at n. 
 This accumulation may 
 thus go on until the 
 potential at the sur- 
 face, p, is equal to that 
 of the machine, as it 
 was when A was ab- 
 sent. Interrupting 
 communication by x 
 and y, both plates are 
 charged. The vertical 
 pendulum, a, shows no 
 free electricity, the 
 electricity of A being 
 all bound at n ; the 
 pendulum at b shows 
 some free electricity, 
 
 although the greater part of the electricity of B is bound at m. Re- 
 move A and B from each other and the bound electricity of each is 
 set free and both a and b fly out as the discs are separated. The 
 pith balls thus seem to indicate that the discs are more highly elec- 
 trified when they are thus separated, but no additional charge has 
 been given to either A or B. The fact is that while B was near A, 
 the capacity of B was largely increased. On moving it away from A, 
 its capacity was diminished and the same quantity of electricity elec- 
 trified it to a higher potential than before. The presence of an earth 
 connected plate near an insulated conductor largely increases the elec- 
 tric capacity of the latter, enabling it to condense electricity upon the 
 surface nearest the opposing plate, at which surface the electrical den- 
 sity becomes very great. 
 
 (b.) If A and B are pushed up close to C, the decrease of distance 
 will work an increase of the inductive action and a still larger quan- 
 tity may be accumulated in the plates. Thus, the capacity of a con- 
 denser depends, in part, upon the nearness of the plates to each other. 
 
 352. Dielectrics and Specific Inductive 
 Capacity. Substances that permit inductive electric 
 influences to act across or through them as just described 
 are called dielectrics. All dielectrics are insulators, but 
 
FRICTIONAL ELECTRICITY. 
 
 227 
 
 equally good insulators are not always equally good dielec- 
 trics. Glass is a better dielectric than ebonite and ebonite 
 is better than air. The capacity of a condenser is greater 
 when the dielectric is glass than it is when the dielectric 
 is air. The ratio of the capacity in the former case 
 to the capacity in the latter case is called the 
 specific inductive capacity (or specific inductivity) 
 of glass. Air (at C. and 760 mm. ) is taken as the 
 standard, its specific inductive capacity being unity. 
 
 (a.) The old idea that electric induction is " action at a distance" 
 is wholly disproved* by the fact that different substances have dif- 
 ferent specific inductive capacities, for it is evident that the dielec- 
 tric itself is concerned in the process. Otherwise, all media would 
 allow induction to take place across them with equal facility. 
 
 (6.) The specific inductivity (sometimes called dielectric capacity) 
 assigned to various substances by different observers varies widely. 
 Gordon gives the following results : 
 
 Air 1.00 I Ebonite 2.284 
 
 Paraffin (solid).l. 9936 Gutta percha. .2.462 
 
 India rubber.. 2.22 I Sulphur 2.58 
 
 Schiller gives the specific inductivity of white mirror glass as 5.88 
 to 6.34. 
 
 Shellac 2.74 
 
 Glass, from 3.013 
 
 " to 3.258 
 
 353. The Leydeii Jar. The most com- 
 mon and, for many purposes, the most con- 
 venient 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, communicating 
 by means of a small chain with the inner coat 
 and terminating above in a knob. The upper 
 part of the jar and the cork which closes the 
 mouth of the jar and supports the rod are generally coated 
 with sealing-wax or shellac varnish to lessen the deposition 
 
 FIG. 148. 
 
228 FRICTION A L ELECTRICITY. 
 
 of moisture from the air. The inner coat represents the 
 collecting plate, B\ the glass jar, the insulating plate, (7; 
 the outer coat, the condensing plate, A, of Fig. 146. 
 
 (a.) Select a candy or fruit jar of greenish glass ; paste tin-foil 
 within and without, as above described, using flour paste ; thrust a 
 wire through a dry cork ; bend the wire so that, when the cork is in 
 its place, the wire shall touch the tin-foil on the inside of the bottle 
 without tearing it ; solder the upper end of the wire to a smooth 
 button or thrust it into a lead bullet ; charge your Leyden jar with 
 a few sparks from the electrophorus and take a shock. 
 
 354. Charging the Leydeii Jar. To charge 
 the jar, hold it in the hand, as shown in Fig. 149, and bring 
 the knob near the prime conductor of an electrical machine 
 that is in action or into contact with it. 
 
 (a.) The + charge thus developed on the inner coat acts in- 
 ductively through the glass, repelling the + electricity which escapes 
 through the hand to the earth and binding its electricity to the 
 surface in contact with the glass. This " bound " negative elec- 
 tricity of the outer coat, in turn, binds the positive of the inner coat, 
 which then may receive a further charge and so on. The inner 
 coat will receive a much greater quantity of electricity than it pos- 
 sibly could were it not for the attraction of its opposite on the outer 
 coat. If, instead of holding the outer coat in the hand, the jar be 
 supported upon a pane of glass so that the repelled electricity of the 
 outer coat cannot escape, the jar cannot be very intensely charged. 
 
 FIG. 
 
 (&.) Thus we see again that the capacity of a conductor is greatly 
 increased when it is placed near a conductor charged with the oppo- 
 
FRICTIONAL ELECTRICITY. 
 
 site kind of electricity. Its capacity being increased, it can receive a 
 greater quantity of electricity without any increase of potential. Of 
 course, the potential of the charged jar cannot exceed that of the 
 prime conductor or other charging body. 
 
 355. Discharging the Leyden Jar. If the jar 
 
 be of good glass, dry and free from dust, it will retain its 
 charge for hours. But if a path be provided by which the 
 opposite and mutually attracting electricities can flow 
 together, they will do so and 
 the jar will be instantaneously 
 and almost completely dis- 
 charged. The jar might be 
 discharged by touching the 
 knob with the finger, the sep- 
 arated electricities coming to- 
 gether through the person of 
 
 the experimenter and the earth. In this case, the experi- 
 menter will feel a "shock." If the charge be intense, the 
 shock will be painful or even dangerous. It is better to 
 use a " discharger," two forms of which are represented in 
 Fig. 150. This consists of two metal arms hinged to- 
 gether, bearing knobs at their free ends and carried by 
 insulating handles. The outer coat of the jar should be 
 touched first. Why ? 
 
 (a.) A good discharger may be made by passing a piece of stout, 
 copper wire, about a foot long, through apiece of rubber tubing and 
 providing a metal knob for each end of the wire. The flexibility of 
 the wire avoids the necessity for a hinged joint. 
 
 356. The Residual Charge. If a Leyden jar be 
 charged, discharged and left for a little time to itself, it 
 will be found that a small, second spark can be obtained. 
 
230 
 
 FRICTIONAL ELECTRICITY. 
 
 TJiere is a residual charge which seems to have 
 soaked into the glass. The return of the residual charge 
 is hastened by tapping the jar. The 
 amount of the residual charge varies 
 with the time that the jar has been 
 left charged ; it also depends on the 
 kind of glass of which the jar is 
 made. (See Appendix J.) 
 
 357. The Leyden Jar with 
 Movable Coats. This piece of appara- 
 tus is represented by Fig. 151. The upper 
 part of the glass jar, B, is coated with shel- 
 lac varnish. The three parts being placed 
 together in proper order, B within A and G 
 within B, the jar is charged in the usual man- 
 ner. The inner coat, (7, is then removed 
 with a glass rod and touched with the hand 
 to discharge it fully. B is then lifted out 
 from A and the outer coat fully discharged. 
 The three parts are then put together again 
 and found to be able to give nearly as strong 
 a spark as at first. This seems to indicate 
 upon the surfaces of the glass rather than upon 
 the surfaces of the coats. If, when the charged jar is in pieces, the 
 thumb be placed on the outer surface of the glass and the forefinger 
 of the same hand on the inner surface, a very slight shock is per- 
 ceptible. The oppositely charged glass molecules that come into 
 actual contact with thumb and finger respectively are discharged. 
 By changing the position of the thumb and finger, successive little 
 shocks may be felt as successive portions of the inner and outer sur- 
 faces of the glass are discharged. The inner coat furnishes a means 
 for the simultaneous discharge of the inner layer of glass molecules ; 
 the outer coat does the same for the outer layer of glass molecules. 
 Thus all or nearly all of the electrified glass molecules may be dis- 
 charged simultaneously instead of successively. 
 
 FIG. 151. 
 
 that the charge 
 
 358. The Leyden Battery, The effect that may 
 be produced with a Leyden jar or other condenser depends 
 
FRICTIONAL ELECTRICITY. 
 
 231 
 
 upon the size of the coats, the thinness and the inductive 
 capacity of the glass. But a large jar is expensive and 
 requires great care ; thin glass is liable to perforation by 
 
 the condensed and strongly attracting electricities of its 
 two coats. To obviate both of these d ifficulties, a collection 
 of jars is used. When their outer coats are in electric 
 communication, which may be secured by placing them 
 in a tray the bottom of which is covered with tin-foil, and 
 their inner coats are connected by wires or metal strips 
 passing from rod to rod, or from knob to knob, the ap- 
 paratus is called a Leyden or electric battery. "Tough- 
 ened glass" is less easily pierced than ordinary glass. 
 Hence, Leyden jars made of it may be made thinner and, 
 consequently, Avill hold a greater charge than otherwise. 
 The battery is charged and discharged in the same way as 
 a single jar. Great care is needed, for if the discharge 
 
232 FRICTIONAL ELECTRICITY. 
 
 were to take place through the human body the result 
 would be serious and possibly fatal. The "universal 
 discharger," as employed with the Leyden battery, is 
 shown at A G in Fig. 152. (See Exp. 50.) 
 
 (a.) The horizontal rods of the universal discharger may be sup- 
 ported by passing them through corks in the mouths of two bottles. 
 When a table is wanted for the support of bodies to be operated 
 upon by the discharge, it may be made by placing a small plate of 
 glass upon the open mouth of a bottle of the same height as those 
 that carry the rods and placing the third bottle between the other 
 two. 
 
 359. The Farad. The farad is the capacity of a 
 condenser that will be raised to a potential of one volt by 
 a charge of one coulomb of electricity ( 382, 387). Such 
 a condenser would be too large to be constructed. The 
 micro-farad (=0.000001 farad) is, therefore, chosen as 
 the practical unit of electrical capacity. The ca- 
 pacity of three miles of an Atlantic cable is about one 
 micro-farad. A micro-farad condenser contains about 
 3,600 square inches of tin-foil. A farad equals 10~ 9 of an 
 electro-magnetic unit of capacity ( 451). See App. M (5). 
 
 (a.) A coulomb in a farad gives a volt. 
 Coulombs 
 
 Farads = 
 
 Volts 
 
 36O. Submarine Cable Condensers. An 
 
 ocean cable forms a condenser, the water forming the 
 outer coating ; the conducting wire, the inner coating ; 
 while the insulating layers of gutta-percha correspond 
 to the glass of the Leyden jar. When, for example, one 
 end of a submerged cable is connected to the -f pole of 
 a powerful battery, + electricity flows into it. Before 
 any signal can be received at the other end, enough elec- 
 
FRICTIONAL ELECTRICITY. 233 
 
 tricity must flow in to charge the cable to a considerable 
 potential, an operation which may, in the case of long 
 cables, require some seconds. It is a serious obstacle to 
 signalling with speed through the Atlantic cables. 
 
 (a.) Imagine a mile of insulated cable wire to be coiled up in a tub 
 of water (Fig. 153), one end, JV". being insulated. The other end is 
 joined up through a long 
 coil galvanometer, G, to 
 the + pole of a large bat- 
 tery., whose pole is 
 joined by a wire to the 
 water in the tub. As 
 soon as this is done, the 
 needle of the galvanom- JT IG jg^. 
 
 eter will show a violent 
 
 deflection, + electricity rushing through it into the interior of the 
 cable and a charge being accumulated on the outside of it where 
 the water touches the gutta-percha. The flow will go on, though 
 diminishing, until the cab.le is fully charged, taking, perhaps, an 
 hour. Now remove the battery and close the circuit. The charge 
 in the cable will rush out through the galvanometer, which will 
 show an opposite deflection. The charge will continue "to soak 
 out " for a long time. 
 
 361. Modes of Discharge. An electrified con- 
 ductor may be discharged in at least three ways, viz., by 
 the disi*uptive> discharge, by the convective discharge 
 and by the conductive discharge. The discharge in any 
 of these ways is accompanied by a transformation of .en- 
 ergy. Sound, light, heat, chemical action and other phe- 
 nomena are produced. 
 
 Experiment 35. Present a knuckle of the hand or a metal knob 
 fco the prime conductor of an electric machine and "draw sparks" 
 therefrom. (See Fig. 169.) For short distances, the spark is straight. 
 If the distance be made somewhat greater, the spark takes a sinuous 
 and forked form as though floating dust particles served as stepping- 
 stones and rendered a crooked path the easiest. If the charge be 
 
234 
 
 FRICTION AL ELECTRICITY. 
 
 very powerful, the spark will take the zigzag form so familiar in the 
 
 lightning-stroke. When the machine is vigorously worked in the 
 dark, the apparently continuous discharge into 
 the air produces a luminous appearance at the 
 ends of the conductor. This appearance, known 
 as a brush, may be improved by holding a large, 
 smooth, metal globe at a distance a little too great 
 for the passage of a spark. When the discharge 
 takes place from the rounded end of a wire ex- 
 tending from the conductor, a quiet, phosphor- 
 
 escent glow, as shown in Fig. 154, will often appear at and near the 
 
 end of the wira 
 
 FIG. 154. 
 
 362. The Disruptive Discharge. A discharge 
 of electricity taking place suddenly through a non-con- 
 ductor is called a disruptive discharge, e.g., the spark and 
 brush drawn from an electric machine in action. The 
 glow is either a continuous discharge or one of exceed- 
 ingly small period. Perhaps, it is a high order of con- 
 vective discharge. 
 
 Experiment 36. Attach a pointed wire to the prime conductor 
 of the electric machine. The flame of a candle held near will be 
 blown away, as shown in 
 Fig. 155. If the candle be 
 placed upon the prime 
 conductor and a pointed 
 conductor be held in the 
 hand near the candle, the 
 flame will still be blown 
 away. 
 
 363. The Con- 
 vective Dis- 
 charge. When elec- 
 tricity of high poten- 
 tial accumulates with 
 
 so great a density as to electrify the neighboring particles 
 of air which, driven by electric repulsion, fly off carrying 
 
 FlG 
 
FRICTIONAL ELECTRICITY. 235 
 
 part of the charge with them, we have what is called the 
 convective discharge. Such discharges are best mani- 
 fested in gases at low pressure, in tubes exhausted by an 
 air-pump. (Exp. 70.) 
 
 364. The Conductive Discharge. The flow 
 of a continuous current of electricity constitutes the con- 
 ductive discharge. When electricity flows through a wire 
 from the prime conductor of an electric machine to the 
 rubbers or from the positive pole of a voltaic cell or bat- 
 tery to the negative, we have a conductive discharge. It 
 will be considered in the section especially devoted to 
 voltaic electricity. 
 
 365. Atmospheric Electricity. The phenom- 
 ena of atmospheric electricity are of three kinds : 
 
 1. A continual slight electrification of the air, best ob- 
 
 served in fair weather. 
 
 2. The familiar phenomena of thunder storms. 
 
 3. The Aurora Borealis. 
 
 366. The First Kind. During fair weather, the 
 air above the surface of the earth is usually electrified posi- 
 tively, a negative electrification being extremely rare. In 
 stormy weather, it is more often than -f and frequently 
 changes from one kind to the other several times in an 
 hour. The higher up we go to observe the usual + elec- 
 tricity of the air, the higher its potential is found to be. 
 The evaporation of water by the sun's heat and the fric= 
 tion of moving masses of air probably contribute to the 
 presence of atmospheric electricity. 
 
 367. Thunder Storms. We have already seen 
 (g 341) that a solid conductor can not be charged through- 
 
236 FRICTION AL ELECTRICITY. 
 
 out its substance, the charge residing upon the surface. 
 The same is true of liquids, but aeriform bodies may be 
 charged bodily, the individual molecules being so much 
 more widely separated. Dry air being a poor conductor, 
 the air particles discharge their electricity into each 
 other slowly and with difficulty. The electricity thus 
 prevented from accumulating has a low potential and, 
 hence, gives few manifestations of its presence. The 
 minute particles of water floating in the air being better 
 conductors than the air itself become more highly charged. 
 As they fall and unite, the potential of their charges in- 
 creases. 
 
 (a.) "Suppose eight small drops to join into one. That one will 
 have eight times the quantity of electricity distributed over the sur- 
 face of a single sphere of twice the radius and, therefore, of twice 
 the capacity (for the electrical capacities of spheres are proportional 
 to their radii) of the original drops." The capacity being thus in- 
 creased only two fold while the quantity is increased eight fold, the 
 potential becomes four times as great. Thus the potential of a 
 cloud may rise by the union of electrified drops. 
 
 368. Lightning 1 , When an electrified cloud floats 
 over the earth, separated from it by a layer of insulating 
 air, the inductive influence of the cloud renders the ground 
 beneath oppositely electrified. Then the cloud, ground 
 and insulating air correspond respectively to the inner 
 and outer coatings and the insulating glass of a Leyden 
 jar. As the charge of a Leyden jar may be made so in- 
 tense that the mutual attraction of the separated elec- 
 tricities will result in their rushing together and thus 
 piercing the jar (| 358), so the charge of a cloud may be- 
 come sufficiently intense to overcome the resistance of the 
 air and a lightning stroke ensues. Two clouds charged 
 
FRICTIONAL ELECTRICITY. 237 
 
 with opposite electricities may float near each other. 
 Then they, with the intervening air, may be looked upon 
 as constituting a huge Leyden jar. Thus, we may see 
 the lightning leaping from cloud to earth, or from clond 
 to cloud. Such electric sparks are sometimes more than 
 a mile in length, showing a difference of potential greater 
 than that of 3,000,000 Daniell's cells. The duration of 
 the spark or flash is not more than 0.00001 of a second. 
 The danger from any lightning stroke has passed when we 
 hear the crash. The identity of lightning with electricity, 
 though long suspected, was first proved by Franklin's 
 famous kite experiment. (See Exp. 64.) 
 
 Experiment 37. Bring the point of a knife-blade near the con 
 ductor of an electric machine in operation and notice the instant cessa- 
 tion of sparks. The quiet passage of electricity from the earth 
 neutralizes the charge of the conductor and restores the electric 
 equilibrium. In the same way, a lightning-rod tends to restore the 
 electric equilibrium of the cloud and prevent the dangerous dis- 
 charge. 
 
 369. Lightiiing-Rods. The value of lightning- 
 rods depends upon the tendency of electricity to follow 
 the best conductor and upon the effect of pointed con- 
 ductors upon electrical density ( 342). The lightning- 
 rod should, therefore, be made of a good conductor ; 
 copper is better than iron. It should terminate above in 
 one or more points, tipped with some substance that may 
 be corroded or fused only with extreme difficulty. Plati- 
 num and iridium are metals that satisfy these conditions 
 very well. The rod should extend above the highest point 
 of the building in order to offer the electricity the easiest 
 path to the ground. It is important to have each pro- 
 jecting part of the building, as chimneys, towers and 
 
238 FRICTIONAL ELECTRICITY. 
 
 gables, protected by a separate rod. All metal work about 
 the roof or chimneys should be connected with the rod. 
 The rod should afford an unbroken connection ; the joints, 
 if there be any, should be carefully made. The rod 
 should terminate below in water, or in earth that is always 
 moist. It is well to connect it with underground water- 
 pipes when possible or with a large metal plate. Personal 
 attention should be given to this matter when the rod is 
 put up as, being under ground and out of sight, this part 
 of the rod is not easily inspected subsequently. A rod 
 having a Hunted tip, a broken joint or terminating 
 in dry earth is more dangerous than no rod at all. 
 Lightning-rod insulators are undesirable. 
 
 (a.) The greatest value of a lightning-rod is due to its quiet work 
 in the prevention of the lightning stroke. For this quiet but very 
 valuable service, few persons ever give the rod any credit. Every 
 leaf of the forest and every blade of grass is a pointed conductor 
 acting in the same way. 
 
 (6.) There is some question as to the space protected by a rod, but 
 the following is a good rule : The protected space is a cone having 
 its apex at the tip of the rod and having a base the radius of which 
 is equal to the height of the cone. 
 
 37O. The Aurora Borealis. The aurora borealis 
 or "northern light" is frequently seen in northern re- 
 gions; beyond the Arctic circle it is of almost nightly 
 occurrence. Sometimes its streamers of light radiate like 
 the ribs of a fan or form an arch across the northern sky, 
 as shown in Fig. 156. But, as seen in this country, it 
 more often appears as a few streamers of a pale tint. 
 Similar lights are seen in south polar regions and are 
 called aurora australis. 
 
 The atmosphere, in its upper strata, is highly rarefied 
 and conducts electricity as do the rarefied gases in Geissler 
 
FRICTIONAL ELECTRICITY. 
 
 tubes (Exp. 70). There is little doubt that the aurora ig 
 due to electric discharges in this rarefied air. The appear- 
 
 FIG. 156. 
 
 ance of an aurora is generally accompanied by a " mag- 
 netic storm" or irregular disturbance that affects all of 
 the compass needles over a considerable part of the earth. 
 
 371. Apparatus and Experiments. It is 
 
 neither necessary nor very desirable that all of the follow- 
 ing experiments be performed. Several of them involve 
 the same principle ; but one teacher may have one piece of 
 apparatus and another, another piece. Additional experi- 
 ments may be found in " The First Principles of Natural 
 Philosophy," pp. 174-176. 
 
 Experiment 38. Place a tin plate containing a handful of small 
 bits of tissue paper upon the prime conductor of an electric machine. 
 Work the machine and thus produce an imitation snow storm. 
 
240 
 
 FRl CTIONAL ELECTRICITY. 
 
 Experiment 39. The " metallic plates and dancing images " are 
 represented in Fig. 157. The images are made of pith. The upper 
 plate is in communication with the prime conductor , 
 the lower one, with the earth. When the machine 
 is worked, the images dance in a very ludicrous 
 manner. Explain. Pith balls may be substituted 
 for the images, the resulting phenomena being known 
 as " Volta's hail." The experiment may be simplified 
 by electrifying the inner surface of a glass tumbler 
 by rubbing it upon the knob of the prime conductor 
 and placing the tumbler over some pith balls on the 
 table. 
 
 Experiment 40. Place a dozen pith balls or some 
 FIG. 157. bits of tissue paper on a table between two books 
 about 2 inches (5 cm.) thick. Place a pane of glass 
 upon the books as shown in Fig. 158. 
 Rub the upper surface of the glass 
 with the silk pad mentioned in 302 
 (or a silk handkerchief) and notice 
 the lively dance of the pith balls. FIG. 158. 
 
 Experiment 41. In the "electric chime," represented in Fig. 
 159, the outer bells are to be put into communication with the prime 
 conductor; the central bell is in communication with the earth. 
 
 FIG. 159. 
 
 FIG. 160. 
 
 The clappers are suspended by silk threads. Work the machine 
 slowly ; the bells will begin to ring. Explain. 
 
miCTIONAL ELtiCTtttClTY. 241 
 
 Experiment 42. In the "Leyden jar and bells," shown in Fig. 
 180, the left-hand bell is in communication with the outer coat of the 
 jar; the clapper is suspended by a silk thread. When the jar is 
 charged and placed in position as represented, the bells begin to 
 ring and continue to do so for a considerable time. Explain. 
 
 Experiment 43. In the " electric swing," shown in Fig. 161, 
 the boy is suspended by silk cords. One of the 
 insulated knobs is in communication with the 
 earth; the other with the prime conductor. 
 When the machine is worked, the boy swings to 
 and fro. Explain. 
 
 Experiment 44. If a pupil hold a Leyden 
 jar by the outer coat and, by a wire, connect the 
 knob of the jar with the prime conductor, his p IG 
 
 knuckle will attract the balanced lath (Exp. 5) 
 when the machine is worked. Explain. 
 
 Experiment 45. Fasten a small paper kite by a linen thread to 
 the prime conductor. When the machine is worked, the kite wilV 
 float around the knob. Explain. 
 
 Experiment 46. Fasten one end of a long, small, copper wire to 
 the prime conductor. Near the other end of the wire, tie a silk cord 
 and hang it from the ceiling or other support so that the end of the 
 vertical part of the wire shall be at a convenient height. To this 
 end of the wire attach a tassel about four or five inches long made 
 of many strips of light tissue paper. Work the machine and the 
 leaves will diverge. Explain. Extend toward it your clenched fist ; 
 the leaves seek the fist. Explain. Instead of your fist, hold a needle 
 toward the tassel ; it will be blown away. Explain. Hold the 
 needle upright under the tassel. The strips will collapse. Explain. 
 
 Experiment 47. Stand upon the insulating stool and place your 
 left hand upon the prime conductor of the electric machine. Hold in 
 your right hand a sewing-needle with the tip of the forefinger cover- 
 ing the end of the needle. Bring the right hand cautiously near the 
 gold-leaf electroscope. Notice the divergence of the leaves. Now 
 uncover the point of the needle and bring it near the electroscope. 
 Notice the marked and immediate increase in the divergence of the 
 leaves. Explain. 
 
 Experiment 48. Place an "electric whirl" (which consists of 
 a set of horizontal wire arms radiating from a pivot-supported centre, 
 
242 
 
 FRICTIONAL ELECTRICITY. 
 
 the pointed ends being all bent in the same direction) upon the prime 
 conductor. Work the machine and the arms will revolve. (Fig. 
 162.) Explain. 
 
 Experiment 49. The "electric or- 
 rery," represented in Fig. 163, is a pret- 
 ty modification of the " electric whirl." 
 The short, balanced bar is provided with 
 a pointed conductor to produce rotary 
 motion upon its supporting pivot, which 
 is one end of the long balanced bar. 
 This longer bar 
 is also provided 
 with a pointed 
 conductor and 
 supported i n 
 turn upon a 
 pivot, which 
 
 FIG. 162. 
 
 may be attached FIG. 163. 
 
 to the prime 
 
 conductor. When the machine is worked, the long bar revolves 
 upon its fixed pivot ; the short bar revolves upon its moving pivot. 
 
 Experiment 50. Half fill a wide, glass vessel with water. Within 
 this, place a glass beaker and fill it to the same level with water. 
 By a wire, connect the water in the outer vessel with the earth ; in 
 similar manner, connect the water in the beaker with the electric 
 machine. Give the handle of the machine a single turn. Dipping 
 one finger into the outer water and another into the inner water, a 
 shock is felt. Explain. 
 
 Experiment 51. Let a pupil stand upon an insulating stool (a 
 board supported by four warm tumblers will answer) and place his 
 left hand upon the prime conductor. Let him, with his right hand, 
 clasp the left hand of another pupil not insulated, their hands being 
 prevented from actual contact by an intervening sheet of india-rub- 
 ber cloth. After the machine has been worked a moment, let the 
 insulated pupil remove his left hand from the prime conductor and 
 clasp the free hand of his companion. At this moment of clasping 
 hands, a shock will be felt Explain. 
 
 Experiment 52. Cover one knob of the discharger with gun cot- 
 ton sprinkled with powdered rosin. When the Ley den jar is dis- 
 charged with this discharger, the cotton and rosin are ignited 
 
FRICTIO NA L ELECTRICITY. 
 
 243 
 
 Bring the covered knob of the discharger into contact with the knob 
 of the jar with a quick motion. 
 
 Experiment 53. The " electric bomb," represented in Fig. 104, 
 may be made of ivory, heavy glass, or thorough- 
 ly seasoned wood. The ends of the two metal 
 wires are rounded and placed a short distance 
 apart. The bomb may be filled with gun- 
 powder. One wire is connected by a chain 
 with the outer coat of a charged Leyden jar. 
 The other wire is to be connected with the 
 inner coat by a wet string and the discharger. 
 The spark between the ends of the two wires 
 ignites the powder. Then try the experiment 
 with air instead of powder. FIG. 164. 
 
 Experiment 54. Fig, 165 illustrates a method of igniting an 
 
 inflammable liquid, like 
 ether or alcohol, by the 
 electric spark. Through 
 the bottom of a small 
 glass vessel, a, passes a 
 metal rod, having a knob 
 at its upper extremity. 
 The lower end of this 
 rod may be brought into 
 electrical connection with 
 the outer coat of a Ley- 
 den jar. Enough ether 
 or alcohol is poured into 
 a just to cover the knob. 
 When the jar is dis- 
 charged in the way 
 shown in the figure, the 
 spark ignites the liquid. 
 If alcohol is used, it may 
 have to be warmed to 
 render the experiment 
 successful. 
 
 Experiment 55. Let 
 FIG. 165. a pupil, standing on an 
 
 insulating stool, become 
 charged by holding one hand on the prime conductor when the 
 
244 FRICTION AL ELECTRICITY. 
 
 machine is in operation. If he then bring his knuckle to a metal 
 burner from which a jet of gas is issuing, a spark will pass be- 
 tween the knuckle and the burner, igniting the gas. An Argand 
 or Bunsen burner answers well for this experiment. The experi- 
 ment may be modified by using, instead of the knuckle, an icicle 
 held in the hand. The gas burner may be replaced by a pupil (not 
 insulated) holding a spoonful of ether or of chloroform which readily 
 gives off an easily combustible vapor. 
 
 Experiment 56. The "universal discharger," shown in Fig. 166, 
 consists of a glass table and two insulated metal rods. (See 358 a.) 
 
 Balls, points and pincers are 
 provided for use at the adja- 
 cent ends of the rods which are 
 supported upon sliding and 
 hinged joints, so that they may 
 be easily placed in any desir- 
 able position. Cover the ad- 
 jacent ends of the two rods 
 FIG. 166. with metal balls and place them 
 
 upon the glass table, a small 
 
 distance apart. Connect the balls by a very fine wire. One of the 
 rods is to be connected by a wire or chain with the outer coats of a 
 powerful battery ; the other rod is to be connected, by the discharger, 
 (Fig. 150) with the inner coats of the battery. The current thus 
 passed along the fine wire may heat it to incandescence, melt or 
 even vaporize it. 
 
 Experiment 57. Prick a profile portrait of Franklin or some other 
 design in a sheet of thin card board. Paste two pieces of tin-foil to 
 the ends of the card and join them with a piece of gold leaf placed 
 over the pricked design. Place a piece of white paper or silk on the 
 other side of the card and have the whole tightly screwed up be- 
 tween two boards, leaving the edges of the tin-foil strips accessible. 
 Discharge a Leyden battery through the gold leaf, thus volatizing 
 it, sending the disintegrated particles through the holes in the card 
 board and obtaining an impression of the portrait. 
 
 Experiment 58. Fig. 167 represents "Volta's pistol," which 
 consists of a metal vessel through one side of which passes an in- 
 sulated metal rod with knobs at both ends. The knob at the inner 
 end of this rod is near the opposite wall, so that a spark may easily 
 be made to pass between the knob and the body of the pistol. The 
 pistol being filled with a mixture of illuminating gas and common 
 
24G 
 
 FRICTIONAL ELECTRICITY. 
 
 sulated support, lower a second pointed conductor until it touches 
 the pane at the oil. Through these two pointed conductors (Fijr. 
 168), discharge a Leyden jar or battery. Unless the glass is very thin, 
 .a single jar will not be sufficient. If the experiment fails the first 
 time, do not use the same piece of glass for the second trial. A plate 
 of glass, 6 cm. thick, has been pierced by means of a powerful in 
 duction coil. 
 
 Experiment 61. With corks, plug the ends of a glass tube filled 
 with water. Through the corks, introduce copper wires until the 
 ends in the water are within a quarter of an inch of each other. 
 Through these wires, discharge a Leyden jar. The mechanical shock 
 due to the repulsion of the electrified water molecules will often 
 break the tube. 
 
 Experiment 62. Charge a Leyden jar. In discharging it, hold 
 a stiff card between the knob of the jar and the knob of the di 
 
 FIG. 169. 
 
 charger. A hole will be pierced through the card. By the side of 
 tW Uole in the card, make another with a pin. Any one can tell 
 
FRICTIONAL ELECTRICITY. 
 
 247 
 
 by examination of the pin-hole from which side of the card it waa 
 pierced ; it is burred on only one side. Not so with the perforation 
 made by this discharge ; it is burred on both sides. 
 
 Experiment 63. One of the inevitable experiments with an elec- 
 tric machine consists in " drawing sparks " from the conductor by 
 the hand (Fig. 169). When the potential of the separated electrici 
 ties becomes sufficient to overcome the resistance of the intervening 
 air, they recombine with a sharp, explosive sound and brilliant flasi: 
 t)f light. (362.) 
 
 Experiment 64. Divide a circle 
 into black and white sectors, as shown 
 in Fig. 170, and attach it to a whirl- 
 ing table ($ 74). Revolve it so rapidly 
 that the colors blend and the disc ap- 
 pears a uniform gray. Darken the 
 room and illuminate the rapidly re- 
 volving disc by the electric spark 
 from a Ley den jar. The disc will 
 appear at rest and each sector will 
 appear separate from its neighbors. 
 This shows that the duration of the 
 electric spark is less than the persist- 
 ence of vision. 
 
 FIG. 170. 
 
 Experiment 65. In a dark room, place a piece 
 of loaf sugar in contact with the outside coat of a 
 charged Leyden jar. Place one knob of the dis- 
 charger upon the sugar and bring the other near 
 the knob of the jar. When the jar is discharged 
 thus through the sugar, the sugar will glow for 
 some time. 
 
 Experiment 66. The "luminous jar," repre 
 sented in Fig. 171, is a modified Leyden jar. The 
 outer coat consists chiefly of a layer of varnish 
 sprinkled over with metallic powder. A strip of 
 tin-foil at the bottom affords means of communica- 
 tion with the earth. A similar band at the upper 
 edge of the outer coat is provided with an arm, as 
 shown in the figure. The rod of the jar is curved 
 
 so as to bring the knob near the projecting arm of the outer coat. 
 
 The jar is suspended by the curved rod from the prime conductor 
 
248 
 
 FRICTIONAL ELECTRICITY. 
 
 FIG. 172. 
 
 FIG. 173. 
 
 and its lower strip of tin-foil connected 
 with the earth. When the machine is 
 worked, sparks pass between the knob 
 and the projecting arm. In a dark room, 
 the metallic powder coat will be beauti- 
 fully illuminated at the passage of each 
 such spark. 
 
 Experiment 67. The " luminous 
 pane" is represented in Fig. 172. A. 
 continuous tin-foil strip is pasted back 
 and forth upon the surface of a plate of 
 glass. The upper end of this strip is con- 
 nected with the prime conductor ; the 
 lower end with the earth. A series of 
 breaks in this continuous conductor may 
 be made by cutting it across with a sharp 
 pen-knife. When the machine is worked, 
 a small spark will appear at each break 
 thus made. These breaks may be ar- 
 ranged so as to represent a flower, star, 
 arch, word or other de- 
 sign. The sparks are 
 really successive, but 
 they seem to be simul- 
 taneous. 
 
 Experiment 68. 
 
 The "luminous globe " 
 is represented in Fig. 
 173 and the " luminous 
 tube "in Fig. 174. The 
 first of these consists 
 of a hollow glass globe, 
 on the inner surface of 
 which small discs of 
 tin-foil are placed very 
 near each other. The 
 first disc is in connec- 
 tion with the prime 
 conductor, and the last 
 one with the ground. 
 When the machine is 
 
 FIG. 174. 
 
miCTIONAL ELECTRICITY. 
 
 249 
 
 worked, bright sparks appear at each break between the discs. The 
 construction and action of the luminous tube are similar. All of 
 these luminous effects are best exhibited in the dark. 
 
 Experiment 69. If two barometer 
 tubes, united at the top, be filled with 
 mercury and inverted over two cups of 
 mercury, as shown in Fig. 175, a Torri- 
 cellian vacuum will be formed at the 
 bend. When the mercury of one cup is 
 connected with the prime conductor and 
 that of the other with the earth, the up- 
 per part of fhe tube (containing only mer- 
 curic and other vapors) is filled with light. 
 The luminosity may be increased by 
 raising the temperature and thus in- 
 creasing the density of the aeriform con- 
 ductor. (A true vacuum will not con- 
 duct electricity.) The apparatus may 
 be put into the circuit of an induction 
 coil instead of connecting it with the 
 prime conductor and the earth. 
 
 Experiment 70. "Geissler's Tubes" 
 are sealed glass tubes containing a 
 highly rarefied vapor or gas. Platinum 
 wires are sealed into the glass at each 
 end, to conduct the electric current to 
 the interior of the tube. The brilliancy FlG> I75> 
 
 and beauty of the light, the great variety 
 
 of effects, color and fluorescence, are indescribable. They are made 
 in great variety of form and size and filled with rarefied vapors and 
 gases of many kinds. A few of the forms are represented in. Fig. 
 
 FIG. 176. 
 
 176. They may be used in the dark with an electric machine or an 
 induction coil ( 459). 
 
250 
 
 FRICTIONAL ELECTRICITY. 
 
 Experiment 71. In "Crookes's Tubes," devised in many forms 
 by Prof. Crookes for his investigations of the phenomena of " radiant 
 matter" ( 59 6), the tension of the contained gas is reduced to about 
 one millionth of an atmosphere, far below that of Geissler's tubes, 
 Under the influence of the electric discharge, matter seems to be 
 radiated from the negative pole in straight lines and in directions 
 perpendicular to the radiating surface. 
 
 FIG. 177. 
 
 (a.) One of these tubes, used to show that radiant matter " may 
 exert mechanical action, is shown in Fig. 177. It consists of a highly 
 f-xhausted glass tube containing a glass railway. The axle of a 
 small wheel revolves on the rails, the spokes of the wheels carrying 
 
 FIG. 178. 
 
 mica paddles. Pole pieces are fused in through the glass, as repre- 
 sented. Whichever pole is made negative, " radiant matter " darts 
 
FRICTIONAL ELECTRICITY. 251 
 
 from it along the tube, strikes the upper paddles, causing the wheel 
 to roll along the railway. By reversing the poles, the motion of the 
 wheel may be stopped and reversed. 
 
 (6.) To show that "radiant matter" may* be deflected from a 
 straight line, he devised the tube shown in Fig. 178. The negative 
 pole, a &, is in the form of a shallow cup. A mica screen, c, shields 
 the mica paddle-wheel, ef. By holding one pole of the magnet, g, 
 over the tube, the matter radiated from a b is deflected upward and 
 the wheel caused to revolve like an overshot water-wheel. By hold- 
 ing the other pole of the magnet over the tube, the molecular stream 
 is deflected downward and the wheel caused to revolve as an under- 
 shot water-wheel. (See Appendix C.) 
 
 312. Relation of Electricity to Energy- 
 
 The work necessarily performed in operating an electric 
 machine is not all expended in overcoming inertia and 
 friction. Much of it is employed in producing electric 
 separation. It matters not whether this separation be 
 the separation of two fluids or of something else. What- 
 ever be the nature of the realities separated, me- 
 chanical, kinetic energy is employed in the separa- 
 tion and converted into the potential variety ( 159). 
 An electrified pith hall or a charged Leyden jar is simply 
 an electro statical reservoir of potential energy. In the 
 discharging of such a body, the passage of the current is 
 accompanied by a loss of potential energy. What becomes 
 of this energy ? This leads us to look for effects due to 
 it, to work done by it. Many illustrations of work- thus 
 done have been furnished in the experiments just de- 
 scribed. In every case of electric attraction or repulsion, 
 we have an evident reconversion of this potential energy 
 into mechanical kinetic energy. We shall soon see that 
 the sound, heat and light accompanying electric dis- 
 charges are forms of energy due to the conversion of the 
 potential energy of electric separation. We shall see other 
 
252 FRICTION AL ELECTRICITY. 
 
 effects, more or less powerful, when we come to study 
 voltaic and other forms of current electricity. 
 
 EXERCISES. 
 
 1. (a.) If a gold-leaf electroscope be placed within a tin pail which 
 is insulated and electrified, what will be the action of the electro- 
 scope? (&.) Explain. 
 
 2. (a.) Why may one obtain a stronger spark from a Leyden jar 
 than from the machine by which it is charged? (&.) A Leyden jar 
 standing upon a glass plate cannot be strongly charged. Why ? 
 
 3. (a.) A globe that is polished will remain electrified longer than 
 one that is not polished. Why? (&.) Can you devise an appendage 
 to the outer coat of a Leyden jar, so that it may be charged when 
 standing upon a plate of glass ? 
 
 4. (a.) Describe the plate electric machine. (&.) Explain its ac- 
 tion, (c.) Explain the action of the electrophorus. 
 
 5. (a.) A minute after the discharge of a Leyden jar, a second and 
 feebler spark may generally be obtained. Explain. (&.) State two 
 uses of lightning-rods. 
 
 6. (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 ? (&.) How could you charge posi- 
 tively one of tne dozen without affecting the charge of the first? 
 
 7. Can you devise a plan by which a series of Leyden jars, placed 
 upon a glass plate, may be simultaneously charged, the first posi- 
 tively, the second negatively, the third positively, the next nega- 
 tively and so on? 
 
 8. How would you prove that there is no electrification within a 
 closed conductor? 
 
 9. At what distance from a small sphere charged with 28 units of 
 electricity 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. 
 
 10. If a number of Leyden jars be separately charged in the or- 
 dinary way and then connected in series, so that the outer coating 
 of one is connected with the inner coating of the next, will the po- 
 tential of the battery be changed and in what way ? 
 
 11. Will the " striking distance" of a battery of Leyden jars in 
 series be less or greater than the striking distance (i.e., the greatest 
 distance at which the discharge by spark will take place through 
 air) of a battery of the same number of similar cells arranged abreast 
 as shown in Fig. 152 ? 
 
FRICTIONAL ELECTRICITY. 253 
 
 12. In what way may an electric charge be divided into three 
 equal parts ? 
 
 13. Suppose two similar conductors to be electrified, one with a 
 + charge of 5 units and the other with a charge of 3 units. 
 They are made to touch each other. When they are separated, 
 what will be the charge of each ? 
 
 Ans. One unit of + electricity. 
 
 14. "Why are telegraphic signals through a submerged cable re- 
 tarded in transmission ? 
 
254 FRICTIONAL ELECTRICITY. 
 
 Recapitulation. To be amplified by the pupil for 
 review. 
 
 KINDS AND NAMES. 
 ELECTROSTATIC LAWS. 
 ELECTRICAL UNITS AND TESTS. 
 ELECTROSCOPES. 
 
 s>rtMrMin-ris\iu ( CONDUCTORS, NON-ELECTRICS. 
 
 CONDUCTION \ INSULATORS, ELECTRICS. 
 
 TENSION, POTENTIAL AND CAPACITY. 
 
 f BY CONTACT. 
 ELECTRIFICATION. | [ POLARIZATION. 
 
 ELECTROPHORUS. 
 
 CJ 
 
 BY INDUCTION. 
 
 ELECTRIC MACHINES 
 
 Q 
 
 } L SOURCE OF ENERGY, 
 
 U 
 
 PROVISIONAL THEORY. 
 
 Q \ 
 
 DISTRIBUTION OF j ON SURFACE. 
 CHARGE. 1 DENSITY. 
 
 CONDENSERS 
 
 DIELECTRICS. 
 INDUCTIVE CAPACITY. 
 
 LEYDEN JAR. 
 LEYDEN BATTERY. 
 
 SUBMARINE CABLES. 
 
 f DISRUPTIVE. 
 
 DISCHARGE ........ I CONVECTIVE. 
 
 [ CONDUCTIVE. 
 
 f THUNDER STORMS. J LIGHTNING. 
 
 ATMOSPHERIC E. J ' LIGHTNING-RODS 
 
 I AURORA BOREALIS. 
 
 L RELATION TO ENERGY. 
 
HI, 
 
 VOLTAIC AND THERMO-ELECTRICITY. 
 
 373. Chemical Action. All chemical changes are 
 accompanied by electric separation. The substances acted 
 upon may be solid, liquid or aeriform, but the chemical 
 action between liquids and metals gives results the most 
 satisfactory. Electricity thus developed is called voltaic 
 or galvanic electricity. Its energy is derived from the 
 potential energy of chemical affinity ( 7). 
 
 374. Current Electricity. The principal classes 
 of electric currents are as follows: 
 
 (1.) Currents produced by chemical action, i. e., 
 
 voltaic electricity. 
 (2.) Currents produced by heat, i. e., thermo- 
 
 electricity. 
 (3.) Cuwents produced by other electric currents 
 
 or by magnets, i. e., induced electricity. 
 
 (a.) We have seen that, when a body having an electrical charge 
 is properly connected with another of lower potential, there is a 
 transfer of electricity from the former to the latter. This implies 
 that there is an electric current. But this current is only momentary 
 and of little importance in comparison with the currents that we are 
 about to consider. Current electricity may differ from static elec- 
 tricity in quantity, electromotive force, etc., but not in its nature. 
 
 375. The Voltaic Current. When a strip of 
 copper and one of zinc are placed in dilute sulphuric acid 
 
 25 
 
256 VOLTAIC ELECTRICITY. 
 
 or in a battery solution like the one already used, the two 
 strips being connected above the acid by a wire conductor, 
 
 a current of electricity is produced. 
 
 The apparatus here described 
 
 is called a voltaic or galvanic 
 
 element or cell. 
 
 (a) For voltaic purposes, the sulphuric 
 acid should be diluted by slowly pouring 
 the acid into ten or twelve times its bulk 
 of soft water. Do not pour the water 
 into the acid. 
 
 FIG 179 376 Wnence the Energy 
 
 of Current ? The energy of the current is due to the 
 potential energy of chemical affinity existing between the 
 acid and the zinc. As the chemical affinity between coal 
 and oxygen develops, in the furnace, a form of kinetic en- 
 ergy that we call heat, so the potential energy of chemical 
 separation between the acid and the zinc develops, in the 
 cell, the two varieties of kinetic energy, heat and electric 
 current. The coal is consumed in the one case ; the zinc, 
 in the other. 
 
 377. Direction of the Current. For this pro- 
 duction of the electric current, it is necessary that the 
 liquid have a greater action upon one plate than upon the 
 other. The plate that is more vigorously acted upon by 
 the liquid constitutes the generating or positive plate ; the 
 other, the collecting or negative plate. This relation of 
 the plates determines the direction of the current. In 
 the liquid, the current is from the positive to the 
 negative plate; in the wire, the current is from 
 the positive to the negative electrode. In each 
 
VOLTAIC ELECTRICITY. 257 
 
 case, the current passes from -f to . The direction 
 of the current is indicated by arrows in Fig. 179. 
 
 When the wires from the two plates are in contact, it 
 is said that the circuit is closed ; when the plates are not 
 thus in electric connection, it is said that the circuit is 
 broken. 
 
 378. Electrodes. It may help the memory to sup- 
 pose that, in a voltaic cell, two currents, opposite in kind 
 and direction, are simultaneously produced. It will be 
 readily understood, by keeping in mind the direction of 
 these two currents, that, if the circuit be broken, negative 
 electricity will accumulate at the end of the wire attached 
 to the positive plate and positive electricity at the end of 
 the wire attached to the negative plate. Tliese ends of 
 the wires are then called poles or electrodes. The 
 negative pole is attached to the positive plate and 
 vice versa. The plate or electrode from which the 
 current flows is -f ; that toward which the current 
 flows is . Strips of platinum are often fastened to the 
 ends of the wires; these platinum strips then constitute 
 the electrodes. 
 
 379. Resistance. Every electric circuit offers a re- 
 sistance to the passage of the current. This resistance 
 will, of course, depend largely upon the materials used for 
 the circuit. (See Appendix K.) 
 
 ( 1.) With a conducting wire of a given material, 
 the resistance is proportional to the length. If the 
 resistance of a mile of telegraph wire be 13 ohms, the re- 
 sistance of 50 miles of such wire will be (13 ohms x 50 =) 
 650 ohms. 
 
 ( 2. ) With a conducting wire of a given material, 
 
258 VOLTAIC ELECTRICITY. 
 
 the resistance is inversely proportional to its sec* 
 tional area, to the square of its diameter or to its 
 weight per linear unit. If one conductor be twice the 
 diameter of another made of the same length and material, 
 the sectional area or the weight per foot or yard will be 
 (2 2 =) four times as great and the resistance of the first 
 will be one-fourth as great as that of the second. If they 
 be made of the same material and length, one weighing 
 twice as much per foot as the latter, the resistance of the 
 former will be half as great as that of the latter. (See 
 Appendix I.) 
 
 (3.) The resistance of a conducting wire of given 
 length and thickness depends upon the material 
 of which it is made, i. e., upon the specific resist- 
 ance of the material. (See Appendix K, [2].) 
 
 (4.) The resistance of a given conductor may vary with 
 its temperature. (See Appendix K, [3].) 
 
 (a.} Conductivity and resistance are reciprocals, but it is more 
 common to speak of the resistances of conductors than of their con- 
 ductivities. 
 
 38O. The Practical Unit of Resistance.. 
 
 The practical unit of resistance is called an ohm. 
 A. m>egohm is a million ohms. A. microhm is one- 
 millionth of an ohm. The ohm is the resistance of a 
 column of mercury one square millimeter in section and at 
 the freezing temperature (0 0.). The exact length of this 
 column is to be determined experimentally by an interna- 
 tional commission. A recent determination of the value 
 of the ohm (probably the best yet made) gives the mercury 
 column a length of 106.3 cm. If the pupil will get, from 
 some dealer ia electrical supplies, 40 ft. of No. 24 insulated 
 
VOLTAIC ELECTRICITY. 259 
 
 copper wire (see Appendix I), he will have a very good 
 standard ohm. 
 
 (a.) A galvanized iron (telegraph) wire, 4 millimeters in diameter 
 and 100 meters long, or a pure copper wire, 1 millimeter in diameter 
 and 48 meters long, has a resistance of about one ohm. An ohm 
 equals 10 9 absolute electro-magnetic units ( 452). (For the measure- 
 ment of resistances, see Appendix M, [2 and 3].) 
 
 381. Examples. (a.) If the resistance of 130 yd. of copper 
 wire, y 1 ^ inch in diameter, be one ohm, what is the resistance of 260 
 yd. of copper wire, -fa inch in diameter ? Since the diameter of the 
 first wire is twice that of the second, the sectional area of the first will 
 be four times that of the second. (Areas of circles are proportional 
 to the squares of their diameters.) Therefore, the resistance of the 
 same length (130 yds.) of the smaller wire will be four times that of 
 the larger wire, or 4 ohms. But the second or smaller wire is twice 
 as long. Therefore, its resistance will be twice (ff$) as great, or 8 
 ohms. Ans. 8 ohms. 
 
 (b.) What is the resistance of 20 yd. of platinum wire, 0.016 inch 
 in diameter, if the resistance of 200 yd. of copper wire, 134 mils in 
 diameter, is 0.34 ohm and the relative resistances of platinum and 
 copper are as 11.8 : 1 ? (A mil is the one -thousandth of an inch. 
 The term is frequently used in descriptions of wire.) 
 
 on /1Q4\ 2 1 1 Q 
 
 0.34 ohm x ~ x I ^ ) x ^ = 26.95 ohms. 
 200 \ 16 / 
 
 Ans. 26.95 ohms. 
 
 382. Electromotive Force. Electromotive force 
 (often written E. M. F. or simply E.) is the mysterious 
 power that causes a transfer of electricity from one point 
 to another. It is somewhat analogous to hydrostatic pres- 
 sure. Wherever there is difference of potential, there is 
 E. M. F. The terms are not synonymous, although, for 
 convenience, E. M. F. is often expressed as difference of 
 potential and vice versa. The E. M. F. of a voltaic 
 cell depends upon the nature of the materials used and 
 not upon the size of the plates or the distance between 
 them, 
 
260 VOLTAIC ELECTRICITY. 
 
 Tl%e unit of electromotive force is called, a volt. 
 A microvolt is one-millionth of a volt. 
 
 A volt is a little less than the E. M. F. of a Daniell cell 
 ( 394), which measures 1.079 volts. 
 
 (a.) A volt equals 10 8 absolute electro-magnetic units ( 452). 
 (For the measurement of E. M. F. see Appendix M, [4].) 
 
 383. Internal Resistance. We may imagine 
 that the two plates of a voltaic cell are connected by a 
 liquid prism. The greater the distance between the plates, 
 the longer this prism and the greater its resistance. The 
 larger the plates, the larger the prism and the less its re- 
 sistance. (See Appendix M, [3].) 
 
 When the circuit is closed, hydrogen is set free by the 
 decomposition of the liquid and rises from the surface of 
 the negative plate. Gases are poor conductors. Hence, 
 the hydrogen bubbles that often adhere to the negative 
 plate increase the internal resistance of the cell by lessen- 
 ing the effective surface of the plate ( 389). This ten- 
 dency of the hydrogen to adhere to the plate is one of 
 the practical difficulties to be overcome in working a 
 voltaic cell or battery. 
 
 384. Fall of Potential. The existence of a cur- 
 
 rent is evidence of a 
 difference of potential 
 at any two consecu- 
 tive points of the cir- 
 cuit. It may he well 
 to compare the flow 
 of electricity with the 
 flow of water in hori- 
 zontal pipes and difference of potential with difference of 
 
VOLTAIC ELECTRICITY. 2G1 
 
 hydrostatic pressure. Let Fig. 180 represent a vessel filled 
 with water. The tap at is closed and the water stands at 
 the same level in all of the vertical tubes ( 234) showing 
 that there is no difference of pressure and, consequently, no 
 liquid flow. Similarly, 
 when there is no differ- 
 ence of potential there is 
 no electric flow. But 
 when the tap at C is 
 opened, as represented 
 
 in Fig. 181, it is noticed 
 
 ',> : i , . ., FIG. 181 
 
 that the level in the ver- 
 tical tubes becomes lower as we pass from A toward C. The 
 height of water in each vertical tube indicates the pressure 
 at that part of the tube, B. This difference in hydrostatic 
 pressure produces a flow of water. In much the same way, 
 if the electric potential of a voltaic circuit be measured at 
 different points, it will be found to decrease from the + pole 
 to the pole. If the circuit be a wire of uniform size 
 and material, the resistance offered by it will be uniform 
 and the potential will fall uniformly. If, however, the cir- 
 cuit be made to have a varying resistance in different parts, 
 the potential will fall most rapidly along the parts of 
 greatest resistance. For the whole or any part of the 
 circuit, the fall of potential will be proportional to the 
 resistance. 
 
 (a.) A number of hydraulic motors may be worked " hi series " 
 upon a given water pipe, the outflow of the first being the supply of 
 the second. The work done in any motor may be determined from 
 the quantity of water flowing through the pipe or motor per second 
 and tJie difference between the supply pressure and the back pressure 
 at the motor. There will be a fall of pressure between the two sides 
 of the motor at work. The more work the motor has to do, the more 
 
262 VOLTAIC ELECTRICITY. 
 
 resistance it will offer to the flow of water and the greater the fall of 
 pressure. Similarly, a number of telegraphic instruments or electric 
 lamps may be placed in series upon an electric circuit. The work 
 done in each instrument or lamp will depend upon the current 
 strength and the difference of potential between the two terminals 
 of the instrument or lamp. There will be a fall of a certain number 
 of volts between the two terminals, depending upon the intervening 
 resistance. 
 
 385. The Ampere. The strength of current or its 
 rate of flow (often called its intensity) will depend upon 
 electromotive force and resistance, increasing with the 
 former and decreasing with the latter. The unit of 
 current is called an ampere. One-thousandth of 
 an ampere is called a milli-ainpere. At any given 
 instant, the current is the same at every part of the circuit. 
 
 (a.) The telegraphic currents commonly used on main lines vary 
 from 5 to 15 milli-amperes. The currents commonly used in electric 
 arc lamps vary from 7 to 20 amperes. 
 
 (&.) The strength of a current may be measured by its heating 
 <-Tect (471) or by the products of electrolysis, as in the case of the 
 wa c er voltameter ( 410). But currents are generally measured by in- 
 s ruments like the galvanometer (418), or by their electro-magnetic 
 effects. An instrument so used is called an ammeter (abbreviated 
 from ampere-meter). An ampere equals 0.1 or 10" 1 of an absolute 
 electro-magnetic unit ( 452). 
 
 386. Ohm's Law. The strength of current 
 varies directly as the E. M. F. and inversely as 
 the resistance. This resistance is the total resistance of 
 the circuit, including the internal resistance of the cells 
 or dynamo and the resistance of the external circuit. 
 
 Volts E E 
 
 - = Amperes, or Q -5- .-. E= C x R ; R -7,- 
 (trims H 
 
 Standards for strength of current have not yet been 
 made. 
 
VOLTAIC ELECTRICITY. 263 
 
 (a.) Ohm's great service (A.D., 1827) to electrical science consisted 
 largely in the introduction of the accurate ideas, electromotive 
 force, current strength and resistance. "Before his time, the 
 quantitative circumstances of the electric current had been indicated 
 in a very vague way by the use of the terms ' intensity ' and 
 ' quantity/ to which no accurately defined meaning was attached." 
 
 (6.) If we have a difference of potential that secures an E. M. F. 
 of 18 volts, and if the total resistance of the circuit be 3 ohms, the 
 strength of the current will be 6 amperes, 18 -f- 3 = 6. The 
 analogy of flowing water will again help us. The rate at which the 
 water is delivered will depend upon, not only the head or pressure 
 (corresponding to E. M. F.), but also upon the resistance it meets with 
 in flowing, If the pipe be small and crooked or if it be choked with 
 sand or sawdust, the water will flow in a small stream even though 
 the pressure be great. 
 
 Experiment 72. Make four coils or spools of insulated wire as 
 follows : (See Appendix I.) 
 
 No. 1, of 100 feet of No. 16 gauge, copper. 
 
 No. 2, of 100 " " 30 " 
 
 No. 3, of 50 " " 30 " 
 
 No. 4, of 50 " " 30 " german silver. 
 
 Place the wire of the first spool and a galvanometer ( 418) in the 
 circuit of one cell and note the number of degrees of deflection of 
 the galvanometer needle. Put the second spool in place of the first. 
 The smaller deflection shows that (other things being equal) the 
 No. 16 wire transmits more current than the No. 30. Why ? Then 
 add the third spool to the circuit. The still smaller deflection shows 
 that (other things being equal) a long wire transmits less current 
 than a shorter one. Why ? Remove the second spool from the 
 circuit and note the deflection of the galvanometer. Put the fourth 
 spool in place of the third. The diminished deflection shows that 
 (other things being equal) a german silver wire transmits less current 
 than a copper wire. Why ? With any one of the spools in the cir- 
 cuit, compare the galvanometer deflections produced by a Bunsen 
 cell and by a gravity cell and notice that the former gives the 
 stronger current. 
 
 Note. These experimens give very crude results but, such as 
 they are, they fairly represent the measurements that prevailed 
 until recently. More accurate measurements with numerical repre- 
 sentations of the results are now demanded. The rapid advances of 
 
264 VOLTAIC ELECTRICITY. 
 
 electrical science within the last few decades have been very largely 
 due to the adoption of definite units and accurate determinations. 
 (See Appendix M.) 
 
 387. The Coulomb. The unit of quantity is 
 called the coulomb. It is the quantity of elec- 
 tricity given by a one ampere current in one 
 second. A ten ampere current will give thirty coulombs 
 in three seconds. 
 
 (a.) The word " quantity " was formerly used in the sense in 
 which the word "intensity" was used in 385, while the latter 
 word was used as if it depended upon E. M. F. alone. But quantity 
 of electricity, clearly, depends upon the strength of the current and 
 the time that the current flows. A coulomb equals 0.1 or 10" 1 of an 
 absolute electro-magnetic unit of quantity ( 452). 
 
 EXEKCISES. 
 
 1. What length of No. 10 pure copper wire (B. & S.) will have a 
 resistance of 1 ohm ? (See Appendix I.) Ans. 961.54 ft. 
 
 2. A given battery has an E. M. F. of 12 volts. The internal 
 resistance is 8 ohms. The resistance of the external circuit is 4 
 ohms. What is the strength of the current ? 
 
 3. The 4 cells of a given battery are connected so that the total 
 E. M. F. is 4 volts and the internal resistance is 20 ohms. The 
 external circuit has a resistance of 20 ohms. What is the strength 
 of the current ? Ans. 0.1 ampere. 
 
 4. What length of copper wire 4 mm. in diameter will have the 
 same resistance as 12 yd. of copper wire 1 mm. in diameter ? 
 
 Ans. 192yd. 
 
 5. The 4 cells of a given battery are connected so as to give an 
 E. M. F. of 2 volts and to have a total internal resistance of 10 ohms. 
 The external circuit is a stout copper wire with a resistance so small 
 that it may be ignored. What is the current strength ? 
 
 6. The same battery is used with a telegraphic sounder in the 
 circuit. This instrument has a resistance of 5 ohms. What is the 
 current strength ? Ans. 133 milli-amperes. 
 
 7. The resistance of 47 ft. of copper wire, 22 mils in diameter, 
 being 1 ohm, find the resistance of 200 yd. of copper wire 134 mils 
 in diameter. Ans. 0.34 ohm. 
 
 If you do not know what a mil is, consult the Index. 
 
VOLTAIC ELECTRICITY. 265 
 
 $. A battery has a current of 2 amperes flowing through a total 
 resistance of 9 ohms. What is the E. M. F. ? 
 
 9. The E. M. F. of a battery is 10 volts. The current is 1 ampere. 
 The external resistance is 5 ohms. What is the internal resistance 
 of the battery ? Ans. 5 ohms. 
 
 10. The potential of a current falls 45 volts between the two 
 terminals of an incandescence lamp. The current measures 1.25 
 amperes. What is the resistance of the lamp ? Ans. 36 ohms. 
 
 Jgp^ If you do not know what an incandescence lamp is, consult 
 the Index. 
 
266 VOLTAIC ELECTRICITY. 
 
 388. Amalgamating the Zinc. Ordinary com- 
 mercial zinc is far from being pure. The chemically 
 pure metal is expensive. When impure zinc is used, small 
 closed circuits are formed between the particles of foreign 
 matter and the particles of zinc. This local action, which 
 takes place even when the circuit of the cell or battery is 
 broken, rapidly destroys the zinc plate and contributes 
 nothing to the general current. This waste, which would 
 not occur if pure zinc were used, is prevented by fre- 
 quently amalgamating the zinc. This is done by clean- 
 ing the plate in dilute acid and then rubbing it with 
 mercury. 
 
 (a.) The method of amalgamating battery zincs practised by the 
 author is as follows : In a glass vessel placed in hot water, dissolve 
 15 cu. cm. of mercury in a mixture of 170 cu. cm. of strong nitric 
 acid and 625 cu. cm. of hydrochloric (muriatic) acid. When the 
 mercury is dissolved, add 830 cu. cm. of hydrochloric acid. When 
 the liquid has cooled, immerse the battery zinc in it for a few 
 minutes, remove and rinse thoroughly with water. The liquid may 
 be used over and over until the mercury is exhausted. The quan- 
 tity here mentioned will suffice for 200 ordinary zincs or more. 
 Keep the liquid, when not in use, in a glass-stoppered bottle. 
 
 389. Polarization. It was stated in 383 that the 
 accumulation of hydrogen bubbles at the negative plate 
 increases the internal resistance of the cell. But the 
 hydrogen affects the current in another way. It acts like 
 a positive plate (being almost as oxidizable as the zinc) 
 and sets up an opposing electromotive force that tends 
 to set a current in the opposite direction. A cell or bat- 
 tery in this condition is said to be polarized. Some- 
 times, as a result of polarization, the strength of the cur- 
 rent falls off very greatly within a few minutes after clos- 
 ing the circuit. (See 414.) 
 
VOLTAIC ELECTRICITY. 26? 
 
 390. Varieties of Voltaic Cells. All voltaic 
 belong to one of two classes : 
 
 (1.) Those using only one liquid. 
 (2.) Those using two liquids. 
 
 All of the earlier batteries were composed of one-liquid 
 3ells. 
 
 Note. When dilute sulphuric acid is mentioned in connection with 
 cells and batteries, it may be understood that one volume of acid to 
 ten or twelve volumes of water is meant. 
 
 391. Smee's Cell. A Smee's cell 
 is represented by Fig. 182. It consists of 
 a platinized silver plate placed between 
 two zinc plates hung in dilute sulphuric 
 acid. The hydrogen bubbles accumulate 
 at the points of the rough platinum sur- 
 face and are more quickly carried up to 
 the surface of the liquid and thus gotten 
 rid of. The cell has an available electro- 
 motive force of about 0.47 volt. FIG. 182. 
 
 392. Potassium Di-chromate Cell. The po- 
 tassium di-chromate cell has a zinc plate hung between 
 two carbon plates. A solution of potassium di-chromate 
 (bi-chromate of potash) in dilute sulphuric acid is the 
 liquid used. The hydrogen is given an opportunity for 
 chemical union as fast as it is liberated. The E. M. F. of 
 this cell is great to start with (from 1.8 to 2.3 volts), but 
 it falls very quickly when the external resistance is small. 
 It quickly recovers and may be used with advantage 
 where powerful currents of short duration are often 
 wanted. It is the only single liquid cell that is free from 
 polarization. It is sometimes called the Grenet cell. 
 
268 
 
 ELtiCTRtClTY. 
 
 FIG. 183. 
 
 (a.) The bottle form of this cell, represented in Fig. 183, is the 
 most, convenient for the laboratory or lecture table. By means of the 
 sliding rod, the zinc plate may be raised out 
 of the solution when not in use. Thus ad- 
 justed, the cell may remain for months with- 
 out any action, if desired, and be ready at a 
 moment's notice. 
 
 (6.) One of the best proportions for the solu- 
 tion is as follows : One gallon of water, one 
 pound of potassium di-chromate and from a 
 half pint to a pint of sulphuric acid, according 
 to the energy of action desired. A small 
 quantity of nitric acid added to the solution 
 increases the constancy of the battery by oxi- 
 dizing the nascent hydrogen and thus forming 
 water. 
 
 (c.) The following recipe is good : Pour 167 
 cu. cm. of sulphuric acid into 500 cu. cm. of 
 water and let the mixture cool. Dissolve 115 
 g. of potassium di-chromate in 335 CM. cm. of 
 boiling water and pour, while hot, into the dilute acid. When cool, 
 it is ready for use. 
 
 393. The Leclaiiche Cell. This cell, shown in 
 Fig. 184, contains a zinc plate or rod and a porous, earthen- 
 ware cup containing the carbon plate. 
 The space between the carbon plate 
 and the cup is filled with fragments 
 of carbon and powdered peroxide of 
 manganese. This cup replaces the 
 second metal plate. The liquid used 
 is a solution of ammonium chloride 
 (sal-ammoniac) in water. This cell 
 is tolerably constant if it be not used 
 to produce very strong currents, but 
 its great merit is that it is very permanent. It will keep 
 in good condition for months with very little attention, 
 furnishing a current for a short time whenever wanted. 
 
 FIG. 184. 
 
VOLTAIC ELECTRICITY. 
 
 It is much used for working telephones, electric bells 
 (Fig. 232) and clocks, railway signals, etc. The man- 
 ganese oxide prevents polarization by destroying the 
 hydrogen bubbles. If the cell be used continuously for 
 some time, its power weakens owing to the accumulation 
 of hydrogen, but if left to itself it gradually recovers 
 as the hydrogen is oxidized. Sometimes the manga- 
 nese oxide is applied to the face of the carbon and the 
 porous cup dispensed with. This cell has an E. M. F. of 
 about 1.5 volts. It should be left on open circuit when not 
 in use. 
 
 394. Daiiiell's Cell. This cell consists of a copper 
 plate immersed in a saturated solution of copper sulphate 
 (blue vitriol) and a zinc plate immersed in dilute sul- 
 phuric acid or a solution of zinc sulphate (white vitriol). 
 The two liquids are separated ; usually 
 one liquid is contained in a porous 
 cup placed in the other liquid. Cry- 
 stals of copper sulphate are placed in 
 the solution of copper sulphate to 
 keep the lafcter saturated. Such a 
 cell will furnish a nearly constant 
 current, with an E. M. F. of 1.079 
 volts and keep in order for a long 
 time. It should be kept on closed cir- 
 cuit when not in use. The hydrogen passes through the 
 porous cell and acts upon the solution of copper sulphate. 
 Copper, instead of hydrogen, is deposited upon the copper 
 plate. Polarization is thus avoided. If an incrustation 
 forms near the zinc plate, remove some of the solution of 
 zinc sulphate and dilute what remains with water. 
 
 FIG. 185. 
 
270 
 
 VOLTAIC ELECTRICITY. 
 
 (a.) In Fig. 186, the copper plate is represented as a cleft cylinder 
 within the porous cup, the crystals being piled up around it. It is 
 common to interchange the plates, the zinc heing in dilute sulphuric 
 acid within the porous cup, and the copper plate in the saturated 
 acid outside the porous cup. Sometimes the outer vessel itself is 
 made of copper instead of glass and serves as the copper plate as is 
 shown in Fig. 185. 
 
 FIG. 1 86. 
 
 FIG. 187. 
 
 395 The Gravity Cell. This is a modification 
 of the Daniell's cell, no porous cup being used. The cop- 
 per plate is placed at the bottom of the cell and the zinc 
 plate near the top Crystals of copper sulphate are piled 
 upon the copper plate and covered with a saturated solu- 
 tion of copper sulphate. Water or, preferably, a weak 
 solution of zinc sulphate rests upon the blue solution be- 
 low and covers the zinc plate. The two solutions are of 
 different specific gravities and remain clearly separated if 
 the cell be kept on closed circuit when not in use. (Fig 
 187.) This cell is very largely used in working telegraph 
 lines. It is sometimes called the Callaud cell. 
 
 396. Grove's Cell. The outer vessel of a Grove's 
 cell contains dilute sulphuric acid. In this is placed a 
 
VOLTAIC ELECTRICITY. 
 
 271 
 
 hollow cylinder of zinc. Within the zinc cylinder is 
 placed a porous cup containing strong nitric acid. The 
 negative plate is a strip of platinum placed in the nitric 
 acid. The hydrogen passes through the porous cup and 
 reduces the nitric acid to nitrogen peroxide, which escapes 
 as brownish-red fumes. These nitrogen fumes are dis- 
 agreeable and injuribus ; it is well, therefore, to place the 
 battery in a ventilating chamber or outside the experiment- 
 ing room. The E. M. F. of the Grove cell, under favor- 
 able conditions, is nearly two volts, while its internal re- 
 sistance is small, being about one-fifth that of a Daniell's 
 cell. It is much used for working induction coils (consult 
 the Index), for generating the electric light, etc. It is, 
 however, troublesome to fit up and should have its liquids 
 renewed every day that it is used. Fig. 189 represents a 
 Grove's battery with cells joined in series. 
 
 397. Bunsen's Cell. -**>. 
 
 Bunsen's cell (Fig. 188) dif- | 
 
 fers from Grove's in the use I 
 
 of carbon instead of expensive 
 
 platinum for the negative 
 
 plate, thus reducing the cost. 
 
 The plates are made larger 
 
 than for Grove's battery. Its 
 
 E. M. F. is about the same as 
 
 that of the Grove cell but its 
 
 internal resistance is greater. FIG. 188. 
 
 Fig. 190 represents a battery of Bunsen's cells joined in 
 
 multiple arc. 
 
 Note. There are scores of different kinds of cells in the market 
 competing for favor. Those here described are among the ones 
 most commonly used. 
 
272 VOLTAIC ELECTRICITY. 
 
 398. A Voltaic Battery. A number of similar 
 voltaic elements connected in such a manner that 
 the current has the same direction in all, constitutes 
 a voltaic battery. The usual method is to connect the 
 positive plate of one element with the negative plate of 
 the next, as shown in Fig. 189. When thus connected, 
 they are said to be coupled "tandem" or "in series." 
 Sometimes all of the positive plates are connected by a 
 wire and all of the negative plates by another wire. The 
 cells are then said to be joined " parallel/' " abreast " or 
 in multiple arc." (See Fig. 190.) 
 
 (a.) When two or more cells are joined together, the points of 
 Contact should be as large as is convenient and kept perfectly clean. 
 The connecting wire should be of good size and, for the sake of 
 pliability, a part of it may well be given a spiral form by winding it 
 upon a pencil or other small rod. 
 
 399. Batteries of High Internal Resist- 
 ance. Each kind of galvanic cell has an internal resist- 
 
 FIG. 189. 
 
 ance, as explained in 383. A battery of cells joined in 
 series is called a "battery of high internal resistance." 
 (Fig. 189). This method of joining the cells increases 
 
VOLTAIC ELECTRICITY. 273 
 
 the length of the liquid conductor through which the 
 current passes. 
 
 (a.) In a battery of cells joined in series, the E. M. F. and the 
 internal resistance are those of a single cell multiplied by the num- 
 ber of cells. For a circuit of great external resistance, a battery of 
 high internal resistance is needed. 
 
 4OO. Batteries of Low Internal Resist- 
 ance. A battery of cells joined parallel is called a 
 "battery of low internal resistance." (Fig. 190.) This 
 method of joining the cells does not increase the length 
 of the liquid conductor traversed by the current but is 
 equivalent to increasing its diameter or sectional area. 
 
 (a.) In a battery of cells joined parallel, the E. M. F. is that of a 
 single cell, but the internal, resistance is that of a single cell divided 
 by the number of cells. For a circuit of small external resistance, 
 large cells, or several cells joined parallel, are preferable. 
 
 FIG. 190. 
 
 (&.) A battery of high internal resistance was formerly called an 
 intensity battery, while a battery of low internal resistance was 
 called a quantity battery. 
 
 4O1. Requisites of a Good Battery. The 
 
 following conditions should be met by a battery : 
 
 ( 1.) Its electromotive force should be high and constant, 
 (2.) Its internal resistance should be small. 
 
274 VOLTAIC ELECTRICITY. 
 
 (3.) It should give a constant current and, therefore, 
 
 must be free from polarization ; it should not be 
 
 liable to rapid exhaustion, requiring frequent re- 
 
 newal of the acid. 
 
 (4.) It should be perfectly quiescent when the circuit 
 
 is open. 
 
 ( 5.) It should be cheap and of durable materials. 
 (6.) It should be easily manageable and, if possible, 
 
 should not emit corrosive fumes. 
 
 As no single battery fulfills all these conditions, some 
 batteries are better for one purpose and some for another. 
 Thus, for telegraphing through a long line of wire a con- 
 siderable internal resistance in the battery is no great 
 disadvantage ; while, for producing an electric light, much 
 internal resistance is absolutely fatal. 
 
 4O2. The Best Arrangement of Cells. The 
 best method of coupling cells in any given case depends 
 on the work to be done by the battery. The maximum 
 effect is attained when the resistance of the ex- 
 ternal circuit is made equal to the internal resist- 
 ance of the battery. 
 
 (a.) For example, suppose that in a given battery of eight cells : 
 
 (1.) Each cell has an E. M. F. of two volts. 
 
 (2.) Each cell has the very high internal resistance of eight ohms. 
 
 (3.) The battery is to work through a wire that has a resistance 
 of sixteen ohms. 
 
 (&.) First, couple the cells parallel. The E. M. F. of the battery 
 is that of a single cell, 2 volts. The internal resistance is 8 ohms 
 -4-8 = 1 ohm. Adding the external resistance, we have a total 
 resistance of 17 ohms. (See 386.) 
 
 This arrangement gives a current of 04176+ amperes. 
 
VOLTAIC ELECTRICITY. 275 
 
 (<0 Next, couple the cells in series. The E. M. F. of the battery 
 is 8 times 2 volts, or 16 volts. The internal resistance is 8 times 8 
 ohms or 64 ohms. Adding the external resistance, we have a total 
 resistance of 80 ohms. 
 
 . 
 
 This arrangement gives a current of 0.2 amperes. 
 
 (d.) Finally, join the cells in two rows (each row being a series 
 of four cells) and join the rows parallel. The E. M. F. of the battery 
 will be 4 times 2 volts or 8 volts. The internal resistance will be 
 4 times 8 ohms or 32 ohms for each row, but only half that, or 16 
 ohms, for the whole battery. Adding the external resistance, we 
 have a total resistance of 32 ohms. 
 
 *'p^ ;-*=! =i6TT6=- 25 - ;/ - ; - ; - 
 
 This arrangement, in which the internal and the external resistances 
 are equal, gives a current of 0.25 amperes, the greatest possible 
 under the given conditions. 
 
 (e.} A similar application of Ohm's law shows that when the 
 external resistance is large, there is little gain from joining cells 
 parallel, and thai; when the external resistance is very smatt, there is 
 little gain in joining cells in series. 
 
 EXERCISES. 
 
 1. Given ten cells, each with an electromotive force of 1 volt and 
 an internal resistance of 5 ohms. What is the current (in amperes) 
 of a single cell, the external resistance being 0.001 ohm ? 
 
 Ans. 0.19996+ amperes. 
 
 2. The ten cells above mentioned are joined abreast. The exter- 
 nal resistance is 0.001 ohm. What is the current of the battery ? 
 
 Ans. 1.996+ amperes. 
 
 3. The ten cells above mentioned are joined tandem, the external 
 resistance remaining the same. What is the current of the battery ? 
 
 Ans. 0.19999+ amperes. 
 
 4. What is the current given by one of the above mentioned cells 
 when the external circuit has a resistance of 1000 ohms ? 
 
 Ans. 0.00099502 amperes. 
 
 5. When the ten cells are joined abreast with an external resist 
 ance of 1000 ohms, what is the current of the battery ? 
 
 Ans. 0.0009995 amperes. 
 
276 VOLTAIC ELECTRICITY. 
 
 6. When the ten cells are joined in series with an external resist- 
 ance of 1000 ohms, what is the current of the battery ? 
 
 Am. 0.00952 amperes. 
 
 Note. Compare the results in Exercises 1, 2 and 3, where we 
 have a small external resistance. Then compare the results in Ex- 
 ercises 4, 5 and 6, where we have a high external resistance. 
 
 7. Why are cells arranged tandem for use on a long telegraphic 
 line? 
 
 8. What is the resistance of 2 miles of No. 6 electric light wire 
 (copper of ordinary commercial quality)? (See Appendix I.) 
 
 Ans. 4.56 ohms. 
 
 9. A Brush dynamo, No. 8, will operate 65 arc lamps on a short 
 circuit. Each lamp has a resistance of about 4.52 ohms. If the 
 lamps be put on a 10 mile circuit of No. 6 copper wire, how many 
 lamps should be " cut out " of the circuit, the dynamo running at 
 the same speed and the current strength remaining the same ? 
 
 Ans. 5 lamps. 
 
 10. Show, by a diagram, how a battery of three cells should be 
 arranged when the internal resistance is the principal one to be 
 overcome. 
 
 11. What is the resistance of a mile of ordinary No. 6 iron tele, 
 graph wire? (See Appendix K, [2].) Ans. 13.3 ohms. 
 
 12. Show that the conductivity of water is increased more than 50 
 times by adding half its volume of sulphuric acid. (See Appendix 
 K> [2].) 
 
 13. How much is the conductivity of water increased by adding 
 ^ ite volume of sulphuric acid ? Am. About 22 times. 
 
VOLTAIC ELECTRICITY. 277 
 
 403. Long and Short Coil Instruments. 
 
 A "long coil" galvanometer, or a "long coil" electro- 
 magnet, or an instrument of any kind in which the con- 
 ductor is a long, thin wire of high resistance, should not 
 be employed on circuits the other resistances of which are 
 small. Conversely, on circuits of great length, or where 
 there is a high resistance, " short coil " instruments are of 
 little service for, though they add little to the resistances, 
 their few turns of wire are not enough with the small 
 currents that circulate in high-resistance circuits ; " long 
 coil " instruments are here appropriate, as they multiply 
 the effects of the currents by their many turns. Their 
 resistance, though perhaps large, is not a serious addition 
 to the existing resistances of the circuit. 
 
 404. Divided Circuits and Shunts. The cas'e 
 of several wires forming a multiple arc often occurs in 
 practice. In such cases, the current flowing in each 
 branch is inversely proportional to the resistance 
 of that branch. Either of two such branches is called 
 a shunt. Evidently, the joint resistance of all the branches 
 is less than the resistance of any one of them. 
 
 FIG. 191. 
 
 (a.) A current flowing along a conductor divides at A, part going 
 through a galvanometer or electro-magnet at G and the rest going 
 through the branch, B. The currents unite at C. If the conductor, 
 AGO, has a resistance of 99 ohms and the conductor, ABC, has a 
 
278 VOLTAIC ELECTRICITY. 
 
 resistance of 1 ohm, 1 per cent, of the total current will go through 
 G and 99 per cent, will go by way of B. 
 
 (6.) If we have two wires, the separate resistances of which are 
 respectively 28 ohms and 24 ohms, placed abreast in a circuit, find 
 their joint resistance. The joint conductivity will be the sum of the 
 separate conductivities and conductivity is the reciprocal of resist- 
 ance. Call the joint resistance JR. 
 
 -I-J- JL. = 2t4.^?_^. 7?_??2 no 
 
 R ~ 28 24 672 672 ~ 672' ~ 52 ~ 
 
 The joint resistance will be 12.92 ohms. 
 
 (c.) The joint resistance of the two branches of a divided conductor 
 is equal to the product of the separate resistances divided by their 
 sum. If there are more than two branches, the method employed 
 above may be used. 
 
 (d.) It is often necessary to use a sensitive galvanometer or other 
 instrument with a current so strong that the current would give in- 
 dications too large for accurate measurement or even ruin the instru- 
 ment. Under such circumstances, the greater part of the current 
 may be shunted around the galvanometer. The resistance of the 
 shunt having a known ratio to that of the galvanometer and its 
 branch, the total current strength may be computed from the strength 
 of the current flowing through the instrument. Shunt circuits may 
 be found in almost all arc lamps. 
 
 4O5. Mechanical Effects of the Electric 
 Current. The piercing of the glass walls of an over- 
 charged Leyden jar affords a good, though expensive, 
 illustration of the mechanical effects of electricity. Trees 
 and telegraph poles shattered by lightning are not un- 
 familiar. But, by far, more important for our considera- 
 tion are the mechanical effects produced by voltaic or 
 dynamic electricity and, especially, the numerical rela- 
 tion between the electricity used and the work done. 
 This subject will be considered in Section VI. of this 
 chapter. 
 
 Experiment 73. Through a long, thin platinum wire, send a 
 current that will heat it to dull redness. Apply a piece of ice to the 
 
VOLTAIC ELECTRICITY. 279 
 
 wire and notice that the rest of the wire glows more brightly than it 
 did before. Then heat a part of the wire with the flame .of a spirit 
 lamp and notice that the rest of the wire glows less brightly than 
 before. In the first case, the current is strengthened by the in- 
 creased conductivity of the cooled part ; in the second case, the cur- 
 rent is decreased by the increased resistance of the part heated by 
 the lamp. 
 
 Experiment 74. When two curved metal surfaces rest upon each 
 other, a current passing from one to the other encounters considera- 
 ble resistance at the small area of contact. The heat consequently 
 developed causes the parts in the neighborhood to expand very 
 quickly when the contact is made. This often gives rise to rapid 
 vibratory movements in the conductors. Gore's railway consists of 
 two concentric copper hoops, whose edges are worked very truly 
 into a horizontal plane. A light copper ball is placed on the rails 
 thus formed. One rail is connected with the + pole of a battery 
 of two or three Grove cells and the other rail with the pole. The 
 ball is then set rolling around the track. If the ball be true and the 
 track well leveled, the energy supplied by the swelling (expansion) 
 at the continually changing point of contact is sufficient to keep up 
 the motion. The ball will roll round and round, giving a crackling 
 sound as it goes. 
 
 Experiment 75. From the poles of a potassium di-chromate bat- 
 tery, lead two stout copper wires and connect their free ends by two 
 or three inches of very fine iron or platinum tmre. Coil the iron wire 
 around a lead pencil and thrust a small quantity of gun-cotton into 
 the loop thus formed. Plunge the zinc plate of the battery into the 
 liquid and the iron wire will be heated enough to explode the gun- 
 cotton ; it may be heated to redness or even to fusion. 
 
 4O6. Thermal Effects of the Electric Cur- 
 rent. Whenever an electric current flows through a 
 conductor, part of the electric energy is changed 
 into heat energy. TJie amount of electricity thus 
 changed into heat will depend upon the amount 
 of resistance offered by the conductor. In the last 
 experiment, the stout copper wires were good conductors, 
 offered but little resistance and converted but little of the 
 
280 VOLTAIC ELECTRICITY. 
 
 electrical energy into heat energy. The change of ma- 
 terial from copper to iron increased that resistance. This 
 increased resistance was again increased by reducing the 
 size of the conductor. For this double reason, the fine 
 wire offered so much resistance that a considerable of the 
 current energy was transformed into heat. Resistance 
 in an electric circuit always produces heat at the 
 expense of the electric current. Thus, electricity is 
 often used in firing mines in military operations and in 
 blasting. All known metals have been melted in this way, 
 while carbon rods have been heated by a battery of 600 
 Bunsen's elements until they softened enough for welding. 
 By means of a Leyden jar battery and a universal dis- 
 charger, remarkable thermal effects may be obtained. 
 Houses are sometimes set on fire by lightning. The nu- 
 merical relations between electricity and heat are con- 
 sidered in Section VI. of this chapter. 
 
 4O7. Luminous Effects of the Electric 
 Current. The electric spark, the glow seen when elec- 
 tricity escapes .from a pointed conductor in the dark and 
 the various forms of lightning are some of the now 
 familiar luminous effects of electricity. Whenever an 
 electric circuit is closed or broken, there is a spark at the 
 point of contact, due to the heating of a part of the con- 
 ductor to incandescence. We have seen luminous effects 
 produced by winding the wire from one plate of a voltaic 
 cell round one end of a file and drawing the other electrode 
 along the side of the file, thus rapidly closing and break- 
 ing the circuit. If the iron wire used in the last experi- 
 ment was heated sufficiently, it also gave a luminous effect 
 
VOLTAIC ELECTRICITY. 281 
 
 and illustrated the fundamental principle of the incandes- 
 cence electric lamp ( 466). 
 
 (a.) The most important luminous effects of electricity will be 
 considered in connection with dynamo-electric machines ( 465). It 
 will be noticed that all of these are secondary thermal effects. 
 
 4O8. Galvani's Experiment. In 1786, Galvani, 
 a physician of Bologna, noticed convulsive kicks in a 
 
 FIG. 192. 
 
 frog's legs when acted upon by an electric current. A frog 
 was killed and the hind limbs cut away and skinned, the 
 crural nerves and their attachments to the lumbar vertebrae 
 remaining. Two dissimilar metals were held in contact and 
 their free ends brought into contact with nerve and muscle 
 respectively, as shown in Fig. 192. Convulsive muscular 
 contractions brought the legs into a position similar to 
 
282 VOLTAIC ELECTRICITY. 
 
 that represented by the dotted lines in the figure. A frog's 
 legs thus prepared make a very sensitive galvanoscope. 
 It is said that they show even the very feeble induction 
 currents of the telephone, though the best galvanometers 
 barely detect them. 
 
 4O9. Physiological Effects of the Electric 
 Current. An electric current may produce muscular 
 convulsions in a recently killed animal. Experiments 
 with the Leyden jar and the induction coil show that 
 similar effects may be produced upon the living animal. 
 The " electric shock," which is physiological in its nature, 
 is familiar to most persons. The sensation thus produced 
 cannot be described, forgotten or produced by any other 
 agency. 
 
 Electricity is largely used as an agent for the cure of 
 disease; experiments of this kind may do injury and 
 would better be left to the educated physician. The dis- 
 charge of a large battery may be fatal and a number of 
 persons have lost their lives within the last few years by 
 coming, accidentally or otherwise, into the circuit of a 
 dynamo-electric machine. Interrupted and alternating cur- 
 rents are more serious in their physiological effects than 
 continuous currents. 
 
 (a.) If the members of a class form a chain by joining hands, the 
 first member holding a feebly -charged Leyden jar by its outer coat 
 and the last member touching the knob, a simultaneous shock will 
 be felt by each person in the chain. A similar experiment may be 
 made with a Ruhmkorff coil. A single Leyden jar has been dis- 
 charged through a regiment of 1500 men, each soldier receiving a 
 shock. Dr. Priestley killed a rat with a battery of seven feet of 
 coated surface, and a cat with a battery of forty feet of coated 
 surface. 
 
VOLTAIC ELECTRICITY. 283 
 
 Experiment 76. Into a bent tube (known to dealers in chemical 
 glassware as a TJ tube), put a solution of any 
 neutral salt, e. g., sodium sulphate. Color the 
 contents of the tube with the solution from 
 purple cabbage. In the arms of the tube, place 
 the platinum electrodes of a battery, as shown in 
 Fig. 193. Close the circuit and presently the 
 liquid at the + electrode will be colored red and 
 that at the electrode, green. If, instead of 
 coloring ths solution, a strip of blue litmus paper 
 be hung near the + electrode it will be reddened, 
 while a strip of reddened litmus paper hung near FIG. 193. 
 
 the 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 77. 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 bath of a dilute solution of 
 tin chloride, introduce two platinum electrodes from a battery of a 
 few cells. A remarkable growth of tin crystals will shoot out from 
 the electrode and spread towards the +, bearing a strong resem- 
 blance to vegetable growth. Hence, it is called the " tin tree." 
 Repeat the experiment with solutions of lead acetate ("sugar of 
 lead ") and of silver nitrate. 
 
 41O. Chemical Effects of the Electric Cur- 
 rent. The electric spark may be made to produce chem- 
 ical combination or chemical decomposition. Ammonia 
 (NH 3 ), or carbon-dioxide (C0 3 ), may be decomposed by 
 passing a series of sparks through it. A mixture of oxygen 
 and hydrogen may be caused to enter into chemical union 
 by the electric spark, the product of the union being water. 
 (See Chemistry, Exp. 53.) Many chemical compounds 
 may be decomposed by passing the current through them. 
 The compound must be in the liquid condition, either by 
 solution or by fusion. Substances that are thus decom- 
 posed are called electrolytes ; the process is called 
 
284 
 
 VOLTAIC ELECTRICITY. 
 
 trolysis ; the compound is said to be electrolyzed. The 
 electrolysis of acidulated water is easily accomplished with 
 a current from three or four Grove's or Bunsen's cells. 
 The water is decomposed into oxygen and hydrogen. The 
 apparatus, shown in Fig. 194, may be called a water- 
 voltameter. 
 
 FIG. 194. 
 
 (a.) The apparatus consists of a vessel containing water (to which 
 a little acid has been added to increase its conductivity) in which 
 are immersed two platinum strips that constitute the two elec- 
 trodes of a battery. When the circuit is closed, bubbles of oxygen 
 escape from the positive electrode and bubbles of hydrogen from 
 the negative. The gases may be collected separately by inverting, 
 over the electrodes, tubes filled with water, as shown in the figure. 
 The volume of hydrogen thus collected will be about twice as great 
 as that of the oxygen. 
 
 (6.) A water- voltameter may be made by cutting off the bottom of 
 a wide-mouthed glass bottle (Chemistry, App. 4, h.) and passing two 
 insulated wires, varnished and terminating in platinum strips, 
 through a cork that closes the mouth of the inverted bottle. Two 
 test tubes will complete the instrument. When a sufficient quantity 
 of the gases has been collected, they may be tested ; the hydrogen, 
 by bringing a lighted match to the mouth of the test tube, where- 
 upon the hydrogen will burn ; the oxygen, by thrusting a splinter 
 
VOLTAIC ELECTRICITY. xJ85 
 
 with a glowing spark into the test tube, whereupon the splinter will 
 kindle into a flame. 
 
 (e.) Each coulomb of electricity liberates 0.1176 cu. cm. of hydrogen 
 and 0.0588 cu. cm. of oxygen, or a total of 0.1764 cu. cm. of the 
 mixed gases. The electrolysis of 9 g. of water requires 95,050 
 coulombs. 
 
 411. Ions. The products of electrolysis, like the oxy- 
 gen and hydrogen, are called ions; the one that goes to 
 the + electrode (or anode) is called the anion; the one 
 that goes to the electrode (kathode or cathode) is called 
 the Icathion or cathion. 
 
 (a.) The amount of chemical action in a cell is proportional to the 
 strength of current while it passes. One coulomb of electricity, in 
 passing through a cell, liberates 0.0000105 gram of hydrogen and 
 dissolves 0.00034125 gram of zinc. 
 
 (&.) One coulomb will cause the deposition of 0.0003307 gram of 
 copper. To deposit 1 gram of copper requires 3024 coulombs. This 
 principle has been used in the Edison meter for electric lighting 
 purposes, a certain proportion of the current being shunted through 
 a " copper voltameter " or bath of copper sulphate solution, as de- 
 scribed in the next experiment. 
 
 Experiment 78. From the + pole of a voltaic battery or dy- 
 namo-electric machine, suspend a plate of copper ; from the pole, 
 
 FIG. 195. 
 
 suspend a silver coin. Place the copper and silver electrodes in a 
 strong solution of copper sulphate (blue vitriol). When the circuit 
 
286 VOLTAIC ELECTRICITY. 
 
 is closed, the salt of copper is electrolyzed, the copper from the salt 
 being deposited upon the silver coin and the sulphuric acid going to 
 the copper or + electrode. The silver is thus electro-plated with 
 copper. (Fig. 195.) 
 
 412. Electro -Metallurgy. The many applica- 
 tions of this process of depositing a metallic coat on a 
 body prepared for its reception, constitute the important 
 art of electro-metallurgy. If, with the apparatus used in 
 the last experiment, a solution of some silver salt be used 
 instead of the copper sulphate solution and the direction 
 of the current be reversed, silver will be deposited upon 
 the copper plate, which will thus be silver-plated. If the 
 positive electrode be a plate of gold and the bath a solu- 
 tion of some salt of gold (cyanide of gold dissolved in a 
 solution of cyanide of potassium), gold will be deposited 
 upon the copper of the negative electrode, which will be 
 thus electro-gilded. In electrotyping, impressions of type 
 or engravings are taken in wax, or any other plastic ma- 
 terial that is impervious to water. A conducting surface 
 is given to such a mould by brushing finely powdered 
 graphite over it ; it is then placed in a solution of sulphate 
 of copper facing a copper plate. The mould is then con- 
 nected with the pole of a dynamo or a vol taic battery and 
 the copper, with the -f- pole; when the current passes 
 through the bath, copper will be deposited upon the mould. 
 When the copper film is thick enough (say as thick as an 
 ordinary visiting card), it is removed from the mould 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 amalgam of equal parts of tin and 
 lead. The copper-faced plate thus produced is an exact 
 
VOLTAIC ELECTRICITY. 287 
 
 reproduction of the type and engravings from which the 
 mould was made. 
 
 (a.) In all these cases, the metal is carried in the direction of the 
 current and deposited upon the negative electrode. In electro- 
 plating and gilding, the technicalities of the art refer chiefly to the 
 means of making the deposit firmly adherent. In electrotyping, 
 they refer chiefly to the preparation of the mould or matrix. 
 
 413. Electro-Chemical Series. The facts just 
 considered suggest a division of substances into two 
 classes, electro-positive and electro- negative. Tlie ion 
 that goes to the negative electrode is called electro- 
 positive ; that which goes to the positive electrode 
 is called electro-negative. 
 
 (a.) Kathions are called electro-positive because they seem to be 
 attracted to the negative pole of the battery (kathode), the idea be- 
 ing that of attraction between opposite electricities. Hydrogen and 
 the metals are kathions or electro-positive. They seem to move with 
 the current, going as far as possible and being deposited where the 
 current leaves the " bath " or electrolytic cell. Similarly, anions 
 are said to be electro-negative. 
 
 414. The E. M. F. of Polarization. The prod- 
 ucts of electrolysis have a tendency to reunite by virtue 
 of their chemical affinity. (Chemistry, 8.) For exam- 
 ple, the electrolysis of zinc sulphate gives zinc and sul- 
 phuric acid. But we now well know that the chemical 
 action of these two substances has an electro-motive force 
 of its own. This E. M. F. of the ions acts in opposition 
 to that of the electrolyzing current. In some cases, it 
 rises higher than the E. M. F. of the original current and 
 reverses the direction of the current. The oxygen and 
 hydrogen, yielded by the electrolysis of water, tend to re- 
 unite and set up an opposing E. M. F. of about 1.45 volts. 
 
288 VOLTAIC ELECTRICITY. 
 
 Thus we see that it requires a battery or cell with an E. 
 M. F. of more than 1.45 volts to decompose water. This 
 electro-motive force of the ions is called the E. M. 
 F. of Polarization. It may be observed by putting a 
 galvanometer in the place of the battery of the water- 
 voltameter (Fig. 194). The polarization in a voltaic cell 
 acts in the same way. 
 
 (a.) There is no opposing E. M. F. of polarization when the kathion 
 and the anode are of the same metal. For example, the feeblest 
 current will deposit copper from a solution of copper sulphate, when 
 ihe anode is a copper plate. 
 
 Experiment 79. Suspend two strips of bright sheet lead facing 
 each other in dilute sulphuric acid. Pass a current through these 
 plates by connecting them with a battery of 4 or 5 cells in series. A 
 dark peroxide of lead will form on one of the bright plates. Then 
 remove the battery and, in its place, put a short coil galvanometer or 
 electro-magnet. It will be found that the lead-plate cell is supply- 
 ing a current, the direction of which is the reverse of the charging 
 battery previously used. 
 
 415. Secondary Batteries. When a voltameter 
 or an electro-plating bath is supplying a current of elec- 
 tricity, as mentioned in the last paragraph, it constitutes 
 a secondary battery. As the ions do not reunite when the 
 circuit is open, the energy of the decomposing current 
 may be stored up as energy of chemical affinity. When 
 a current is again wanted, the circuit may be 
 closed and the energy of chemical affinity at once 
 appears as energy of electric current. Secondary 
 batteries are, consequently, often called storage 
 batteries. 
 
 (a.) The Faure battery consists of two plates of sheet lead coated 
 with red lead (lead sesqui-oxide, Pb 8 4 ). These plates are septi- 
 
VOLTAIC ELECTRICITY. 289 
 
 rated by a layer of paper or cloth, rolled up in a loose coil like a roll 
 of carpet and immersed in dilute sulphuric acid. 
 
 (b.) When a current from a dynamo-electric machine or a voltaic 
 battery is sent through such a cell, chemical action is produced. 
 Oxygen acts on the coating of the anode plate and converts it into a 
 higher oxide of lead (the peroxide, PbO 2 ). Hydrogen acts upon 
 the coating of the kathode plate and reduces it to metallic lead in a- 
 spongy condition. When these changes have gone as far as possi- 
 ble, the battery is said to be ' charged." The charged plates will 
 remain in this condition for days if the circuit be left open. 
 
 (c,) By closing the circuit, the plates will, at any time, furnish a 
 current until they are changed to their original chemical condition. 
 As the lead plates and the acid are not rapidly destroyed, the battery 
 may be charged and discharged many times. 
 
 FIG. 
 
 (d.) Many serious defects in the Faure battery have been obviated 
 in the Brush battery (Fig. 196). These batteries are composed of a 
 number of cells containing cast lead plates of a peculiar construction, 
 electro-chemically prepared and immersed in dilute sulphuric acid. 
 These cells may be connected together, tandem or abreast, so as to 
 produce any desired result. A large number of these batteries may 
 be placed in one circuit and charged by the current of one dynamo. It 
 will thus be seen that the dynamo may be made to do double duty, 
 charging batteries by day for use in connection with the incandes- 
 cence lamps and supplying arc lamps direct, at night. The E. M. F. 
 
290 VOLTAIC ELECTRICITY. 
 
 of each Brush cell is about two volts. For electric lighting, they 
 are generally prepared in batteries of twenty or more cells. An 
 automatic current " manipulator " or switch is provided with each 
 Brush battery and is arranged so as to retain the battery in circuit 
 
 until it is charged and 
 then to disconnect it from 
 the circuit. When the 
 charge has been exhausted 
 to a certain point, it brings 
 the battery into the cir- 
 cuit again and holds it till 
 it has been recharged and 
 then cuts it out as before. 
 The same operation is re- 
 peated with every battery 
 in circuit. The operation 
 is automatic. Each bat- 
 tery has a clock attached, 
 which registers the time 
 thaf; the charging current 
 has been passing through 
 FlG - T 97- the cells. The incandes- 
 
 cence lamps are connected with the batteries through the " manipu- 
 lator," as shown in Fig. 197. The quantity of electricity capable 
 of being "stored" may be increased by increasing the number of 
 cells and the size of the plates. 
 
 416. Magnetic Effects of the Electric Cur- 
 rent. Any conductor is rendered magnetic by passing 
 a current of electricity through it. A common needle 
 may be magnetized by winding about it an insulated cop- 
 per wire and discharging a Leyden jar through the wire. 
 We have already seen that a bar of soft iron may be tem- 
 porarily magnetized by the influence of the voltaic current. 
 It may be further shown by the action of the bar and 
 helix. 
 
 (a.) This apparatus consists of a movable bar of soft iron surrounded 
 by a coil of insulated copper wire (Fig. 198). When the wire of the 
 coil is placed in the closed circuit of a battery, the iron bar becomes 
 
VOLTAIC ELECTRICITY. 
 
 291 
 
 FIG. 198. 
 
 strongly magnetized ; when the circuit is broken, the bar instantly 
 
 loses its magnetic power. The bar may be a 
 
 straight piece of stout iron wire ; the helix may 
 
 be made by winding insulated copper wire upon 
 
 a piece of glass tubing large enough to admit 
 
 the wire and not quite as long as the iron. 
 
 (&.) A good helix, convenient for many pur- 
 poses, may be made upon an ordinary wooden 
 
 spool. With a sharp knife, make the shank of 
 
 the spool as thin as possible and then wind the 
 
 spool full of insulated copper wire about as large as ordinary broom 
 
 or stove-pipe wire. The iron bar must be small enough to pass 
 
 easily through the hole in the spool and long enough to project a 
 
 little ways beyond each end. 
 
 (c.) Either of these helices may be placed in the circuit of a cell 
 
 and held in a vertical position, when it will act as a " sucking " 
 
 magnet. The movable iron core will be held in mid-air " without 
 
 any visible means of support." 
 
 (d.) The " helix and ring armature " is shown in Fig. 199. The 
 armature is of soft iron divided into two semicircles 
 with brass handles. When the helix is placed in a 
 closed circuit, the semicircles resist a considerable 
 force tending to draw them apart ; when the circuit 
 is broken, they fall asunder of their own weight. 
 The iron ring may be made without handles by any 
 blacksmith. Stout cords will answer for handles. 
 The helix may be made by winding insulated wire 
 upon a pasteboard cylinder an inch or an inch and a 
 half long There should be four or five layers of 
 stout, copper wire which may be tied together with 
 
 strings passing through the hole in the helix. 
 (e.) Such temporary magnets as these are called electro-magnets. 
 
 The subject of electro-magnets will be further considered in 442- 
 
 448. 
 
 FIG. 199. 
 
 417. Deflection of the Magnetic Needle. 
 
 We have already seen that the voltaic current has a 
 marked effect in turning the magnetic needle from its north 
 and south position, tending to place the needle at right 
 angles to the direction of the current. This may be easily 
 shown by Oersted's apparatus represented in Fig. 200. It 
 
292 VOLTAIC ELECTRICITY. 
 
 consists of a magnetic needle and a brass wire frame with 
 three pole-cups, permitting the current to be passed over, 
 under, or around the magnet. The 
 space immediately surround- 
 ing a wire carrying an electric 
 current is a field of magnetic 
 force as truly as is the space 
 around a magnetized body 
 ( 433). 
 
 Flo. 200. (a.) If the current pass above the needle 
 
 from north to south, the north-seeking or 
 
 end of the magnet will be deflected toward the east ; if it pass 
 from south to north, the end of the needle will be deflected toward 
 the west. If the current pass below the needle, the deflections will 
 be the opposite of those just mentioned. The wires are insulated 
 where they cross at a. 
 
 418. The Astatic Galvanometer. This gal- 
 vanometer depends upon the principles set forth in the 
 last paragraph. It is a very delicate instrument for 
 detecting the presence of an electric current and 
 determining its direction and strength. In Oersted's 
 apparatus, the needle is heavy and a considerable force is 
 needed to set it in motion ; in the galvanometer, the needle 
 is very light and suspended so as to turn easily. In Oersted's 
 apparatus, the needle is held in the magnetic meridian by 
 the directive influence of the earth ; in the galvanometer, 
 this is obviated almost wholly by the use of an astatic needle 
 ( 439). In Oersted's apparatus, the current makes but a 
 single course about the needle ; in the galvanometer, the 
 wire is insulated and coiled many times about the needle ; 
 thus the effect is multiplied. One of the needles is within 
 the coil while the other swings above it, the two being 
 connected by a vertical axis passing through an appro- 
 
VOLTAIC ELECTRICITY.' 
 
 293 
 
 FIG. 201. 
 
 priate slit in the coil. If both needles were within the 
 coil, since their poles are reversed, the same current would 
 tend to deflect them in opposite directions and thus the 
 action of one needle would neutralize 
 that of the other. The astatic needle 
 is suspended by an untwisted silk 
 fibre from a hook which may be low- 
 ered when the instrument is not in 
 use until the upper needle rests upon 
 the dial plate beneath it. The ends 
 of the coiled wire are connected with 
 binding screws ; leveling screws are 
 provided, by means of which the in- 
 strument may be adjusted so that the 
 needles shall swing clear of all obstructions. A glass 
 cover protects from dust and disturbance by air currents. 
 The instrument is represented in Fig. 201. 
 
 (a.) When the deflections of tlie astatic galvanometer are less than 
 10 or 15, they are very nearly proportional to the strengths of the 
 currents that produce said deflections. A current that deflects the 
 needle 6 is about three times as strong as one that deflects it 2. 
 
 (&.) That a galvanometer shall be good, it must be able to meas- 
 ure the strength of the current in some certain way. It must be 
 adapted to the currents to be measured by it. A galvanometer fitted 
 for the measurement of small currents (e. g., five or six milliamperes) 
 would not be suitable for measuring a ten ampere arc electric 
 light current. If the current to be measured has passed through 
 a circuit of great resistance (e. g., several miles of telegraph wire), 
 a short coil galvanometer consisting of only a few turns of wire will 
 not answer; a long-coil galvanometer, with many turns of wire 
 about the needle, must be used. Hence, it will be seen that differ- 
 ent kinds of galvanometers are needed for different kinds of work. 
 (See Appendix L.) 
 
 Experiment 80. Connect an iron and a German silver wire to 
 the binding posts of a sensitive, short-coil, astatic galvanometer. 
 Twist the free ends of the wires together and heat the junction in 
 
294 THERMO-ELECTRICITY. 
 
 the flame of an alcohol lamp. The deflection of the galvanometer- 
 needle will show that an electric current is traversing the circuit. 
 Cool the junction with a piece of ice. The galvanometer will show 
 that a second current is flowing in the opposite direction. 
 
 419. Thermo-Electricity. // a circuit be 
 made of two metals and one of the junctions be 
 heated or chilled, a current of electricity is pro- 
 duced. 
 
 (a.) This may be further illustrated by the apparatus shown 
 
 in Fig. 202. The 
 upper bar, m n, 
 having its ends 
 bent, is made of 
 copper ; the low- 
 er, op, is of bis- 
 muth. This rect- 
 angular frame is 
 to be placed in the 
 magnetic merid- 
 ian and a mag- 
 n et ic needle 
 placed within it. 
 FIG. 202. Upon heating one 
 
 of the junctions, 
 
 a current will be produced, the existence of which is satisfactorily 
 shown by the deflection of the needle as indicated in the figure. The 
 junction may be chilled with a piece of ice or by placing upon it 
 some cotton wool moistened with ether. In this case, a current, 
 opposite in direction to the first, will be produced ; the needle will 
 be turned the other way. The frame may be simplified by bend- 
 ing a strip of copper twice at right angles to make the top, bottom 
 and one end of the frame, the other end being a cylinder of bis- 
 muth. But the form shown in Fig. 202 is preferable, as the same 
 junction may be heated by the lamp below or chilled by laying a 
 piece of ice on the upper side. 
 
 420. A Thermo-electric Pair. If a bar of 
 
 antimony, A, be soldered to a bar of bismuth, B, and the 
 free ends joined by a wire, we evidently have a circuit 
 
THERMO-ELECTRICITY. 
 
 equivalent to the one considered in the last paragraph. 
 When the junction, (7, is heated, a current will pass, from 
 bismuth to antimony across the junction and from anti- 
 mony to bismuth through the wire, as shown in Fig. 203. 
 
 (a.) The arrangement is analogous to a voltaic element, the 
 antimony representing the plate and 
 carrying the + electrode, the bismuth rep- 
 resenting the + plate and carrying the 
 electrode, while the solder takes the place 
 of the liquid. The E. M. F. of an antimony- 
 bismuth pair for 1 C. difference of temper- 
 ature is about 117 microvolts. Just as a number of voltaic elements 
 may be connected, so may a number of thermo-electric pairs be 
 connected to form a thermo-electric series. 
 
 421. The Thermo-electric Pile. Several 
 thermo-electric pairs, generally five, six, or seven, are 
 arranged in a vertical series, as shown in Fig. 204, the 
 intervening spaces being much reduced, the successive 
 bars separated by strips of varnished paper only and the 
 wire connection omitted. A similar series may be united 
 to this by soldering the free end of the antimony bar of 
 one series to the free end of the bis- 
 muth bar of the other, the two series 
 being separated by a strip of varn- 
 ished paper. Any desirable number 
 of such series may be thus united, 
 compactly insulated and set in a 
 metal frame so that only the sold- 
 ered ends are open to view. The free end of the antimony 
 bar, representing the -f electrode, and the free end of 
 the bismuth bar, representing the -* electrode, are con- 
 nected with binding screws, whicfh may be connected with 
 a sensitive short-coil galvanometer. The thermo-electric 
 
296 
 
 THERMO-ELECTRICITY. 
 
 pile, with the addition of conical reflectors, is shown 
 in Fig. 205. A change of temperature at either exposed 
 face of the pile produces a feeble current of electricity 
 which is manifested by the movement of the needle of the 
 
 galvanometer. The instrument 
 is much used in scientific work 
 for detecting differences in tem- 
 perature, being much more 
 ' sensitive than the mercury ther- 
 mometer. 
 
 FIG. 205. 
 
 423. The Peltier Ef- 
 fect. When .an electric cur- 
 rent passes over a junction 
 from antimony to bismuth, 
 there is an evolution of heat at 
 the junction, the temperature 
 of which rises. When the current passes in the op- 
 posite direction (from bismuth to antimony), there is an 
 absorption of heat and the temperature of the junction 
 falls. In other words, if the current be sent through the 
 circuit in the direction in which the thermo-electromotive 
 force would naturally send it, the heated junctions will be 
 cooled and the cooled junctions will be heated. 
 
 EXERCISES. 
 
 1. (a.) Draw a figure of a simple voltaic element. (6.) State 
 what is meant by the electric current, (c.) Indicate, upon the 
 figure, the direction of the current, (d.) What are the electrodes ? 
 (e.) Indicate them by their proper signs upon the figure. 
 
 2. (a.) Describe or figure a high resistance battery of Grove's ele- 
 ments. (&.) A low resistance battery of Bunsen's elements, (c.) 
 What is the peculiar advantage of the Daniell's battery ? 
 
VOLTAIC AND THERMO-ELECTRICITY. 297 
 
 3. Describe an experiment illustrating the heating effects of cur- 
 rent electricity. 
 
 4. (a.) How may a very feeble current be detected ? (&.) Describe 
 the apparatus used, (c.) Mention the features contributing to its 
 delicacy. 
 
 5. (a.) If the resistance of one mile of a certain electric light wire 
 is 3.58 ohms, what is the resistance of 4.4 miles of the same wire? 
 (6.) The resistance of a certain wire is 5 ohms per 100 yd. What 
 length of the same wire will have a resistance of 13.2 ohms? 
 
 Ans. (a.) 15.75 ohms. (&.) 264 yd. 
 
 6. What is the resistance of a mile of copper wire that has a 
 diameter of 65 mils if the resistance of a mile of copper wire 80 mils 
 in diameter is 8.29 ohms ? Ans. 12-56 ohms. 
 
 7. If the resistance of 700 yd. of a certain wire is 0.91 ohm, what 
 is the resistance of 1,320 yd.? Ans. 1.72 ohm. 
 
 8. (a.) Define electrolyte. (6.) What term is applied to chemical 
 decomposition when effected by means of an electric current? (c.) 
 How would you go about the task of determining for yourself the 
 electro-chemical nature of a substance ? 
 
 9. The resistance of a certain wire is 4.55 ohms. The resistance 
 of a mile of the same wire is 1.3 ohms. What is the length of the 
 first wire ? Ans. 3.5 mi. 
 
 10. The resistance of a mile of copper wire 70 mils in diameter is 
 10.82 ohms. What is the diameter of a copper wire a mile long and 
 having a resistance of 23 ohms ? Ans. 0.048 inch or 48 mils. 
 
 11. What should be the length of a silver wire so that it may 
 have the same resistance as 10 inches of copper wire of the same 
 thickness, the conductivity of silver being 1.0467 times that of 
 copper ? 
 
 12. Find the resistance, at the freezing temperature, of 20 m. of 
 German silver wire weighing 52.5 grams, having given that the resist- 
 ance, at the same temperature, of a wire of the same material 1 m. 
 long and weighing 1 g. is 1.85 ohms. Ans. 14.1 ohm. 
 
 13. When a piece of fine platinum wire and a galvanometer are 
 put in the circuit of a galvanic cell, the needle is deflected. Remove 
 the platinum wire and close the circuit with stout copper wire ; 
 the needle is deflected more than before. Explain. 
 
 14. Find the resistance of 500 yd. of copper wire 165 mils in 
 diameter, the resistance of one mile of copper wire 230 mils in 
 diameter being one ohm. Ans. 0.55 ohm. 
 
 15. If 1,000 ft. of wire 95 mils in diameter have a resistance of 
 1.15 ohm, what is the diameter of a wire of the same material that 
 has a resistance of 10.09 ohms per 1,000 ft.? Ans. 32 mils. 
 
298 
 
 VOLTAIC AND THERMO-ELECTRICITY. 
 
 16. Under what circumstances is it desirable to arrange cells 
 as shown in Fig. 206 ? 
 
 17. A copper wire 6 m. long has a diameter of 0.74 mm. What 
 is the length of a copper wire of 1 mm. diameter that has the same 
 
 electrical resistance ? Ans. 10.957 m. 
 
 18. Given 8 cells, each with an E. M. F. of 2 volts 
 and an internal resistance of 8 ohms. The resistance 
 of the external circuit is to be 16 ohms. How shall 
 the cells be arranged to give maximum current and 
 what will that current be? Ans. 0.25 ampere. 
 
 19. What is the length of an iron wire having a 
 sectional area of 4 sq. mm. and the same resistance as 
 a copper wire 1,000 yd. long, the latter having a sec- 
 tional area of 1 sq. mm., the conductivity of iron 
 being |- that of copper? Ans. 571 f yd. 
 
 20. Two incandescence lamps of 31 and 37 ohms 
 respectively are placed abreast in a circuit. Find the 
 joint resistance of the two lamps. Ans. 16.87 ohms. 
 
 21. How thick must an iron wire he so that it and 
 a copper wire that has the same length and a diame- 
 ter of 2.5 mm. shall have the same resistance, the re- 
 
 FIG. 206. sistance of iron being 7 times that of copper? 
 
 Ans. 6.61 mm. 
 
 22. How many coulombs will be furnished by the consumption of 
 20 g. of zinc ? 
 
 23. What weight of zinc must be consumed in each cell of a 
 voltaic battery of 3 Daniell's cells to enable the electrolysis of 9 g. 
 of water? (Neglect loss by local action.) Ans. About 32.5 #. 
 
 24. What weight of copper will be deposited in each cell of the 
 battery mentioned in the last problem? Ans. About 31.5 g. 
 
 25. Three wires, the respective resistances of which are 5, 7 and 
 9 ohms are joined in multiple arc. Find the resultant resistance of 
 this compound conductor. Ans. 2.2 ohms. 
 
 26. What is the necessary E. M. F. of a dynamo that is to furnish 
 a 10 ampere current for 60 arc lamps (in series), each of which has a 
 resistance of 4.5 ohms, the resistance of the line wire being 10 ohms 
 and the internal resistance of the dynamo being 22 ohms ? 
 
 27. A piece of zinc, at the lower end of which a piece of copper 
 wire is fixed, is suspended in a glass jar containing a solution of 
 acetate of lead (sugar of lead). After a few hours, a deposit of lead 
 in tree-like form grows downward from the copper wire. Explain 
 this. ,.;.-: 
 
 28. Liquids increase in conductivity with an increase of temper- 
 
VOLTAIC AND THERMO-ELECTRICITY. 299 
 
 ature. Will a given battery give a stronger current at C. or at 
 20 C.? 
 
 29. What should be the length of a lead wire so that it may have 
 the same resistance as 10 inches of copper wire of the same thickness, 
 the conductivity of lead being 0.0923 times that of copper ? 
 
 30. Four wires are joined together in multiple arc, their resist- 
 ances being 5.5, 18, 3.7 and 2.9 ohms respectively. Find the result 
 ant resistance of the compound conductor thus formed. 
 
 Ans. 1.17 ohm. 
 
 HONORARY PROBLEM. 
 
 31. Find the number of incandescence lamps that may be worked 
 in multiple arc by a dynamo-electric machine that has an internal 
 resistance of 0.032 ohm. The E. M. F. of the dynamo is 55 volts 
 and the resistance of each lamp is 28 ohms. The current must be 
 1.6 amperes in each lamp. Ans. 199 lamps. 
 
300 
 
 VOLTAIC AND THERMO-ELECTRICITY. 
 
 Recapitulation. To be amplified by the pupil for 
 review. 
 
 
 
 
 Smee's. 
 
 
 
 ' One Liquid. . 
 
 Potassium 
 di-chromate. 
 
 
 
 
 Leclanche. 
 
 
 
 
 Daniell's. 
 
 
 CEL-. H 
 
 Two Liquids. 
 
 Callaud's. 
 Grove's. 
 
 
 
 
 
 Bunsen's. 
 
 
 
 \ 
 
 Tandem. 
 
 
 
 Joined. - 
 
 Abreast. 
 Best Method. 
 
 
 r VOLTAIC - 
 
 SOURCE OF ENERGY. 
 
 
 
 
 ( High Internal Resistanct. 
 BATTERY. . . < Low Internal Resistance. 
 
 
 
 \ Requisites. 
 
 
 
 CURRENT.. . 
 
 Direction 
 Strength 
 
 Unit. 
 Ohm's Law, 
 
 
 1 ^ 
 
 
 1 SIMPLE. 
 
 
 
 
 
 
 CIRCUIT - 
 
 DIVIDED. 
 
 SHUNT. 
 
 
 
 
 
 
 PLATE. 
 
 
 
 
 
 
 POLE. 
 ELECTRODE. 
 
 A node. 
 Kathode. 
 
 
 
 o 
 
 POTENTIAL ; 
 
 FALL OF E. 
 
 M F j Unit. 
 ' | Measurement. 
 
 J>H 
 
 s 
 
 ' EXTERNAL. 
 
 t^^ 
 
 C i 
 
 111 
 
 INTERNAL. 
 
 G 
 
 X 
 o 
 
 RESISTANCE . 
 
 LAWS. 
 ' UNIT. 
 
 
 
 
 
 
 MEASURE 
 
 WENT. 
 
 
 2 
 
 
 LONG AND SHORT-COIL INSTRUMENTS. 
 
 PH 
 
 
 QUANTITY 
 
 UNIT. 
 
 
 
 u 
 
 
 
 ( r* . ... 
 
 
 
 w 
 
 
 LOCAL ACTION. -J JJJj y 
 
 a- 
 
 
 L POLARIZATION. j R ME E DV . 
 
 ^ 
 
 
 f MECHANICAL 
 
 
 
 
 jgj 
 
 
 THERMAL;.... 
 
 RELATION TO RESISTANCE. 
 
 w 
 
 
 LUMINOUS. 
 
 f ELECTROLYSIS, -j jj& 
 
 , h ns - 
 
 * 
 
 
 
 PHYSIOLOGICAL. ELECTRO .METALLURGV":'" 
 
 P5 
 
 r^ 
 
 o 
 
 CHEMICAL... 
 
 .. . ELECTRO-CHEMICAL SERIES. 
 
 ** 
 
 Ul 
 
 E. M. F. OF POLARIZA- 
 
 
 u. 
 
 
 TION. 
 
 
 f Faure's. 
 
 
 u. 
 
 Ul 
 
 SECONDARY BATTERIES.. 
 
 \ Brush's. 
 \ Uses. 
 
 
 
 
 
 
 \ Advantages, 
 
 
 
 MAGNETIC. . . 
 
 ( ELECTRO-MAGNETS. 
 . . -< ELECTRIC TELEGRAPH. 
 
 
 ( GALVANOMETER. 
 
 TUCDMn Cl COTOI/MTV 
 
 (For Induced Currents^ see Section V. of this Chapter.) 
 
iv. 
 
 MAGNETISM. 
 
 Natural Magnets. One of the most valua- 
 ble iron ores is called magnetite (Fe 3 4 ). Occasional 
 specimens of magnetite will attract filings and other pieces 
 of iron. Such a specimen is called a lodestone. 
 It is a natural magnet. 
 
 424. Artificial Magnets. Artificial magnets are 
 either temporary or permanent. A temporary magnet 
 is usually made of soft iron and is called an electro- 
 magnet. A permanent magnet is usually made of steel. 
 Artificial magnets have all the 
 
 properties of natural magnets 
 and are more powerful and con- 
 venient. They are, therefore, FIG. 207. 
 preferable for general use. The 
 
 most common forms are the straight or "bar magnet and 
 the horseshoe magnet. The first of these is a straight bar 
 of iron or steel; the second is shaped like a letter U, the 
 ends being thus brought near together, as shown in Fig. 
 207. A piece of iron placed across the two poles of a 
 horseshoe magnet is called an armature. We have already 
 learned how to make artificial magnets. 
 
 425. Reteiitivity. It is more difficult to get the 
 magnetism into steel than into iron. It is also more dim*- 
 
302 
 
 MAGNETISM. 
 
 cult to get it out. This power of resisting magneti- 
 zation or demagnetization is called coercive force 
 or retentivity. The harder the steel, the greater its re- 
 tentivity. Soft wrought iron has but little retentivity. 
 
 426. Distribution of Magnetism. If a ba* 
 
 magnet be rolled in iron filings and then withdrawn, the 
 
 FIG. 208. 
 
 filings cling to the ends of the bar but not to the middle. 
 This form of attraction is not evenly distributed through- 
 out the bar. It is greatest at or near the ends. 
 These points of greatest attraction are called the 
 poles of the magnet. It is impossible, by any known 
 means, to develop one magnetic pole without simultane- 
 
MAGNETISM. 303 
 
 ously developing another pole of opposite sign. The mid- 
 dle of the magnet does not attract iron and is called the 
 equator or neutral point. 
 
 Experiment 81. Bring either end of a bar magnet near the end 
 of a floating piece of iron, AB ; the iron is 
 attracted. Bring the same end of the 
 magnet near the middle of the iron ; the 
 iron is attracted. Bring the same end of 
 the magnet near the other end of the iron ; 
 the iron is attracted. Repeat the experi- 
 ments with the other end of the magnet ; 
 in each case, the iron is attracted. FIG. 
 
 427. Attraction between a Magnet and 
 
 Iron. ^Either pole of a magnet will attract or- 
 dinary iron. 
 
 Experiment 82. Freely suspend three bar magnets, A, B and C, 
 at some distance from each other. This may be done by placing each 
 magnet in a stout paper stirrup supported by a cord or horse-hair or 
 upon a board or cork floating on water. (See Fig. 209.) When they have 
 come to rest, each will lie in a north and south line. Magnets for this 
 experiment may be made by magnetizing ( 448) three stout knitting- 
 needles. If there is any electric light apparatus in your neighbor- 
 hood in charge of a good-natured man, he will probably magnetize 
 the needles for you. Each needle may be suspended by means of a 
 triangular piece of stiff writing-paper. Pass the needle through the 
 paper near the lower corners ; at the other corner, affix, by wax, the 
 end of a horse-hair. The poles may be indicated by little bits of red 
 and of white paper, fastened by means of wax to the ends of the 
 needles. Mark the north -seeking poles, and the south-seeking 
 poles, +. 
 I > 
 
 428. Characteristics of Magnets. Magnets 
 are chiefly characterized by the property of attract- 
 ing iron and by a tendency to assume a partic- 
 ular direction of position when freely suspended. 
 
 Experiment 83. (a.) Take magnet A of Experiment 82 from its 
 
304 
 
 MAGNETISM. 
 
 support and bring its + end near the end of B or C. Notice the 
 attraction. 
 
 (b.) Bring the + end of A near the + end of B or G. Notice the 
 repulsion. 
 
 (c.) Bring the end of A near the end of B or G. Notice the 
 repulsion. 
 
 (d.) Bring the end of A near the + end of B or C. Notice the 
 attraction. 
 
 (e.) From (.), we learned that the ends of B and G were each 
 attracted by the + end of A. Bring the end of B near the 
 end of C. Notice that they now repel. 
 
 (/.) From (&.), we learned that the + ends of B and G were each 
 repelled by the + end of A. Bring the + end of B near the + end 
 G. Notice that they now repel. 
 
 (g.) In similar manner, show that the + end of B will attract the 
 - end of C', that the end of B will attract the + end of G. 
 
 Record the results of your experiments in tabular form thus; 
 
 (a.) + attracts . 
 (d.) attracts +. 
 etc. 
 
 (b.) + repels +. 
 (c.) . repels . 
 etc. 
 
 Experiment 84. Magnetize a number of fine sewing-needles by 
 drawing the + end of a bar magnet three or four times from the eye 
 ^____^^ to the point of each. 
 
 Cut several small 
 corks into slices 
 about an eighth of 
 an inch thick. 
 Through each cork 
 disc, push a needle 
 up to its eye, point 
 downward, and 
 place them in a 
 round dish of water. 
 These little mag- 1 
 nets have their like 
 
 poles presented to each other and they mutually repel. Bring the 
 bar magnet, with its + end downward, over the needles ; they will 
 be driven to the sides. Similarly, bring the end over them ; they 
 will be attracted toward the centre. 
 
 FIG. 210. 
 
 429. Laws of Magnets. (1.) Every magnet 
 
MAGNETISM. 305 
 
 has two similar poles; like poles repel each other', 
 unlike poles attract each other. 
 
 (2.) Magnetic force, like other forms of attrac- 
 tion and repulsion, varies inversely as the square 
 of the distance. 
 
 Experiment 85. Dip one of the magnetized knitting-needles into 
 iron filings. Notice that filings cling to the ends, near the paper 
 discs, but that none cling to the middle. Break the needle in the 
 middle and dip each piece into iron filings. Notice that the un- 
 marked ends, which were at the middle of the unbroken magnet, 
 now attract iron filings as well as do the marked ends. Poles have 
 been developed in parts of the needle that previously showed no mag- 
 netic attraction. 
 
 43O. Effect of Breaking a Magnet. If a 
 
 magnet be broken, each piece becomes a magnet with two 
 poles and an equator of its own. These pieces may be 
 repeatedly subdivided and each fragment will be a perfect 
 magnet. 
 
 It is probable that every jnolecule has its poles 
 or is polarized and that, could one be isolated, it 
 would be a perfect magnet. We may, thus, conceive 
 a magnet as made up of molecules each of which is a 
 magnet, the action of the molar magnet being due to the 
 combined action of all the molecular magnets of which it 
 is composed. 
 
 431. Magnetized, Magnetic and Diamag- 
 lietic Substances, A magnetized body is one that 
 
306 MAGNETISM. 
 
 can be made to repel a pole of a freely suspended magnet 
 Substances that are attracted by a magnet are called mag- 
 netic; e.g., iron or steel and nickel. Substances that are 
 repelled by a magnet are called diamagnetic ; e.g., bismuth, 
 antimony, zinc, tin, mercury, lead, silver, copper, gold 
 and arsenic. Of these, iron is by far the most magnetic, 
 while bismuth is the most diamagnetic. The magnetic 
 properties of iron or steel are easily shown ; diamagnetic 
 properties require a powerful magnet for satisfactory illus- 
 tration. 
 
 Experiment 86. Wrap a bar magnet in a piece of cloth. With 
 it, attract and repel the poles of a suspended magnet. 
 
 Experiment 87. Repeat the last experiment, holding a slate or 
 sheet of zinc between the two magnets. 
 
 Experiment 88. Put one piece of the broken magnet into a bot- 
 tle ; cork the bottle tightly. With it, attract and repel the poles of 
 a suspended magnet. 
 
 432. Magnetic Screens. Nothing but a mag- 
 netic body can cut off the inductive action of a 
 magnet. If a small magnet be suspended inside a hol- 
 low iron ball, no outside magnet will affect it. 
 
 Experiment 89. With the end of a good bar magnet, write your 
 name upon the blade of a handsaw. The invisible characters may 
 be made visible by sifting fine iron filings upon the blade. 
 
 Experiment 90. Place a piece of card-board or rough drawing 
 paper over a good bar magnet. Sift fine iron filings through a piece 
 of muslin upon the card-board and tap it lightly. The iron particles 
 will move and arrange themselves in well defined curved lines. (See 
 Fig. 212.) By using two bar magnets placed side by side, first, with 
 like poles near each other and, secondly, with unlike poles near each 
 other, their combined effect on the iron filings may be easily ob 
 served. The figures will be widely different. 
 
MAGNETISM. 
 
 307 
 
 4:33. Magnetic Field. A maguet seems to be sur- 
 rounded by an atmosphere of magnetic influence called 
 the magnetic field. (See 450^ and Appendix N.) 
 The magnetic curves, formed in the above experiment, 
 are very interesting and instructive for they show the 
 direction of the lines of magnetic force. The filings 
 in any one of these curves are temporary magnets with 
 
 FIG. 212. / 
 
 adjoining poles opposite and therefore attracting. If a 
 small magnetic needle be suspended over the card board 
 at any point, its length will tend to lie in the direction 
 of the lines of magnetic force at that point as mapped out 
 by the iron filings. 
 
 (a.) The figures may be permanently fixed by using a sheet of 
 glass that has been gummed and dried, instead of the sheet of 
 paper. Tlie filings are sifted evenly over the surface ; then the glass 
 is tapped ; then a jet of steam is caused to play gently above the 
 sheet, softening the surface of the gum, which, as it hardens, fixes 
 the filings in their places. 
 
 (6.) Since the lines of force are made of little magnetic particles 
 that set themselves thus in obedience to the attractions and re- 
 pulsions in the field, they represent the resultant direction of said 
 forces at each point. They map out the magnetic field, showing the 
 f]irection of the magnetic force by their position and its intensity b^ 
 
308 MAGNETISM. 
 
 their number. If a small pole could be obtained alone and put 
 down on any one of these lines of force, it would tend to move along 
 that line from + to ; a single + pole would tend to move along 
 the line in an opposite direction. 
 
 Experiment 91. Rub one end of a steel pen against the end of a 
 magnet. Dip the pen into iron filings and notice that the newly 
 made magnet has a pole at each end. Determine the sign of each of 
 these poles, as indicated in Experiment 82. 
 
 434. Magnetization by Contact. A bar of 
 
 iron or steel may be magnetized by rubbing it 
 against a magnet. Pure or soft iron is easily magnet- 
 ized but quickly loses its magnetism when the magnetiz- 
 ing influence is removed. Hardened steel is magnetized 
 with more difficulty but retains its magnetism after the 
 removal of the magnetizing influence. 
 
 Experiment 92. Move the point of an unmagnetized steel pen to 
 and fro very near one end of a magnet but without touching it to 
 the magnet. Dip the pen into iron filings and determine whether 
 or not it has been magnetized. Tf it has, determine the sign of each 
 pole, as in the last experiment and notice whether the point of the 
 pen is of the same polarity as the end of the magnet near which it 
 was moved. 
 
 Experiment 93. Bring a short bar of soft iron, I, very near a 
 strong bar magnet, M, end to end, as shown in the figure. Sprinkle 
 
 FIG. 213. 
 
 iron filings over the ends of the iron bar and they will cling as they 
 would to a magnet. The iron bar is a magnet, while it remains in 
 this position. 
 
 435. Magnetic Induction. If the end of a bar 
 
 of soft iron be brought near one of the poles of a strong 
 
MAGNETISM. 
 
 magnet, the iron becomes, for the time being, a mag- 
 net. The poles of the temporary magnet will be opposite 
 to those of the permanent magnet, i.e., if the -f or posi- 
 tive pole of the magnet be presented to the iron bar, it 
 will develop a or negative pole in the nearest end of the 
 iron bar and a + pole at the further end. Bring the iron 
 bar nearer the magnet and this effect will be increased. 
 Actual contact is not necessary, but when the iron and 
 the magnet touch, the magnetizing force is the greatest. 
 If a steel bar be used instead of an iron bar, it will be per- 
 manently instead of temporarily magnetized. The iron 
 or the steel is induced to become a magnet by the 
 influence of the rnaguet used. It is said to be 
 magnetized by induction. This, like other forms of 
 attraction, varies inversely as the square of the distance. 
 We have already seen that magnetic induction takes place 
 in certain directions called lines of magnetic force 
 ( 433.) 
 
 Experiment 94. Bring a soft iron ring to the end of a magnet. 
 It will be supported. Bring a second ring into contact with the 
 first ring and it will be sup- 
 ported. In this way, quite 
 a number of rings may be 
 supported, each ring being 
 magnetized by the bar or 
 
 ring magnet above it. Of FIG. 214. 
 
 course, the attractive force 
 
 is continually weakening from the first to the last ring. Sup- 
 port the upper ring upon your finger and remove the magnet. 
 Each ring ceases to be a magnet and the chain is broken into 
 its separate links. Vary the experiment by using, instead of 
 the rings : (1,) Soft iron nails ; (2,) Steel sewing- needles ; and 
 see if there is any difference in the results. 
 
 Experiment 95. Suspend an iron key from the positive end of 
 a bar magnet. The key is inductively magnetized, the relation of 
 
310 
 
 MAGNETISM. 
 
 its poles to each other and to the magnet being as shown in Fig. 
 215. A second bar magnet of about the same power, with its poles 
 opposite, is moved along the first magnet. When the end of the 
 second magnet comes over the key, the key drops. 
 
 FIG. 215. 
 
 The first magnet tends to induce a - pole at the upper end of the 
 key. The second magnet tends to induce a + pole at the same 
 point. The effect of each magnet neutralizes that of the other. 
 
 Experiment 96. Magnetize a piece of watch spring about, six 
 inches long (easily obtainable at the watch repairer's) by drawing it 
 several times between the thumb and the end of a magnet. Dip it 
 into iron filings. Lift it carefully with its load. Bring the poles of 
 t'.ie spring magnet together, bending the magnet into a ring. The 
 magnet drops its load. 
 
 436. Induction Precedes At- 
 traction. We now see why a magnet 
 attracts ordinary iron; it first magnetizes 
 it and then attracts it. The attraction be- 
 tween unlike poles is greater than the re- 
 pulsion between like poles because of the 
 smaller distance between them. Compare 
 336. 
 
 Experiment 97. Test a common fire poker for 
 magnetism by bringing a small magnetic needle near 
 its ends and seeing whether the poker repels either 
 pole of the compass needle or whether the two ends of the poker 
 attract different poles of the needle. If the poker is not even slightly 
 magnetic, place it with its upper end sloping toward the south so as 
 
MAGNETISM. 311 
 
 to make an angle of a little less than half a right angle. In other 
 words, place it in the position assumed by the dipping needle. 
 ( 439.) While the poker is in this position, strike it a few blows 
 with a wooden block or mallet. Test it again for magnetism. A 
 steel poker that has usually stood in a nearly vertical position may, 
 thus, often be shown to have acquired magnetism. 
 
 437. The Earth is a Magnet. The earth acts 
 like a huge magnet in determining the direction of com- 
 pass and dipping needles. Its inductive influence, as 
 shown in the last experiment, strengthens the belief that 
 it has such action. If a small dipping needle be placed 
 over the end of a bar magnet, the needle will take a 
 vertical position with its -f end down. As the needle is 
 moved toward the other end of the bar, it turns from its 
 
 FIG. 217. 
 
 vertical position. When over the neutral line, the needle 
 is horizontal. As it approaches the + end of the magnet, 
 the needle again becomes vertical, but the end of the 
 needle is drawn down. If a dipping needle be carried 
 from far southern to far northern latitudes, it will act in a 
 similar way. Many facts seem to teach that the earth is 
 a great magnet with magnetic poles near its geo- 
 graphical poles. The magnetic pole in the northern 
 hemisphere was found in 1832 by Capt. Ross. It was then 
 a little north and west of Hudson's Bay, in latitude 
 
312 MA GNETfSM. 
 
 70 05' N., and longitude 96 45' W. A place in the south- 
 ern hemisphere has been found where the dipping needle 
 is nearly vertical. 
 
 438. Names of Magnetic Poles. We have now learned 
 to regard the earth as a huge magnet, with one pole in the northern 
 hemisphere and one in the southern. Since unlike poles attract 
 each other, it follows that the earth's magnetic pole situated in the 
 northern hemisphere is opposite, in kind, to the end of a magnetic needle 
 that points to the north. From this fact, great confusion of nomen- 
 clature has arisen. We have spoken of the end of the needle that 
 points north as or negative. Following this nomenclature, the 
 northern magnetic pole of the earth must be + or positive. But 
 popular usage calls the north -seeking end of the needle the north 
 pole and the other end the south pole. This introduces great confu- 
 sion when we wish to speak of the magnetic poles of the earth. 
 The nomenclature that we have adopted obviates this confusion. 
 
 Experiment 98. Make a horizontal needle of a piece of watch 
 spring about six inches long and straightened by drawing it between 
 thumb and finger. Heat the middle of the 
 needle to redness in a flame and bend it 
 double. Bend the ends back into a line 
 with each other, as shown in Fig. 218. 
 Magnetize each end separately and oppo- 
 FIG. 218. sitely. Wind a waxed thread around the 
 
 short bend at the middle to form a socket 
 
 and balance the needle upon the point of a sewing-needle thrust into 
 a cork for support. A little filing, clipping with shears or loading 
 with wax may be necessary to make it balance. The needle will 
 point north and south. 
 
 Experiment 99. By means of a fine wire fork, gently lay one of 
 the magnetized sewing-needles of Experiment 84 on the surface of 
 water. It will float without any cork or similar support and will 
 assume a north and south position. It may be considered the needle 
 of a small compass. 
 
 439. Magnetic Needles..^ small bar magnet 
 suspended in such a manner as to allow it to 
 assume its chose n position is a magnetic needle. 
 It may turn in a horizontal or a vertical plane. 
 
MAGNETISM. 
 
 313 
 
 FIG 219. 
 
 (a.) If it be free to move in a horizontal plane, it is a horizontal 
 needle ; e. g., the mariner's or the survey- 
 or's compass (Fig. 219). It will come to 
 rest pointing nearly north and south. 
 If the magnet be free to move in a ver- 
 tical plane, it constitutes a vertical or 
 dipping needle (Fig. 220). Two magnets 
 fastened to a common axis but having 
 their poles reversed constitute an astatic 
 needle (Fig. 221). An astatic needle as- 
 sumes no particular direction with respect 
 to the earth if the two needles are equally 
 magnetized. ( 418.) 
 
 (&) Make a dipping needle by thrusting a knitting-needle through 
 
 a cork so that the cork shall be at 
 the middle of the needle. Thrust 
 through the cork, at right angles 
 to the knitting-needle, half a knit- 
 ting-needle, or a sewing-needle, 
 for an axis. Support the ends of 
 the axis upon the edges of two 
 glass goblets or other convenient 
 objects. Push the knitting-needle 
 through the cork so that it will 
 balance upon the axis like a scale- 
 beam. Magnetize the knitting- 
 needle and notice the dip. 
 
 (c.) A magnetized sewing- 
 needle, suspended near its middle 
 (at its centre of gravity) by a fine 
 thread or hair or an untwisted 
 fibre will serve as a dipping needle. 
 It should first be suspended so as to hang + 
 horizontal and magnetized afterward. 
 A simple form of dipping needle is repre- - 
 sented in Fig. 222. 
 
 FIG. 220. 
 
 44O. Inclination or Dip. 
 
 The angle that a dipping 
 needle makes with a hori- 
 zontal line is called its in- FI G. 221. 
 elination or dip. The angle in question is indicated 
 
314 
 
 MAGNETISM. 
 
 by the dotted arc of Fig. 
 
 FIG. 222. 
 masked by the effect of gravity. 
 
 At the magnetic poles, the 
 inclination is 90; at 
 the magnetic equator, 
 there is no inclina- 
 tion. The inclination 
 at any given place is 
 not greatly different 
 from the latitude of 
 that place. 
 
 (a.) Experiments for 
 inclination are difficult 
 of execution without spe- 
 cial apparatus. It is diffi- 
 cult to make a needle 
 turn about a point ex- 
 actly coincident with its 
 centre of gravity. In 
 rough experiments, there 
 is danger that the mag- 
 netic effect will be 
 
 NORTH 
 STAR 
 
 fi* 
 
 FIG. 223. 
 
MAGNETISM. 315 
 
 Experiment 100. Set two stakes so that a string joining them 
 will point toward the North Star. The string will run north and 
 south or nearly enough so for our purpose. Place a long magnet 
 suspended as a needle under or over the string. Looking downward 
 at the magnet and the string, it will probably be found that the 
 needle and the string do not point in the same direction. The 
 North Star may be easily found any evening in the direction indi- 
 cated by "The Pointers" of the well known constellation, "The 
 Great Dipper." "The Pointers" are the two stars marked by the 
 Greek letters a and (3 in Fig. 223. 
 
 441. Declination or Variation. The magnetic 
 needle, at most places, does not lie in an exact north and 
 south line. The angle that the needle makes with 
 the geographical meridian is its declination or 
 variation. A line drawn through all places where the 
 needle points to the true north is called a Line of no Vari- 
 ation. Such a line, nearly straight, passes near Cape Hat- 
 teras, a little east of Cleveland, Ohio, through Lake Erie and 
 Lake Huron. It is now slowly moving westward. At all 
 places east of the Line of no Variation, the end of the 
 needle points west of the true north ; at all places west of 
 the Line of no Variation, the variation is easterly. The 
 further a place is from this line, the greater the declina- 
 tion, it being 18 in Maine and more than 20 in Oregon. 
 
 (a.) In order that ships may steer safely by the compass, magnetic 
 charts are prepared. The declination at various places is properly 
 indicated on the chart. The surveyor must recognize not only the 
 declination of his needle but also the changes in declination. Other- 
 wise he would not be able properly to " run 
 the lines " of a given piece of land from the 
 description given in an old deed. 
 
 Experiment 101. Construct a floating 
 cell of zinc and copper plates, about ^ inch 
 apart, the connecting wire being given an 2 . 
 
 elongated spiral or solenoid form, and support ^TG. 22 4- 
 
 it by a large, flat cork resting on the surface of a bowlful of acidu- 
 
316 
 
 MAGNETISM. 
 
 lated water, as shown in Pig. 224. The solenoid may be made by 
 winding the middle part of about 3 yards of No. 20 insulated copper 
 wire around a rod, half an inch in diameter, forming thus a coil, 4 
 or 5 inches long. The current will set the axis of the solenoid in a 
 north and south direction as if it were a magnetic needle. By hold- 
 ing one end of a bar magnet near first one end and then the other 
 end of the solenoid, it will be found that the latter exhibits magnetic 
 polarity. 
 
 FIG. 225. ' 
 
 Experiment 102. Support a solenoid by placing the extremities 
 of its wire (bent into the same vertical axis) in two mercury cups, as 
 shown in Fig. 225, or use the solenoid of the floating battery above 
 described. Bring the end of a second solenoid successively to the 
 ends of the first and notice the exhibition of magnetic polarity. 
 
 Experiment 103. Send a current of electricity from the small 
 cell, mentioned in Experiment 16, through its wire. Pour half a 
 teaspoonful of iron filings upon a sheet of paper and bring the wire 
 conductor of the cell into contact with the filings. Notice that the 
 filings cling to the wire as though it were a magnet. Break the 
 circuit and notice that the filings fall from the wire. 
 
 442. Electro -Magnets. From these experiments, 
 we see that while the wire conductor is carrying an electric 
 current it has the properties of a magnet. We have 
 already seen that, under similar circumstances, the con- 
 ductor deflects a magnetic needle as if it were itself a 
 
MAGNETISM. 
 
 317 
 
 FIG. 226. 
 
 magnet. In fact, such a conductor is a temporary mag- 
 net. The magnetic effect is much increased if a con- 
 siderable length of the conductor be 
 made of insulated wire and wound 
 into a coil, as shown in Fig. 226. 
 Such a coil is called a helix; it is a 
 magnet with a + pole at one end and 
 a -- pole at the other. It has an 
 easily perceptible magnetic field. If 
 a soft iron rod or core be introduced 
 into the coil, it enters the magnetic 
 field of the coil or helix and becomes 
 a magnet. This combination of coil and core consti- 
 tutes an electro-magnet and is more powerfully mag- 
 netic than the coil alone. An electro-magnet is a 
 bar of iron surrounded ~by a coil of insulated wire 
 carrying a current of electricity. It may be made 
 more powerful than any permanent magnet but loses its 
 power as soon as the current 
 ceases to flow through its coil. 
 The fact that the magnetism of 
 this apparatus is under control 
 adapts it to many important uses, 
 such as electric bells and tele- 
 graphic instruments. 
 
 FIG. 227. 
 
 443. Forms of Electro- 
 Magnets. The bar of 416, a, 
 and the ring of Fig. 199, with 
 their helices, are electro-magnets. The electro-magnet 
 more often has the horse-shoe form shown in Fig. 227, so 
 that the attraction of both poles may act upon the same 
 
318 MAGNETISM. 
 
 body at the same time. The middle of the bent bar is 
 bare, the direction of the windings on the ends being such 
 that, were the bar straightened, the current would move 
 in the same direction round every part. More frequently, 
 the two helices, A and B, have separate cores which are 
 joined by a third straight piece into which the ends of the 
 cores are screwed. An armature is often placed across the 
 two poles of the magnet, as shown in the figure. Electro- 
 magnets have been made capable of supporting several 
 tons. 
 
 (a.) When the circuit is broken and the current thus interrupted, 
 the iron is generally not whotty demagnetized. The small magnet- 
 ism remaining is called residual magnetism. The residual magnetism 
 seems to increase with the hardness and impurity of the iron. The 
 cores of electro-magnets for some purposes are made of the softest 
 and purest iron obtainable. 
 
 444. The Electric Telegraph. The electric 
 telegraph consists essentially of an electro-magnet and a 
 "key" placed in the circuit of a battery. The key is an 
 
 instrument by which 
 the circuit may be 
 easily broken or closed 
 at will. The arm at u re, 
 A, of the "register'' 
 magnet, M, is sup- 
 ported by a spring, 8, 
 which lifts it when the 
 FlG 22g circuit is broken. 
 
 When the circuit is 
 
 closed, the armature is drawn down by the attraction of 
 the magnet. Thus, the armature may be made to vibrate 
 up and down at the will of the person at the key. The 
 
MA GNETISM. 
 
 319 
 
 armature may act upon one arm of a lever, the other end 
 of which, being provided with a style or pencil, P, may be 
 pressed against a paper ribbon, R, drawn along by clock- 
 work. Thus, the pencil may be made to record, upon the 
 moving paper, a series of dots and lines at the pleasure of 
 the operator at the key perhaps hundreds of miles away. 
 When the two stations are several miles apart, one of the 
 wires is dispensed with, the circuit being completed by 
 connecting each station with the earth. This arrange- 
 ment saves half the wire and nearly half the cost of the 
 line. As the resistance of the earth is insignificant, there 
 is the further saving of nearly half the battery otherwise 
 necessary. Earth connections are often made by joining 
 the wires to water or gas pipes that run into the ground. 
 When the line is long, there is a battery at each end, the 
 + electrode of one battery and the electrode of the 
 other battery being joined to the line wire. The same 
 principle of communicating signals by making and break- 
 ing an electric circuit is used in fire and burglar alarms, 
 hotel annunciators, etc. 
 
 445. Morse's Alphabet. The inventor of the 
 practical electric telegraph was an American, S. F. B. Morse. 
 The code of signals devised by him is given below : 
 
 
 I 
 
 ETTERS. 
 
 a 
 
 k 
 
 
 
 b 
 
 I 
 
 
 
 c - - - 
 
 m 
 
 
 
 d 
 
 n 
 
 
 
 e - 
 
 
 
 . - 
 
 
 71 
 
 
 '. "' 
 
 P 
 
 
 g 
 
 q 
 
 
 
 h 
 
 j . -_ . 
 
 r 
 
 8 
 
 t 
 
 :.: g 
 
 u 
 
 z - 
 
320 
 
 MAGNETISM. 
 
 (a.) To prevent confusion, a small space is left between successiva 
 letters, a longer one between words and a still longer one between 
 sentences. We here give a short message written in Roman and in 
 telegraphic characters : 
 
 H 
 
 1 1 
 
 ten 
 
 The ordinary telegraph operator does not punctuate his messages 
 to any considerable extent. Telegraph operators soon become so 
 
 FIG. 229. 
 
 familiar with this alphabet that they understand a message from the 
 mere clicks of the lever and do not use any recording apparatus. 
 Such an operator is said to " read by sound"; his instrument is called 
 a "sounder." Fig. 229 represents one. The sounder is placed on a 
 local circuit and has a usual resistance of from three to five ohms. 
 
 FIG. 230. 
 
 (6.) With a long main line, the resistance is so great that the cur- 
 rent of the inain battery is too feeble to operate the sounders with 
 
MAGNETISM. 
 
 321 
 
 sufficient force. This difficulty is met |4| 
 by introducing a " local battery " and 
 a " relay " at each station on the line. 
 The relay (Fig. 230) is a delicate elec- 
 tro-magnet, of which the terminals, 
 a and 6, are connected with the main 
 line. This magnet operates an ar- 
 mature lever, e, the end of which 
 strikes against a metal contact piece 
 and thus closes the local circuit 
 through the terminals, c and d. The 
 resistance of relays vary from 50 to 
 500 ohms. The " Western Union " 
 standard relay has a resistance of 150 
 ohms. 
 
 (c.) 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 railway 
 station. The general features of the 
 " plant " are represented by the dia- 
 gram shown in Fig. 231. The pupil 
 will probably find the key, sounder 
 and relay on a table and the local 
 battery, 6, under the table. The keys 
 being habitually closed, the current 
 passes through all relays on the line, 
 the current being continuous ( 395) 
 except when a message is being sent 
 from some office. When an operator, 
 in sending a message, opens his key, 
 the breaking of the circuit stops the 
 current, 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 
 
 FIG. 231. 
 
 TL. 
 
 its local circuit, it and the 
 
322 MAGNETISM. 
 
 sounder lever vibrating in obedience to the motions of the key at 
 the sending station. Of course, the sending operator can read his 
 own message from his sounder. The message may also be read from 
 any sounder on the line. 
 
 (d.) If the local circuit at New York (see Fig. 231) be lengthened 
 so as to reach thence to Boston and the local battery, b, be increased 
 to the dimensions of a main battery, B, (ground connections being 
 made, of course), the relay at New York will transmit to Boston the 
 message received from Cleveland. In such cases, the relay at New 
 York becomes a repeater. Messages from New York to Chicago may 
 thus be repeated at Meadville, Pa., without the intervention of any 
 operator. 
 
 446. Duplex and Quadruplex Telegraphy. 
 
 The simple Morse system, just described, is very reliable, 
 but a given wire can transmit 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, at the same 
 time, without conflict. By what is known as the quadru- 
 plex system, a wire may be made to carry four messages, 
 two each way, at the same time. Delany's multiplex sys- 
 tem enables the sending of six messages in the same direc- 
 tion at one time. The student is referred to technical 
 works on telegraphy for an explanation of these systems. 
 A good Morse operator can send or receive thirty or forty 
 words a minute ; by the aid of a combination of recent 
 inventions, fifteen hundred words have been transmitted 
 over a single wire in one minute. 
 
 447. Electric Bells. The construction of the 
 trembler or electric bell will be clearly seen by an exam- 
 ination of Fig. 232. When the button at P (anywhere 
 on the circuit) is pushed, two metal pieces are brought 
 into contact and the circuit is thus completed. The spring 
 carried by the armature of the magnet, E, makes contact 
 
MAGNETISM. 
 
 323 
 
 with the tip of the screw at (7, except when it is drawn 
 away by the attraction of the magnet. 
 
 FIG. 232. 
 
 (a.) When the spring rests against the end of the screw at C (the 
 circuit being closed at P), the cores of E are magnetized. They 
 then draw the armature away from the end of the screw and break 
 the circuit at C. E, being thus demagnetized, no longer attracts 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 released, thus vibrating rapidly and striking a blow upon the 
 bell at H at every vibration. (See 459, a.) 
 
324 MAGNETISM. 
 
 448. Making Permanent Magnets. A com- 
 mon way of magnetizing a steel bar is to draw one 
 end of a strong magnet from one end of the bar 
 to the other, repeating the operation several times, 
 always in the same direction. A second method is to 
 bring together the opposite poles of two magnets at the 
 middle of the bar to be magnetized and simultaneously 
 drawing them in opposite directions from the middle to 
 the ends. A steel bar may be magnetized by striking it 
 on end with a wooden mallet while it is held in the direc- 
 tion assumed by the dipping needle. If a bar of steel be 
 heated to redness and cooled, either slowly or suddenly, 
 while lying in the magnetic meridian, it acquires magnetic 
 polarity. But better than any of these can give are the 
 effects produced by electro-magnetism. 
 
 FIG. 233. 
 
 The bar may be permanently magnetized by drawing it, 
 from its centre, in one direction over one pole of a power- 
 ful electro-magnet and then, from its centre, in the oppo- 
 site direction over the other pole and repeating the pro- 
 cess a few times (Fig. 233). 
 
 A bar of steel placed within a helix through which a 
 
MAGNETISM. 
 
 325 
 
 strong current is passing will be permanently magnetized. 
 The bar should be passed into one end of the helix and 
 removed from the other end. 
 
 (a.) A long, thin, steel magnet is more powerful in proportion to 
 its weight than a thicker one is. Compound magnets are, therefore, 
 made of thin pieces of steel, separately magnetized and then bound 
 together in bundles. A horse-shoe magnet will lift a load three or 
 four times as heavy as will a bar magnet of the same weight. The 
 lifting power is increased if the area of contact between the poles and 
 the armature is increased. The lifting power of a magnet is strength- 
 ened, in an unexplained way, by gradually increasing the load on its 
 armature day by day until it bears a load which at the outset it 
 could not have borne. If the load be so increased that the armature 
 is torn off, the power of the magnet falls at once to its original 
 value. The attraction between a powerful electro-magnet and its 
 armature may amount to 200 Ib. per square inch, or 14,000 g. per 
 sq. cm. Small magnets lift a greater load in proportion to their own 
 weight than large ones. A good steel horse-shoe magnet weighing 
 one pound ought to lift twenty pounds' weight. 
 A steel magnet loses part of its magnetism by be- 
 ing jarred or knocked about and all of it by being 
 heated to redness. 
 
 449. Armatures. Magnets left to them- 
 selves soon lose their magnetism. They should, 
 therefore, be provided with armatures. Armatures 
 are pieces of soft iron placed in contact with opposite 
 poles, as shown in Fig. 234. The two pojes of the 
 magnet (or magnets, for two bar magnets may be 
 thus protected) act inductively upon the armature 
 and produce in it poles opposite in kind to those 
 with which they come in contact. The poles of the 
 armature in turn react upon the magnet and, by 
 their power of attraction, aid in retaining the mag- 
 netism. 
 
 FIG. 234. 
 
 45O. Magnetic Units, All magnetic quantities, strength of 
 poles, intensity of magnetization, etc., are expressed in terms of 
 special units derived from the fundamental units of length, mass and 
 time, i.e., they are 0. G. S. units. 
 
 (a.) Unit Strength of Magnetic Pole. The unit magnetic pole is 
 
326 MAGNETISM. 
 
 one of such strength that it repels a similar pole of equal strength 
 with a force of one dyne when it is placed at a distance of one centi- 
 meter from it. 
 
 (&.) Magnetic Potential being measured by work done in moving 
 a unit magnetic pole against the magnetic forces, the unit of mag- 
 netic potential will be measured by the unit of work, the erg. 
 
 (c.) Unit Difference of Magnetic Potential exists between two 
 points when it requires the expenditure of one erg of work to 
 bring a unit magnetic pole from one point to the other against 
 the magnetic forces. 
 
 (d.) Intensity of Magnetic Field is measured by the force it exerts 
 upon a unit magnetic pole ; hence, 
 
 (e.) Unit Intensity of Field is that which acts on a unit pole 
 with a force of one dyne. 
 
 451. Electro-Magnetic Units. The magnetic units just 
 described give rise to a set of electrical units, in which the strength 
 of currents, etc., are expressed in magnetic measures. (See 320.) 
 
 (a.) Unit Strength of Current. A current has unit strength when 
 1 cm. length of its circuit bent into an arc of 1 cm. radius (so as to 
 be always 1 cm. away from the magnet-pole) exerts a force of one 
 dyne on a unit magnet-pole placed at the centre. 
 
 (b.) Unit of Quantity of Electricity is that quantity which is con- 
 veyed by unit current in one second. 
 
 (c.) Unit of Difference of Potential (or of E. M. F.) is that which 
 exists between two points when it requires the expenditure of one 
 erg of work to bring a unit of + electricity from one point to the 
 other against the electric force. 
 
 (d.) Unit of Resistance. A conductor possesses unit resistance 
 when unit difference of potential between its ends causes a current 
 of unit strength to flow through it. 
 
 452. Practical Units. As some of these "abso- 
 lute" electro-magnetic units are too large for common, 
 convenient use and others are too small, the practical 
 units, the volt, the ohm, the ampere, the coulomb and 
 the farad have been chosen and are generally used. These 
 units have been already described, the value of each in 
 absolute electro-magnetic units being given. 
 
MAGNETISM. 327 
 
 453. Molecular Changes in a Magnet. 
 
 When a steel or iron bar is strongly magnetized, it in- 
 creases in length and diminishes in thickness. This effect 
 is probably due to the magnetization of the individual mole- 
 cules, which tend to set themselves parallel to the length 
 of the bar. This supposition is confirmed by the observa- 
 tion that at the moment when a bar is magnetized or 
 demagnetized, a faint metallic click is heard in the bar. 
 When a tube containing water rendered muddy with finely 
 divided magnetic oxide of iron is magnetized, the liquid 
 becomes clearer in the direction of magnetization, the par- 
 ticles apparently setting themselves end to end and al- 
 lowing more light to pass between them. A piece of iron, 
 when powerfully magnetized and demagnetized in rapid 
 succession, grows hot, as if the changes were accompanied 
 by internal friction. 
 
 454. Theory of Magnetism. These and other 
 phenomena point to a theory of magnetism very different 
 from the old notion of " magnetic fluids." It appears that 
 every molecule of a magnet is itself a magnet and that the 
 molar magnet becomes a magnet only by the molecular 
 magnets being turned so as to point one way. This con- 
 clusion is supported by the observation that if a glass tube 
 full of iron filings be magnetized, the filings may be seen 
 to set themselves endwise and that, when thus once set, 
 they act as a magnet until they are shaken up. 
 
 455. Relation of Magnetism to Energy. A 
 
 magnet is a reservoir of potential energy. This energy is 
 due to tHe expenditure, at some time, of a definite amount 
 of energy, of some kind. By virtue of its potential energy, 
 
328 MAGNETISM. 
 
 it can do a definite amount of work and no more. For in- 
 stance, it may attract a certain amount of iron. When 
 thus fully loaded, the magnet has done its full work and 
 can do no more. When the iron is torn from the 
 magnet, more energy is expended and the magnet 
 thus endowed again with potential energy. A 
 magnet has not an inexhaustible supply of energy, 
 as some have supposed. 
 
 EXERCISES. 
 
 1. (a.) What is a magnetic pole? (6.) A magnetic equator? 
 (c.) How does a magnet behave toward soft iron? (d.) How does 
 soft iron behave toward a magnet ? 
 
 2. (a.) State carefully the various effects that one magnet may 
 exert upon a second magnet. (&.) Generalize these observed facts 
 into a law. 
 
 3. On board an iron ship that is laying a submarine telegraph 
 cable, there is a galvanometer used for testing the continuity of the 
 cable. It is necessary to prevent the magnetized needle of the gal- 
 vanometer from being affected by the magnetism of the ship. How 
 can this be done ? 
 
 4 (a.) Given a bar magnet, how would you determine the sign of 
 either of its poles? (6.) What is a diamagnetic substance ? 
 
 5. If a magnetic needle be freely suspended from its centre of 
 gravity, what position will it assume? 
 
 6. (a.) Do you think that the earth is a magnet? (&.) Give a good 
 reason for your answer, (c.) Do the magnetic and the geographical 
 meridians ever coincide? (d.) Do they always coincide? (e.) If 
 they do not coincide, what name would you give to their difference 
 in direction ? 
 
 7. (a.) Does the magnetic attraction of the earth upon a ship's 
 compass tend to float the ship northward ? (&.) If so, why? If not, 
 why not ? 
 
 8. (a.) State and illustrate the second law of motion. (6.) State 
 and illustrate the law of universal gravitation, (e.) A body falls to 
 the ground from rest in 11 seconds ; what is the space passed over? 
 
 9. An electric bell in Cleveland, Ohio, is to be rung by a battery 
 in New York City. Should the magnet coils of the bell be made of 
 fine or coarse wire ? 
 
MAGNETISM. 
 
 329 
 
 10. Would you use a long coil or a short coil galvanometer to 
 measure the current used to ring the bell above mentioned? 
 
 11. Would it make any difference whether the galvanometer were 
 put into the circuit at New York or at Cleveland if the line be thor- 
 oughly insulated ? 
 
 12. With a local battery of 2 cells, each having an internal resist- 
 ance of 2 ohms, what should be the resistance of the sounder ? 
 
 13. The cells represented in Fig. 235 have each an E. M. F. of 2 
 volts and an internal resistance of 3 ohms. 
 
 What is the resistance of the external cir- 
 cuit, G, if the battery is arranged in the best 
 possible way ? Ans. 2 ohms. 
 
 14. Why is it that when there is little other 
 resistance in the circuit, a stout wire with few 
 turns will make a stronger electro-magnet than 
 a very fine wire with many more turns? 
 
 15. A battery of 5 Leclanche cells was con- 
 nected in simple circuit with a galvanometer 
 and a box of resistance coils. A deflection of 
 40 having been obtained by adjustment of the 
 resistances, it was found that the introduction 
 of 150 additional ohms of resistance brought 
 down the deflection to 29. A battery of ten 
 Daniell's cells was then substituted in the cir- 
 cuit and adjusted until the resistance was 40 
 as before. But this time it was found that 216 
 
 ohms had to be added before the deflection was brought down to 
 29. Taking the E. M. F. of a single Daniell's cell as 1.079 volt, 
 calculate that of a single Leclanche cell. Ans. 1.499 volt. 
 
 16. An electric bell has a resistance of 0.5 ohm. It requires a 
 current of 20 milliamperes to ring it. It is on a line of 1 mile 
 of No. 20 copper wire (see Appendix I). Ignoring the internal re- 
 sistance of the battery, find how many Leclanche cells (E. M. F. 
 = 1.6 volts) will be required. 
 
 17. We have to send a current through a telegraph line, 100 miles 
 long, the resistance of which is 13 ohms per mile. The battery is 
 composed of Daniell cells, each having an E. M. F. of 1.079 volts and 
 an internal resistance of 2 ohms. The telegraphic instrument offers 
 a resistance of 130 ohms and requires a current of 10 milliamperes 
 to work it. Will one cell of battery answer our purpose? Why ? 
 
 18. Under what circumstances will a magnet repel an unmag- 
 netized piece of iron ? 
 
 FIG. 235. 
 
330 MAGNETISM. 
 
 19. Give two or three differences between electric attractions and 
 repulsions and magnetic attractions and repulsions. 
 
 20. A zinc and a copper plate are respectively united by copper 
 wires to the terminals of a galvanometer. They are dipped, side by 
 side, into a glass containing dilute sulphuric acid. The galva- 
 nometer needle, at first, shows a deflection of 28, but five minutes 
 later the deflection has fallen to 11. How do you account for this 
 falling off ? 
 
 21. A wire, the resistance of which was to be determined, was 
 placed in a Wheatstone's bridge, in which resistances of 10 and 100 
 ohms respectively were used as the fixed resistances. Its resistance 
 was balanced when the adjustable coils were arranged to throw 281 
 ohms into circuit. What was its resistance ? (See Appendix M, (>.].) 
 
 Ana. 28.1 ohms. 
 
 22. Relays are wound with long, fine wire and sounders with 
 short, stout wire. Why is there this difference ? 
 
MAGNETISM. 331 
 
 Recapitulation. To be amplified by the pupil for 
 
 review. 
 
 f MAGNETS. 
 
 OQ 
 
 * i 
 
 w 
 
 125 
 
 NATUKAL. 
 ( Forms. 
 
 
 PERMANENT < 
 ( How Made. 
 
 
 
 Definition. 
 
 ARTIFICIAL. . . - 
 
 
 Advantages. 
 
 
 TEMPORARY OR 
 
 Forms. 
 
 
 ELECTRO-MAGNETS. 
 
 Residual 
 
 
 Magnetism. 
 
 
 Telegraph. 
 
 
 Electric Bells. 
 
 {MAGNETS. 
 
 CHANGES. 
 
 POLES. 
 
 CHARACTERISTICS. 
 
 LAWS. 
 
 ( MAGNETIC . ) 
 
 (.RELATION TO-J \Substances. 
 
 DlAMAGNETIC. 
 
 RETENTIVITY. 
 
 THEORY. 
 
 fBY CONTACT. 
 
 MAGNETIZATION. \ MODES OF. 
 
 I BY INDUCTION. -I 
 
 .MAGNETIC FIELD. 
 LINES OF FORCE. 
 PRECEDES ATTRACTION. 
 MAGNETIC SCREENS. 
 
 TERRESTRIAL.. 
 
 POLES. f COMPASS. 
 
 MAGNETIC NEEDLES. \ DIPPING. 
 DIP. [ ASTATIC. 
 
 DECLINATION. 
 
 MAGNETIC AND ELECTRO-MAGNETIC UNITS. 
 RELATION TO ENERGY, 
 
-3 
 
 ECTFON V. 
 
 INDUCED E LECTRI CITY. 
 
 456. Induced Currents. From our study of 
 frictional electricity and magnetism, we are familiar with 
 the term induction, by which we understand the influence 
 that an electrified body exerts upon a neighboring un elec- 
 trified body or that a magnetized body exerts upon a 
 neighboring magnetic but unmagnetized body. In 1831, 
 Faraday discovered an analogous class of phenomena 
 which we are now about to consider. An induced, cur- 
 rent is a current produced in a conductor by the 
 influence of a neighboring current or magnet. A 
 current used to produce such an effect is called an in- 
 ducing current. 
 
 457. Inductive Effect of Closing or Break- 
 ing a Circuit. In Fig. 236, B represents a double 
 coil made as follows: On a hollow cylinder of wood or 
 card-board are wound several layers of stout, insulated, 
 copper wire. The two ends of this wire, which constitutes 
 the primary coil, are seen dipping into the cups, gg'. Upon 
 this coil and carefully insulated from it, is wound a much 
 greater length of finer, insulated copper wire. The two ends 
 of this wire, which constitutes the secondary coil, are seen 
 connecting with a delicate, long coil galvanometer, G. 
 
INDUCED ELECTRICITY. 
 
 333 
 
 Remember that there is no electrical connection between 
 the two coils. Wires from, the poles of a voltaic cell, P, 
 dip into mercury in the cups g g', thus closing a circuit 
 through the primary coil of B. While this circuit is closed, 
 the galvanometer needle is at rest, showing that no 
 current is passing through the secondary coil. By lifting- 
 one of the wires from its cup, the inducing current is 
 interrupted. At this instant, the galvanometer needle 
 
 FIG. 236. 
 
 is deflected, as by a sudden impulse that immediately 
 passes away. This movement of the galvanometer needle 
 shows the existence of a momentary, induced current in 
 the secondary coil. The direction in which the needle 
 turns, shows that the secondary current is direct, i. e., 
 that it has the same direction as the inducing cur- 
 rent. If the wire just removed from the cup be replaced 
 and the inducing current thus re-established, the galva- 
 nometer needle will be momentarily turned in the direction 
 opposite to that in which it was previously turned. When 
 a current begins to flow through the primary coil, 
 it induces a current in the secondary coil. When 
 
334 INDUCED ELECTRICITY. 
 
 it ceases to flow through the primary coil, a cur- 
 rent flowing in the opposite direction is induced 
 in the secondary coil. Both induced currents are 
 merely momentary in duration. 
 
 458. The Extra Current. When a circuit is 
 made or broken, each convolution of a coil placed in he 
 circuit acts inductively upon the other convolutions of 
 the coil as if they were portions of two unconnected cir- 
 cuits. This action is called the induction of a 
 current upon itself ; the current thus produced is 
 vailed the extra current. 
 
 (a.) When the circuit is made, the extra current is inverse or 
 opposite in direction to the primary current and acts against it. 
 The extra current at the breaking of the circuit is direct and adds 
 its effect to that of the primary current. Hence, a spark is more 
 often seen on breaking than on making contact. Increasing the 
 number of coils or convolutions in the circuit will increase the brill- 
 i-mcy of the spark. If the coil has an iron core (electro-magnet) 
 the effect is especially marked. 
 
 459. Ruhmkorff's Coil. The induction coil, 
 often called, from the name of its inventor, Ruhmkorff's 
 coil, is a contrivance for producing induced, cur- 
 rents in a secondary coil by closing and opening, 
 in rapid succession, the circuit of a current in 
 the primary coil. The essential parts are described in 
 457. In the complete instrument, the axis of the coils 
 is a bundle of soft iron wires. These wires usually ter- 
 minate in two small plates of soft iron which thus form 
 the ends of the wire bundle. Around this bundle, is wound 
 the primary coil of stout, insulated, copper wire. Upon 
 the primary coil, but carefully insulated from it, is wound 
 
INDUCED ELECTRICITY. 
 
 335 
 
 the secondary coil which is made of a great many turns of 
 fine, silk covered, copper wire. 
 
 (a.) The wire bundle (M, Fig. 238) becomes magnetized by the 
 action of the battery current in the primary coil and then adds its 
 Inductive effect 
 upon the secondary 
 coil to the effect of 
 tKe primary itself. 
 The primary cir- 
 cuit is rapidly 
 broken and closed 
 by an automatic in- 
 terrupter or contact 
 breaker, repre- 
 sented at the left 
 hand of the coil, 
 Fig. 237, and at the FIG. 237. 
 
 right hand of the 
 
 diagram in Fig. 238. One of the posts there seen carries an elastic, 
 metallic, vibrating plate with an iron hammer, b, at its end. This 
 hammer vibrates back and forth between the end of the iron core of 
 the coils and the end of the metal adjusting screw, d, which is car- 
 ried by the other post seen in the figure. These posts are in the 
 
 primary circuit. When 
 the hammer rests against 
 the end of the adjusting 
 screw, the circuit is closed 
 and the iron core is mag- 
 netized. As soon as the 
 
 *\ j^ core is magnetized, it at- 
 
 tracts the hammer, thus 
 drawing it away from the 
 end of the screw and break- 
 ing the circuit. As soon as the circuit is broken, the bar is de- 
 magnetized and the plate, by virtue of its elasticity, throws the 
 hammer back against the screw, closing the circuit and again mag- 
 netizing the core. The plate is thus made to vibrate with great 
 rapidity, each oscillation making or breaking the primary circuit and 
 creating a series of induced currents in the secondary coil. 
 
 (6.) The condenser (C G, Fig. 238), which is generally placed in 
 the pedestal or base of the coil, consists of a number of sheets of 
 tinfoil insulated from each other by thin sheets of varnished paper 
 
336 INDUCED ELECTRICITY. 
 
 or oiled silk. Alternate layers of the tinfoil are connected, i. e., the 
 first, third, fifth, seventh, etc., layers are connected, as also are the 
 second, fourth, sixth, eighth, etc., thus forming two separate, in- 
 sulated series. One series (e. g., the odd numbered sheets) is con- 
 nected with one of the posts of the contact breaker ; the other series, 
 with the other post. Thus, the plates of the condenser do not 
 form a part of the primary circuit but are, as it were, lateral expan- 
 sions of that circuit, one on each side of the contact breaker. The 
 effect of the condenser is to lessen the spark when the primary cir- 
 cuit is made or broken and to increase the force of the discharge of 
 the secondary coil. 
 
 (c.) For an ordinary Ruhmkorff's coil, one to three Bunsen or 
 potassim di-chromate elements will suffice. 
 
 (d.) Most induction coils are provided with a commutator, for the 
 purpose of changing the direction of the current through the primary 
 coil and, consequently, the direction of the currents induced in the 
 secondary coil. One form of the commutator is shown at the right 
 hand end of Fig. 237. It is not an essential part of the instrument. 
 
 Experiment 104. Let the members of the class join bare hands. 
 Let the pupil at one end of the line place a finger on one of the 
 binding posts or electrodes of the secondary coil of a small induction 
 coil. Then let the pupil at the other end of the line, momentarily 
 touch the other electrode. Each person in the line will feel a 
 "shock." The experiment should not be tried with a powerful coil, 
 as the spasmodic, muscular contractions thus produced are sometimes 
 painful and permanently injurious. 
 
 46O. Spark from the Induction Coil. If the 
 
 ends of the secondary coil be connected, opposite current* 
 alternately traverse the connecting wire. When the ends 
 are disconnected, the inverse current cannot overcome the 
 resistance of the intervening air because of its low electro- 
 motive power ( 458, a). The direct current, produced 
 by breaking the primary circuit, is alone able to 
 force its way in the form of a spark. The sparks 
 vary with the power of the instrument. 
 
 (a.) Mr. Spottiswoode, of London, has made an induction coil, the 
 secondary coil of which contains 280 miles of wire wound in 340,000 
 turns. This magnificent instrument has a resistance of more than 
 
INDUCED ELECTRICITY. 
 
 337 
 
 100,000 ohms, and, when worked with a battery of 30 Grove cells, 
 yields a spark 42| inches long, a result greater than that obtainable 
 from any electric machine. The induction coil may be used to pro- 
 duce any of the effects of frictional electricity, it being at the same 
 time nearly free from the limitations that atmospheric moisture 
 places upon ordinary electric machines. 
 
 (6.) For many instructive and beautiful experiments with this in- 
 strument and other information relating thereto, see the little book, 
 " Induction coils : How made and how used," published by D. Van 
 Nostrand, New York ; Price, 50 cents. 
 
 461. Currents Induced by Change of Dis- 
 tance. If the primary coil be made movable, as shown 
 in Fig. 239, and, with a current passing through it, be 
 suddenly placed within the sec- 
 ondary coil, the galvanometer 
 will show that an inverse current 
 is induced in the outer coil. 
 When the needle has come to 
 rest, let the primary coil be re- 
 moved and the galvanometer 
 will show that a direct current 
 is induced. From this we see 
 that when the primary coil, 
 bearing a current, is brought 
 near or thrust into the sec- 
 ondary coil, an inverse cur- 
 rent is induced in the latter ; 
 that when the coils are sep- 
 arated, a direct current is 
 
 induced in the secondary coil; that the induced 
 currents flow while a change of distance is varying 
 the inductive effect of the primary current. Re- 
 moving the primary coil to an infinite distance is equiva- 
 lent to breaking its circuit, as in 457. 
 
 FIG. 239. 
 
338 
 
 INDUCED ELECTRICITY. 
 
 462. Magneto -Electric Currents. We have 
 already noticed that there is an intimate relation between 
 electric and magnetic action. We have seen that an elec- 
 tric current may develop magnetism. Faraday found that 
 electricity may he developed by magnets ; the results of this 
 discovery have already become of incalculable commercial 
 importance. If, instead of the primary coil bearing the 
 
 FIG. 240. 
 
 inducing current, a bar magnet be used, as shown in Fig. 
 240, the effects produced will be like those stated in the 
 last paragraph. WTien the magnet is thrust into the 
 interior of the coil, an induced current will flow 
 while the motion of the magnet continues. When 
 the magnet becomes stationary, the current ceases to 
 flow and the needle of the galvanometer gradually 
 comes to rest. When the magnet is withdrawn, an 
 induced current flows in the opposite direction. 
 Of course, it makes no difference whether the magnet be 
 
TNDVCED ELECTRICITY. 
 
 339 
 
 moved toward the coil or the coil be moved toward the 
 magnet. The more rapid the motion, the greater will be 
 the electromotive force of the induced currents. 
 
 463. The Inductive Action of a Temporary 
 Magnet. If within the coil, a soft iron bar (or still 
 better, a bundle of straight, soft, iron wires) be placed, 
 as shown in Fig. 241, the induced current may be more 
 
 FIG. 241. 
 
 effectively produced by bringing one end of a permanent 
 magnet near the end of the soft iron. In this case, the 
 induced currents are due to the varying magnetism of the 
 soft iron, this magnetism being due, in turn, to the in- 
 ductive influence of the permanent magnet. Thus we 
 see that when the intensity of the magnetism of a 
 bar of iron or steel is increased or diminished, 
 currents are induced in the neighboring coil. 
 Similar effects may be produced by moving one pole of 
 the magnet across the face of the coil from end to end. 
 
.140 
 
 INDUCED ELECTRICITY. 
 
 464. The Wheel Armature. Imagine the soft 
 iron bar in the helix of Fig. 241 to be grooved and several 
 times as long as the helix through which it passes. Imag- 
 ine the ends of this bar to be brought together so as to 
 
 form a complete iron 
 ring carrying one helix. 
 If the number of helices 
 upon the ring be in- 
 creased to twelve we 
 shall have the wheel 
 armature, shown, in an 
 unfinished condition, in 
 Fig. 242. If the pole 
 of a magnet be passed 
 around the face of this 
 wheel, it will pass twelve 
 coils of wire and induce 
 a current of electricity as it approaches each coil and an 
 opposite current as it leaves each coil, thus inducing 
 twenty-four currents for each revolution. Of course, it 
 makes no difference whether the magnet be permanent or 
 temporary, whether the pole of the magnet moves by the 
 coil or the coil passes by the pole of the magnet. Then, if 
 the magnet be fixed and the wheel turn upon its axis in 
 such a way as to carry its coils across the end of the 
 magnet, we shall be inducing twenty-four currents of 
 electricity for each revolution of the wheel. This is what 
 happens in the operation of a dynamo-electric machine. 
 When a closed circuit conductor moves in a mag- 
 netic field so as to cut across the lines of magnetic 
 force ( 433), an induced current of electricity flows 
 through the conductor in on direction while the 
 
INDUCED ELECTRICITY. 
 
 341 
 
 conductor is approaching the point of greatest 
 magnetic intensity and in the opposite direction 
 while the conductor is moving away from such 
 point of maximum intensity. The varying magnetic 
 intensity of the iron core of each moving coil increases 
 this effect as explained in 463. Of course, the number 
 of coils on the armature may be more or less than twelve, 
 or the armature may be of a form almost wholly different 
 from that just described, but, in every case, the principle 
 of its action is as above stated. The dynamo represented 
 in Fig. 243 has only eight armature helices and diametric* 
 ally opposite coils are joined so as to form four pairs. 
 
 FIG. 243. 
 
 465. Dynamo-Electric Machines. In the 
 
 Brush dynamo-electric machine, represented in Fig. 243, a 
 shaft runs through the machine from end to end, carrying 
 a, pulley, P, at one end, a commutator, c, at the other, 
 and a wheel armature, R, at the middle. The armature, 
 R, carries eight or more helices of insulated wire, H H. 
 
342 INDUCED ELECTRICITY. 
 
 As the shaft is turned by the belt acting upon P, R and 
 c are turned with it. As R turns around, it carries the 
 eight coils, H H, rapidly across the poles of the four 
 powerful field magnets, M M. 
 
 As each coil passes each pole, it necessarily tra- 
 verses the magnetic field and cuts across the lines 
 of magnetic force; consequently, currents are in- 
 duced in the coil. These currents are carried on insu- 
 lated wires to the commutator rings, c c, where they are 
 united in such a way as all to flow in the same direction, 
 forming a continuous current. The electricity is taken 
 from the revolving commutator, c c, by the four or more 
 fixed, copper plates, i i, technically called " brushes," then 
 carried down the flexible copper strips, s s, then passed 
 through the insulated wire of the electro-magnets, M M, 
 and, finally, to the + binding post. Thence the current 
 passes by a wire -to the external circuit, e. g., to an arc 
 lamp (Fig. 246) and from this to a second lamp, and so on 
 through all of the lamps of the circuit and from the last 
 lamp back to the binding post of the dynamo-electric 
 machine, thus making the circuit complete. Sixty or 
 more arc lamps in series may be worked by one of these 
 machines. No part of the circuit of a dynamo should 
 have an earth connection. The complete circuit (except 
 through the lamp carbons) should be of carefully insu- 
 lated wire. 
 
 Dynamo-electric machines are being rapidly introduced 
 for purposes of electric lighting, electro-plating, motive 
 power, telegraphy, etc. They are made in various forms, 
 but tfye principle underlying the action of them all i& the 
 same as that stated in the last paragraph. After master- 
 ing the action of one dynamo-electric machine the pupil 
 
INDUCED ELECTRICITY. 343 
 
 will have little trouble in understanding the action of any 
 other that he may have a chance to examine. Dynamo- 
 electric machines are often called " dynamos." A small, 
 hand power dynamo, suitable for school use, may be had 
 for $30 or more. 
 
 (a.) In cases where a high E. M. F. is needed (as in arc electric 
 lighting), the armature helices are wound with many turns of wire 
 which gives a high internal resistance. Compare 399. When a 
 smaller E. M. F. is wanted (as in direct, incandescence electric light- 
 ing or in electro-plating), fewer turns of wire of greater diameter 
 are used. This reduces the internal resistance of the dynamo. 
 Compare 400. The E. M. F. will vary with the strength of the 
 magnetic field and the speed at which the armature is revolved. 
 Thus, a given dynamo may be run slowly for a few lamps and at a 
 higher speed for a greater number of lamps. In practice, however, 
 special automatic devices are generally provided for adapting the 
 E. M. F. to the varying resistances of the external circuk without 
 changing the speed of the dynamo. 
 
 (b.) If permanent magnets are used instead of electro-magnets, 
 the machine is called a magneto -electric instead of a dynamo-electric 
 machine. Small magnetos (armatures wound with long, thin wires) 
 are much used for electro-medical purposes. The patient holds two 
 metallic handles connected with the terminals of the instrument 
 and receives a rapid succession of shocks when the armature is 
 turned. 
 
 (c.) If, instead of expending mechanical energy to turn the shaft 
 of the dynamo and thus produce an electric current, we pass a strong 
 current of electricity through the dynamo, the shaft of the dynamo 
 will be turned in the opposite direction and may be made to drive 
 ordinary machinery as an electric motor. In the former case, we 
 convert mechanical energy into electric energy ; in the latter case, 
 we convert electric energy into mechanical energy ( 473). 
 
 466. Incandescence Electric Lamps. When 
 
 a conductor of high resistance is heated to incandescence 
 by the passage of a current, we have an illustration of the 
 fundamental principle of incandescence electric light- 
 ing. To prevent the fusion of the conductor, a carbon 
 
344 
 
 INDUCED ELECTRICITY. 
 
 THE SWAN ELECTRIC LAMP. 
 
 filament, about the size of a horse-hair, is used carbon 
 never having been melted. To prevent the combustion of 
 the carbon filament, it is enclosed 
 in a glass globe containing either 
 a high vacuum or only some inert 
 gas, incapable of acting chemic- 
 ally upon the carbon at even the 
 high temperature to which it is 
 to be subjected. The ends of the 
 carbon are connected with plat- 
 inum wires that are fused into 
 and passed through the glass. 
 
 (a.) The filament is carbonized in 
 different ways and given different 
 shapes by different inventors. The 
 Edison carbon is made of bamboo fibre 
 and is in the shape of an ordinary hair 
 pin. The Swan carbon is made of 
 parchmentized cotton thread. Fig. 
 244 represents the Swan incandescence 
 lamp and is half the actual size of the 
 standard sixteen candle power lamp. 
 Incandescence lamps are generally 
 operated abreast, as shown in Fig. 245, 
 being placed, as it were, in little 
 bridges of wire connecting the two conductor "mains." Thus, the 
 resistance of the circuit is reduced by the successive addition of lamps. 
 
 (b.) The resistance of carbon is 
 lowered by heating the conductor. ^, m ^ 
 The "hot" resistance of an incan- If r I I ! I 
 
 descence lamp is about | its "cold" 9999 9 9 
 
 resistance. 
 
 FIG. 244. 
 
 FIG. 245. 
 
 467. The Voltaic Arc. 
 
 The most brilliant luminous effect of current electricity is 
 the arc of an electric lamp. This lamp consists essentially 
 of two pointed bars of hard carbon, generally copper coated 
 
INDUCED ELECTRICITY. 
 
 345 
 
 (Experiment 78), placed end to end in the circuit of a 
 powerful current. If the ends of the carbons be separated 
 a short distance while 
 the current is passing, 
 the carbon points be- 
 come intensely heated 
 and the current will 
 not be interrupted 
 thereby. When the 
 carbons are thus 
 separated, their tips 
 glow with a brill- 
 iancy which ex- 
 ceeds that of any 
 other light under 
 human control, 
 while the tempera- 
 ture of the inter- 
 vening arc is un- 
 equalled' by any 
 other source of ar- 
 tificial heat. 
 
 The mechanism 
 shown in the upper 
 part of Fig. 246, is for 
 the purpose of auto- 
 matically separating the carbons and "feeding" them 
 together as they are burned away at their tips and for the 
 purpose of cutting the lamp out of the circuit in case of 
 any irregularity or accident. Such lamps of from one to 
 two thousand candle power and requiring an expenditure, 
 at the dynamo, of about one-horse power per lamp are 
 
 FIG. 246. 
 
346 
 
 INDUCED ELECTRICITY. 
 
 now quite common. Lamps of a hundred thousand can- 
 dle power have been made. The current may be furnished 
 by a battery of forty or more Grove's cells but, for eco- 
 nomical reasons, it is almost universally supplied by a dy- 
 namo-electric machine. 
 
 (a.) It is necessary to bring the carbons into contact to start th 
 light. The tips of the carbons become intensely heated on account 
 of their small area of contact and the consequent high resistance at 
 that point. The carbon (and its usual copper coating) begins to 
 volatilize. When the carbons are separated, the current is kept up 
 by this intervening layer of vapor and the accompanying disin- 
 tegrated matter, which act as a conductor. Arc lamps 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 
 successive addition of lamps. 
 
 (&.) The constitution of the 
 voltaic arc may be studied by 
 projecting its image on a screen 
 with a lens. Three parts will 
 be noticed : 
 
 1. The dazzling white, con- 
 
 cave extremity of the 
 positive carbon. 
 
 2. The less brilliant and more 
 
 pointed tip of the nega- 
 tive 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 direc 
 tion of the current, the positive 
 
 carbon wasting away more than 
 
 FIG. 247. twice as rapidly as the negative. 
 
 Most of the light of the lamp is 
 
 radiated from the crater at the end of the positive carbon. If the 
 arc be too short, many of these rays will be intercepted by the nega- 
 tive (generally the lower) carbon, thus lessening the efficiency of the 
 
INDUCED ELECTRICITY. 347 
 
 Jamp. If the arc become too long, it will "flame" and much of 
 the light thus be lost. If the electrodes be horizontal, the arc will 
 be curved upward by r.scending air currents. Arc lamps are now 
 largely used for lighting streets, factories, stores, etc., many thou- 
 sands having been sold in every quarter of the globe ( 000). 
 
 468. The Telephonic Current. An electric cur- 
 rent may be induced in a coil of insulated wire surround- 
 ing a bar magnet by the 
 
 approach and withdrawal 
 of a disc of soft iron. The 
 disc, a (Fig. 248), is mag- 
 netized by the inductive 
 influence of the magnet, m, 
 
 ( 435). The disc, thus magnetized, reacts upon the 
 magnet, m, and changes the distribution of magnetism 
 therein. By varying the distance between a and m, the 
 successive changes in the distribution of the magnetism of 
 m induce to-and-fro currents in the surrounding coil 
 ( 463). When a approaches m, a current flows in one 
 direction ; when it recedes, the current flows in the oppo- 
 site direction. 
 
 469. The Telephonic Circuit. If the wire sur- 
 rounding the magnet mentioned in the last paragraph be 
 continued to a distance and then wound around a second 
 bar magnet, as shown in Fig. 249, tbe currents induced at 
 M would affect the magnetism of the bar at M' or the in- 
 tensity of its attraction for the neighboring disc, a'. . A 
 vibratory motion in the disc, a, would induce electric 
 currents at M ; these currents, when transmitted to M', 
 perhaps several miles distant, would affect the magnetism 
 of the bar there and tend to produce exactly similar vibra- 
 
348 
 
 INDUCED ELECTRICITY. 
 
 tions in a'. " It is as if the close approach and quick 
 oscillation of the piece of soft iron fretted or tantalized 
 
 FIG. 249. 
 
 the magnet and sent a series of electrical shudders through 
 the iron nerve/' When the current generated at M flows 
 in such a direction as to reinforce the magnet at M', the 
 latter attracts a' more strongly than it did before. When 
 the current flows in the opposite direction, it weakens the 
 magnetism of M' t which then attracts a' less. The disc, 
 therefore, flies back. Thus, the vibrations of a' are like 
 those of a. 
 
 (a.) We have here the principle of the telephone, so far as electric 
 action is involved. Further consideration of this instrument must 
 be deferred until we have learned more concerning sound. (See 
 505.) 
 
INDUCED ELECTRICITY. 349 
 
 EXERCISES. 
 
 1. A dynamo is feeding 16 arc lamps, the average resistance oi 
 each of which is 4.56 ohms. The internal resistance of the dynamo 
 (i.e., of the wire conductors of the armature and field magnets) is 
 10.55 ohms. What current does the dynamo yield with an E. M. F. 
 of 838.44 volts? An*. 10.04 amperes. 
 
 2. If a wire about 18 inches long be 
 attached to one electrode of a potassium 
 dichromate cell and the other electrode 
 momentarily touched with the other end 
 of the wire, a minute spark may be 
 
 noticed at the instant of breaking the cir- JT IG< 
 
 cuit. If the wire be bent into a scalari- 
 form or ladder like shape and the experiment repeated, the spark will 
 be greater than before. If the form of the external circuit be again 
 changed by winding the wire into a spiral (as shown in Fig. 250), the 
 spark will be still greater. Explain the repeated increase in the spark. 
 8. A dynamo is run at 450 revolutions, developing a current of 
 9.925 amperes. This current deflects the needle of a tangent gal- 
 vanometer, 60. (See Appendix L.) When the speed of the dynamo 
 is sufficiently increased, the galvanometer shows a deflection of 74. 
 What is the current developed at the higher speed? 
 
 Am. 20 amperes. 
 
 4. The current running through the carbon filament of an incan 
 descence lamp was found to be 1 ampere. The difference of poten- 
 tial between the two terminals of the lamp was found to be 30 volts. 
 What was the resistance of the lamp ? 
 
 5. A yard of silver wire weighs 7.2 grains and has a resistance of 
 0.3 ohm. What is the resistance of a foot of silver wire that weighs 
 one grain? Ans. 0.24 ohm. 
 
 6. If a pure copper wire has a weight of one grain and a resistance 
 of 0.2106 ohms per foot and a commercial copper wire has a weight 
 of 164 grains and a resistance of 0.547 ohms per 20 ft., what is the 
 percentage conductivity of the latter as compared with pure copper ? 
 
 Ans. 93.9 per cent. 
 
 7. I want to place, in series, 10 incandescence lamps, each of 25 
 ohms resistance ; the line wire is to be 200 feet long and must have 
 not more than 2 per cent, of the resistance of the lamps. Determine 
 from the table in Appendix I what size of wire (American gauge) 
 should be used. Ans. No. 23. 
 
350 INDUCED ELECTRICITY. 
 
 8. 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, that 
 of the lamps. Determine from the table what size wire should be 
 used. Am. No. 4 (B. & S.) 
 
 9. What length of No. 0000 pure copper wire (B. & S.) will have a 
 resistance of 1 ohm? (See Appendix I.) Am. 19607.84 ft. 
 
 10. A dynamo has an E. M. F. of 206 volts and an internal (or in 
 terpolar) 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 
 wire has a resistance of 1.1 ohms and joins the dynamo to 3 arc lamps 
 in series, each lamp having a resistance 3.12 ohms. Under such 
 conditions, the dynamo develops a current of 14.8 amperes. What 
 is the E. M. F. ? Ans. 196.25 volts. 
 
 12. A dynamo, run at a certain speed, gives an E. M. F. of 200 
 volts. It has an internal resistance of 0.5 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 ohm. I want a current of just 
 25 amperes. Must I increase or lessen the speed of 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 re- 
 sistance of the dynamo ? Ans. 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. The same lamps were placed in multiple arc with another 
 dynamo. The line wire was adjusted so that its resistance with the 
 internal resistance of the machine was 11.2 ohms as before. The 
 current was 1.2 amperes. What was the E. M. F.? 
 
 Ans. 29.16 volts. 
 
 17. A dynamo supplies current for two incandescence lamps in 
 series, each having a hot resistance of 97 ohms. The other resist- 
 ances 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. ? 
 
 18. 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 potential between the carbon tips, Ans. 38 volts. 
 
INDUCED ELECTRICITY. 351 
 
 10. The resistance of the arc lamp above mentioned, when the 
 carbons are held together, is 0.62 ohm. When it is burning with 
 normal arc and a 10 ampere current, what is the difference of poten- 
 tial between the terminals of the lamp ? Ans. 44.2 volts. 
 
 HONORARY PROBLEMS. 
 
 20. Four arc lamps, with a resistance of 6 ohms each, are joined 
 in series, 150 feet apart. The first lamp is 1,500 feet and the last 
 is 1,350 feet from the dynamo. The line wire has a conductivity 
 of 96 per cent, that of pure copper. Its resistance must not exceed 
 8 per cent, of that of the lamps. The resistance of a foot of pure 
 copper wire 1 mil in diameter being 9.94 ohms, what must be the 
 diameter of the line wire ? Ans. 133 mils or 0.133 inch. 
 
 Use No. 10 wire, B. W. G. (App. I). 
 
 21. Twenty-five similar voltaic cells having an internal resistance 
 of 15 ohms each were joined in series, by short and stout copper 
 wires to a 70 ohms incandescence lamp and produced a current of 
 0.112 ampere. What would be the strength of the current sent by 
 a series of 30 such cells through a series of 2 lamps, each of 30 ohms 
 resistance? Ans. 0.118 ampere. 
 
 22. What would have been the strength of current through the 
 two lamps if the area of each of the battery plates had been doubled, 
 all things else remaining the same ? Ans. 0.2105 ampere. 
 
 23. I join 50 arc lamps in series. Each lamp has a resistance of 
 4.5 ohms. The line wire connecting them with the dynamo is 3| 
 miles long and its conductivity is 90 per cent, that of pure copper. 
 One tenth of the total energy of the external circuit is lost in heat- 
 ing this line wire. What is its diameter, it being assumed that 1 foot 
 of pure copper wire. 1 mil in diameter has a resistance of 9.94 ohms. 
 
 Ans. 90.3 mils. 
 Use No. 11 wire (B. & S.) 
 
352 INDUCED ELECTRICITY. 
 
 Recapitulation. To be amplified by the pupil foi 
 
 review. 
 
 fc Q 
 
 w g 
 
 r^ 
 
 * 
 
 ffi U 
 
 CLOSING. 
 
 BREAKING. 
 
 PRIMARY CIRCUIT. 
 
 PRIMARY. 
 
 SECONDARY. 
 
 Coils. 
 
 RUHMKORFF. 
 EXTRA CURRENT. 
 
 CHANGE OF DISTANCE OF PRIMARY CIRCUIT. 
 
 (Current. 
 Circuit. 
 PERMANENT, f 
 
 * MAGNETO-ELECTRIC MACHINES 
 f WHEEL ARMATURE. 
 MAGNETS. "I r Electro-Plating 
 
 Incandescence 
 Electric Light 
 ing. 
 
 DYNAMO-ELEC- 
 TRIC MACHINES, \ Arc Electric 
 USED FOR.... Lighting. 
 
 -TEMPORARY. 
 
 Charging Stor- 
 age Batteries. 
 
 Motive Power. 
 ELECTRIC MOTORS. 
 
*AV~ 
 
 ELECTRIC CURRENTS AS RELATED TO HEAT 
 AND MECHANICAL WORK. 
 
 4W. The Convertibility of Electric En- 
 ergy. Whenever an electric current does work of any 
 kind, it does it at the expense of a part "of its own energy. 
 Anything that increases the resistance of a circuit, decreases 
 the strength of the current ( 386). But such a diminu- 
 tion may be caused by a counter electromotive force set up 
 somewhere in the circuit. The E. M. F. of polarization 
 is an example of the truth under consideration. When- 
 ever a current is used to drive an electric motor, the action 
 of the motor generates a back current that diminishes the 
 current of the battery or dynamo. All of the current 
 that is not expended in some such way, in exter- 
 nal work, is dissipated as heat. The dissipation may 
 be in the battery (or dynamo), in the external circuit or 
 in both. The heat will appear wherever there is resistance. 
 If the poles of a battery or dynamo be short circuited, most 
 of the heat will be developed in the battery or dynamo. 
 If the external circuit be a thin wire of high resistance, it 
 will grow hot while the generator will remain compara- 
 tively cool. 
 
354 
 
 ELECTRICITY AND HEAT. 
 
 471. Joule's Law. The quantity of heat developed 
 in a conductor by the passage of an electric current is 
 proportional : 
 
 (1.) To the resistance of the conductor. 
 
 (2.) To the square of the strength of the current. 
 
 ( 3. ) To the time the current is flowing. 
 
 A current of one ampere flowing through a resistance 
 of one ohm, develops therein, per second, a quantity of heat 
 which (or its mechanical equivalent) is called a joule. It is 
 equal to 0.7373 of a foot-pound or to 0.24 of a lesser calorie 
 ( 579). A lesser calorie is, therefore, equal to 4.17 joules. 
 
 These facts are concisely stated by the following equa- 
 tion, known as Joule's Law : 
 
 H = C*Rt x 0.24, 
 
 in which # represents the number of lesser calories; C, the 
 number of amperes ; R, the number of ohms and t, the 
 number of seconds. In other words, a current of one 
 ampere flowing through a resistance of one ohm 
 develops therein 0.24 of a lesser calorie per second. 
 Foot-pounds =C*Rtx 0.737335. 
 
 (a.) In investigating this subject, 
 Joule used instruments on the prin- 
 ciple indicated in Fig. 251, in which 
 a thin wire joined to two stout con- 
 ductors is enclosed within a glasa 
 vessel containing alcohol, into which 
 a thermometer dips. The resist- 
 ance of the wire being known, its 
 relation to the other resistances may 
 be calculated. 
 
 Experiment 105. Send the cur- 
 rent from a few cells through a 
 chain made of alternate links of 
 silver and platinum wires. The platinum links grow red-hot while 
 
ELECTRICITY AND HEAT. 355 
 
 the silver links remain comparatively cool. The explanation is that 
 the specific resistance (Appendix K, [2]) of platinum is about six 
 times that of silver and that 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. 
 
 472. Heating Wires by the Current. The 
 
 resistance of metals increases with the temperature. Con- 
 sequently, a thin wire heated by the current will resist 
 more and more and grow hotter and hotter until it 
 loses heat by conduction and radiation into the surround- 
 ing air as rapidly as heat is supplied by the current. 
 Thin wires heat much more rapidly than thick. 
 The rise of temperature in different parts of a 
 wire of uniform material hut varying diameter 
 (the current remaining the same) will he in- 
 versely proportional to the fourth power of the 
 diameters. 
 
 (a.) Suppose a wire at any point to become reduced to Jidlf 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 (16 = 2 4 ). 
 
 (&.) A thin platinum wire, heated white-hot by a current, is some- 
 times used in surgery, instead of a knife, as it sears the ends of the 
 severed blood vessels and thus prevents hemorrhage. Platinum is 
 chosen on account of its infusibility, but even platinum* wires are 
 fused by too strong a current. Carbon is the only conductor that 
 resists all attempts at fusion ( 466). 
 
 (c.) Sometimes stout conducting wires are laid from a battery at a 
 safe distance to a fuse connected with a blast of powder or other ex- 
 plosive. In the fuse, is a thin platinum wire, forming part of the 
 electric circuit. The fuse is ignited by heating the platinum wire 
 by sending the current through it. Such methods are frequently 
 used in the operations of both peace and war. 
 
356 ELECTRICITY AND MOTIVE POWER. 
 
 473. Electric Motors. An electric motor is a 
 device for converting the energy of an electric cur- 
 rent into motive power by means of electro-magnets. 
 Illustrative apparatus of this kind may be found in many 
 school laboratories or will be gladly supplied by dealers in 
 philosophical apparatus. But the best electric motors are the 
 now common dynamo electric machines or slight modifica- 
 tions thereof. Such "electro-magnetic engines "are rap- 
 idly coming into use for operating sewing machines and 
 other light machinery, the current being supplied indirectly 
 by a storage battery or directly by a voltaic battery or 
 dynamo. Some "Electric Light and Power Companies " 
 now run such motors on their arc light circuits, selling 
 current to some for power and to others for light. In 
 many cases where it is undesirable to use a steam engine, 
 an electric motor may be made available. Such motors, 
 up to the capacity of 40 H. P., are now in the market. 
 Some of them have been successfully and economically 
 used in propelling street railway cars. 
 
 474. Electric Transmission of Power. A 
 
 water fall, perhaps at a point not easily accessible, may be 
 made to turn a turbine or other water wheel, which shall 
 drive a dynamo, which shall generate a current, which 
 shall be carried by wire to some available point and there 
 converted- into mechanical power again by means of an 
 electric motor. Thus, an otherwise waste water-power 
 may be made a source of profit. The scheme of thus dis- 
 tributing part of the power of Niagara over the State of 
 New York has been seriously considered. It may be pos- 
 sible (as a profitable commercial undertaking) to burn 
 cheap fuel at the coal mine for running large stationary 
 
ELECTRICITY AND POWER. 357 
 
 engines and thus deliver the power to consumers at great 
 distances. 
 
 475. The Watt. The electric unit of power (rate 
 of doing work) is called a watt. A. watt is the amount 
 of power conveyed by a current of one ampere 
 through a difference of potential of one volt. It 
 equals (10" 1 x 10 8 =) 10 7 ergs or ^-g- horse-power, 
 
 W=C x E = ' E ^- = C*R 9 
 1 
 
 in which W equals the number of watts; C, the number 
 of amperes ; E 9 the number of volts and R, the number 
 of ohms. 
 
 For example, if the difference of potential (Appendix M, 
 [4 .]) between the terminals of an arc lamp that is sup- 
 plied with a ten ampere current be 45.8 volts, how much 
 of the power used in driving the dynamo is consumed in 
 the lamp ? 
 
 W*=CxE=10x 45.8 = 458, the number of watts. 
 458 ~ 746 = 0.614, the number of horse-powers. 
 
 (a.) The formula W C x E is determined by the definition of 
 
 77T 
 
 the watt. From Ohm's law, we see that G . Substituting this 
 
 ET Etg 
 
 value of 0, the formula becomes TF x E = , as above. This 
 
 R R 
 
 shows that the power varies as the square of the E. M. F. when the 
 resistance remains constant, or that the power varies inversely as the 
 resistance when the E. M. F. remains constant. 
 
 (6.) W= C x E. But E = C R. Substituting this value of E, 
 the formula becomes TF= C x G R = C S R, as above. This shows 
 that tlie power varies as the square of the current when the resistance 
 remains constant or that the power varies as the resistance when the 
 current remains constant. 
 
358 ECONOMY OF CONDUCTION. 
 
 476. Relation of Conductors to E. M. F. 
 
 This subject may be well studied by means of an example. 
 The energy of a ten ampere current with an E. M. F. of 
 fifty volts is equal to that of a five ampere current with 
 an E. M. F. of one hundred volts. 
 
 W= C x E= 10 x 50 = 100 x 5 = 500. 
 
 These equivalent currents (500 watts each), flowing through 
 similar wires, will develop widely different quantities of 
 heat. If we take any convenient wire, say one of fifteen 
 ohms, the heat developed in each case will be as follows: 
 
 H= C 2 x Rb x 0.24. ( 471.) 
 
 10 2 x 15 x 0.24=360, the number of heat units per second. 
 52x15x0.24= 90, " " 
 
 . 
 In other words, the same electric energy develops only 
 
 one-fourth as much heat with the current of high electro- 
 motive force as it does with the current of low E. M. F., 
 the same wire being used. It is easily evident that a great 
 saving in the cost of conductors may be made possible by 
 the use of currents of high E. M. F. (See 474.) But 
 such currents are more dangerous to handle and require 
 careful insulation and special precautions to lessen the 
 risk of serious accident. 
 
ELECTRICITY, HEAT AND WORK. 359 
 
 EXERCISES. 
 
 1. What shorter name may be given for a volt-ampere ? 
 
 2. What electrical horse-power is required to send a current of 10 
 amperes through 10 arc lamps (in series) each having a resistance ol 
 4.476 ohms? Ana. 6.H. P. 
 
 3. How many joules will be developed per minute by a 10 ampere 
 current in a lamp of 4.42 ohms resistance? Ana. 26520 joules. 
 
 4. How many calories will be developed in a 40 ohm incandescence 
 lamp by the passage of a current of 1.2 amperes through it for a 
 minute? Ans. 0.82944 calories. 
 
 5. Find the mechanical equivalent (in foot-pounds) of the work 
 done by a 5 ampere current working for a minute against 100 ohms 
 resistance? Ans. 110600| foot-pounds. 
 
 6. A 30,000 watt dynamo develops an E. M. F. of 3000 volts. 
 What is the current strength ? Ans. 10 amperes. 
 
 7. How much power is required properly to operate an arc lamp 
 that has a difference of potential of 45.2 volts between its terminals, 
 it having been adjusted for a 10 ampere current? 
 
 8. The difference, of potential between the two terminals of an 
 arc lamp was found to be 37.7 volts. A 25 ampere current was 
 passing through the lamp. What is the power consumed in the 
 lamp? Ans. 942.5 watts, or 1| H. P. 
 
 9. A certain Edison incandescence lamp has a resistance of 125 
 ohms. The difference of potential between the terminals of the 
 carbon is 110 volts, (a.) What is the current strength? (6.) What 
 amount of heat is developed in the lamp per second ? 
 
 Ans. (a.) 0.88 ampere ; (b.) 23.23 lesser calories. 
 
 10. A Grove cell has an E. M. F. of 1.9 volts and a resistance of 
 0.4 ohm. Its plates are joined, first, by a 3 ohms wire ; second, by 
 a 30 ohms wire, (a.) What is the current in each case ? (b.) What 
 amount of heat per second is developed in each case ? 
 
 (a.) .559 amperes in first case. 
 
 Ans. 
 
 .0625 " second case. 
 
 (b.) .125 joules " first case. 
 
 .00625 " " second case. 
 About 80 times as much. 
 
360 
 
 ELECTRICITY, HEAT AND WORK. 
 
 Recapitulation. To be amplified by the pupil for 
 review. 
 
 
 
 
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REVIEW. 361 
 
 REVIEW QUESTIONS AHD EXERCISES. 
 
 1. (a.) Give the laws for pressure of liquids and (&.) explain each 
 by some fact or experiment. 
 
 2. (a.) What is a natural magnet? (&.) An artificial magnet? 
 (c.) How does a magnet behave toward soft iron? (d.) How does 
 one magnet behave toward another magnet ? 
 
 3. Give the facts in regard to the variation of the magnetic needle. 
 
 4. (a.) What are conductors in electricity ? (b.) In what ways may 
 electrical separation be effected? 
 
 5. (a.) What conditions in the construction and erection of light- 
 ning-rods are necessary to insure safety from lightning ? (6.) Give 
 the elements of a simple voltaic cell and (c.) the electric condition of 
 those elements within and without the liquid. 
 
 6. (a.) A body weighs at the surface of the earth 1014 Ib. ; what 
 would it weigh 1200 miles above the surface? (&.) Give the velocity 
 of water issuing from an orifice, under a head of 81 feet, (c.) If 5 
 quarts of water weigh as much as 7 of alcohol, what is the specific 
 gravity of the alcohol ? 
 
 7. Find the kinetic energy of a 25 Ib. ball that has fallen 3600 feet 
 in vacuo. Am. 90,000 foot-pounds. 
 
 8. Give the fundamental principle of Mechanics and illustrate its 
 application by one of the mechanical powers. 
 
 9. (a.) Over how high a ridge can you continuously carry water 
 in a siphon, where the minimum range of the barometer is 27 inches? 
 (&.) Explain. 
 
 10. (a.) What is specific gravity? (&.) How do you find that of 
 solids? (c.) What principle is involved in your method ? 
 
 11. (a.) How much water per hour will be delivered from an 
 orifice of 2 inches area, 25 feet below the surface of a tank kept full 
 of water, not allowing for resistance? (&.) Give the law of magnetic 
 attraction and repulsion. Ans. 14,998.44 gal. 
 
 12. (a.} State what you have been taught concerning the dipping 
 needle. (&.) Define and illustrate magnetic induction. 
 
 13. (a.) Give the law of electric attraction and repulsion and illus- 
 trate by the pith-ball electroscope. (6.) Define conductors and non- 
 conductors, electrics and non-electrics, (c.) Illustrate by an example 
 of each. 
 
 14. (a.} Explain (by figures) electric induction, (b.) Explain the 
 charging of a Leyden jar. (c.) When charged, what is the electric 
 condition of the outside and inside of the jar ? 
 
362 REVIEW, 
 
 15. (a.} Give the sources of atmospheric electricity and (&.) the 
 effects of lightning. 
 
 16. (a.) What is the effect of breaking a magnet? (6.) Give a 
 theory of magnetism that is competent to account for the properties 
 of magnets, broken or unbroken. 
 
 17. (a.) How do soft iron and tempered steel differ as to suscep- 
 tibility to magnetism ? (6.) Describe one method of magnetizing a 
 steel bar. 
 
 18. The influence of the earth's magnetism upon a magnetic 
 needle is merely directive, (a.) Explain what this means. (&.) 
 Show why it is so. 
 
 19. (a.) What is meant by electromotive force? (b.) Describe 
 Grove's battery and its mode of action, (c.) Why are battery zincs 
 generally amalgamated ? 
 
 20. (a.) Describe Oersted's apparatus and (6.) tell what its use 
 teaches, (c.) Describe the construction of the astatic galvanom- 
 eter. 
 
 21. (a.) Describe an electro-magnet and (&.) tell what its advan- 
 tages are. (c.) State the principle of the electric telegraph. 
 
 22. (a.) Describe a RuhmkorfFs coil and (&.) explain its action. 
 
 23. (a.) Define electrolysis and electrolyte. (&.) Describe the elec- 
 trolysis of water, (c.) Give a clear account of some branch of elec- 
 tro-metallurgy, (d.) What is meant by the terms electropositive and 
 electro-negative ? 
 
 24. (.) Define physics. (&.) Name and define the three conditions 
 of matter, (e.) What do you understand by energy? (d.) Explain 
 what is meant by foot-pound. 
 
 25. (a.) What condition of the atmosphere is desirable for experi- 
 ments in frictional electricity? (&.) Why? (c.) How could you 
 show, experimentally, that there are two opposite kinds of elec- 
 tricity ? 
 
 26. (a.) Describe the experiment with Faraday's bag and (6.) state 
 what it teaches, (c.) Describe the dielectric machine and (d.) ex- 
 plain its action. 
 
 27. In an air-pump, the capacity cf the cylinder is one-fourth that 
 of the receiver. Under ordinary atmospheric conditions, they to- 
 gether contain 62 grains of air. Find the capacity (a.) of the re- 
 ceiver, (&.) of the cylinder. After 5 strokes of the piston, (c.) how 
 many grains of air would be left in the receiver? What would be 
 its tension (d.) in pounds per square inch ? (e.) In Kg. per sq. cm. ? 
 (/.) In inches of mercury? Ana. (.) 827.68 g. 
 
 28. (a.) Supposing we had two Leyden jars, one charged on the 
 inside with positive electricity and the other with negative on the 
 
363 
 
 inside ; the two jars being insulated, can the jars be fully discharged 
 by connecting the inner coats? (b.) Give reasons for your answer. 
 
 29. In a vessel having the dimensions of a cubic foot, sulphuric 
 acid (sp. gr. = 1.83) stands eight inches high ; give the pressure on 
 the bottom and each side. 
 
 30. The lever of a hydrostatic press is six feet long, the fulcrum 
 being at the end and one foot from the piston rod. The diameter of 
 the tube is one inch ; that of the cylinder, ten inches. The power is 
 25 Ib. ; give the effect. (See Appendix A.) 
 
 31. Find the joint resistance of three conductors of 10, 12 and 18 
 ohms arranged in multiple arc. Ans. 4.18 ohms. 
 
 32. (a.) Define equilibrium and its kinds. (&.) Give examples. 
 (c.) How does the centre of gravity of any system, acted upon by 
 an exterior force, move ? (d.) Give an example. 
 
 33. (a.) Figure a simple barometer. (&.) Explain why the mer- 
 cury stands above its level, (c.) What atmospheric pressure will 
 sustain a column of mercury 24 inches high ? 
 
 34. (a.} How is it proved that air has weight? (b.) What is the 
 weight of air in a room 30 feet long, 20 feet wide and 10 feet high. 
 
 35. When a 1000 gram flask, containing 700 g. of water, was filled 
 with the fragments of a mineral, it weighed 1450 g. Give the 
 specific gravity of the mineral. Ans. 2.5. 
 
 36. A tank measuring 1 meter each way is filled with water : 
 what will be the pressure on the bottom and sides ? 
 
 37. (a.) What is meant by kinetic energy? (b.) By potential 
 energy ? 
 
 38. Two inelastic bodies are moving in opposite directions, one 
 weighing 31 grams and having a velocity of 24 meters per second, 
 the other weighing 22 grams and having a velocity of 18 meters 
 per second: what is the united energy (a.) before and (6.) after 
 impact? Ans. (a.) 1.27; (6.) 0.116 kilogrammeters. 
 
 39. Regarding the same bodies as moving in the same direction, 
 what would be the energy (a.) before and (b.) after impact ? 
 
 40. (a.) Draw a simple figure showing the essential parts of an 
 air-pump and (b.) explain the process of forming a vacuum, (c.) If 
 the capacity of the barrel be that of the receiver, how much air 
 will remain in the receiver at the end of the fourth stroke of the 
 piston ? and (d.) what would be its elastic force compared with that 
 of the external air ? Ans. (d.) fff. 
 
 41. The current of a Grove's battery with a certain resistance in the 
 circuit is known to be $ ampere. Passing this current through a 
 sine galvanometer, the coils had to be turned 9 to bring them par- 
 allel with the needle. (See Appendix L [2]). Some of the resistance 
 
364 REVIEW. 
 
 being removed, it is found that the coils have to be turned 70 to 
 bring them parallel. What is the current in the latter case? 
 
 Ans. 1 ampere. 
 
 42. If a positively electrified ball be hung at the centre of a room, 
 its charge will attract an equal amount of electricity to the walls 
 of the room. To what common piece of physical apparatus is this 
 arrangement analogous ? 
 
 43. What length of No. 6 pure copper wire (B. & S.) will have a 
 resistance of 1 ohm? (See Appendix I.) Ans. 2433.09 ft. 
 
 44 If a foot of pure copper wire weighing 1 grain has a resistance 
 of 0.2106 ohm and 20 feet of commercial copper wire weighing 150 
 grains has a resistance of 0.613 ohms, what is the percentage con- 
 ductivity of the latter as compared with pure copper ? 
 
 Ans. 91.6 per cent. 
 
 45. Sketch an arrangement by which a single line of wire can be 
 used by an operator at either end to signal to the other ; the condi- 
 tion of working being that whenever either operator is not sending 
 a message, his instrument shall be in circuit with the line wire 
 and out o/' circuit with the battery at his end. 
 
 46. Calculate, by Joule's law, the number of heat units developed 
 in a wire whose resistance is 4 ohms when a steady current of 0.14 
 ampere is passed through it for ten minutes. Ans. 11.2 units of heat. 
 
 47. A dynamo has an E. M. F. of 839 volts and an internal (or in- 
 terpolar) resistance of 10.9 ohms. Find the current strength when 
 the external resistance is 73 ohms. Ans. 10 amperes. 
 
 48. I have 48 cells, each of 1.2 volts E. M. F. and each of 2 ohms 
 internal resistance. What is the best way of grouping them together 
 when it is desired to send the strongest possible current through a 
 circuit whose resistance is 12 ohms? Ans. Group them three abreast. 
 
 49. The current from a certain dynamo (E. M. F. = 839.02 volts) 
 was sent through a series of 16 arc lamps each having a resistance 
 of 4.51 ohms. The line wire had a resistance of 0.8 ohm. The 
 current measured 10.04 amperes. What was the resistance of the 
 dynamo? Ans. 10.61 ohms. 
 
 50. Immediately after the discharge of a Leyden jar, the potential 
 of its knob is zero. It, however, begins to rise and soon has a value 
 that is a considerable part of the potential before discharge and with 
 the same sign. Explain this. 
 
 51. What three varieties of energy appear when a Leyden jar is 
 discharged ? 
 
 52. How many heat units (calories) will be developed by a 10 am- 
 pere current flowing through a coil of 50 ohms resistance in a quar- 
 ter of an hour ? Ans. 1,080 calories. 
 
REVIEW. 365 
 
 53. A current of 9 amperes worked an electric arc light and on 
 measuring the difference of potential between the two carbons by 
 an electrometer it was found to be 140 volts. What was the 
 amount of power absorbed in the arc? Ans. 1.69 H. P. 
 
 54. If the cells represented in Fig. 252 
 have each an internal resistance of 4 ohms, 
 what is the resistance of the external cir- 
 cuit, G, if the battery is working at its great- 
 est possible efficiency? Ans. 6 ohms. 
 
 55. The same strength of current that 
 will heat an inch of platinum wire to white- 
 ness will similarly heat a yard of the same 
 wire. Explain why it is necessary to use 
 more cells thus to heat a yard than it does 
 to heat an inch of the wire. 
 
 56. Five Daniel cells, each with an E. M. p IG 252. 
 F. or L.i volts and an internal resistance of 
 
 2.2 ohms are joined in series. The external circuit consists of 16743 
 feet of No. 14 copper wire (B. & S.) (See Appendix I.) (a.) What 
 is the resistance of the external circuit? (6.) What is the current 
 strength? Ans. (6.) 0.1 ampere. 
 
 57. Show that with an unlimited number of cells like that just 
 described, joined in series, the current cannot exceed 0.5 amperes. 
 
 58. What is the total energy of the current of the dynamo, operated 
 as described in Exercise 1, page 349 ? ^ g ( 8417.94 watts. 
 
 (11.28 horse-power. 
 
 59. Explain the use and construction of a relay. 
 
 60. Suppose 1000 incandescence lamps to be placed parallel in the 
 circuit of a dynamo. Each lamp has a hot resistance of 50 ohms 
 and requires a current of 1 ampere, (a.) What will be the current 
 strength developed by the dynamo? (6.) What is the resistance of 
 the lamp circuit, ignoring the resistance of the leading \vires ? (e.) 
 What is the necessary difference of potential between the binding 
 posts of the dynamo ? (d ) If the resistance of the dynamo itself is 
 0.005 ohm, what is the total E. M. F. ? (e.) How many watts will be 
 expended in each lamp? (/.) If 500 of the lamps be turned off 
 (open circuited), what will the resistance of the lamp circuit become ? 
 (g.) If the E. M. F. of the dynamo be kept constant by change of 
 speed or otherwise, what will be the current developed by the 
 dynamo with the 500 lamps? (h.) What will be the current then, 
 supplied to each lamp ? 
 
 Ans. (a.) 1000 amperes; (&.) 0.05 ohm ; (c.) 50 volts ; (d.) 55 volts; 
 (e-) 50; (/.) 0.1 ohm ; (#.) 523.81 amperes; (h.) 1.047 amperes, 
 
3G6 REVIEW. 
 
 HONORARY PROBLEMS. 
 
 61. Two incandescence lamps with resistances of 16.9 and 32 ohms 
 respectively were joined in series with a series of 40 similar voltaic 
 cells having a total resistance of 20 ohms. The current measured 
 1.16 amperes. What will be the strength of current that a series of 
 60 such cells will send through a series of four lamps having resist- 
 ances of 16.9, 82, 20 and 16 ohms respectively ? 
 
 Ans. 1.043 amperes. 
 
 62. What would have been the strength of current in this case if 
 the area of the battery plates had been doubled, all things else re- 
 maining the same ? Ans. 1.2 amperes. 
 
 63. It required 15.3 H. P. to drive a certain dynamo that had a 
 resistance of 10.5 ohms and developed a current of 10 amperes 
 through an external resistance of 73 ohms. (The " duty " of a dy- 
 namo is the ratio between the total electrical energy developed and 
 the work performed in turning the armature in the magnetic field). 
 What is the duty of the dynamo in question ? Ans. 73 per cent. 
 
 64. The " commercial efficiency " of a dynamo is the ratio be- 
 tween the electrical energy appearing in the external circuit and the 
 work performed in turning the armature in the magnetic field. The 
 energy expended in any part of the circuit will, of course, depend 
 upon the resistances of that part and of the whole circuit. What is 
 the commercial efficiency of the dynamo above mentioned ? 
 
 Ans. 64 per cent. 
 
VII. 
 
 SOUND. 
 
 ECTJON I. 
 
 V. 
 
 NATURE, REFRACTION AND REFLECTION 
 OF SOUND. 
 
 477. Definition of Sound. Sound is the mode 
 of motion that is capable of affecting the auditory 
 nerve. 
 
 (a.) The word sound is used in two different senses. It is often 
 used to designate a sensation caused by waves of air beating upon 
 the organ of hearing ; it is also used to designate these aerial waves 
 themselves. The former meaning refers to a physiological or 
 psychological process ; the latter to a physical phenomenon. If 
 every living creature were deaf there could be no sound in the 
 former sense, while in the latter sense the sound would exist but 
 would be unheard. The definition above considers sound in the 
 physical sense only. 
 
 478. Umlulations. In beginning the study of 
 acoustics, ic is very important to acquire a clear idea of 
 the nature of undulatory motion. 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 give his attention to a piece of 
 wood floating upon the water, he will notice that it merely 
 
368 NATURE OF SOUND. 
 
 rises and falls without approaching the shore. He may 
 thus be enabled to correct his erroneous idea of the onward 
 motion of the water. Again, he may stand beside a field 
 of ripening grain and, as the breezes blow, he will see a 
 series of waves pass before him. But if he observe care- 
 fully and reflect, he will see clearly that there is no move- 
 ment of matter 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 motion, but that motion is vibratory, not progres- 
 sive. The only thing that has an onward movement 
 is the pulse or wave, which is only a form or change 
 in the relative positions of the particles of the un- 
 dulating substance. 
 
 (a.) The motion of the wave must be clearly distinguished from 
 the motion of particles which constitute the wave. The wave may 
 travel to a great distance ; the journey of the individual particle is 
 very limited. 
 
 479. Wave Period. When a medium is traversed 
 by a series of similar waves, each particle is in a state of 
 continued vibration. These vibrations are alike, they 
 being as truly isochronous ( 143) as those of the pen- 
 dulum. The time required for a complete vibra- 
 tion is called ttie period, and is th& same for 
 all the particles. 
 
 480. Wave Length. In such a series of similar 
 waves, measuring in the direction in which the waves are 
 travelling, the distance from any vibrating particle to 
 the next particle that is in the same relative posi- 
 tion or " phase " is called a wave length. In the case 
 
NATURE OF SOUND. 
 
 369 
 
 of water waves, the distance from one crest to the next is 
 a wave length. (See First Prin. Nat. Phil, 321, a.) 
 
 481. Amplitude. Amplitude means the dis- 
 tance between the extreme positions of the vibrating 
 particle, or the length of its journey. As in the case of 
 the pendulum, amplitude and period are independent of 
 each other. Amplitude is also independent of wave length. 
 
 482. Relation of Period, Wave Length and 
 Velocity. During one period there will be one com- 
 plete vibration, and the wave will advance one wave length. 
 The velocity of the wave may be found by multiplying the 
 wave length by the number of vibrations per second. 
 Conversely, the wave length may be found by divid- 
 ing the velocity by the number of vibrations. 
 
 483. Cause of Sound. Ml sound may be traced 
 to the vibrations of some material body. When a 
 
 bell is struck, the edges of the 
 bell are set in rapid vibration, 
 as may be seen by holding a 
 card or finger nail lightly upon 
 the edge. The particles of the 
 bell strike the adjacent parti- 
 cles of air, these pass the 
 motion thus received on to the 
 air particles next beyond, and 
 these to those beyond. 
 
 (a.) That sound is due to vibra- 
 tory motion may be shown by nu- 
 merous experiments. Holding one 
 end of a straight spring, as a hick- 
 FIG. 253. ory stick, in a vise, pull the free 
 
 ' 3) 
 
370 NATURE OF SOUND. 
 
 end to one side and let it go. Elasticity will return it to its position 
 of rest, kinetic energy will carry it beyond, and so on, a vibratory 
 motion being thus produced. When the spring is long, the vibra- 
 tions may be seen. By lowering the spring in the vise, the vibrating 
 part is shortened, the vibrations reduced in amplitude and increased 
 in rapidity. As the spring is shortened, the vibrations become 
 invisible but audible, showing that a sufficiently rapid vibratory 
 \notion may produce a sound. 
 
 (&.) Suspend a pith ball by a thread so that it shall hang lightly 
 against one prong of a tuning-fork. When the fork is sounded, the 
 pith ball will be thrown off by the vibrations of the prongs. Other 
 illustrations of the same truth will be observed as we go on. 
 
 (c.) The vibrations of a tuning-fork may be represented in the 
 following manner : A glass plate which has been blackened by 
 holding it in a petroleum flame is arranged so as to slide easily in 
 the grooved frame F. A pointed piece of metal is attached to one 
 
 FIG. 254. 
 
 of the prongs of the fork. When the fork is made to vibrate, the 
 point placed against the smoked plate and the plate drawn along 
 rapidly in the grooves, the point traces on the glass an undulating 
 line which represents fairly the vibratory movement of the prong. 
 
 484. Propagation of Sound. Sound is ordi- 
 narily propagated 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 motion to the particles of 
 the next layer, and so on until the particles of the last 
 'ayer strike upon the drum of the ear. 
 
 (a.) This idea is beautifully illustrated by Prof. Tyndall. He 
 
NATURE OF SOUND. 
 
 371 
 
 imagines five boys placed in a row as shown in Fig. 255. " I sud- 
 denly push A ; A pushes B and regains his upright position ; B 
 pushes ; pushes 
 D ; D pushes E ; 
 each boy after the 
 transmission of the 
 push, becoming him- 
 self erect. E, hav- 
 ing nobody in front, 
 is thrown forward. 
 Had he been stand- 
 ing on the edge of 
 a precipice he would 
 
 have fallen over; had FiG 255. 
 
 he stood in contact 
 
 with a window, he would have broken the glass ; had he been close 
 to a drum-head, 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." (See First Prin., Exps. 141-144.) 
 
 485. Sound Waves. The layers of air are crowded 
 more closely together by each outward vibration of the 
 
 m 
 
 188! 
 
 FIG. 256, 
 
 sounding body; a condensation of the air is thus produced 
 As the sonorous body vibrates in the opposite direction, 
 
372 
 
 NATURE OF SOUND. 
 
 the nearest layer of air particles follows it; a rarefaction 
 of the air is thus produced. A sound wave, therefore, 
 consists of two parts, a condensation and a rarefac- 
 tion. The motion of any air particle is backward and 
 forward in the line of propagation, and not " up and down " 
 across that line, as in the case of water waves. A series ol 
 complete sound waves consists of alternate condensations 
 and rarefactions in the form of continually increasing 
 spherical shells, at the common centre of which is the 
 sounding body. Any line of propagation of the sound 
 would be a radius of the sphere. 
 
 486. Sound Media. The air particles impart their 
 motion to other particles because of their elasticity. Any 
 elastic substance may become the medium for the 
 transmission of sound, but such a medium is neces- 
 sary. The elasticity of a body 
 may be measured by the re- 
 sistance it opposes to compres- 
 sion. The less the compres- 
 sibility, the 
 greater the 
 elasticity. 
 
 FIG. 
 
 (a.) That sound 
 is not transmit- 
 ted in a vacuum 
 is shown as fol- 
 
 lows: A lar S e 
 glass globe, pro- 
 vided with a stop-cock, contains a 
 small bell suspended by a thread. 
 When the air is pumped from the 
 globe and the globe shaken, no 
 sound is heard, although the clap- 
 per of the bell is seen to strike 
 
 FIG. 258. 
 
NATURE OF SOUND. 373 
 
 against the bell. Readmitting the air, and again shaking the globe, 
 the sound is plainly heard. (See Fig. 257.) 
 
 (6.) A small music box, or a clock-work arrangement for striking 
 a bell (Fig. 258), may be supported upon a thick cushion of felt or 
 cotton-batting, and placed under the capped receiver of an air-pump 
 When the receiver is exhausted, and the machinery started by the 
 rod g, the motion may be seen but hardly any sound will be heard. 
 If the support were perfectly inelastic and the exhaustion complete, 
 no sound would be audible. The experiment may be made more 
 perfect by filling the exhausted receiver with hydrogen and again 
 exhausting the gas. (See First Prin. Nat. Phil, Exps. 146-148.) 
 
 487. Velocity of Sound in Air. It is a familiar 
 fact that the transmission of sound is not instantaneous. 
 The blow of a hammer is often seen several second before 
 the consequent sound is heard ; steam escaping from the 
 whistle of a distant locomotive becomes visible before the 
 shrill scream is audible; the lightning precedes the thunder. 
 As we shall see further on, the time required for the 
 propagation of light through terrestrial distances is inap- 
 preciable. Hence the interval between the two sensations 
 of seeing and hearing is required for the transmission of 
 the sound. This interval being observed and the distance 
 being known, the velocity is easily computed. By such 
 means it has been found that the velocity of sound in 
 air at the freezing temperature is about 332 m., or 
 1090 ft. per second. There is some reason for believing 
 that very loud sounds travel somewhat more rapidly than 
 sounds of ordinary loudness. "With this exception it may 
 be said that, in a given medium, all sounds travel with the 
 same velocity. 
 
 488. Velocity in Other Media. The velocity 
 of sound depends upon two considerations the 
 elasticity and the density of the medium. It varies 
 directly as fijie square root of the elasticity, and 
 
374 NATURE OF SOUND. 
 
 inversely as the square root of the density. At the 
 freezing temperature, sound travels through oxygen with a 
 velocity of 1040 feet, and through hydrogen with a velocity 
 of 4164 feet per second. 
 
 -VS 
 
 (a.) It is a very common mistake to think that an increase of 
 density causes an increase of velocity. It is known, e.g., that sound 
 travels more rapidiy in water than in air ; that water is more dense 
 than air ; hence, say the superficial, sound travels most rapidly in 
 the densest bodies. It does not follow. Other things being equal, 
 the denser the medium, the less the velocity of the motion. A little 
 reflection will show that this must be so ; experiments will verify 
 the conclusion. In wave motion, the particles of the medium con- 
 stitute the thing that is moved. With a given expenditure of energy, 
 a number of light particles is moved more rapidly than an equal 
 number of heavy particles ( 157). 
 
 489. Effect of Temperature Upon Velocity. 
 
 An increase of the temperature of the air increases its 
 elasticity and decreases its density. We might, therefore, 
 expect sound to travel more rapidly in warm than in cold 
 air. Experiment confirms the conclusion. There is an 
 added velocity of about 1.12 feet for every Fah- 
 renheit degree, or of about 2 feet for every centi- 
 grade degree of increase of temperature. (The 
 freezing temperature is 32 F, or 0. ) 
 
 490. Momentary and Continuous Sounds. 
 
 A sound may be momentary or continuous. A momen- 
 tary sound consists of a single pulse produced by a single 
 and sudden blow. A continuous sound consists of a 
 rapid succession of pulses. The ear is so constructed 
 that its vibrations disappear very rapidly but the disap- 
 pearance is not instantaneous. If the motion imparted 
 
NATURE OF SOUND. 375 
 
 to the auditory nerve by each individual pulse con- 
 tinue until the arrival of its successor, the sound 
 will be continuous. 
 
 (a.) Momentary sounds may be produced by pounding with a 
 hammer, stamping with the foot, clapping the hands or drawing a 
 stick slowly along the pickets of a fence. Continuous sounds may 
 be produced by sawing boards or filing saws. They constitute the 
 rattling of wheels over a stony pavement, the roar of waves or the 
 crackling of a large fire. 
 
 491. Noise and Music. The sensation produced 
 by a series of blows coming at irregular intervals, is 
 unpleasant and the sound is called a noise. But when 
 the air waves come with sufficient rapidity to render the 
 sound continuous and with perfect regularity, the sensa- 
 tion is pleasant and the sound is said to be musical. 
 To secure this pleasing smoothness of music, the 
 sounding body must vibrate with the unerring reg- 
 ularity of the pendulum, but impart much sharper 
 and quicker shocks to the air. Every musical 
 sound has a well-defined period and wave length. 
 
 492. Elements of Musical Sounds. Musical sounds or 
 tones have three elements intensity or loudness, pitch, and timbre 
 or quality. The first two of these we shall consider at once, the 
 third, a little further on. 
 
 493. Intensity and Amplitude. Intensity or 
 loudness of sound depends upon the amplitude of 
 vibration. The greater the amplitude, ' the louder the 
 sound. 
 
 (a.) If the middle of a tightly-stretched cord or wire, as a guitar 
 string, be drawn aside from its position of rest and then set free, it- 
 will vibrate to and fro across its place of rest, striking the air and 
 sending sound waves to the ear. If the middle of the string be 
 drawn aside to a greater distance and then set free, the swing to 
 and fro will be increased, harder blows will be struck upon the air. 
 
376 
 
 NATURE OF SOUND. 
 
 and tlie air particles will move forward and backward through 
 greater distance. In other words, the amplitude of vibration has 
 been increased. But this change in the aerial wave produces a 
 change in the sensation. We still recognize the pitch to be the 
 same as before ; the tone is neither higher nor lower. We even 
 recognize it still as being produced by a guitar string. The only 
 Ufference is that the sensation is more intense ; we say that the 
 is louder. 
 
 494. Intensity and Distance. The intensity 
 of sound varies inversely as the square of the dis- 
 tance from the sounding body. Hence, the distance 
 to which a sound may be heard depends upon its intensity. 
 
 " !' j- : "' -T "' ! ;: .iMiiM.K'jiii ||, 
 
 FIG. 259. 
 
 495. Acoustic Tubes. If the sound wave be not 
 allowed to expand as a spherical shell, the energy of the 
 wave cannot be diffused. This means that its intensity 
 will be maintained. In acoustic tubes (Fig. 217) this 
 diffusion is prevented ; the waves are propagated in 
 
NATURE OF SOUND. 377 
 
 only one direction. In this way, sound may be trans- 
 mitted to great distances without considerable loss of 
 intensity. (See First Principles, Exp. 149.) 
 
 496. Pitch. The second element of a musical sound 
 !.s pitch, by which we mean the quality that constitutes 
 the difference between a low or grave tone and a high 
 tone. All persons are more or less able to recognize 
 differences in pitch. A person who is able to judge 
 accurately of the pitch of sounds is said to have a "good 
 ear for music." The pitch of a sound depends upon 
 the rapidity of vibration of the sounding body, 
 or, in other words, upon the rate at which sound pulses 
 follow each other. The more rapid the vibrations, the 
 higher the tone. 
 
 497. Experimental Proof of the Cause of 
 Pitch. That pitch depends upon 
 
 rapidity of vibration, may be roughly 
 
 shown by drawing the finger nail across 
 
 the teeth of a comb, slowly the first time 
 
 and rapidly the second time. It may be 
 
 shown more satisfactorily by means of 
 
 Savart's wheel, shown in Fig. 260. This 
 
 consists of a heavy metal ratchet-wheel, 
 
 supported on an iron frame and pedestal. The wheel may 
 
 be set in rapid revolution by a cord wound around the axis. 
 
 By holding a card against the teeth, when in rapid motion, 
 
 a shrill tone will be produced, gradually falling in pitch as 
 
 the speed is lessened. 
 
 (a.) 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 
 
378 NATURE OF SOUND. 
 
 sounding 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. 
 
 498. Relation between Pitch and Period. 
 
 Rate of vibration and period are reciprocals. If the 
 rate of vibration be 256 per second, the period is yj 01 a 
 second. The period may, therefore, be used to measure 
 the pitch ; the greater the period, the lower the pitch. 
 
 499. Relation between Pitch and Wave 
 Length. Since, in a given medium, all sounds travel 
 with the same velocity, the rate of vibration determines 
 the wave length. If the sounding body vibrate 224 times 
 per second, 224 waves will be started each second. If the 
 velocity of the sound be 1120 feet, the total length of these 
 224 waves must be 1120 feet, or the length of each wave 
 must be five feet. If another body vibrate twice as fast, 
 it will crowd twice as many waves into the 1120 feet; each 
 wave will be only two and a half feet long. Thus wave 
 length may be used to measure the pitch the greater the 
 wave length, the lower the pitch. 
 
 500. Refraction of Sound. We have a clear 
 idea of sound waves advancing as concentric, spherical 
 shells, but we are far more familiar with the idea of sound 
 advancing in definite straight lines. This idea is also cor- 
 rect, the lines being radii of the sphere. We may thus 
 speak of lines or "rays" of sound, meaning thereby the 
 direction in which the sonorous pulses are propagated. 
 The ray is necessarily perpendicular to the wave. When 
 the noise of the street is heard by a person in a closed room, 
 the sound must have passed from the air without to the 
 
NATURE OF SOUND. 379 
 
 solid matter of the walls, and from this to the air within. 
 When sound thus passes obliquely from one medium to 
 another, the rays are bent. This bending of a sound 
 ray is called refraction of sound. 
 
 5O1. A Sound Focus. Ordinarily, sound rays are 
 divergent. The sound is therefore continually diminishing 
 in intensity. By means of their refrangibility, they may 
 be made convergent. If the divergent rays strike the side 
 of a sack shaped like a double convex lens, made of two 
 Sims of collodion, or very thin India rubber, and filled 
 with carbonic acid gas (C0 2 ), their divergence will be di- 
 minished ; they may thus be made parallel, or even con- 
 vergent, after passing through the sack. At the point 
 where these rays converge their total energy will be con- 
 centrated, and the intensity of the sound be thus increased, 
 The point where the refracted rays intersect is called the 
 focus of the lens. The laws of refracted sound are the 
 same as those of refracted light, to be studied further on. 
 
 (a.) If a watch be hung near such a refractor, its ticking may be 
 heard by placing the ear at the focus on the other side of the sack ; 
 when the sack is re- 
 moved, the ticking is 
 no longer audible. A 
 few trials will enable 
 the experimenter to 
 determine the proper 
 positions for the watch, 
 the lens and the ear. 
 The refraction directs 
 to the ear all the en 
 
 ergy exerted upon the p IG< 26l 
 
 anterior surface of the 
 
 sack. This energy is sufficient to excite the sensation of hearing. 
 A little reflection will show that when the sack is removed, the 
 energy exerted upon the smaller surface of the tympanum at the 
 
380 NATURE OF SOUND. 
 
 greater distance is very much diminished. This lesser energy is 
 unable to excite the auditory nerve to action, and the ticking of the 
 watch is unheard. 
 
 502. Reflection of Sound. When a sound ray 
 strikes an obstacle, it is reflected in obedience to the prin- 
 ciple given in 97. This fact is turned to account in the 
 case of "conjugate reflectors" of sound. Fig. 262 repre- 
 sents the section of two parabolic reflectors mn and op. 
 It is a peculiarity of such reflect- 
 ors 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 F' . \L 
 
 Hence, two such reflectors may ^^ 
 be placed in such a position that FJG 
 
 sound waves starting from one 
 
 focus shall, after two reflections, be converged at the other 
 focus. Two reflectors so placed are said to be con- 
 jugate to each other. This principle underlies the 
 phenomena of whispering galleries. 
 
 (a.) " The great dome of St. Paul's Cathedral in London is so con- 
 structed that two persons at opposite points of the internal gallery, 
 placed in the drum of the dome, can talk together in a mere whisper. 
 The sound is transmitted from one to the other by successive reflec- 
 tions along the course of the dome." A similar phenomenon is 
 observable in the dome of the Capitol at Washington. 
 
 503. Experiment. At the focus of a curved re- 
 flector, place a watch or other suitable sounding body. 
 Directly facing it, but at a distance so great that the 
 ticking is unheard, place a similar reflector. When the 
 ear is placed at the focus of the second mirror, as shown in 
 Fig. 263, the ticking is plainly heard. 
 
NATURE OF SOUND. 
 
 381 
 
 FIG. 263. 
 
 (a.) In the experiment above described, it is plain that many of 
 the rays reflected by the first mirror are intercepted before they 
 reach the second mirror. This may be remedied, in part, by the 
 use of an ear-trumpet, the larger end being held at the focus of the 
 second reflector. The ear-trumpet may be a glass funnel, with a 
 piece of rubber tubing leading from its smaller end to the ear. The 
 experiment may be modified by using a single reflector, the watch 
 being placed a little further from the reflector. The proper positions 
 for the watch and the funnel are easily determined by experiment. 
 They are conjugate foci. 
 
 5O4. Echo. When a sound, after reflection, is 
 audible, it is called an echo. The distinctness with 
 which it is heard depends upon the distance of the ear 
 from the reflecting surface. A very quick, sharp sound 
 may produce an echo even when the reflecting surface is 
 not more than fifty or sixty feet away, but for articulate 
 sounds a greater distance is necessary. 
 
 (a.} Few, if any, persons can pronounce distinctly more than 
 about five syllables in a second. At the ordinary temperature, 
 sound travels about 1120 feet per second. In a fifth of that time 
 it would travel about 224 feet. If, therefore, the reflecting surface 
 be 112 feet distant, the articulate sound will go and return before 
 the next syllable is pronounced. The two sounds will not inter- 
 fere, and the echo will be distinctly heard. If the reflecting sur- 
 face be less than this distance, the reflected sound will return before 
 
382 KATURE Of SOUND. 
 
 the articulation is complete and confusedly blend with it. If th 
 reflector be 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. The echo may be heard 
 sometimes when the direct sound cannot be heard. 
 
 (&.) Suppose the speaker to stand 1120 feet from the reflecting 
 substance. If then he speak ten syllables in two seconds, the echo 
 of the first will return just as the last is spoken ; the echo of each 
 syllable will be distinct. But if he continues to speak, the direct 
 and the reflected sounds will become blended and confused. The 
 reflecting surface should be a large, vertical wall, or similar object, 
 as a huge rock. 
 
 (c.) When two opposite surfaces, as parallel walls, successively 
 reflect the sound, multiple echoes are heard. Sometimes an echo is 
 thus repeated 20 or 30 times. 
 
 EXERCISES. 
 
 1. If 18 seconds intervene between the flash and report of a gun, 
 what is its distance, the temperature being 82 F.? 
 
 2. What will be the length of the sound waves propagated through 
 air at a temperature of 15 C. by a tuning-fork that vibrates 224 
 times per second ? 
 
 3. State clearly the difference between a transverse and a longi 
 tudinal wave. 
 
 4. Determine the temperature of the air when the velocity of 
 sound is 1150 feet per second. 
 
 5. If A is 50 m. from a bell, and B is 70 m. from it, how will the 
 loudness of the sound as heard by B compare with the loudness as 
 heard by A ? 
 
 6. A shot is fired before a cliff, and the echo heard in six seconds. 
 The temperature being 15 C. find the distance of the cliff. 
 
 7. A certain musical instrument makes 1100 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 forma- 
 tion of sound waves four feet long, the velocity of sound being 
 1120 feet ? What will be the temperature at the time of the experi- 
 ment? 
 
 9. Taking the velocity of sound as 332 m., find the length of a 
 wave if there are 830 vibrations per second. 
 
 10. The waves produced by a man's voice in common conversation 
 are from eight to twelve feet long. If the velocity of sound be 
 
COMPOSITION OF SOVND WAVES. 
 
 1128 feet, find the corresponding numbers of vibrations of vocal 
 chords. 
 
 11. A person stands before a cliflf and claps his hands. In f of a 
 second he hears the echo. How far distant was the cliff? 
 
 Recapitulation. To be amplified by the pupil for 
 review. 
 
 DEFINITION AND CAUSE. 
 
 SOUND. 
 
 WAVES. 
 
 MEDIA. 
 
 VELOCITY 
 
 MOMENTARY. 
 
 CONTINUOUS. " 
 
 UNDULATIONS. 
 
 MODE OF PROPAGATION. 
 
 PERIOD AND LENGTH. 
 
 AMPLITUDE. 
 
 ( CONDENSATION. 
 PARTS.. J 
 
 ( RAREFACTION. 
 
 {AT FREEZING TEMPERATURE. . 
 AT OTHER TEMPERATURES. 
 IN OTHER MEDIA. 
 
 NOISY. 
 
 MUSICAL. 
 
 ( Cause. 
 
 LOUDNESS. < 
 
 ( Acoustic Tubes 
 PITCH Cause. 
 
 RELATION BETWEEN PITCH 
 AND PERIOD. 
 
 QUALITY OR TIMBRE. 
 
 REFRACTION AND ACOUSTIC FOCI. 
 
 f LAW. 
 
 REFLECTION.. \ WHISPERING GALLERIES. 
 1 ECHOES. 
 
384 
 
 THE TELEPHONE. 
 
 s 
 
 ECTfON IK 
 
 THE TELEPHONE AND PHONOGRAPH. COMPOSI- 
 TION AND ANALYSIS OF SOUNDS. 
 
 Note. Before beginning the study of the telephone, the pupil 
 should carefully review 468, 469. 
 
 5O5. The Telephone. This instrument is repre- 
 sented in section by Fig. 264. A is a permanent bar 
 
 magnet, around 
 one end of which 
 is wound a coil, 
 />, of fine copper 
 wire carefully 
 insulated. The 
 ends of this 
 coiled wire are 
 
 PIG. 264. 
 
 attached to the larger wires, (7(7, which communicate with 
 the binding posts, DD. In front of the magnet and coil 
 is the soft iron diaphragm, E, which corresponds to the 
 disc, 0, of Fig. 249. The distance between E and the 
 end of A is delicately adjusted by the screw, S. In front 
 of the diaphragm, is a wooden mouth-piece with a hole 
 about the size of a dime, at the middle of the diaphragm 
 and opposite the end of the magnet. The outer case is 
 made of wood or of hard rubber. The external appearance 
 of the complete instrument is represented by Fig. 265. 
 
THE TELEPHONE. 385 
 
 The binding posts of one instrument being connected by 
 wires with the binding posts of another at a distance, con- 
 versation may be carried on between 
 them. 
 
 5O6. Action of the Tele- 
 phone. When the mouth-piece is 
 brought before the lips of a person 
 who is talking, air 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 diaphragm induces an electric 
 current in the wire of B. These cur- 
 rents are transmitted to the coil of the 
 connected telephone, at a distance of, 
 perhaps, several miles, and there produce, in the diaphragm 
 of the instrument, vibrations exactly like the original 
 vibrations produced by the voice of the speaker. These 
 vibrations of the second diaphragm send out new air 
 waves that are very faithful counterparts of the original 
 air waves that fell upon the first diaphragm. The two 
 sets of air waves being alike, the resulting sensations pro- 
 duced in the hearers are alike. Not only different words 
 but also different voices may be recognized. The arrange- 
 ment being the same at both stations, the apparatus works 
 in either direction. No battery is necessary with this 
 arrangement. (See Appendix 0.) 
 
 (a.) The reproduced sound is somewhat feeble but remarkably 
 clear and distinct. The second telephone should be held close to 
 the ear of the listener. Sometimes there are, in the same circuit, 
 
386 
 
 THE TELEPHONE. 
 
 two or more instruments at each station, so that each operator maj 
 hold one to the ear and the other to the month ; or the listener may 
 place one at each ear. When the stations are a considerable dis 
 tance apart, one binding post of each instrument may be connected 
 with the earth, as in the case of the telegraph ( 444). 
 
 (b.) It is to be distinctly noticed that the sound waves are not 
 transmitted from one station to the other. " The air waves are 
 spent in producing mechanical vibrations of the metal ; these create 
 magnetic disturbances that excite electrical acuon in the wire, 
 and this again gives rise to magnetic changes that are still further 
 converted into the tremors of the distant diaphragm, and these 
 finally reappear as new trains of air waves that affect the listener." 
 
 TO THf caoufjo 
 
 FIG. 266. 
 
 5O7. The Transmitter. In practice, a transmit- 
 ter, shown at C in Fig. 266, is generally used. The vibra- 
 tions of the diaphragm of C, when acted upon by sound 
 waves, produce a varying pressure upon a carbon button 
 placed in the circuit of a galvanic battery, />. This vary- 
 
THE PHONOGRAPH. 38? 
 
 ing pressure results in a varying resistance to the passage 
 of the current through the button and, consequently, in 
 variations in the current itself. This varying current, 
 passing through the primary circuit of a small induction 
 coil in the box, C, induces a current in the secondary cir- 
 cuit thereof. This current, thus induced, flows over the 
 telephone wires and, at the other station, passes through a 
 telephone like that shown at B, which is held close to 
 the ear of the listener. The message is transmitted by C 
 at one station and received by B, of a similar instrument, 
 at the other station. 
 
 At each station is placed an electric bell, A, which may 
 be rung from the other station, for the purpose of at- 
 tracting attention. When the stations are a considerable 
 distance apart, one binding post of each instrument 
 may be connected with the earth, as in the case of the 
 telegraph. 
 
 (a.) In most of our cities, the telephones are connected by wire 
 with a central station, called a telephone exchange. The " Ex- 
 change " may thus be connected with the houses of hundreds of 
 patrons in all parts of the city or even in different cities. Upon re- 
 quest by telephone, the attendant at the central station connects 
 the line from any instrument with that running to any other instru- 
 ment. Thus, each subscriber may communicate directly with any 
 other subscriber to the exchange. 
 
 5O8. The Phonograph. This is an instrument 
 for recording sounds and reproducing them after any 
 length of time. (See Appendix P.) 
 
 (a.) The receiving apparatus consists of a mouth-piece and 
 vibrating disc like those of the telephone. At the back of the 
 disc is a short needle or style for recording the vibrations upon a 
 sheet of tin-foil moving under it. This tin-foil is placed upon a metal 
 cylinder about a foot (30 cm.) long. The cylinder has a spiral 
 
THE PHOXOGHAPB. 
 
 groove upon its curved surface and a similar thread upon its axis, 
 which turns in a fixed nut. As the cylinder is turned by a crank, 
 the threads upon the axis give the cylinder a lengthwise motion. 
 The style is placed in position over one of the tin-foil covered 
 grooves of the cylinder. As the cylinder revolves, a projection in 
 front of the style crowds the foil down into the groove. The needle 
 follows in the channel thus made and, as it vibrates, records a suc- 
 cession of dots in the tin-foil. These dots constitute the record. To 
 the naked eye they look alike, but the microscope reveals differences 
 corresponding to pitch, loudnees, and timbre. 
 
 (b.) To reproduce the sound, the style is lifted from the foil, the 
 cylinder turned back to its starting point, the style placed in the 
 beginning of the groove and the crank turned. The style passes 
 through the channel and drops into the first indentation ; the disc 
 follows it. The style rises and drops into each of the succeeding 
 indentations, the disc following its every motion with a vibration. 
 The original vibrations made the dots ; the dots are now making 
 similar vibrations. Sound waves made the original vibrations ; now 
 the reproduced vibrations create similar sound waves. The repro- 
 duced sounds are a little muffled but remarkably distinct, each of the 
 three qualities ( 492) being recognizable. The principle may be 
 applied to any implement or toy that makes a sound as well as to 
 the voice. Perfectly simple ; equally wonderful. 
 
 Experiment I. The effect of repeated impulses, each feeble 
 but acting at the right instant, may be forcibly illustrated as follows : 
 Support a heavy weight, as a bucket of coal, by a long string or 
 wire. To the handle of a bucket, fasten a fine cotton thread. By 
 repeated pulls upon the thread, each pull, after the first one, being 
 given just as the pendulum is beginning to swing toward you 
 from the effect of the previous pull, the weight may be made to 
 swing through a large arc, while a single pull out of time will 
 snap the thread. A little practice will enable you to perform the 
 experiment neatly. 
 
 Experiment 2. Vary the last experiment by setting the pendu- 
 lum in motion by well-timed puffs of air from the mouth or from a 
 hand bellows. The same principle is illustrated in the action of the 
 spring board, familiar to most boys, who know that the desired 
 effect can be secured only by " keeping time." Soldiers are often 
 ordered to "break step" in crossing a bridge, lest the accumulated 
 energy of many footfalls in unison break the bridge. 
 
 Experiment 3. Suspend several pendulums from a frame as 
 
SYMPATHETIC VIBRATIONS. 
 
 389 
 
 d c b 
 
 shown in Fig. 267. 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 vibra- 
 tions in the frame which will, in turn, trans- 
 mit them to the other pendulums. As the 
 successive impulses thus imparted by a keep 
 time with the vibrations of &, this energy ac- 
 cumulates 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 accumulation of energy 
 in them, for many of the impulses will act in 
 opposition to the motions produced by previous 
 impulses and tend to destroy them. 
 
 Experiment 4. Tune to unison two strings 
 upon the same sonometer (Fig. 268). Upon 
 one string, place two or three paper riders. 
 With a violin bow, set the other string- in vi- 
 bration. The sympathetic vibrations thus 
 produced will be shown by the dismounting 
 of the riders, whether the vibrations be audible JT IG 267 
 
 or not. Change the tension of one of the 
 
 strings, thus destroying the unison. Repeat the experiment and 
 notice that the sympathetic vibrations are not produced. See App. Q. 
 
 FIG. 268. 
 
 Experiment 5. Place, several feet apart, two tuning-forks 
 mounted upon resonant cases. The forks should have the same 
 tone and the cases should rest upon pieces of rubber tubing to pre- 
 vent thie transferrence of vibratory motion to and through the table, 
 
390 SYMPATHETIC VIBRATIONS. 
 
 Sound the first fork by rapidly separating the two prongs with a 
 rod or by rubbing it with a violin bow. Notice the pitch. At the 
 end of a second or two, touch the prongs to 
 stop their motion and sound. It will be found 
 that the second fork has been set in motion by 
 the repeated blows of the air and is giving 
 forth a sound of the same pitch as that orig- 
 inally produced by the first fork. Fasten, 
 by means of wax, a 3-cent silver piece or 
 other small weight to one of the prongs of 
 the second fork. An attempt to repeat the 
 FIG. 269. experiment will fail. When the two forks are 
 
 in unison, 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 predecessors. If the forks be not in unison, their periods 
 will be different and but few of the successive pulses can strike the 
 second fork in the same phase of vibration ; the greater number 
 will strike it at the wrong instant. 
 
 5O9. Sympathetic Vibrations. The string of a 
 violin may be made to vibrate audibly by sounding near 
 it a tuning-fork of the same tone. By prolonging a vocal 
 tone near a piano, one of the wires seems to take up the 
 note and give it back of its own accord. If the tone be 
 changed, another wire will give it back. In each case, 
 that wire is excited to audible action, which is able to 
 vibrate at the same rate as do the sonorous waves that set 
 it in motion. Thus the vibrations of the strings may pro- 
 duce sonorous waves and the waves, in turn, may produce 
 vibrations in another string. The most important feature 
 of the phenomenon is that the string absorbs only the 
 particular kind of vibration that it is capable of 
 producing. 
 
 Experiment 6. Strike a tuning-fork held in the hand. Notice 
 the feeble sound. Strike the fork again and place the end of tht? 
 
SOUNDING BOARDS. 391 
 
 handle upon a table. The loudness of the sound heard is remark 
 ably increased. 
 
 Experiment 7. 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. 
 
 51O. Sounding-Boards. In the case of 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 them- 
 selves. The strings are too thin to impart enough motion 
 to the air to be sensible at any considerable 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; the sounds are of shorter 
 duration. 
 
 (#.) This sounding apparatus usually consists of thin pieces of 
 wood that are capable of vibrating in any period within certain 
 limits. The vibrations of these large surfaces and of the enclosed 
 air produce the sonorous vibrations. The excellence of a Cremona 
 violin does not lie in the strings, which may have to be replaced 
 daily. The strings are valuable to determine the rate of vibration 
 that shall be produced ( 519). The excellence of the instrument 
 depends upon the sonorous character of the wood, which seems to 
 improve with age and use. 
 
 (6.) Similar remarks apply to the tuning-fork. Hence, for class 
 or lecture experiments, tuning-forks should be mounted as shown 
 in Fig. 269. 
 
 Experiment 8. Support horizontally, between two fixed sup- 
 ports, a soft cotton rope a few yards in length. With a stick, 
 strike the rope near one end a blow from below and a crest will 
 be formed as shown in Fig. 270. Vary the tension of the rope, if 
 
392 COINCIDENT SOUND WAVES. 
 
 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 
 
 B 
 
 FIG. 270. 
 
 By striking the rope from above, a trough may be started which 
 will be reflected as a crest. 
 
 Experiment 9. From A, start a trough. At the moment of its 
 reflection as a crest at B, start a crest at A as shown in Fig. 271. 
 The two crests will meet near the middle of the rope. The crest 
 at the point and moment of meeting results from two forces acting 
 
 FIG. 271. 
 
 in the same direction, consequently it will be greater than either 
 of the component crests. 
 
 511. Coincident Waves. In the case of water 
 waves, when crest coincides with crest the water reaches a 
 greater height. So. with sound waves, when condensation 
 coincides with condensation, this part of the wave will be 
 more condensed; when rarefaction coincides with rarefac- 
 tion, this part of the wave will be more rarefied. This 
 increased difference of density in the two parts of the 
 wave means increased loudness of the sound, because 
 there is an increased amplitude of vibration for the par- 
 ticles constituting the wave. 
 
 512. Reinforcement of Sound. This increased 
 intensity may result from the blending of two or more 
 series of similar waves in like phases, or from the union of 
 
RESONANCE. 
 
 393 
 
 direct and reflected waves in like phases. Under such 
 circumstances, one set of waves is said to reinforce the 
 other. The phenomenon i spoken of as a reinforce- 
 ment of sound. 
 
 Experiment 10. Hold a sounding tuning-fork over the mouth of 
 a glass jar, 18 or 20 inches - v 
 
 deep ; a feeble sound is 
 heard. On carefully pour- 
 ing 1 in water, we notice 
 that when the liquid 
 reaches a certain level, 
 the sound suddenly be- 
 comes much louder. The 
 water has shortened the 
 air column until it is able 
 to vibrate in unison with 
 the fork. If more water 
 be now poured in, the in- 
 tensity of the sound is 
 lessened. If a fork of dif- 
 ferent vibration be used, 
 the column of air that 
 gives the maximum reso- 
 nance will vary, the air 
 column becoming shorter 
 as the rate of vibration of 
 the fork increases. The 
 length of the air column 
 is one-fourth the length of the wave produced by the fork. 
 
 FIG. 272. 
 
 513. Resonance. Resonance is a variety of the 
 reinforcement of sound due to sympathetic vibrations. 
 The resonant effects of solids were shown in 510. 
 The resonance of an air column was well shown by the 
 last experiment. 
 
 (a.) Fig. 273 represents Savart's bell and resonator. The bell, 
 on being rubbed with the bow, produces a loud tone. The resonator 
 is a tube with a movable bottom. The length of the resonant air 
 column is changed by means of this movable bottom. The point 
 
394 
 
 RESONANCE. 
 
 at which the reinforcement of sound is greatest is easily found by 
 trial. If, when the sound of the bell has become hardly audible, 
 
 the tube be brought near, 
 the resonant effect is very 
 marked. 
 
 514. Helmholtz's 
 Resonators. Helm- 
 holtz, the German 
 physicist, constructed a 
 series of resonators, 
 each one of which re- 
 
 FIG. 273. 
 
 sounds powerfully to a single tone of certain pitch or 
 wave length. They are metallic vessels, nearly spherical, 
 having a large opening, 
 as at A in Fig. 274, 
 for the admission of 
 the sound waves. The 
 funnel-shaped projec- 
 tion at B has a small 
 opening and is inserted 
 in the outer ear of the 
 observer. 
 
 FIG. 274. 
 
 Experiment II. Using 
 
 the rope as described in Experiment 8, start a crest at A. At the 
 moment of its reflection at B as a trough, start a second crest at A. 
 The trough and crest will meet near the middle of the rope. The 
 
 FIG. 275. 
 
 rope at this time and place will be urged upward by the crest and 
 downward by the trough. The resultant effect of these opposing 
 forces will, of course, be equal to their difference. If crest and 
 trough exert equal forces, the difference will be zero. Consequently 
 
INTERFERENCE OF SOUND. 
 
 395 
 
 the motion of the rope at the meeting of crest and trough will be 
 little or nothing. Thus one wave motion may be made to destroy the 
 effect of another wave motion. 
 
 Experiment 12. 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 perfect 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 ear, the waves from one prong completely destroy the waves started 
 by the other. The interference is complete. 
 
 Experiment 13. Over a resonant jar, as shown in Fig. 272, slowly 
 turn a vibrating tuning-fork. In four positions of the fork we have 
 
 FIG. 
 
 loud, resonant tones ; in four other positions we have complete 
 interference. If, while the fork is in one of these positions of inter- 
 ference, a pasteboard tube be placed around one of the vibrating 
 prongs, a resonant tone is instantly heard ; the cause of the inter- 
 ference has been removed. (Fig. 276.) 
 
 515. Interference of Sound. If, while a tuning- 
 fork is vibrating, a second fork be set in vibration, the 
 
396 
 
 INTERFERENCE OF SOUND. 
 
 waves from the second must traverse the air set in motion 
 by the former. If the waves from the two forks be of 
 
 FIG. 277. 
 
 equal length, as will be the case when the two forks have 
 the same pitch, and the forks be any number of whole 
 wave lengths apart (Fig. 277), the two sets of waves will 
 unite in like phases (condensation with condensation, 
 etc.), and a reinforcement of sound will ensue. But -if the 
 second fork be placed an odd number of half wave lengths 
 behind the other, the two series of waves will meet in 
 opposite phases ; where the first fork requires a condensa- 
 tion, the second will require a rarefaction. The two sets 
 of waves will interfere, the one with the other. If the 
 waves be of equal intensity, the algebraic sum of these 
 component forces will be zero. The air particles, thus 
 acted upon, will remain at rest ; this means silence. In 
 
 FIG. 278. 
 
 Fig. 278, an attempt is made to represent this effect to 
 the eye, the uniformity of tint indicating the absence of. 
 condensations and rarefactions. Thus, by adding sound 
 to sound, both may be destroyed. This is the lead- 
 
BEATS. 397 
 
 ing characteristic property of wave motion. The 
 phenomenon here described is called interference 
 of sound. 
 
 (a.) The sound of a vibrating tuning-fork held in the hand is 
 almost inaudible. The feebleness results largely from interference. 
 As the prongs always vibrate in opposite directions at the same 
 time, one demands a rarefaction where the other demands a con- 
 densation. By covering one vibrating prong with a pasteboard 
 tube, the sound is more easily heard. 
 
 Experiment 14. In a quiet room, strike simultaneously one of 
 the lower white keys of a piano and the adjoining black key. A 
 series of palpitations or beats will be heard. 
 
 Experiment 15. Simultaneously sound the two tuning-forks 
 described in Experiment 5, one being loaded as there mentioned ; 
 the beats will be very perceptible. Replacing the 3-cent piece suc- 
 cessively by a silver half-dime and a dime, the number of beats will 
 be successively increased. 
 
 516. Beats. If two tuning-forks, A and B, vibrating 
 respectively 255 and 256 times a second, be set in vibration 
 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 reinforcement ; at 
 the middle of the next second another interference. This 
 peculiar palpitating effect is due to a succession 
 of reinforcements and interferences, and is called 
 a beat. The number of beats per second equals the dif- 
 ference of the two numbers of vibration. 
 
 (a.) If two large organ pipes, having exactly the same tone, be 
 simultaneously sounded, a low, loud, uniform sound will be pro- 
 duced. If an aperture be made in the upper part of one of the 
 walls of one of the pipes and closed by a movable plate, the tone 
 
398 VIBRATIONS OF STRINGS. 
 
 produced by the pipe may be changed at will. The more the aper- 
 ture is opened, the higher the pitch. In this manner, digliily raise 
 the pitch of one of the pipes. If the pipes be sounded in succession, 
 even a trained ear would probably fail to detect any difference. If 
 they be sounded simultaneously, the sound will be of varying loud- 
 ness, very marked jerks or palpitations being perceptible. 
 
 517. Practical Effect of Beats. The human 
 ear may recognize about 38,000 different sounds. If a 
 string, for example, vibrating 400 times per second were 
 sounded, and one vibrating 401 times per second were 
 subsequently sounded, the ear would probably fail to detect 
 any difference between them. But if they were sounded 
 simultaneously, the presence of one beat each second would 
 clearly indicate the difference. Unaided by the beats, the 
 ear can detect about one per cent, of the 38,000 sounds 
 lying within the range of the human ear. Beats are, 
 therefore, very important to the tuner of musical instru- 
 ments. To bring two slightly different tones into unison, 
 he has only to tune them so that the beats cease. 
 
 518. Vibrations of String's. The laws of musical tones 
 are most conveniently studied by means of stringed instruments. 
 In the violin, etc., the strings are set in vibration by bowing them. 
 The hairs of the bow, being rubbed with rosin, adhere to the string 
 and draw it aside until slipping takes place. In springing back, 
 the string is quickly caught again by the bow and the same action 
 repeated. In the harp and guitar, the strings are plucked with the 
 finger. In the piano, the wires are struck by little leather-faced 
 hammers worked by the keys, The vibrations of the string, and 
 consequently the pitch, depend upon the string itself. The manner 
 of producing the vibrations has no effect upon the pitch. 
 
 519. Laws of the Vibrations of Strings. 
 
 The following are important laws of musical strings: 
 (1.) Other conditions being the same, the number of 
 
VIBRATIONS OF STRINGS. 399 
 
 vibrations per second varies inversely as the length of the 
 string. 
 
 (2.) Other conditions being the same, the number of 
 vibrations per second varies directly as the square root of 
 the stretching weight, or tension. 
 
 (3.) Other conditions being the same, the number 01 
 vibrations per second varies inversely as the square root of 
 the weight of the string per linear unit. 
 
 (a.) All of these laws may be roughly illustrated by means of a 
 violin. The length of the string may be altered by fingering ; the 
 tension may be changed by means of the screws or keys ; the effects 
 of the third law may be shown by the aid of the four strings. 
 
 (&.) For the illustration of these laws, the sonometer, shown in 
 Fig. 279, is generally used. The length of the string is determined 
 
 FIG. 279. 
 
 by the two fixed bridges, or by one of them and the movable bridge 
 which may be employed for changing the length of the vibrating part 
 of the string ; the tension is regulated by pegs or by weights that 
 may be changed at pleasure ; the third law may be verified by using 
 different strings of known weights. Iron and platinum wires of the 
 same diameters are frequently used for this purpose. (Appendix Q.) 
 (c.) From these laws it follows, for example, that a string of half 
 the length, or four times the tension, or one-fourth the weight of a 
 given string will vibrate just twice as fast as the given string, i.e., 
 twice as fast on account of any one, of these three variations. A 
 string of one-third the length, or nine times the tension, or one 
 ninth the weight of a given string, will vibrate three times as fast 
 as the given string ; and so on, 
 
400 THE MUSICAL SCALE. 
 
 520. The Musical Scale. Starting from any 
 arbitrary tone or absolute pitch, the voice rises or falls in 
 
 a manner very pleasing to the ear, by eight steps or inter- 
 vals. The whole series of musical tones may be divided 
 into octaves, or groups of eight tones each, the relation 
 between any two members of one group being the same as 
 the relation between the corresponding members of any 
 other group. The eighth of the first group becomes the 
 first of the second. The intervals between the successive 
 tones are not the same, as will be seen from the next 
 paragraph. 
 
 521. Relative Numbers of Vibrations. A 
 
 string vibrating half as rapidly as a given string, will give 
 its octave below ; one vibrating twice as rapidly, its octave 
 above. The ratio of the number of vibrations correspond- 
 ing to the interval of an octave is, therefore, 1:2. The 
 relative number of vibrations corresponding to the tones 
 that constitute the major diatonic scale (gamut) are as 
 follows : 
 
 
 Relative Names, - - - 1, 2, 3, 4, 5, 6, 7, 8. 
 
 Absolute Names, - - C, D, E, F, G, A, B, C. 
 
 Syllables, - do, re, mi, fa, sol, la, si, do. 
 
 Relative Numbers of Vibrations, \, f , , |, f , f , - 1 /, 2. 
 
 24, 27, 30, 32, 36, 40, 45, 48. 
 
 522. Absolute Numbers of Vibrations. 
 
 Knowing the number of vibrations that constitute the 
 tone called do, the absolute number of vibrations of any 
 of the other tones of the scale may be obtained by multi- 
 plying the number of vibrations of do by the ratio between 
 it and that of the given tone, as shown above. Thus, if C 
 
ABSOLUTE PITCH. 401 
 
 have 256 vibrations per second, G will have 256 x f = 384 
 vibrations per second ; its octave will have 512 ; the fifth 
 of its octave will have 512 x f 768. If F be given 352 
 vibrations, C will have 352 -j- ^ = 264. Thus, knowing C, 
 any given tone may have its number of vibrations deter- 
 mined by multiplying by the proper ratio. 
 
 523. Absolute Pitch. The number of vibrations 
 constituting the tone called is purely arbitrary. The 
 assignment of 256 complete vibrations to middle G is com- 
 mon, but the practice of musicians is not uniform. A 
 certain tuning-fork deposited in the Conservatory of Music 
 at Paris is the standard for France ; it assigns 261 vibra- 
 tions per second to middle C. The standard tuning-fork 
 adopted by English musicians and deposited with the 
 Society of Arts in London, gives 264 vibrations to middle 
 C. Multiplying the numbers in the last line of 521 by 
 11, we shall have the absolute numbers of vibration for the 
 several tones of the gamut corresponding to this standard. 
 
 (a.) Whatever be the standard thus adopted, an instrument will 
 be in tune when the relative number of vibrations is correct. The 
 string that produces the tone G must always vibrate three times 
 while the one producing C vibrates twice, or 36 times, while the 
 latter vibrates 24 times. While the string yielding D vibrates 27 
 times, the string yielding B must vibrate 45 times ; and so on. 
 
 (&.) Middle G is the tone sounded by the key of a piano at the left 
 of the two black keys near the middle of the key-board. It is 
 designated by Ci. (See Exp. 16, p. 404.) Its octaves below and above 
 are designated as follows : 
 
 CL 2 , CLi, 0, Ci, C 2 , Cs, G,. 
 
 524:. Fundamental Tones and Overtones. 
 
 A string may vibrate transversely as a whole, or as inde- 
 pendent segments. Such segments will be aliquot parts 
 of the whole string and separated from each other by points 
 
402 FUNDAMENTALS AND HARMONICS. 
 
 of no motion, called nodes or nodal points. The tone 
 produced by the vibrations of the whole length of 
 a string is called its fundamental tone. The tones 
 produced by the vibrations of the segments of a 
 string are called its overtones or harmonics. 
 
 (a.) The fact that a string may thus vibrate in segments, with the 
 further fact that a string, or other sounding body, can hardly be made 
 to vibrate as a whole without vibrating in segments at the same time, 
 furnishes a means of explaining quality or timbre of sound. ( 492.) 
 
 525. Fundamental Tones. When a string 
 vibrates so as to produce its fundamental tone, its extreme 
 
 positions may be represented 
 by the continuous and the 
 FlG - 28a dotted lines of Fig. 280. 
 
 This effect is obtained by leaving the string free and 
 bowing it near one of its ends. If a number of little 
 strips of paper, doubled in the middle, be placed like riders 
 upon the string, and the string bowed as just described, 
 all of the riders will be thrown up and most of them off. 
 This shows that the whole string vibrates as one string ; 
 that there is no part of it between the fixed ends that is 
 not in vibration. 
 
 526. The First Overtone. If the string of the 
 sonometer be touched exactly at its middle with a finger, 
 or better, with a feather, a higher tone is produced when 
 the string is bowed. This higher tone is the octave of the 
 fundamental. The string now vibrates in such a way that 
 the point touched remains Own 
 
 at rest. Its extreme posi- ~ f ~~~~ ~~~^*~~~ ^ 
 
 tions may be represented FlG - 2Sl - 
 
 by the lines of Fig. 281. The point N is acted upon by 
 two equal and opposite forces ; it is urged to move both 
 
FUNDAMENTALS AND HARMONICS. 403 
 
 ways at the same time and, consequently, does not move 
 at all, but remains at rest as a node. The tone is due to 
 the vibrations of the two halves of the string, which thus 
 give the octave instead of the fundamental. The existence 
 of the node and segments will continue for some time after 
 the finger is removed. If riders be placed at (7, JVand Z), 
 the one at N will remain at rest while those at G and D 
 will probably be dismounted. 
 
 527. Higher Overtones. In like manner, if the 
 vibrating string be touched at exactly one-third, one-fourth 
 
 FIG. 282. 
 
 or one-fifth of its length from one end, it will divide into 
 three, four or five segments, with vibrations three, four or 
 five times as rapid as the fundamental vibrations. If 
 touched at one-third its length, as represented in Fig. 282, 
 the tone will be the fifth to the octave of the fundamental ; 
 
404 
 
 QUALITY OF SOUND. 
 
 if touched at one-fourth its length, the tone will be the 
 second octave above. Of course, any other aliquot part of 
 the length of the string may be used. In any case, the 
 experiment with riders may be repeated to indicate the 
 position of the segments and nodes. 
 
 528. Qnality or Timbre. As a sounding body 
 vibrates as a whole and in segments at the same time, the 
 fundamental and the harmonics blend. The resultant 
 effect of this blending of fundamentals and harmonics con- 
 stitutes what we call the quality or timbre of the sound. 
 We recognize the voice of a friend, not by its loudness nor 
 by its pitch, but by its quality. When a piano arid violin 
 sound the same tone, we easily distinguish the sound of 
 one from that of the other, because, while the fundamentals 
 are alike, the harmonics are different. Hence, the total 
 effects of the fundamentals and the harmonics, or the 
 qualities, are different. The possible combinations of fun- 
 damentals and harmonics, or forms of vibratory motion, 
 are innumerable. 
 
 Experiment 16. Take your seat before the key-board of a piano. 
 Press and hold down the key of "middle C," marked 1 in Fig. 283, 
 
 which represents part of the key -board. This will lift the damper 
 from the corresponding piano wire and leave it free to vibrate. 
 Strongly strike the key of C", 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 0' has died away, a swuid of higher pitch is heard. The tone 
 
ANALYSIS OP SOVtf&S. 405 
 
 Corresponds to the wire of 1, which wire is now vibrating. These 
 vibrations are sympathetic with those that produced the first over- 
 tones of the wire that was struck. These vibrations in the wire of 
 1 prove the presence of the first overtone in the vibrating wire of C'. 
 (See 509.) 
 
 In similar manner, successively raise the dampers from the wires 
 of 2, 3, 4, 5, 6 and 7, striking C' each time. These wires will accu- 
 mulate the energy of the waves that correspond to the respective 
 overtones of the wire of C' and give forth each its 'proper tone. 
 Thus we analyze the sound of the wire of C' and prove that at least 
 seven overtones are blended with its fundamental. 
 
 Some of these tones of higher pitch, thus produced by vibrations 
 sympathetic with the vibrations of the segments of the wire of C", 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. 
 
 529. Simple and Compound Tones. The 
 
 well trained ear can detect several sounds of different 
 pitch when a single key of a piano is struck. In other 
 words, the sound of a vibrating piano wire is a compound 
 sound. The sound of a tuning-fork is a fairly good 
 example of a simple sound. Simple sounds all have the 
 same quality, differing only in loudness and pitch. 
 
 (a.) A series of Helrnholtz's resonators enables the student of 
 acoustics to analyze any compound sound. Each component tone 
 may be reproduced by a tuning-fork of appropriate pitch. By 
 sounding simultaneously the necessary number of forks, each of 
 proper pitch and with appropriate relative intensity, Helmholtz 
 showed that the sounds of musical instruments, including even the 
 most wonderful one of all (the human voice), may be produced 
 synthetically. 
 
 530. Classes of Musical Instruments. 
 
 Musical instruments may be divided into two classes, 
 stringed instruments and wind instruments. The sounds 
 sent forth by stringed instruments are due to the regular 
 vibrations of solids ; those sent forth by wind instruments, 
 
406 MUSICAL 
 
 to the regular vibrations of columns of air confined in 
 sonorous tubes. 
 
 531. Sonorous Tubes. The material of which a 
 sonorous tube is made does not affect the pitch or loud- 
 ness of the sound, but does determine its timbre or 
 quality. Sonorous tubes are called mouth pipes or reed 
 pipes, according to the way in which the column of air is 
 made to vibrate. 
 
 532. Stopped Pipes. A. sonorous tube may have 
 one end stopped or both ends open. In either case, the 
 tones are due to waves of condensation and rarefaction 
 transmitted through the length of the tube. In a stopped 
 pipe, the air particles at the closed end have no oppor- 
 tunity for vibration ; this end of the tube is, therefore, a 
 node. The mouth of the tube affords opportunity for the 
 greatest amplitude. The length of such a pipe is one- 
 fourth the wave length of its fundamental tone. 
 
 533. Open Pipes. In an open pipe, the ends 
 afford opportunity for the greatest amplitude ; the node 
 will fall at the middle. The air column will now equal 
 one-half the wave length; the tone will be an octave 
 higher than that produced by a stopped pipe of the same 
 length. 
 
 534. Organ Pipes. The organ pipe affords the 
 best illustration of mouth pipes. Fig. 284 represents the 
 most common kind of organ pipe, which may be of wood 
 or metal, rectangular or cylindrical. The air current from 
 the bellows enters through P, passes into a small chamber, 
 
MUSICAL INSTRUMENTS. 
 
 407 
 
 emerges through the narrow slit, i, and escapes in puffs 
 
 between a and I, the two lips of the mouth. The puffs 
 
 are due to the fact that the air cur- M 
 
 rent from i strikes upon the bevelled 
 
 lip, a, and breaks into a flutter. The 
 
 puffing sound thus produced consists 
 
 of a confused mixture of many faint 
 
 sounds. The air column of the pipe 
 
 can resound to only one of these 
 
 tones. The resonance of the air 
 
 column, brought about in this way, 
 
 constitutes the tone of the pipe. 
 
 (a.) We see, from the above, that it 
 makes little difference how the pulses of 
 air are produced. A vibrating tuning-fork 
 held at the mouth of a pipe of the same 
 pitch is enough to make the pipe sound 
 forth its tone. The production of the tone 
 is strictly analogous to the phenomena 
 mentioned in 513. 
 
 535. Reed Pipes. A simple 
 reed pipe may be made 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 
 
 FIG. 285. 
 
 from the knot, cut inward about a quarter of the straw's 
 diameter; turn the knife-blade flat and draw it toward 
 the 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 
 
408 MUSICAL INSTRUMENTS. 
 
 r and s and the breath driven through the apparatus, the 
 reed vibrates and thus produces vibrations in the air col- 
 umn of the wheaten pipe. Notice the pitch of the musical 
 sound thus produced. Cut off two inches from the end 
 of the pipe at s. Blow through the pipe as before and 
 notice that the pitch is raised. Cut off, now, two inches 
 more, and upon sounding* the pipe the pitch will be found 
 to be still higher. We thus see that the pipe and not the 
 reed determines the pitch. In these three cases we had 
 the same reed which was obliged to adapt itself to the 
 different vibrations of the different air columns. 
 
 (a.) It will be easily seen how reeds may be used in musical 
 instruments. The accordeon, clarionet and vocal apparatus are reed 
 instruments. 
 
 536. Effect of Lateral Openings. Certain 
 
 wind instruments, like the flute, fife and clarionet, have 
 holes in the sides of the tube. On opening one of these 
 holes, opportunity is given for greatest amplitude at that 
 point. This changes the distribution of nodes, affects the 
 length of the segments of the vibrating air columns, and 
 thus determines the wave length or pitch of the tone. 
 
 EXERCISES. 
 
 1. If a musical sound be due to 144 vibrations, to how many vibra- 
 tions will its 3d, 5th and octave, respectively, be due? 
 
 2. Determine the length of a tube open at both ends that can 
 resound to the tone of a tuning-fork vibrating 512 times a second. 
 
 3. A certain string vibrates 100 times a second, (a.) Find the 
 number Of vibrations of a similar string, twice as long, stretched 
 by the same weight. (6.) Of one half as long. 
 
 4. A certain string vibrates 100 times per second. Find the num- 
 ber of vibrations 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 musical string vibrates 200 times a second. State (a.) what 
 
EXERCISES. 409 
 
 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. 
 
 6. A tube open at both ends is to produce a tone corresponding 
 (a.} to 32 vibrations per second. Taking the velocity of sound as 
 1120 ft., find the length of the tube. (6.) If the number of vibra- 
 tions be 4480, find the length of the tube. 
 
 7. (a.) Find the length of an organ pipe whose waves are four 
 feet long, the pipe being open at both ends. (&.) Find the length, 
 the pipe being closed at one end. 
 
 8. 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. 
 
 9. If two tuning-forks vibrating respectively 256 and 259 times 
 per second be simultaneously sounded near each other, what phe- 
 nomena would follow ? 
 
 10. 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, (a.) Are the strings in unison? (&.) If not, what is 
 the rate of vibration of the second string ? 
 
 11. If a tone be produced by 256 vibrations per second, what num- 
 bers will correspond to its third, fifth and octave respectively ? 
 
 12. If a tone be produced by 264 vibrations per second, what 
 number will represent the vibrations of the tone a fifth above its 
 octave. Ans. 792. 
 
 Recapitulation. In this section we have considered 
 the Telephone and Phonograph ; Sympa- 
 thetic Vibrations and the Resonance of 
 Sounding Boards and Air Columns ; Re- 
 inforcement and Interference of superposed 
 waves, including the phenomenon of Beats ; Vi- 
 brating Strings ; The Musical Scale and its 
 relation to Number of Vibrations and Pitch ; 
 Timbre and its dependence upon Fundamentals 
 and Harmonies ; Simple and Compound 
 Tones, their Synthesis and Analysis; Musi- 
 cal Instruments 
 
410 REVIEW. 
 
 REVIEW QUESTIONS AND EXERCISES. 
 
 1. (a.) Define sound ; (b.) give its cause; (c.) mode of propagation 
 and (d.) velocity. 
 
 2. (a.) Give the rate at which sound is transmitted in air. (6.) 
 How is it affected by temperature? (c.) Give the law of Reflection. 
 (d.) How may it be illustrated? 
 
 3. (a.) What is capillary attraction ? (b.) Give three illustrations 
 of the importance of capillary action in the operations of nature. 
 
 4. (#.) Describe an experiment showing the expansibility of the 
 air. (b.) Give the laws of the Pendulum. 
 
 5. (a.) On what does the loudness of sound depend? (6.) How 
 may the pitch of strings be varied ? (c.) Give the relative number 
 of vibrations in the major diatonic scale and (d.) find the number of 
 vibrations for A2. 
 
 6. (a.) Represent by a diagram, a lever of the first class, in which 
 one pound will balance five. (&.) Give the laws of falling bodies. 
 
 7. Explain the Artesian well by a diagram. 
 
 8. (a.) What will be the momentum of a ball weighing two ounces 
 after falling 4^ seconds ? (b.) A stone weighing 20 Ib. on the sur- 
 face of the earth, would weigh how much at an elevation of 2000 
 miles from the surface ? 
 
 9. Define (a.} wave length ; (6.) wave period ; (c.) amplitude of 
 vibration ; (d.) phase of a vibrating particle. 
 
 10. (a.) What would be the effect of making a small hole at the 
 highest point of a siphon in action ? (6.) What effect upon the action 
 of a siphon would be produced by carrying it up a mountain? (c.) 
 What effect would follow if the atmosphere were suddenly to become 
 denser than the liquid being moved ? 
 
 11. Describe (a.) a complete sound wave and (6.) its manner of 
 propagation, (c.) How does the transmission of sound through a 
 smooth tube differ from its transmission through the open air ? 
 
 12. Give the laws for pressure of liquids and explain each by 
 some fact or experiment. 
 
 13. (a.) Distinguish clearly between noise and music. (6.) What 
 is meant by timbre ? (c.) By pitch ? 
 
 14. Give three examples of musical sounds that agree in one 
 and differ in two elements or characteristics, making a different ele- 
 ment agree each time. 
 
 15. Give three examples of musical sounds that differ in one and 
 agree in two elements, making a different element differ each time. 
 
REVIEW. 411 
 
 16. (a.) What are sympathetic vibrations ? (&.) How may they be 
 produced? (c.) What are beats ? (d.) How may they be produced 1 
 
 17. (a.) What is Archimedes' Principle ? (b.) How is it applied in 
 finding the specific gravity of a solid ? 
 
 18. How much water per hour will be delivered from an orifice of 
 2 inches area 49 feet below the surface of a tank kept full ? 
 
 19. Describe the telephone. 
 
 20. (a.) Describe the electrophorus. (6.) Explain its action. 
 
 21. (a.) Describe an organ pipe. (&.) Make a reed pipe. 
 
 22. (a.) Explain the charging of the Leyden jar; (b.) when 
 charged, what is the electric condition of the outside and inside of 
 the jar? 
 
 23. (a.) A body falls for six seconds ; find the distance traversed 
 in the last two seconds of its fall, (b.) How far will a body fall in 
 T a of a second beginning at the end of four seconds? (c.) Explain 
 the " kick " of a gun. 
 
 24. (a.) Show that if, in an Attwood's machine, one weight be f 
 as heavy as the other, its increment of velocity will be that of a 
 freely falling body, (b.) That if the lighter weight be f of the 
 heavier, its increment of velocity will be | g. 
 
 25. A telegraph line from New York City to Meadville, Pa., is 510 
 miles long. The wire has a resistance of 4 ohms per mile. There 
 are, on this line, 19 relays of 150 ohms each and one repeater of 250 
 ohms. The current is supplied by a series of 40 gravity cells with 
 an E. M. F. of 1 volt each. Suppose that the battery and the 
 ground and other connections offer a resistance of 574 ohms. What 
 is the strength of the current ? Ans. 7 milliamperes. 
 
 26. Explain the electrical phenomena described in 323 (b). 
 
 27. An arc lamp has a difference of potential of 36 volts between 
 the carbon tips. The resistance of the arc is 3.6 ohms, (a.) What 
 is the current strength ? (b.) What amount of heat is developed in 
 the arc per second. 
 
 Ans. (a.) 10 amperes ; (b.) 86.4 lesser calories. 
 
 28. A coil of fine wire with a resistance of 46.64 ohms was placed 
 in 100 grams of ice-cold water. A current from a varies of 50 
 voltaic cells was sent through the wire for 10 minutes. Each cell 
 had an E. M. F. of 1 volt and a resistance of 6 ohms. [The water 
 would not short circuit the wire. See Appendix K (2)]. (a.) What 
 was the current strength ? (6.) Find the rise of temperature of the 
 water assuming that no heat is lost by the water. 
 
 Ans. (a.) 0.144 amperes ; (6.) 1.39 C. 
 
H EAT. 
 
 X8>MECTK)N I. 
 
 J\. 
 
 TEMPERATURE, THERMOMETERS, EXPANSION. 
 
 537, Introductory Quotation." There are other forces 
 besides gravity, and one of the most active of these is chemical affin- 
 ity. Thus, for instance, an atom of oxygen has a very strong attrac- 
 tion for one of carbon, and we may compare these two atoms to the 
 < arth and a stone lodged upon the top of a house. Within certain 
 limits, this attraction is intensly powerful, so that when an atom of 
 carbon and one of oxygen have been separated from each other, we 
 have a species of energy of position just as truly as when a stone 
 has been separated from the earth. Thus by having a large quan- 
 tity of oxygen and a large quantity of carbon in separate states, we 
 are in possession of a large store of energy of position. When we 
 allowed the stone and the earth to rush together, the energy of 
 position was transformed into that of actual motion ( 159), and we 
 should therefore expect something similar to happen when the 
 separated carbon and oxygen are allowed to rush together. This 
 takes place when we burn coal in our fires, and the primary result, 
 as far as energy is concerned, is the production of a large amount of 
 heat. We are, therefore, led to conjecture that heat may denote a 
 motion of particles on the small scale just as the rushing together of 
 the stone and the earth denotes a motion on the large. It thus 
 appears that we may have invisible molecular energy as well as 
 visible mechanical energy." Balfour Stewart. 
 
 538. What is Heat tHeat is a form of en- 
 ergy. It consists of vibratory motions of the mole- 
 cules of matter or results from such motions, and 
 
TEMPERATURE. 413 
 
 gives rise to the well known sensations of warmth 
 and cold. By means of these effects upon the animal 
 body it is generally recognized. Being a form of energy, 
 it is a measurable quantity but not a material substance. 
 
 539. What is Temperature IThe tempera- 
 ture of ct body is its state considered with refer- 
 ence to its ability to communicate heat to other 
 bodies. It is a term used to indicate how hot or cold 
 a body is. When a body receives heat its temperature 
 generally rises, but sometimes a change of condition 
 ( 53) results instead. When a body gives up heat, its 
 temperature falls or its physical condition changes. 
 
 540. An Unsafe Standard. When we put a very warm 
 hand into water at the ordinary temperature, we say that the water 
 is cold. If another person should put a very cold hand into the 
 Bame water he would say that the water is warm. If a person place 
 one hand in water freezing cold and the other hand in water as hot 
 as he can endure, and, after holding them there some time, plunge 
 them simultaneously into water at the ordinary temperature, the 
 hand from tlje cold water feels warm while the hand from the hot 
 water feels cold. These experiments show that bodily sensations 
 cannot be trusted to measure this form of energy that we call heat. 
 
 541. Thermometers. An instrument for 
 measuring temperature is called a thermometer. 
 The mercury thermometer is the most common. Its ac- 
 tion depends upon the facts that heat expands mercury 
 more than it does glass, and that when two bodies of dif- 
 ferent temperatures are brought into contact, the warmer 
 one will give heat to the colder one until they have a com- 
 mon temperature. 
 
 542. Graduation of Thermometers. Ther- 
 mometers are graduated in different ways, but in all cases 
 there are two fixed points, viz., the freezing and the boiling 
 
414 
 
 TEMPERATURE. 
 
 FIG. 286. 
 
 points of water ; or, more accurately, the temperature of 
 melting ice and the temper- 
 ature of steam as it escapes 
 from water boiling under 
 a pressure of one atmos- 
 phere. 
 
 543. Determination 
 of the Freezing Point. 
 
 Ice in contact with water cannot 
 be raised above a certain tem- 
 perature ; water in contact with 
 ice cannot be reduced below the 
 same temperature. Here, then, 
 is a temperature fixed and easily 
 produced. The thermometer is 
 placed in melting ice or snow 
 contained in a perforated vessel. 
 When the mercury column has come to rest, a mark is made on the 
 glass tube at the level of the mercury. This point is, for the sake 
 tf brevity, called the freezing point. 
 
 544. Determination of the Boiling Point. The 
 
 temperature of steam issuing from water boiling under any given 
 pressure is invariable. Fig. 287 represents a metal vessel in which 
 water is made to boil briskly. The thermom- 
 eter being supported as represented is sur- 
 rounded by the steam but does not touch the 
 water. That the steam may not cool before 
 it comes into contact with the thermometer, 
 the sides of the vessel are surrounded by what 
 is called a "steam-jacket." A bent tube open 
 at both ends and containing mercury in the 
 bend is sometimes added. When the mercury 
 stands at the same level in both arms, the 
 pressure upon the surface of the boiling liquid 
 is just equal to the external atmospheric pres- 
 sure, which should be 760 mm. When the 
 mercury column has come to rest, a mark is 
 made on the glass tube at the level of the 
 mercury. This point is, for the sake of 
 FIG. 287. brevity, called the boiling point, 
 
TEMPERATURE. 415 
 
 545. Thermometric Scales. There are two 
 ecales used in this country, the centigrade and 
 Fahrenheit's. For these scales, the fixed points, de- 
 termined as just explained, are marked as follows t 
 
 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 Fahrenheit's. Hence a change of 
 temperature of 5 0. is equal to a change of 9 F., 
 or an interval of one centigrade degree is equal to 
 FIG. 288. an i nterva l f -f of a Fahrenheit degree. 
 
 546. Thermometric Readings. To change 
 the readings of a centigrade thermometer to those of 
 Fahrenheit's, or vice versa, is a little more complicated 
 than to determine the relation between the intervals of 
 temperature. This complication arises from the fact that 
 Fahrenheit's zero is not at the freezing point but 32 de- 
 grees below. To reduce Fahrenheit readings to centigrade 
 readings, subtract 32 from the number of Fahrenheit de- 
 grees and multiply the remainder by j. 
 
 To reduce centigrade readings to Fahrenheit readings, 
 multiply the number of centigrade degrees by $ and add 33. 
 
 F. = lc. + 32. 
 5 
 
 (a.) Suppose that we desire to find the equivalent centigrade 
 reading for 50 P. Subtracting 32, we see that this temperature is 
 18 Fahrenheit degrees above the freezing point. But one Fahren- 
 heit degree being equal to jj of a centigrade degree, this temperature 
 
416 
 
 TEMPERA TUR E. 
 
 is f of 18, or 10 centigrade degrees above the freezing point. Henca 
 the reading will be 10 C. 
 
 (6.) Suppose that we desire to find the equivalent Fahrenheit 
 reading for 45 C. This, temperature is 45 centigrade degrees above 
 the freezing point, or 81 Fahrenheit degrees above the freezing 
 point. Hence the reading will be (81 + 32 =) 113 F. (See Fig. 288.) 
 
 (e.) The centigrade thermometer is the most convenient and is 
 adopted in all countries as the standard scale for scientific reference 
 Like the metric system, its general use in this country is probab]} 
 only a question of time. 
 
 Note. It is desirable that this class be provided with several 
 "chemical" thermometers; i. e., thermometers having the scale 
 marked on the glass tube instead of a metal frame. 
 
 547. Differential Thermometer. Leslie's dif- 
 ferential thermometer (Fig. 289) shows the difference in 
 temperature of two neighboring places by 
 
 the expansion of air in one of two bulbs. 
 These bulbs are connected by a bent glass 
 tube containing some liquid not easily 
 volatile. It is an instrument of simple 
 Donstruction (See Appendix, M.) and great 
 delicacy of action, but has been largely 
 superseded by the thermopile and galvan- 
 ometer (414,391). 
 
 548. Expansion. Heat consists 
 generally of molecular vibrations. "What- FIG. 289. 
 ever raises the temperature of a body 
 
 increases the energy with which the molecules of that 
 body swing to and fro. These molecules are too small ( 5), 
 and their range of motion too minute to be visible, and we 
 must call upon our imaginations to make good the defect 
 of our senses. We must conceive these invisible molecules 
 as held together by the force of cohesion, yet vibrating 
 to and fro. The more intense the heat, the greater the 
 
TEMPERA TURE. 
 
 417 
 
 energy of these molecular motions. Molecules thus vi- 
 brating must push each other further apart, and thus cause 
 the body which they constitute to expand. This expansion, 
 or increase of volume, is the first effect of heat upon 
 bodies. 
 
 (a.) Imagine, if possible, twenty -five quiet boys standing closely 
 crowded together. Upon the floor draw a chalk line enclosing the 
 group. If these boys be suddenly set shaking, as by the ague, they 
 will force some of their number over the chalk line. From the 
 motions of the individuals has resulted an expansion of the living 
 
 549. Expansion Illustrated. The expansion of 
 solids may be shown by a ball, which, at ordinary tempera- 
 tures, will easily pass through a 
 ring ; on heating the ball it will 
 no longer pass through the ring. 
 If the ball be cooled by plung- 
 ing it into cold water, it will 
 again pass through the ring 
 This illustrates the increase oi 
 volume or cubical expansion. 
 Sometimes the expansion in 
 length only is measured. This 
 is called linear expansion. Ex- 
 pansion is also illustrated in the 
 
 FIG. 290. compensation pendulum ( 149). 
 
 550. Unequal Expansion. Different substances 
 expand at different rates for the same change of temper- 
 ature. This may be shown by heating a bar made by 
 riveting together, side by side, two thin bars of equal size, 
 one of iron and one of brass, so that the compound bar 
 shall be straight at the ordinary temperature. As brass 
 
ilS TEMPERATURE. 
 
 expands and contracts more than iron, when the compound 
 bar is heated it will curve with the brass on the convex 
 eide ; when it is cooled, it will curve with the brass on the 
 concave side. 
 
 (a.) Glass and platinum expand nearly alike. In fact, the rates 
 of expansion are so nearly alike that platinum wires may be fused 
 into glass tubes, as is done in electrolysis apparatus and eudiometers. 
 If we attempt thus to fuse copper wire into glass, the glass will be 
 bi*ken during the unequal contraction from cooling. 
 
 551. Practical Applications of Expansion. The 
 
 energy of expansion and contraction of solids, when heating and 
 cooling, is remarkable. This expansion of metals by heat is 
 ulilized by coopers in setting hoops, by wheelwrights in setting 
 tires, and by builders in straightening bulging walls. When the 
 iron rails of our railways are laid, a small space is left between the 
 endb of each two adjoining rails to provide for their inevitable 
 expansion by the summer heat. The iron tubular bridge over the 
 Menai Straits is about 1800 feet long. Its linear expansion is abort 
 one foot, and is provided for by placing the ends of the huge tube 
 upon /oilers. 
 
 552. Expansion of Liquids. The expansion of 
 liquids may be illustrated as follows : Nearly fill a Florence 
 flask with water, and place it on a retort stand or other 
 convenient support. A long straw is supported by a thread 
 tied near one end. From the short end of this straw lever 
 is suspended a weight nearly balanced by the long arm of 
 the lever. This weight hangs in the neck of the flask, 
 and rests lightly upon the surface of the water ( 238). 
 By placing a spirit-lamp below the flask the water may be 
 heated. As it expands, it rises in the neck of the flask, 
 raises the weight, and lowers the end of the long arm of 
 the lever, which may be seen to move. 
 
 553. Anomalous Expansion of Water. 
 
 Water presents a remarkable exception to the general rule. 
 // water at 0C. b& heated, it will contract until it 
 
TEMPERATURE. 
 
 419 
 
 reaches 4 C., its temperature of greatest density, 
 Heated above this point it expands. 
 
 (a.) Through the cork of a large flask pass a fine glass tube. Fill 
 the flask with water at the ordinary temperature, and insert the 
 
 cork and tube so that the water 
 shall rise some distance in the 
 tube. Place the flask in a freezing 
 mixture, such as salt and pounded 
 ice. The water column in the 
 tube falls, showing that the water 
 is contracting. But before the 
 water freezes the contraction 
 ceases, the column in the tube 
 becomes stationary, and then be- 
 gins to rise again. This shows 
 that water does not contract on 
 being cooled below a certain tem- 
 perature, and that there is a tern- 
 perature of maximum density 
 above the freezing point. 
 
 (&.) Fig. 291 represents a glass 
 cylinder with two thermometers 
 inserted in the side, near the top 
 and bottom, at A and B. Midway 
 between A and B is an envelope C, which may be filled with a 
 sing mixture. The envelope being empty, the cylinder is filled 
 
 FIG. 291. 
 
420 
 
 TEMPERA TUEE. 
 
 the ice would sink and destroy everything living in the 
 water. The entire body of water would soon become a 
 solid mass which the heat of summer could not wholly 
 melt, for, as we shall soon see, water has little power to 
 carry heat downward. As it is, in even the coldest winters, 
 the mass of water in our northern lakes remains at a tem- 
 perature of 4C., the colder water floats upon the warmer 
 layer, ice forms over all, and protects the living things 
 below. 
 
 555. Expansion of Oases. The expansion of 
 gases may be shown by partly filling a bladder with cold 
 air, tying up the opening, and placing the bladder near 
 the fire. The expanded air will fill the bladder. Through 
 the cork of a bottle pass a small glass tube about a foot 
 iong. Warm the bottle a little between the hands and 
 place a drop of ink at the end of the tube. As the air 
 contracts the ink will move down the tube and form a 
 frictionless liquid index. 
 By heating or cooling the 
 bottle the index may be 
 made to move up or down. 
 If a closed flask having a 
 delivery tube terminating 
 under water be heated, 
 some of the expanded air 
 mil he forced to escape, 
 and may be seen bubbling 
 through the water. By 
 "collecting over water" 
 the air thus driven out, 
 it may be accurately 
 measured. (Fig. 292.) 
 14 
 
 FIG. 292. 
 
TEMPERATURE. 421 
 
 556. Practical Results. The ascension of ' ' fire-balloons " 
 and the draft of chimneys are due to the expansion of gases by heat 
 When the air in the chimney of a stove or lamp is heated, it is ren 
 dered lighter than the same bulk of surrounding air, and, therefore, 
 rises. The cooler air comes in to take its place and thus feeds the com- 
 bustion. Sometimes when a fire is first lighted, the chimney is so 
 cold that the current is not quickly established and the smoke 
 escapes into the room. But in a little while the air column rises 
 and the usual action takes place. By the aid of a good thermometer 
 it may be shown that the air near the ceiling of a room is warmer 
 than the air near the floor. When the door of a warmed room is 
 left slightly ajar, there will be an inward current near the floor and 
 an outward current near the top of the door. These currents ma? 
 be shown by holding a lighted candle at these places. Artificial 
 ventilation depends upon the same principles. 
 
 557. Rate of Gaseous Expansion. The rate 
 of expansion is practically the same for all gases, viz., 
 0.00366 or ^^ of the volume at C., for each centigrade 
 degree that the temperature is raised above the freezing 
 point. In other words, a liter of air at C., expands to 
 
 1 I + .00366 I at 1 C., 
 1 I + (.00366 x 2) I at 2 0. 
 
 (.00366 x3)?.at3C., 
 I at 4 C. 
 
 Of course, if we use Fahrenheit degrees the expansion 
 will he only f as great, or about :r J T . A litre of gas at 32 F. 
 expands to 1^ I at 33 F. ; to ff J I at 39 F., etc. 
 
 558. Absolute Zero of Temperature. The 
 
 temperature at which the molecular motions con- 
 stituting heat wholly cease is called the absolute 
 zero. It has never been reached, and has been only ap- 
 proximately determined, but it is convenient as an ideal 
 starting-point. The zero point of the thermometers does 
 not indicate the total absence of heat. A Fahrenheit 
 thermometer, therefore, does not indicate that boiling 
 water is 212 times as hot as ice at 1 F. ; a centigrade. 
 
422 TEMPERATURE. 
 
 thermometer does not indicate that boiling water has 100 
 times as much heat as water at 1 C. 
 
 (a.) Temperature, when reckoned from the absolute zero, is called 
 absolute temperature. Absolute temperatures are obtained by add- 
 ing 460 to the reading of a Fahrenheit thermometer, or 273 to the 
 reading of a centigrade thermometer. 
 
 559. Temperature, Volume and Pressure. 
 
 By raising a gas from 00. to 273 C., its volume will be 
 doubled. To reduce the gas at this temperature to its 
 original volume, the original pressure must be doubled. 
 From our knowledge of pneumatics and gaseous expansion, 
 we are able to solve certain problems relating to the volume 
 of gases under different pressures and temperatures. 
 
 Examples. (1.) A mass of air at C. and under an atmos- 
 pheric pressure of 30 inches, measures 100 cu. inches ; what will be 
 its volume at 40 C. under a pressure of 28 inches ? 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 ( 284). In 
 other words, the volume will be f-f times 100 cubic inches or 107J 
 cu. in. Next, suppose the temperature to change from C. to 
 40 C. The expansion will be ^ of the volume at C. ; the volume 
 will be 1^ of the volume at C. l-ffc times 107 cubic inches 
 =122ff inches. Ans. 
 
 The problem may be worked by proportion as follows : 
 28 : 30 ) 28: 30 
 
 (2.) At 150 C., what will be the volume of a gas that measures 
 10 cu. cm. at 15 C. ? 
 
 273 + 15 : 273 + 150 : : 10 : x. .'. x = 14.69 cu. cm. 
 (3.) If 100 cu. cm. of hydrogen be measured at 100 C. , what will 
 be the volume of the gas at 100 C.? 
 
 273 + 100 : 273 - 100 : : 100 : x. /. x = 46.37 cu. cm. 
 
TEMPERATURE. 423 
 
 (4.) A liter of air is measured at C. and 760 mm. What volume 
 ill it occupy at 740 mm., and 15.5 C. ? 
 
 :: 1,000:,. .-. .- M8S.M*. . 
 EXERCISES. 
 
 1. A rubber balloon, capacity of 1 liter, contains 900 cu. cm. of 
 oxygen at C. When heated to 30 C., what will be the volume 
 of the oxygen ? Ans. 998.9 cu. cm. 
 
 2. If 170 volumes of carbonic acid gas be measured at 10 C., what 
 will be the volume when the temperature sinks to C. ? 
 
 3. A certain weight of air measures a liter at C. How much 
 will the air expand on being heated to 100 C.? Ans. 366.3 cu. cm. 
 
 4. A gas has its temperature raised from 15 C. to 50 C. At the 
 latter temperature it measures 15 liters. What was its original 
 volume? Ans. 13,374.6 cu. cm. 
 
 5. A gas measures 98 cu. cm. at 185 F. What will it measure at 
 10 C. under the same pressure ? Ans. 77.47 cu. cm. 
 
 6. To what volume will a liter of gas contract in cooling from 
 42 F. to 32 F.? Ans. 980 cu. cm. 
 
 7. A certain quantity of gas measures 155 cu. cm. at 10 C., and 
 under a barometric pressure of 530 mm. What will be the volume 
 at 18.7 C., and under a barometric pressure of 590 mm.l 
 
 8. A gallon of air (231 cu. in.) is heated, under constant pressure, 
 from C. to 60 C. What was the volume of the air at the latter 
 temperature ? Ans. 281.77 cu. in. 
 
 9. A fire balloon contains 20 cu. ft. of air. The temperature of 
 the atmosphere being 15 C. and that of the heated air in the bal- 
 loon being 75 C., what weight, including the balloon, may be thus 
 supported? (See Appendix G.) Ans. 1,847 grains. 
 
 10. The difference between the temperatures of two bodies is 
 36" F. Express the difference in centigrade degrees. 
 
 11. The difference between the temperatures of two bodies is 
 35 C. Express the difference in Fahrenheit degrees. 
 
 12. (a.) Express the temperature 68 F. in the centigrade scale. 
 (&.) Express the temperature 20 D C. in the Fahrenheit scale. 
 
 13. What will be the tension at 30 C. of a quantity of gas which 
 at C. has a tension of a million dynes per sq. cm., the volume 
 remaining the same ? ( 69.) Ans. 1109890 dynes. 
 
 14. A liter of gas under a pressure of 1013600 dynes per sq. cm. 
 is allowed to expand until the pressure is reduced to 1000000 dynes 
 per sq. cm. At the same time, the temperature is raised from C 
 to 100 C. Find the final volume. Ans. 1385 cu. cm. nearly. 
 
424 LIQUEFACTION. 
 
 Recapitulation. In this section we have considered 
 the Nature of Heat; the meaning of Tem- 
 perature ; Thermometers and their graduation -, 
 the determination of the Freezing and Boiling 
 Points ; thermometric Scales and Readings ; 
 the Differential Thermometer ; Expansion 
 of Solids ; Expansion of Liquids, especially 
 the Expansion of Water ; the Expansion of 
 Gases and the Rate thereof; Absolute Zero of 
 temperature; the relation between Temperature, 
 Pressure and Volume. 
 
 ECTION II. 
 
 LIQUEFACTION, VAPORIZATION, DISTILLATION. 
 
 56O. Liquefaction. In the last section we learned 
 that heat is a form of energy. As energy, it is able to 
 perform work, such as overcoming or weakening the force 
 of cohesion. It is well known that when a solid is changed 
 to the liquid or aeriform condition, or when a liquid is 
 changed to a vapor, it is done by an increase of heat, and 
 that when the reverse operations are performed, it is by a 
 diminution of heat. Cohesion draws the particles together ; 
 heat pushes them asunder, and on the varying preponder- 
 ance of one or the other of these antagonistic powers, the 
 condition of the body seems to depend. When the firm 
 grip of cohesion has been so far weakened by heat that the 
 molecules easily change their relative positions ( 55), the 
 body passes from the solid into the liquid condition. This 
 change of condition is called liquefaction. 
 
LIQ UEFA CTIO& 
 
 425 
 
 561. Laws of Fusion. It has been found by 
 experiment that the following statements are true : 
 
 (1.) Every solid begins to melt at a certain temperature 
 vrfrich is invariable for the given substance if the pressure 
 be constant. When cooling, the substance will solidify at 
 the temperature of fusion. 
 
 (2.) The temperature of the solid, or liquid, remains at 
 the melting point from the moment that fusion or solidi- 
 fication begins until it is complete. 
 
 (a.) If a flask containing ice be placed over a fire, it will be found 
 that the hotter the fire the more rapid the liquefaction, but that if 
 the contents of the flask be continually stirred, the thermometei 
 will remain at C. until the last bit of ice is melted ( 543-). If 
 sulphur be used instead of ice, the tem- 
 perature will remain at 115 C. until the 
 sulphur is all melted. (Fig. 293.) 
 
 5O2. Reference Table of Melt* 
 ing- Points : 
 
 Alcohol, .... Never frozen. 
 Mercury, .... 38.8C. 
 Sulphuric acid, - - 344 
 
 Ice, ^'^ 0. 
 
 Sulphur, .... 115. 
 
 Lead, 326 
 
 Zinc, .... 425 
 
 Silver (pure), - - - 1,000 
 Gold (pure), - 1,250 
 
 Iron (wrought), - - 1,600 
 
 P Note. The higher temperatures in this 
 
 table are only approximate. Certain 
 
 bodies soften and become plastic before they melt. In this condition 
 
 glass is worked and iror. is welded. 
 
 563. Vaporization. If, after liquefaction, further 
 additions of heat be made, a point will be reached at which 
 the heat will overbalance both the cohesion and the 
 pressure of the atmosphere and the liquid pass into the 
 aeriform condition. This change of form is called vapor 
 
426 
 
 VAPORIZA TION. 
 
 ization. Vaporization may be of two kinds evaporation 
 and ebullition. 
 
 564. Evaporation. Evaporation signifies the 
 quiet formation of vapor at the surface of a 
 liquid. 
 
 (a.) With reference to the rapidity with which evaporation takes 
 place, it may be remarked that 
 
 (t.) It varies with the temperature. 
 (2.) It varies with the extent of surface. 
 
 (3.) It varies with pressure upon the liquid, being exceedingly 
 rapid in a vacuum. 
 
 565. Evaporation in Vacuo. The rapid forma- 
 tion of vapors in a vacuum is prettily illustrated by the 
 following experiment : 
 
 Torricellian vacua are 
 formed at the top of four 
 barometer tubes, A, B, 
 tfandD, Fig. 294. Into 
 the mouth of B pass a 
 few drops of water. They 
 will rise through the mer- 
 cury to the vacuum at 
 the top. Upon reaching 
 this open space they are 
 instantly vaporized. The 
 tension of the aqueous 
 vapor shows itself by 
 lowering the mercury 
 column. This depression 
 is due to the tension 
 
 rather than to the weight 
 
 FIG. 294. 
 of the vapor, because the 
 
 water weighs scarcely anything compared with the mer 
 
VAPORIZA TION. 
 
 427 
 
 cury it displaces. Introducing the same quantity of 
 alcohol into C, and of ether into D, they are instantly 
 vaporized, but the mercury will be depressed more by the 
 alcohol than by the water, and more by the ether than by 
 the alcohol. 
 
 (a.) At the beginning of the experiment, the four mercury 
 columns indicated the atmospheric pressure ; at the end of the 
 experiment, the column in A indicated the full pressure of the 
 atmosphere ; the columns in B, G and D indicate that pressure 
 minus the tension of their respective vapors. This experiment 
 also shows that, at the same temperature, the vapors of different 
 liquids have different tensions. 
 
 566. Ebullition. Ebullition, or boiling, signi- 
 fies the rapid formation of vapor bubbles in the 
 
 mass of a liquid. 
 When a flask con- 
 taining water i? 
 placed over the flame 
 of a lamp, the ab- 
 sorbed air that is 
 generally to be found 
 in water is driven off 
 in minute bubbles 
 that rise and escape 
 without noise. As 
 the temperature of 
 the water is raised, 
 the liquid molecules 
 in contact with the 
 bottom of the flask 
 
 become so hot that 
 FIG. 295. 
 
 the heat is able to 
 
 overcome the cohesion between the molecules, the pressure 
 
428 VA PORIZA TION. 
 
 of the overlying water, and the pressure of the atmosphere 
 above the water. Then the water boils. 
 
 (a.) When the first bubbles of steam are formed at the bottom of 
 the water, they rise through the water, condense in the cooler layers 
 above, and disappear before reaching the surface. The formation 
 and condensation of these bubbles produce the peculiar sound known 
 as singing or simmering, the well-known herald of ebullition. 
 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. The whole liquid mass is agitated 
 with considerable vehemence, there is a characteristic noisy accom- 
 paniment, the quantity of water in the flask diminishes with every 
 bubble, and finally it all disappears as steam. The water has 
 " boiled away." 
 
 567. Laws of Ebullition. It has been found by 
 experiment that the following statements are true : 
 
 (1.) Every liquid begins to boil at a certain temperature, 
 which is invariable for the given substance if the pressure 
 be constant. When cooling, the substance will liquefy at 
 the temperature of ebullition, or at the boiling point. 
 
 (2.) The temperature of the liquid, or vapor, remains 
 at the boiling point from the moment that it begins to 
 boil or liquefy. 
 
 (3.) An increase of pressure raises the boiling point ; a 
 decrease of pressure lowers the boiling point. 
 
 (a.) In a beaker half full of water, place a ther- 
 mometer and a test tube half filled with ether. 
 Heat the water. When the thermometer shows a 
 temperature of about 60 C., the ether will begin to 
 boil. The water will not boil until the temperature 
 rises to 100 C. The temperature will not rise be- 
 yond this point. 
 FIG. 296. 
 
 568. Vapor Pressure. The pressure 
 of a vapor ( 282) is due to the kinetic energy of its con- 
 stituent molecules. " As a liquid evaporates is a closed 
 
VAPORIZATION. 429 
 
 space, the vapor formed exerts a pressure upon the enclosure 
 and upon the surface of the liquid, which increases as long 
 as the quantity of vapor increases and reaches a maximum 
 when the space is saturated. This maximum pressure of 
 a vapor increases with the temperature. When evapora- 
 tion takes place in a space filled hy another gas that has 
 no action upon the vapor, the pressure of the vapor is 
 added to that of the gas and the pressure of the mixture 
 is, therefore, the sum of the pressures of its constituents." 
 
 569. Effect of Pressure upon Boiling Point. 
 
 We saw in 566 that when a liquid is boiled, the heat 
 has three tasks or three kinds of work to perform, viz., 
 overcoming cohesion, liquid and atmospheric pressures. 
 Nothing can be more evident than the propositions that 
 increasing the work to be done involves an increase in the 
 energy needed to do the work ; that decreasing the work 
 to be done involves a decrease in the energy needed to do 
 the work. In the case of boiling any given liquid, the first 
 of the three tasks can not be varied ; either of the other 
 two easily may. If we increase the pressure, we increase 
 the work to be done and, therefore, increase the necessary 
 amount of heat, the only form of energy competent to do 
 the work. If we lower the pressure, we lessen the work to 
 be done and, therefore, lessen the necessary amount of 
 heat. This means, in the first case, raising the boiling 
 point ; in the second case, lowering the boiling point. 
 
 570. Franklin's Experiment. The boiling of 
 water at a temperature below 100 C. may be shown as 
 follows: Half fill a Florence flask with water. Boil the 
 water until the steam drives the air from the upper part 
 
430 VAP OR 12 A 2TO #. 
 
 of the flask. Cork tightly, remove the lamp and invert 
 the flask. The exclusion of the air may be made more 
 certain by immersing the corked neck of the flask in water 
 
 that has been recently 
 boiled. When the lamp 
 was removed, the tem- 
 perature was not above 
 100 C. By the time 
 that the flask is inverted 
 and the boiling has 
 ceased, the temperature 
 will have fallen below 
 100 C. When the boil- 
 ing stops, pour cold 
 water upon the flask : 
 directly the boiling be- 
 F:c. 297 . gins again. 
 
 (a.) The cold water poured upon the flask lowers the tempera- 
 ture of the water in the flask still further, but it also condenses 
 Borne of the steam in the flask or reduces its tension ( 559). This 
 reduction of the tension lessens the work necessary to boiling. There 
 being enough heat in the water to do this lessened amount of work, 
 the water again boils and increases the pressure until the boiling 
 point is raised above the present temperature of the water. The 
 flask may be drenched and the water made to boil a dozen times in 
 succession with a single heating. The experiment may be made 
 more striking by plunging the whole flask under cool water. 
 
 571. Papin's Digester. At high elevations water boils at 
 a temperature too low for culinary purposes. Persons living there 
 are obliged to boil meats and vegetables (if at all) in closed vessels 
 and under a pressure greater than that of the atmosphere. In the 
 arts, a higher temperature than 100 C. is sometimes required for 
 water, as, for example, in the extraction of gelatine from bones. In 
 a closed vessel, water may be raised to a much higher temperature 
 than in the open air, but, for reasons now obvious, water cannot be 
 
VAPORIZATION. 
 
 431 
 
 kept boiling in Such a vessel. Papin's Digester Consists of a metal 
 vessel of great strength covered with a lid pressed down by a 
 powerful screw. That the joint may be more perfect, a ring of 
 sheet lead is placed between the edges of the cover and of the vessel. 
 It is provided with a safety valve, pressed close by a loaded lever. 
 When the tension of the steam reaches a dangerous point, it opens 
 the valve, lifting the weight and thus allowing some of the steam 
 to escape. 
 
 (a.) In many cases, e. g., sugar refining, it is desirable to boil or 
 evaporate a liquid at as low a temperature as possible. The 
 work is then done in a vacuum pan from which the vapor is 
 pumped, the tension being thus reduced. 
 
 .572. Marcet's Globe. Marcet's globe is represented 
 in Fig. 298. It consists of a spherical metallic boiler, five 
 or six inches in diameter, provided with three openings, 
 through one of which a thermometer, T, passes ; through 
 the second of which a glass manometer tube, M, passes ; the 
 third opening being provided with a stop-cock, S. The 
 thermometer and manometer tubes fit their openings so 
 closely that no steam can escape at those points. The 
 thermometer bulb is exposed directly to 
 the steam. The lower end of the manometer 
 tube dips into mercury placed in the lowei 
 part of the globe. The boiler is to be half 
 filled with water and heated until the 
 water boils, the stop-cock being open. As 
 long as the stop-cock is open, the ther- 
 mometer will not rise above 100 C. When 
 the stop-cock is closed, the steam accumu- 
 lates, the pressure on the water increases, 
 the thermometer shows a rise of temperature 
 beyond 100 0. higher and higher as the 
 FIG 2 s mercury rises in the manometer tube, 
 
432 VAPORIZATION. 
 
 When the mercury in the manometer tube is 760 mm. 
 above the level of the mercury in the boiler, the steam 
 has a tension of two atmospheres, and the thermometer 
 will record a temperature of about 121 C. 
 
 573. Concerning Steam. A given mass of 
 water in the aeriform, condition occupies nearly 
 1700 times as much space under a pressure of 
 one atmosphere as it does in the liquid condition. 
 In other words, a cubic inch of water will yield nearly a 
 cubic foot of steam. Steam is invisible. What is 
 commonly called steam is not true steam, but little globules 
 of water condensed by the cold air and suspended in it. 
 By carefully noticing the steam issuing from the spout of 
 a tea-kettle, it will be observed that for about an inch from 
 the spout there is nothing visible. The steam there 
 has not had opportunity for condensation. The water 
 particles visible beyond this space passed through it as 
 invisible steam. The steam in the flask of Fig. 297 is 
 invisible. 
 
 574. Reference Tables. Boiling Points under a pressure 
 of one atmosphere : 
 
 Ammonia -40 C. 
 
 Sulphurous anhydride. .. 8 
 
 Ether 35 
 
 Carbon bisulphide 48 
 
 Alcohol 78C. 
 
 Water (pure) 100 
 
 Mercury 350 
 
 Sulphur 447 
 
 Some solids, as iodine, arsenic and camphor vaporize without 
 risible intermediate liquefaction. The process is called sublimation 
 Boiling Points of water at different pressures : 
 
 Thermometer. 
 
 Barometer. 
 
 Thermometer. 
 
 Atmospheres 
 
 184 F. 
 
 16.676 inches. 
 
 212 F. 
 
 1 
 
 190 
 
 18.992 
 
 249.5 
 
 2 
 
 200 
 
 23.454 
 
 2733 
 
 3 
 
 210 
 
 28.744 
 
 318.2 
 
 6 
 
 212 
 
 29.922 
 
 356.6 
 
 10 
 
 215 
 
 81.730 1 415.4 
 
 20 
 
VAP ORIZA TION. 
 
 433 
 
 575. Definition of Boiling Point. We ought 
 now to be fully prepared to understand that the boiling 
 point of a liquid is the temperature at which it 
 
 gives off a vapor of the same 
 tension as the surrounding at- 
 mosphere. 
 
 (a.) If there be any doubt or lack of 
 comprehension of this proposition, it may 
 be removed by the following experiment : 
 A A glass tube, bent as shown at A, has its 
 short arm closed and its long arm open. 
 The short arm is nearly filled with mer- 
 cury, the space above the mercury b ^ing 
 filled with water. While water is briskly 
 boiling in a flask, the bent tube is sus- 
 pended in the steam, as shown in Fig. 
 299. Part of the water in the bent ';ube 
 is changed to vapor, the mercury falls in 
 the short arm, and finally assumes the name 
 FIG. 299. level in both branches. 
 
 576. Distillation. Distillation is the process of 
 vaporizing a liquid in a heated vessel and subsequently 
 condensing the vapor in a cool vessel. It is chiefly used 
 for the purpose of separating a liquid from a solid which it 
 holds in solution, or of separating a mixture of two liquids 
 having different boiling points. The process depends upon 
 the fact that different substances are vaporized at different 
 temperatures. The apparatus, called a still, is made in 
 many forms, but consists essentially of two parts the re- 
 tort for producing vaporization, and a condenser for 
 changing the vapor back to the liquid form. Fig. 300 
 represents one form of the apparatus. It consists of a 
 retort, ab, the neck of which is connected with a spiral 
 tube, dd, called the worm. The worm is placed in a vessel 
 containing water. 
 
434 
 
 DISTILLATION. 
 
 ft 
 
 FIG. 300. 
 
 577. Distillation of a Liquid from a Solid, 
 
 Suppose that water is to be separated from the salt it 
 holds in solution. The brine is placed in a retort and 
 heated a little above 212 F. At this temperature the 
 water is vaporized while the salt is not. The steam is 
 driven from the 
 retort through the 
 worm, where it is 
 rapidly condensed 
 and passes into a 
 vessel prepared to 
 receive it. The 
 salt remains in 
 the retort. Of 
 course, the water % 
 of the vessel con- 
 taining the worm FIG. 301. 
 
totsf ILLATION. 435 
 
 must be kept cool. This is done by constantly feeding it 
 at the bottom with cold water, as explained in the last 
 article. 
 
 (a.) Fig. 301 represents a simpler form of apparatus for this pur 
 pose. The retort is a Florence flask, the delivery tube of which 
 passes through a "water-jacket." The method of supplying this 
 condenser with cold water is evident from the figure. Sometimes 
 the delivery tube passes directly into a vessel placed in a cold water 
 bath, this vessel serving as both condenser and receiver. 
 
 578. Distillation of a Liquid from a Liquid. 
 
 Suppose that alcohol is to be separated from water. 
 The solution is placed in the retort and heated to about 
 90 C., which is above the boiling point of alcohol but 
 below that of water. The alcohol will pass over in a state 
 of vapor and be condensed, while the water, etc., remains 
 behind. In practice, the alcohol vapor passes over charged 
 with a certain amount of steam. A receiver placed in a 
 bath containing boiling water is interposed between the 
 retort and the worm or condenser. In this receiver the 
 steam condenses, while the vapor of alcohol passes on to 
 the worm where it also is condensed. This process is known 
 as "fractional distillation." 
 
 Recapitulation. In this section we have considered 
 the meaning of Liquefaction ; the Laws of Fu- 
 sion ; the meaning and kinds of Vaporization ; 
 Evaporation in air and in vacuo ; Ebullition and 
 its Laws; effect of Pressure upon the boiling point; 
 Steam ; definition of Boiling Point ; Distilla- 
 tion. ; 
 
436 LATENT AND SPECIFIC 
 
 SECTION HI. 
 
 LATENT AND SPECIFIC HEAT. 
 
 579. Thermal Units. In 538 it was stated that 
 heat is measurable ; but that we may measure it, a standard 
 or unit of measure is necessary. A thermal or heat 
 unit is the amount of heat necessary to warm a 
 weight unit of water one degree above the freezing 
 point. The weight unit generally used is the gram, 
 kilogram or pound; any other weight unit may be used. 
 The degree may be centigrade or Fahrenheit. 
 
 (a.) We have at least four units in use. They are the amounts 
 of heat necessary to warm 
 
 (1.) A kilogram of water from C. to 1 C. (A calorie.) 
 (2.) A gram of water from C. to 1 C. (A lesser calorie.) 
 (8.) A pound of water from C. to 1 C. 
 (4.) A pound of water from 32 F. to 33 F. 
 
 It makes no practical difference which unit is used, excepting so 
 far as convenience is concerned, but the unit must not be changed 
 during any problem. 
 
 58O. Two Fruitful Questions We have already seen 
 that heat melts ice, and that during the melting the temperature h> 
 constant ; that heat boils water, and that during the boiling the 
 temperature is constant. One feature of this change of condition 
 remains to be noticed more fully. Take a block of ice with a tern, 
 perature of 10 C. (14 F.) and warm it. A thermometer placed in 
 it rises to C. The ice begins to melt, but the mercury no longei 
 rises. Heat is still applied, but there is no increase of temperature ; 
 the mercury in the thermometer remains stationary until the last 
 particle of ice has been liquefied. Then, and not till then, does the 
 temperature begin to rise. It continues to do so until the ther 
 mometer marks 100 C. The liquid then begins to boil, and the 
 temperature a second time becomes fixed. But during all the time 
 that the thermometer stood at C., or while the ice was melting, 
 heat was given by the lamp and received by the ice. Why then did 
 not the temperature rise during that time, instead of remaining the 
 
LATENT AND SPECIFIC HEAT. 43? 
 
 Bame until the last particle of ice was melted? After tlie watel 
 began to boil, heat was continuously supplied. Why then was 
 there not a continued increase of temperature ? 
 
 581. Molecular Energies. Heat is a form of energy and 
 may be kinetic or potential. There can be no doubt that when a 
 body is heated its molecules are thrown into violent motion, and 
 that as the temperature is raised the energy of this molecular motion 
 is increased, or that as this molecular motion is increased, the tern 
 perature is raised. But some of this molecular energy that we call 
 heat, instead of b^ing used to set the molecules of the body in motion, 
 has work of a different kind to perform. That part of the heat 
 which is spent in producing molecular vibrations, which increases 
 the temperature, is called sensible heat. Another part is employed 
 in pushing the molecules of the body asunder, producing expansion 
 and change of condition. In forcing these molecules asunder, in- 
 visible energy of motion is changed to energy of position as truly 
 and as necessarily as visible energy of motion is changed to the 
 potential variety in throwing or carrying a stone from the earth t 
 the house-top. ( 159.) 
 
 582. Transmutation of Molecular Energy. In most 
 cases, but little of the heat communicated to a body is thus changed 
 to potential energy, the greater part remaining energy of motion 
 and increasing the temperature. But there are certain crises, 01 
 " critical occasions," on which the greater part of the heat communi- 
 cated is transformed into energy of position. Thus, at the melting 
 point, a large quantity of heat may be given to ice without affecting 
 the temperature at all ; instead of raising the temperature, it merely 
 melts the ice. The energy used has been changed from the kinetic 
 to the potential variety. In like manner, at the boiling point, a 
 large quantity of heat may be given to the water without affecting 
 the temperature at all. Instead of raising the temperature further, 
 it merely vaporizes the water, and the steam has the same tempera- 
 ture as the water from which it came. The same change of molec- 
 ular energy of motion into molecular energy of position has again 
 taken place. This heat, which is thus used to overcome cohesion 
 and change the condition of matter, does not affect the temperature 
 and therefore is not sensible, but is stored up as potential energy 
 and thus hidden or rendered latent. 
 
 583. Definition of Latent Heat. The latent 
 heat of a substance is the quantity of heat that is 
 
438 LATENT AND SPECIFIC HEAT. 
 
 lost to thermometric measurement during its 
 faction or vaporization, or the amount of heat that 
 must be communicated to a body to change its 
 condition without changing its temperature. It may 
 be made to reappear during the opposite changes after any 
 interval of time. Many solids may undergo two changes 
 of condition. Such solids have a latent heat of liquefac- 
 tion and a latent heat of vaporization. 
 
 584. Latent Heat of Fusion. We are already 
 familiar with the fact that when ice or any other solid is 
 melted by the direct application of heat, much of the heat 
 is rendered latent. In the case of melting ice we shall 
 show how this latent heat is measured, and that its quan- 
 tity is very great We may represent the process of lique- 
 faction of ice as follows : 
 
 Water at 0. = ice at 0" C. + latent heat of water. 
 
 585. Latent Heat of Solution. During the 
 process of solution, as well as during fusion, heat is ren- 
 dered latent. In either case the performance of the work 
 of liquefaction demands an expenditure of kinetic energy. 
 Hence the solution of a solid involves a diminution 
 of temperature. 
 
 (a.} This loss may in some cases be made good by an equal in- 
 crease, or changed to gain by a greater increase of sensible heat 
 from the chemical changes involved ; but in any case, the act of 
 liquefaction considered by itself produces cold. Thus a cup of 
 coffee is cooled by sweetening it with sugar, and a plate of soup is 
 cooled by flavoring it with salt. 
 
 586. Freezing Mixtures.- The latent heat of 
 solution lies at the foundation of the action of 
 freezing mixtures. For example, when ice is melted 
 by salt, and the water thus formed, in turn, dissolves the 
 
LATENT AND SPECIFIC HEAT. 439 
 
 salt itself, the double liquefaction requires a deal of heat 
 which is generally furnished by the cream in the freezer. 
 The freezing mixture most commonly used consists of one 
 weight of salt and two weights of snow or pounded ice. 
 The mixture assumes a temperature of 18 0., which 
 furnished the zero adopted by Fahrenheit. 
 
 (a.) By mixing, at the freezing temperature, three weights of 
 snow with two weights of dilute sulphuric acid, the temperature 
 may be reduced to about 20 F., a diminution of over 50 Fahren- 
 heit degrees. If equal weights of snow and dilute sulphuric acid 
 be thus reduced to a temperature of 20 F. and then mixed, the 
 temperature will fall to about 60 F. By mixing equal weights 
 of sodium sulphate crystals (Glauber's salt), ammonium nitrate and 
 water, all at the ordinary temperature, and stirring the mixture 
 with a thermometer, the temperature will be seen to fall from about 
 65 F. to about 10 F., which is considerably below the freezing point 
 of pure water. Glauber's salt and hydrochloric (muriatic) acid form 
 a good freezing mixture. 
 
 5S7. Solidification. Solidification signifies the 
 passage from the liquid to the solid condition. During 
 solidification there is an increase of temperature. 
 This may seem paradoxical in certain cases, but, even in 
 the case of water, it is true that solidification is a warming 
 process. 
 
 .(#.) The sensible heat that disappeared as latent heat during 
 liquefaction, being no longer employed in doing the work of main- 
 taining liquidity, is reconverted into sensible heat and immediately 
 employed in increasing the molecular vibrations. The molecular 
 potential energy is transmuted into molecular kinetic energy. This 
 is frequently illustrated by the precaution taken in winter to place 
 tubs of water in vegetable cellars that the latent heat of the freez 
 Ing water may be changed into sensible heat and thus protect the 
 vegetables. 
 
 588, Temperature of Solidification. The 
 
 melting point is the highest temperature at which solidi- 
 
440 LATENT AND SPECIFIC HEAT. 
 
 fication can take place, but it is possible to keep substances 
 in the liquid condition at lower temperatures. Water 
 standing perfectly quiet sometimes cools several degrees 
 below the melting point without freezing, but, upon agita- 
 tion in any perceptible degree, solidification immediately 
 takes place. 
 
 (a.) Persons who sleep in cold chambers sometimes notice, upon 
 arising, that as soon as they touch a pitcher of water that has been 
 standing in the room over night, the water quickly freezes. If a 
 particle of ice be dropped into the water the same result follows. 
 We may say that, in this condition, liquids have a tendency to freeze 
 which is kept in check only by the difficulty of making a beginning. 
 
 589. Heat from Solidification. (1.) By surrounding, 
 with a freezing mixture, a small glass vessel containing water, and 
 a mercury thermometer, the temperature of the water may be re- 
 duced to 10 C. or 12 C. without freezing the water. A slight 
 movement of the thermometer in the water starts the freezing and 
 the temperature quickly rises to C. 
 
 (2.) Place a thermometer in a glass vessel containing water at 
 30 C. and a second thermometer in a large bath of mercury at 10 C. 
 Immerse the glass vessel in the mercury. The temperature of the 
 water will gradually fall to 0C., when the water will begin to 
 freeze and its temperature become constant. In the meantime the 
 temperature of the mercury bath rises, and continues to do so while 
 \he water is freezing. 
 
 (3.) Dissolve two weights of Glauber's salt in one weight of hot 
 water, cover the solution with a thin layer of oil and allow to cool, 
 in perfect quiet, to the temperature of the room. By plunging a 
 thermometer into the still liquid substance, solidification (crystal- 
 lization) is started and the temperature rapidly rises. Dr. Arnott 
 found that this experiment was successful after keeping the solu- 
 tion in the liquid condition for five years. 
 
 (4.) Mix equal quantities of dilute sulphuric acid and of a satu- 
 rated solution of calcium chloride (not chloride of lime), the two 
 liquids having been allowed time to acquire the temperature of the 
 room. The two liquids are converted into solid calcium sulphate, 
 with a marked increase of temperature. In this case, as in some 
 of the other cases, part of the heat observed is probably due to 
 chemical action, but more to the conversion of the latent heat of 
 the liquids. 
 
LATENT AND SPECIFIC HEAT. 441 
 
 (5.) To three weights of quicklime add one weight of water 
 The water will be completely solidified in the slaking of the lime 
 with remarkable thermal manifestations. Carts containing quick 
 lime have been set on fire by exposure to heavy rains. 
 
 590. Change of Bulk during Solidification. 
 
 Most substances shrink in size during solidification ; but 
 a few, such as ice, cast-iron, antimony and bismuth, are 
 exceptions. When melted cast-iron is poured into a mould, 
 it expands in solidifying and presses into every part of the 
 mould. The tracings on the casting are, therefore, as clear 
 cut as they were in the mould. A clear-cut casting can 
 not be obtained from lead; this is one of the reasons why 
 antimony is made a constituent of type-metal. Gold coins 
 have to be stamped ; they cannot be cast so as to produce 
 a clear-cut design. The bursting of pipes by freezing water 
 is a common source of annoyance. 
 
 (a.) An army officer at Quebec performed the following experi- 
 ment : He filled a 12-inch 
 
 shell with water and closed 
 the opening with a wooden 
 plug forcibly driven in. The 
 shell was put out of doors ; 
 the temperature being 
 28 C., the water froze, the 
 plug was thrown about 300 
 feet, and a tongue of ice 
 about eight inches long pro- 
 truded from the opening. 
 In a similar experiment, the 
 shell split and a rim of ice 
 FIG. 302. issued from the rent. 
 
 591. Latent Heat of Vaporization. The 
 
 vaporization of a liquid is accompanied by the disappear- 
 ance of a large quantity of heat, and frequently by a diminu- 
 tion of temperature. There is a change of sensible into 
 
442 LATENT AND SPECIFIC HEAT. 
 
 latent heat; of kinetic into potential energy. We 
 represent, for instance, the va- 
 porization of water as follows : 
 Steam at 100 C. = water 
 at 100 C. {- latent heat of 
 steam. 
 
 (a.) The cryophorus, shown in 
 Fig. 254, consists of a bent tube 
 and two bulbs containing a small 
 quantity of water. The air is re- 
 moved by briskly boiling the water. 
 The tube is sealed while the steam 
 is escaping. The instrument thus 
 contains only water and aqueous 
 vapor. When the liquid is poured 
 into B, and A is placed in a freez- p IG 
 
 ing mixture, the vapor is largely 
 condensed in A while more is rapidly formed in B. Crystals of ice 
 soon form on the surface of the water in B. 
 
 (b.) 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 rapidly evaporate it by 
 blowing over its surface a stream of air from a small bellows. So 
 much heat is rendered latent in the vaporization that the watch 
 crystal is firmly frozen to the wooden block. 
 
 (c.) Sulphurous oxide (SO S ) previously dried, is easily liquefied 
 by passing it through a U-tube immersed in a freezing mixture. 
 When some of this liquid is placed upon mercury in a small capsule 
 and rapidly evaporated by blowing over it a stream of air from a 
 bellows, the mercury is frozen ( 562). (See Chemistry, Exp. 146.) 
 
 592. Condensation of Gases. Gases may be 
 condensed by union with some liquid or solid, by cold or 
 by pressure. It has been recently shown that any known 
 gas may be liquefied by cold and pressure. In any case, 
 the condensation of a gas renders sensible a large 
 amount of heat. 
 
LATENT AND SPECIFIC HEAT. 
 
 443 
 
 FIG. 304. 
 
 (a.) The change of latent heat into sensible during the condensa 
 tion of a gas is easily illustrated 
 by the following experiment: 
 Into a gas bottle, A, put a tea- 
 cup full of small pieces of mar- 
 ble, and pour in enough water to 
 cover them and to seal the lower 
 end of the thistle tube. From 
 the gas bottle lead a delivery 
 tube to the lower part of a bot- 
 tle, B, containing a thermome- 
 ter, t. From this bottle lead a 
 tube to the lower part of the 
 bottle (?, which contains a ther- 
 mometer, T, with its lower part embedded in a teacup full of salts 
 of tartar. Through the thistle tube of A pour muriatic acid, about a 
 thimble-full at a time. Carbonic acid gas will be liberated and pass 
 through B into C. There it unites with the potassium carbonate, 
 changing it to potassium bi-carbonate. In this change from the 
 aeriform to the solid condition, the carbonic acid gives up all its 
 latent heat, as is shown by the remarkable rise of the thermometer 
 in C. That this increase of tem perature is not due to the sensible 
 heat of a hot gas is shown by the fact that t is scarcely affected 
 during the experiment, 
 
 (ft.) When the vapor is condensed to the liquid or solid form, the 
 heat previously rendered latent is given out as sensible heat ; that 
 is, the energy of position is changed back to energy of motion. In 
 coming together again, the particles yield the same amount of 
 kinetic energy as was consumed in their separation. 
 
 593. The Heat Equivalent of the Fusion of 
 Ice. If one pound of water at 0. be mixed with one 
 pound of water at 80 C., we shall have two pounds of water 
 at 40 C. But if one pound of ice at C. be mixed with one 
 pound of water at 80 C., we shall have two pounds of water 
 at The heat which might be used to warm the water 
 from to 80 C.. has been used in melting a like weight 
 of ice. Hence, by our definition, we see that the latent 
 heat of one kilogram of water is 80 calories. This means 
 that the amount of heat required to melt a quantity 
 
444 LATENT AND SPECIFIC HEAT. 
 
 of ice without changing its temperature is eighty 
 times as great as the heat required to warm the 
 same quantity of water one centigrade degree. 
 
 (a.) Because of this great latent heat of water, the processes of 
 melting ice and freezing water are necessarily slow. Otherwise, the 
 waters of our northern lakes might freeze to the bottom in a single 
 night, while " the hut of the Esquimaux would vanish like a house 
 in a pantomime," or all the snows of winter be melted in a single 
 day with inundation and destruction. 
 
 594. The Heat Equivalent of the Vaporiza- 
 tion of Water. Experiment has shown that the 
 amount of heat necessary to evaporate one weight unit of 
 water would suffice to raise the temperature of 537 weight 
 units of water 1 C. Hence, we say that the latent heat of 
 one kilogram of steam is 537 calories. This means that 
 the amount of heat required to evaporate a quantity 
 of water without changing its temperature is 537 
 times as great as the heat required to warm the 
 same quantity of water one centigrade degree. 
 
 (a.) When a pound of steam is condensed, 537 heat units (pound - 
 centigrade) are liberated. In this, we see an explanation of the 
 familiar fact that scalding by steam is so painfully severe. Were 
 it not for the latent heat of steam, when water reached its boiling 
 point it would instantly flash into steam with tremendous explosion. 
 
 595. Problems and Solutions. (1.) How many grams 
 of ice at C. can be melted by 1 gram of steam at 100 C. ? One 
 gram of steam at 100 C., in condensing to water at the same tem- 
 perature, parts with all its latent heat, or 537 lesser calories. The 
 gram of water thus formed can give out 100 more heat units. 
 Hence, the whole number of lesser calories given out by the steam 
 in changing to water at C., the temperature at which it can no 
 longer melt ice, is 537 + 100 637. 
 
 Let x = the number of grams of ice that can be melted. Each 
 gram of ice melted will require 80 lesser calories. Hence, 80# the 
 number of heat units necessary. The heat to melt the ice must 
 come from the steam. 
 
 Therefore, SQx = 637. . '. # = 7.96 + grams. Ans. 
 
LATENT AND SPECIFIC HEAT. 44<3 
 
 (jj.) How many pounds of steam at 100 C. will just melt 100 
 pounds of ice at C. ? If x represent the number of pounds of 
 steam required, that quantity of steam at 100 C. will furnish. 637a- 
 heat units. To melt 100 Ibs. of ice, (80 x 100 =) 8,000 heat units 
 will be required. 
 
 Hence, 637 '= 8,000. .'. x = 12.55 + Ibs. Am. 
 
 (3.) What weight of steam at 100 C. would be required to raise 
 500 pounds of water from C. to 10 C. ? 
 Let x = the number of pounds of steam required. 
 (537 + 90)z = 500 x 10. .'. x = 7.97 + Ibs. Ans. 
 
 (4.) If 4 Ibs. of steam at 100 C. be mixed with 200 Ibs. of water at 
 10 C., what will be the temperature of the water ? 
 
 Let x the temperature. In condensing to water at 100 C., the 
 4 Ibs. of steam will give out (537 x 4 =) 2,148 heat units. This 
 4 Ibs. of water will then give out 4(100 x) heat units. Hence, the 
 steam will impart 2,148 + 4(100 x) heat units. The 200 Ibs. of 
 water in rising from 10 C. to x will absorb 200(# 10) heat units. 
 
 Hence, 2,148 + 4(100 -x) = 200(#-10). .'. x = 22.29 C. Ana. 
 
 596. Illustration of Specific Heat. When 
 the temperature of a body changes from 30 to 20, the 
 body loses just as much heat as it gained in passing from 
 20 to 30. This heat lost by a cooling body may be 
 measured, like any other energy, by the work it can per- 
 form. If equal weights of different bodies be raised to the 
 same temperature, the amount of ice that each can melt 
 will be proportional to the number of thermal units they 
 severally contain. A pound of sulphur at 212 F. will 
 melt as much ice as a pound of boiling water. Hence, 
 it required only | as much heat to heat the sulphur from 
 the freezing point to 212 F., as it did to heat the water 
 to the same temperature; in scientific phraseology, the 
 specific heat of sulphur is . 
 
 (a.) In an experiment of this kind, if the cooling substance change 
 its condition, the latent heat set free as sensible heat must be taken 
 into account. Special precaution must also be taken in measuring 
 
446 
 
 LATENT AND SPECIFIC HEAT. 
 
 the heat expended, to avoid melting of the ice by the heal 
 
 of the surrounding air and making proper 
 
 allowance for the heat expended in warming 
 
 the apparatus itself. Fig. 256 represents a 
 
 form of calorimeter frequently used in such 
 
 Bxperiments. M contains the heated body 
 
 whose weight and temperature are known. 
 
 A contains the ice to be melted, the liquid 
 
 thus produced escaping by D. B is an ice 
 
 jacket to prevent melting of the ice in A by 
 
 the heat of the air. 
 
 597. Definition of Specific 
 Heat. The specific heat of a body 
 is the ratio between the quantity 
 
 FIG. 305. 
 
 of heat required to warm that body one degree and 
 the quantity of heat required to "warm an equal 
 weight of water one degree. 
 
 (a.) It is very important to bear in mind that specific heat, like 
 specific gravity, is a ratio ; nothing more nor less. The specific heat 
 of water, the standard, is unity. This ratio will be the same for 
 any given substance, whatever the thermal unit or thermometric 
 scale adopted. 
 
 598. Specific Heat Determined by Mixture. 
 
 One of the simplest methods of measuring specific heat 
 is by mixture. Suppose, e. g., that 3 kilograms of mercury 
 at 100 C. are mixed with 1 kilogram of ice-cold water and 
 that the temperature of the mixture is 9 C. How shall 
 we find the specific heat of mercury ? 
 
 Let x = the specific heat of the mercury, or the amount of heat 
 lost by one kilogram of mercury for each degree of change of 
 temperature. Then will 
 
 3.r = the number of heat units lost by the given amount of mer- 
 cury for every degree of change of temperature, and 91 times 
 3x, or 
 
 273x = the number of heat units lost by the mercury in passing 
 from 100 to 9 C. 
 
 The specific heat of water is 1. This multiplied by the number 
 f kilograms of water taken is 1, which represents the number of 
 
LATENT AND SPECIFIC HEAT. 
 
 447 
 
 heat units gained by that quantity of water for each degree of 
 change of temperature. Then will 9 represent the number of heat 
 units gained by the water in passing from to 9. But no heat 
 has been destroyed or wasted ; what the mercury has lost, the water 
 has gained. 
 
 Mercury. Water. 
 
 Specificheat x 1 
 
 Weights taken 3 1 
 
 No. of degrees of change 91 9 
 
 Heat units 273$ = 9 
 
 .'. x .033, the specific heat of mercury. 
 
 599. Heated Balls Melting Wax. The differ- 
 ence between bodies in respect to specific heat may be 
 roughly illustrated as follows : small balls of equal weight, 
 made severally of iron, copper, tin, lead and bismuth are 
 heated to a temperature of 180 or 200 C. by immersing 
 them in hot oil until they all acquire the temperature of 
 the oil. They are then placed on a cake of beeswax about 
 
 half an inch 
 thick. The iron 
 and copper will 
 melt their way 
 through the 
 wax, the tin will 
 nearly do so, 
 while the lead 
 and bismuth 
 sink not more than half way through the wax. 
 
 600. Reference Tables. (1.) Specific Heat of some sub- 
 stances : 
 
 Iron... .1138 
 
 FIG. 306. 
 
 Hydrogen 3.4090 
 
 Water 1.0000 
 
 Ammonia (gas) 5084 
 
 Air 2375 
 
 Oxygen 2175 
 
 Sulphur 2026 
 
 Diamond 1469 
 
 Copper. 0952 
 
 Silver 0570 
 
 Tin 0562 
 
 Mercury 0333 
 
 Lead 0314 
 
 Bismuth 0308 
 
448 LATENT AND SPECIFIC HEAT. 
 
 (2.) Specific heat of some substances in different states : 
 
 Solid. Liquid. Aeriform 
 
 Water 5050 1.0000 .4805 
 
 Bromine 0843 .1060 .0555 
 
 Alcohol .6050 .4534 
 
 Ether .5467 .4797 
 
 6O1. Specific Heat of Water. Water in iU 
 liquid form has a higher specific heat than any 
 other substance except hydrogen. For this reason the 
 ocean and our lakes are cooled and heated more slowly 
 than the land and atmosphere. They thus modify sudden 
 changes of temperature, and give rise to the well known 
 fact that the climate of the sea-coast is warmer in wintei 
 and cooler in summer than that of inland places of the 
 same latitude. The heat of summer is stored up in the 
 ocean and slowly given out during the winter. This fact 
 also explains a phenomenon familiar to those living on the 
 borders of the ocean or great lakes. Because of its lower 
 specific heat, the land becomes during the day more heated 
 than the water. The air in contact with the land thus 
 becomes more heated, expands, rises and forms an upper 
 current from the land accompanied by a corresponding 
 under current to the land, the latter constituting the 
 welcome sea or lake breezes of summer. After sunset, 
 however, the land cools more rapidly than the water, the 
 process is reversed, and we have an under current from 
 the land constituting the land breeze. 
 
 EXERCISES. 
 
 1. One kilogram of water at 40 C., 2 kilograms at 30 C., 3 kilo- 
 grams at 20 C., and 4 kilograms at 10 C. are mixed. Find the tern 
 perature of the mixture. Am. 20 C. 
 
 2. One pound of mercury at 20 C. was mixed with one pound ol 
 
LATENT AND SPECIFIC HEAT. 449 
 
 water at C., and the temperature of the mixture was 0.634 C. 
 Calculate the specific heat of mercury. 
 
 3. What weight of water at 85 C. will just melt 15 pounds of 
 ice at C. ? Ans. 14.117 Ib. 
 
 4. What weight of water at 95 C. will just melt 10 pounds of ice 
 at 10 C. ? Ana. 8.947 Ib. 
 
 5. What weight of steam at 125 C. will .melt 5 pounds of ice at 
 8 C. and warm the water to 25 C. ? Ans. 0.87 Ib. 
 
 6. How much mercury could be warmed from 10 C. to 20 C. by 
 1 kilogram of steam at 200 C. ? Ans. 1997 Kg. 
 
 7. Equal masses of ice at C. and hot water are mixed. The ice 
 is melted and the temperature of the mixture is C. What was 
 the temperature of the water ? Ans. 80 C. 
 
 8. Ice at C. is mixed with ten times its weight of water at 
 20 C. Find the temperature of the mixture. Ans. 11 C. nearly. 
 
 9. One pound of ice at C. is placed in 5 pounds of water at 
 12 C. What will be the result? 
 
 10. Find the temperature obtained by condensing 10 g. of steam 
 at 100 C. in 1 Kg. of water at C. Ans. 6.3 C. 
 
 11. A gram of steam at 100 C. is condensed in 10 grams of water 
 at C. Find the resulting temperature. Ans. 58 C. nearly. 
 
 12. If 200 g. of iron at 300 C. be plunged into 1 Kg. of water at 
 C., what will be the resulting temperature ? Ans. 6.67 C. 
 
 13. Find the specific heat of a substance, 80 g. of which at 100 C. 
 being immersed in 200 g. of water at 10 gives a temperature of 
 20 C. 
 
 14. If 300 g. of copper at 100 C. be immersed in 700 g. of alcohol 
 at C., what will be the resulting temperature ? ( 600.) 
 
 15. What will be the result of mixing 5 ounces of snow at C. 
 with 23 ounces of water at 20 C. ? 
 
 16. A pound of wet snow mixed with 5 pounds of water at 20 C. 
 yields 6 pounds of water at 10 C. Find the proportions of snow 
 and water in the wet snow. 
 
 17. What weight of mercury at C. will be raised one degree 
 by dropping into it 150 g. of lead at 300 C. ? 
 
 18. Find the result of mixing 6 pounds of snow at C. with 
 7 pounds of water at 50 C. 
 
 Recapitulation. In this section we have considered 
 the definition of Thermal Units ; two Varieties 
 of Molecular Energy ; their mutual Converti- 
 bility ; the definition of Latent Heat ; the latent 
 
450 MODES OF DIFFUSING HEAT. 
 
 heat of Fusion and of Solution ; Freezing Mix- 
 tures ; Solidification, and the Temperature of 
 Solidification ; Heat from Solidification ; 
 Change of Bulk during solidifying; the Latent 
 Heat of Vaporization ; the Condensation of 
 Gases ; the Latent Heat of Water and of 
 Steam; illustration and definition of Specific Heat; 
 specific heat Determined by Mixture; specific 
 heat Determined by Melting Wax; tables of 
 specific heat, and the Specific Heat of Water. 
 
 IV, 
 
 \. 
 MODES OF DIFFUSING HEAT. 
 
 602. Diffusion of Heat. Heat is diffused in three ways . 
 Dy conduction, convection, and radiation. Whatever the mode of 
 diffusion, there is a tendency to produce uniformity of temperature. 
 
 603. Conduction. If one end of an iron poker be 
 thrust into the fire, the other end will soon become too 
 warm to be handled. It has been heated by conduction, 
 the molecules first heated giving some of their heat to those 
 adjacent, and these passing it on to those beyond. There 
 was a transfer of motion from molecule to molecule. The 
 process by which heat thus passes from the hotter 
 to the colder parts of a body is called conduction 
 of heat. The propagation is very gradual, and as rapid 
 through a crooked as through a straight bar. 
 
 604. Differences in Conductivity. If, instead 
 of an iron poker, we use a glass rod or wooden stick, the 
 end of the rofl may be melted or the end of the stick 
 
MODES OF DIFFUSING HEAT. 
 
 451 
 
 FIG. 307- 
 
 burned without rendering the other end uncomfortably 
 warm. We thus see that some substances are good con- 
 ductors of heat while some are not. Thrust a silver and 
 a German silver spoon into the same vessel of hot water, 
 and the handle of the former will become much hotter 
 than that of the latter. 
 
 (a.) Fig. 307 represents a bar of iron and one of copper placed 
 end to end so as to be heated equally by the flame of the lamp. 
 Small balls (or nails) are fastened by wax to the under surfaces of 
 the bars at equal distances apart. More balls can be melted from 
 the copper than from the iron. The number of balls melted off, not 
 the rapidity with which they fall, is the test of conductivity. The 
 rapidity would depend more upon specific heat. 
 
 (&.) Relative thermal conductivity of some metals : 
 
 Silver 100 
 
 Copper 74 
 
 Gold 53 
 
 Brass 24 
 
 Tin... 15 
 
 Iron 12 
 
 Lead 9 
 
 Platinum 8 
 
 German silver 6 
 
 Bismuth . , 2 
 
 The above-named metals arrange themselves in the same order 
 with reference to the conduction of electricity, silver being the best 
 and bismuth the poorest. This relation suggests a similarity of 
 nature between these two agents. 
 
 OO5. Conductivity of Fluids. Liquids and 
 aeriform bodies are poor conductors of Jieat. The 
 surface of a liquid may be intensely heated without sensibly 
 effecting the temperature an inch below. 
 
452 
 
 MODES OF DIFFUSING HEAT. 
 
 FIG. 
 
 Cork the neck of a glass funnel and pass the tube of an 
 inverted thermometer through the cork, or use an air 
 thermometer, as shown in the figure. Cover the ther- 
 mometer bulb to the depth of about half an inch with 
 water. Upon the water pour a little sulphuric ether 
 and ignite it. The heat of the flame will be intense 
 enough to boil a small quantity of water held over it> 
 but the thermometer below will be scarcely affected. 
 Fasten a piece of ice at the bottom of a glass tube, 
 and cover it to the depth of several inches with water. 
 Hold the tube at an angle of about 45, 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. The conductivity of gases is probably lower 
 
 308. than that of liquids. 
 
 6O6. Convection. Fluids (with the exception of 
 mercury, which is a metal) being poor conductors, they 
 cannot be heated as solids gen- 
 erally are. Water, e.g., must be 
 heated from below; the heated 
 molecules expand and rise while 
 the cooler ones descend to take 
 their place at the source of heat. 
 These currents in heating water 
 may be made visible by dropping 
 a small quantity of cochineal or 
 oak sawdust into the vessel con- 
 taining the water. This method 
 of diffusing heat, by actual 
 motion of heated fluid masses, 
 is called convection. Expansion 
 by heat and the force of gravity are essential to convection. 
 Since aeriform bodies are expanded more by heat than 
 liquids are, these currents of heated gases are more active 
 than those of liquids. Hence the drafts of lamps and 
 stoves, the existence of trade winds, etc. 
 
 FIG. 309. 
 
MODES OF DIFFUSING BEAT. 453 
 
 6O7. The Third Mode of Heat Diffusion. When a 
 
 hand is held over a heated stove, heat is carried to the hand by con- 
 vection and given up to the hand by conduction. But when the 
 hand is held before the stove it is also heated, not by conduction, for 
 fluids have little conducting power ; not by convection, for convec- 
 tion currents are ascending. How then does the heat get to the 
 hand ? The query comes to us with still greater force when we 
 consider the transmission of the sun's heat to the earth, for the 
 atmosphere can carry it by neither conduction nor convection. 
 More important yet, how does the sun's heat reach the earth's 
 atmosphere ? This heat passes through the atmosphere without 
 heating it. If along a poker thrust into the fire the hand be moved 
 toward the stove, the temperature increases. If a person ascend 
 through the atmosphere toward the sun the temperature diminishes. 
 We have here a wholly new set of thermal phenomena, heat pass- 
 ing through a substance and leaving the condition of that substance 
 unchanged. 
 
 6O8. Lumiiiiferous Ether. In the case of actual, 
 mechanical energy, the rapid motion of bodies, e. g., a 
 vibrating guitar string, is partly carried off by the air in 
 the shape of sound. When the sound reaches the auditory 
 nerve it represents a certain amount of mechanical energy 
 of motion which has been carried from the string by the 
 air. There is sufficient reason for believing that 
 there is a medium pervading all space which car- 
 ries off part of the invisible motions of molecules, 
 just as the air carries off a portion of the motion 
 of moving masses. This medium, called the luminiferous 
 ether, occupies all space. The gaps between the sun, the 
 planets and their satellites are filled with this ether. " It 
 makes the universe a whole and renders possible the inter- 
 communication of light and energy between star and star." 
 
 OO9. Density and Elasticity of the Ether. This ether 
 is wonderful, not only in its incomprehensible vastness but equally 
 so in its subtleness. While it surrounds the suns of unnumbered 
 systems and fills all interstellar space, it also surrounds the smallest 
 
454 MODES OF DIFFUSING 
 
 particles of matter and fills intennolecular space as well. It is 
 called luminiferous because it is tlie medium by which light ia 
 propagated, it serving as a common carrier for both heat and light. 
 We have seen ( 426) that the velocity of sound depends upon two 
 considerations, the elasticity and the density of the medium. The 
 enormous velocity with which the ether transmits heat and light as 
 wave motion (about 186,000 miles per second), compels us to assume 
 for the ether both extreme elasticity and extreme tenuity. 
 
 610. Radiant Heat. We have seen that the mole- 
 cules of a heated body are in a state of active vibration. 
 The motion of these vibrating molecules is communicated 
 to the ether and transmitted by it, as waves, with wonder- 
 ful velocity. Thus, when you hold your hand before a fire, 
 the warmth that you feel is due to the impact of these 
 ether- waves upon your skin ; they throw the nerves into 
 motion, just as sound-waves excite the auditory nerve, and 
 the consciousness corresponding to this motion is what we 
 popularly call warmth. Heat thus propagated by the 
 ether, instead of by ordinary forms of matter, is 
 Radiant Heat. Tlie process of propagation 
 
 is called radiation. t 
 
 611. The Transmission through a 
 Vacuum. Radiant heat mill traverse a 
 vacuum. "We might infer this from the fact 
 that the sun radiates heat to the earth. It may 
 be also shown experimentally. 
 
 (a.) A thermometer is sealed air-tight in the bottom 
 of a glass globe in such a way that the bulb is near the 
 centre of the globe. The neck of the flask is to be pj Gi 310. 
 about a yard long. The apparatus being filled with 
 mercury and inverted over a mercury bath, a Torricellian vacuum 
 is formed in the globe and upper part of the tube. The tube is 
 then melted off above the mercury. When the globe is immersed 
 In hot water, the thermometer immediately indicates a rise of tern 
 
MODES OF DIFFUSING HEAT. 455 
 
 perature. There is no chance for convection ; conduction acts much 
 more slowly. 
 
 612. Rectilinear Propagation. Radiant heat 
 travels in straight lines through any uniform 
 medium. 
 
 (a.) Between any source of heat and a thermometer place several 
 screens. If holes be made in the screens (See Fig. 321) so that a 
 straight line from the source of heat to the thermometer may pass 
 through them, the thermometer will be affected by the heat. By 
 moving one of the screens so that its opening is at one side of this 
 line, the heat is excluded. In a very warm day a person may step 
 from a sunny into a shady place for the same reason. The heat that 
 moves along a single line is called a ray of heat. 
 
 613. Radiation Equal in all Directions. 
 
 Heat is radiated equally in all directions. If an 
 iron sphere or a kettle of water be heated, and delicate 
 thermometers placed on different sides of it at equal dis- 
 tances, they will all indicate the same temperature. 
 
 614. Radiation Depends upon Tempera- 
 ture of the Source. The intensity of radiant 
 heat is proportional to the temperature of the 
 source. 
 
 (a.) Near a differential thermometer, place a vessel of water 10 
 warmer than the temperature of the room. Notice the effect upon 
 the thermometer. Heat the water 10 more and repeat the experi- 
 ment at the same distance. Then heat the water 10 still more and 
 repeat the experiment again. The effects upon the thermometer will 
 be as the numbers one, two and three. 
 
 615. Effect of Distance. The intensity of 
 radiant heat varies inversely as the square of the 
 distance. 
 
 (a.) Place the differential thermometer at a certain distance from 
 the heated water and note the effect. Removing the thermometei 
 to twice that distance the effect is only one-fourth as great, etc. 
 
456 MODES OF DIFFUSING HEAT. 
 
 616. Incident Rays. When radiant heat falls 
 upon a surface it may be transmitted, absorbed or reflected, 
 ff transmitted, it may be refracted. Kock salt crystal 
 transmits nearly all, reflects very little, and absorbs hardly 
 any. Lampblack absorbs nearly all, reflects very little, and 
 transmits none. Polished silver reflects nearly all, absorbs 
 a little, and transmits none. 
 
 617. Diathermancy. Bodies that transmit ra- 
 diant heat freely are called diathermanous; those 
 that do not are called atherrnanous. These terms 
 are to heat, what transparent and opaque are to light. 
 Rock salt is the most diathermanous substance known. 
 Heat that is radiated from a non-luminous source, as from 
 a ball heated below redness, is called obscure heat ; while 
 part of that radiated from a luminous source, as from the 
 sun or from a ball heated to redness, is called luminous 
 heat. Heat from a luminous source is generally composed 
 of both luminous and obscure rays. 
 
 618. Selective Absorption. The power of any 
 given substance to transmit heat varies with the nature of 
 the heat or of its source. For example, glass, water or 
 alum allows the sun's luminous heat rays to pass, while 
 absorbing nearly all of the heat rays from a vessel filled 
 with boiling water. In other words, these substances are 
 diathermanous for luminous rays, but athermanous for 
 obscure rays. The physical difference between luminous 
 and obscure heat rays will subsequently be explained. 
 
 (a.) A solution of iodine in carbon di-sulphide transmits obscure 
 rays but absorbs luminous rays. By means of these substances, 
 luminous and obscure rays may be sifted or separated from each 
 other. Dry air is highly diathermanous ; watery vapor is highly 
 athermanous for obscure rays. 
 
REFLECTION Of SEAT. 457 
 
 619. Reflection of Heat. When radiant heat 
 falls upon an athermanous body, part of it is generally 
 absorbed and raises the temperature of the body. The 
 rest is reflected, the energy still existing in the ether waves. 
 The angle of incidence equals the angle of reflec- 
 tion ( 97). 
 
 FIG. 311. 
 
 (a.) In Fig. 311, the source of heat at A is a Leslie's cube filled with 
 hot water. S is an athermanous screen with an aperture for the 
 passage of rays from A to the reflector B. The line CB is per- 
 pendicular to the reflector. When D, the bulb of the differential 
 thermometer, is placed so that the angle ABC equals the angle 
 DBG, the reflected rays will strike the bulb and raise the temper- 
 ature. 
 
 62O. Reflection by Concave Mirrors. By the 
 
 use of spherical or parabolic mirrors, remarkable heating 
 effects may be produced. When parallel rays (like the 
 sun's rays) strike directly upon such a mirror, they are 
 reflected to a focus. Any easily combustible substance 
 held at the focus may be thus ignited. 
 
 (a.) Two such mirrors may be placed as shown in Fig. 312. At 
 the focus of one reflector place a hot iron ball ; at the focus of the 
 other, a bit of phosphorus or gun-cotton. If the apparatus be 
 arranged with exactness, the combustible will be quickly ignited. 
 
458 
 
 HEFRACTlON OF BEAf. 
 
 FIG. 312. 
 
 Replace the iron ball with a Leslie's cube containing hot water ; 
 at the focus of the other reflector place one bulb of the differential 
 thermometer. The rise of temperature at this focus will be clearly 
 shown, even when the other bulb is nearer the source of heat than the 
 focus is. 
 
 621. Refraction of Heat. When rays of heat 
 fall obliquely upon a diathermanous body, they will be 
 bent from a straight line on entering and leaving the body. 
 This bending of the ray is called refraction. Many 
 rays of heat may thus be concentrated at a focus, as in the 
 case of a common burning-glass. By the aid of a spectacle- 
 glass, the sun's rays may be made to ignite easily combus- 
 tible substances. The refraction of obscure rays cannot 
 be shown by a glass lens, since glass is athermanous for 
 such rays. But if a rock-salt lens be held before a source 
 of obscure heat, and the face of a thermopile placed at 
 
RADIANT BEAT. 450 
 
 the focus of the lens, the galvanometer needle will at once 
 turn aside, showing a rise of temperature. If the face of 
 the pile be placed anywhere else than at the focus, there 
 vill be no such deflection of the needle. 
 
 622. Change of Radiant into Sensible Heat, 
 
 - -Of all the rays falling upon any substance, only those 
 ihat are absorbed are of effect in heating the body upon 
 which they fall. The motion of the ether waves may be 
 changed into vibrations of molecules of ordinary matter, 
 and thus produce sensible heat, but the same energy can- 
 not exist in waves of ether and in ordinary molecular 
 vibrations at the same time. 
 
 (a.) Phosphorus or gun-cotton may be ignited by solar rays at 
 the focus of a lens made of clear ice. The heat rays pass through 
 the ice without melting it. It is only when the radiation is stopped 
 that the energy of the ray can warm anything. 
 
 623. Determination of Absorbing', Reflecting and 
 Radiating 1 Powers. For experiments in determining the 
 absorbing, reflecting and radiating powers of solids, the apparatus 
 generally used consists of a Leslie's cube, concave mirrors of 
 different materials, and a differential thermometer or a thermopile. 
 The Leslie's cube is a box about three inches on each edge, the 
 sides being made of, or covered with, different materials, to show 
 their differences in radiating power. The cube filled with hot water 
 is placed before the reflector, and a bulb of the thermometer is 
 placed at the focus. By turning different faces of the cube toward 
 the mirror, the relative radiating powers are determined. By using 
 different mirrors, the reflecting powers are determined. By coating 
 the bulb with different substances, their absorbing powers are 
 determined. The relative radiating powers of several common 
 substances are as given below : 
 
 Lampblack 100 
 
 Paper 98 
 
 Crown glass 90 
 
 Tarnished lead. 45 
 
 Mercury 20 
 
 Gold, silver, copper 12 
 
 624. Mutual Relations of Absorption, Re- 
 flection and Radiation. By means like those men- 
 
460 RADIANT HEAT. 
 
 tioned in the last paragraph, it has been shown that 
 good absorbents are good radiators and poor re- 
 flectors, and vice versa ; that the radiating power of a 
 body depends largely upon the nature of its surface ; that 
 smoothing and polishing the surface increases reflecting 
 power, and diminishes absorbing and radiating power; 
 that roughening and tarnishing the surface increases the 
 absorbing and radiating powers, and diminishes the re- 
 flecting power. The poivers of absorption and radi- 
 ation go hand in hand. (See 721, 722.) 
 
 (a.) Make a thick paint of a teaspoonful of lampblack and & 
 little kerosene oil. With this, paint the right-hand face of the 
 left-hand bulb (tin can of the differential thermometer described in 
 Appendix R). Provide another oyster can and paint one side with 
 the lampblack. Fill this third can with boiling water and place 
 it on the wooden strips, midway between the two tin bulbs, the 
 two blackened surfaces facing each other. The heat radiated and 
 absorbed by the two blackened surfaces will exceed the heat radi- 
 ated and absorbed by the two equal unpainted surfaces that face 
 each other. The movement of the colored alcohol in the tube will 
 show this to be true. 
 
 625. Sympathetic Vibrations. The relation 
 between radiation and absorption of heat is closely analo- 
 gous to the relation between the radiation and absorption 
 of sound. If a set of sound waves fall upon a string 
 capable of producing similar waves, the string is set in 
 motion and the sound waves weakened ( 509). When 
 ether waves of a given kind fall upon a body whose mole- 
 cules are able to vibrate at the same rate, and thus to 
 reproduce similar waves, the kinetic energy is transferred 
 from the ether to the molecules, the molecules are heated, 
 the radiant energy absorbed. This ability to absorb wave 
 motion of any particular kind, implies the ability to repro- 
 duce the same kind of waves. It therefore is easily seen 
 
MODES OF DIFFUSING HEAT. 461 
 
 that a body that can absorb any particular kind 
 of heat rays can radiate the same kind. 
 
 . It will be seen further on, that obscure heat rays diffei 
 from light only in the matter of icave length. Most of the phenomena 
 of one may be shown to pertain to the other. Absorption, radiation, 
 reflection, transmission and refraction of rays follow the same laws, 
 whether the agent be called heat or light. Other phenomena, such 
 as interference and polarization, more satisfactorily studied with 
 luminous rays, have been produced with obscure rays. It should 
 be borne in mind that the most delicate instruments yet made are 
 far less sensitive to obscure heat than is the eye to light. A candle 
 flame may be seen a mile away ; any one might well be pleased with 
 an instrument that would detect its heat at the distance of a rod. 
 
 QUESTIONS. 
 
 1. Good conductors feel warmer or cooler to the touch than poor 
 conductors of the same temperature. Why ? 
 
 2. Why is it so oppressively warm when the sun shines after a 
 summer shower ? 
 
 3. Why is there greater probability of frost on a clear than on 
 a cloudy night ? 
 
 4. Can a good absorbent be a good reflector of heat ? Is a good 
 absorbent a good radiator, or otherwise ? 
 
 5. Explain why the glass covering of a hot-bed or conservatory 
 renders the confined air warmer than the atmosphere outside. 
 
 6. From your own experience, decide which is the better con- 
 ductor of heat, linen or woolen goods, oil-cloth or carpet. 
 
 7. Why are the double walls of ice-houses filled with sawdust-? 
 Why do fire-proof safes have double walls inclosing plaster-of- 
 Paris or alum ? 
 
 8. Why do furnace men, firemen and harvesters wear woolen 
 clothing ? Explain the use of double windows. 
 
 9. How may heat be diffused ? How is the surface of the earth 
 and how is the atmosphere heated ? Can you boil water in a vessel 
 with heat applied from above ? Why? 
 
 Recapitulation. In this section we have considered 
 Conduction; the conductivity of Fluids; Con- 
 vection; the Luminiferous Ether, its Den* 
 
4 02 THERMODYNAMICS. 
 
 sity and Elasticity ; Radiant Heat, and 
 diation ; Diathermancy; Selective Absorp- 
 tion ; Reflection from plane and concave surfaces ; 
 Refraction ; the Change from radiant into sensible 
 heat; the determination of Absorbing, Reflecting 
 and Radiating Powers, and their Mutual Re- 
 lations ; Sympathetic Vibrations. 
 
 V, 
 
 THERMODYNAM ICS. 
 
 626. Definition of Thermodynamics. Ther- 
 modynamics is the branch of science that considers 
 the connection between heat and inechanical work. 
 It has especial reference to the numerical relation between 
 the quantity of heat used and the quantity of work done. 
 
 627. Correlation of Heat and Mechanical Energy. 
 
 We know that heat is not a form of matter because it can be 
 created in any desired quantity. We must continually remember 
 that it is a form of energy. When, heat is produced some other 
 kind of energy must be destroyed. Conversely, when heat is de- 
 stroyed, some other form of energy is created. Considered as heat 
 merely, this agent may be annihilated ; considered as energy, it 
 may only be transformed. The most important transformations of 
 energy are those between heat and mechanical energy. The process 
 of working these transformations will be considered directly. It is 
 to be noticed, however, that while we may be able to effect a total 
 conversion of mechanical energy into heat, we are not able to bring 
 about a total conversion of heat into mechanical energy. 
 
 628. Heat from Percussion. A small iron rod 
 placed upon an anvil may he heated to redness hy repeated 
 blows of a hammer. The energy of the moving mass is 
 
THERMOD YNAMICS. 
 
 463 
 
 broken up, so to speak, and distributed among the mole- 
 cules, producing that form of molecular motion that we call 
 heat. The same transformation was 
 illustrated in the kindling of a fire by 
 the "flint and steel " of a century ago, 
 It may be experimentally illustrated 
 by the "air-syringe." 
 
 (a.) The air-syringe consists of a cylinder 
 of metal or glass and an accurately fitting 
 piston. By suddenly driving in the piston, 
 the air is compressed and heat developed. 
 A bit of gun cotton previously placed in 
 the cylinder may thus be ignited. If the 
 cylinder be made of glass, and a bit of ordi- 
 nary cotton dipped in carbon disulphide be 
 used, repeated flashes of light may be pro- 
 duced by successive combustions of ether 
 vapor. The fumes of one combustion 
 must be blown away before the next com- 
 bustion is attempted. 
 
 629. Heat from Friction. 
 
 Common matches are ignited and cold 
 hands warmed by the heat developed 
 by friction. It is said that some savages kindle fires 
 by skilfully rubbing together well-chosen pieces of wood. 
 In the case of the axles of railway cars and ordinary car- 
 riages, this conversion of mechanical energy into heat is 
 not so difficult as its prevention. Lubricants are used to 
 diminish the friction and prevent the waste of energy due 
 to the undesirable transformation. A railway train is 
 really stopped by the conversion of its motion into heat. 
 When this has to be done quickly, the change is hastened 
 by increasing the friction by means of the brakes. Ex- 
 amples of this change are matters of every day experience. 
 
 FIG. 313. 
 
464 
 
 THE R MOD TNAMICS. 
 
 (a.) Attach a brass tube 10 cm. long, about 2 cm. in diameter and 
 closed at the bottom, to a whirling table. Partly fill the tube with 
 alcohol and cork the open end. Press the tube between two pieces 
 of board hinged together as shown in the figure. The boards should 
 
 FIG. 314. 
 
 have two grooves for the reception of the tube ; the inner faces of 
 the boards may be covered with leather. When the machine is set 
 in motion, the friction warms and soon boils the alcohol. The vapor 
 drives out the cork with explosive violence. 
 
 630. First Law of Thermodynamics. -When 
 heat is transformed into mechanical energy or 
 mechanical energy into heat, the quantity of heat 
 equals the quantity of mechanical energy. This 
 principle is the corner-stone of thermodynamics. It is 
 a particular case under the more general law of the Con- 
 servation of Energy. 
 
 631. Joule's Equivalent. It is a matter of great 
 importance to determine the numerical relation between 
 heat and mechanical energy ; to find the equivalent of a 
 heat unit in units of work. This equivalent was first 
 Ascertained by Dr. Joule, of Manchester, England. Hi 
 
THERMODYNAMICS. 465 
 
 experiments were equal in number and variety to the im- 
 portance of the subject. He showed that the mechanical 
 value of the heat required to warm a given weight of 
 
 water 
 
 ( 424 meters against gravity. 
 I'd., would lift the water .......... 1^90 feet 
 
 1 F., would lift the water ............ 772 " 
 
 and represents 41,552,000,000 ergs per calorie. 
 
 Any weight unit may be used without changing the 
 above values which should be remembered. 
 
 Keferring to centigrade degrees, we say that the 
 mechanical value of a calorie is 424 kilogrammeters or 
 that of the third unit ( 579 a) is 1,390 foot-pounds. 
 
 Eef erring to the fourth heat unit mentioned in 579 (), 
 we say that its mechanical value is 772 foot-pounds. 
 
 632. The Use of Joule's Equivalent. The 
 
 use of the mechanical equivalent of heat may be well shown 
 by the solution of a problem. 
 
 (a.) If a cannon-ball weighing 192.96 pounds and moving with a 
 velocity of 2000 feet per second, be suddenly stopped and all of its 
 kinetic energy converted into heat, to what temperature would it 
 warm 100 pounds of ice-cold water ? 
 
 wtf 192.96 x 4000000 
 Kinetic energy = -- = = 12000000 foot-pounds. 
 
 12000000 *- 772 = 15544 + heat units. 
 
 15544 -f- 100 = 155.44 heat units for each pound of water. This 
 would raise the temperature 155.44 R, leaving it at 187.44 F. Ans. 
 
 (6.) Knowing the weight of the earth and its orbital velocity, we 
 may easily compute the amount of heat that would be developed by 
 the impact of the earth against a target strong enough to stop its 
 motion. The heat thus generated from the kinetic energy of the 
 earth would be sufficient to fuse if not vaporize it, equalling 
 that derivable from the combustion of fourteen globes of coal 
 each equal to the earth in size. After the stoppage of its orbital 
 motion it would surely be drawn to the sun with continually 
 increasing velocity. The heat instantaneously developed from 
 
466 
 
 THERMO D YNAMICS. 
 
 this impact of the planetary projectile would equal that derivable 
 from the combustion of 5600 globes of coal each equal to the earth 
 in size. This is the measure of the potential energy of the earth 
 considered as a mass separated from the &un. 
 
 633. Chemical Affinity. We have already seen 
 that there are forces in nature compared with which the 
 force of gravity is insignificant. (Read carefully the first 
 paragraph in this chapter.) When coal is burned, the 
 carbon and oxygen particles rush together with tremendous 
 violence, energy of position being converted into energy of 
 motion. The molecular motions produced by this clashing 
 of particles constitute heat and have a mechanical value. 
 
 634. Heat Equivalent of Chemical Union. 
 
 If a pound of carbon be burned, the heat of the combus- 
 tion would raise about 8,000 pounds of water 1 C. In 
 like manner, the combustion of a gram of hydrogen would 
 yield about 34,000 lesser calories. 
 
 (a.) The following table shows the heating powers of several 
 substances when burned in oxygen : 
 
 Hydrogen 34,462 
 
 Marsh gas (CH 4 ) 13,063 
 
 Petroleum 12,300 
 
 Carbon 8,080 
 
 Alcohol (C 3 H 6 0) 6,850 
 
 Phosphorus .... 5,747 
 
 Carbon protoxide (CO) 2,403 
 
 Sulphur 2,220 
 
 (6.) The calorific powers mentioned above may be adapted to Fah- 
 renheit degrees by multiplying them respectively by f . As they 
 stand, the numbers represent the number of times its own weight 
 of water that could be warmed 1 C. by burning the substance in 
 oxygen. 
 
 635. The Steam -Engine. The steam-engine is a 
 machine for utilizing the tension of steam. Its essential 
 parts are a boiler for the generation of steam, and a cylinder 
 for the application of the tension to a piston. 
 
THE STEAM-ENGINE. 467 
 
 (a.) As in the case of water-power the production of mechanical 
 kinetic energy involves the fall of water from a higher to a lower 
 level, so in the case of steam-power the production of visible 
 energy involves the fall of heat from a higher to a lower temper- 
 ature. 
 
 636. Single-Acting Engine. In a single-acting steam 
 engine, the piston is pushed one way by the tension of the steam, 
 The steam is then condensed and the piston driven back by atmos 
 pli eric pressure. Such engines have gone out of use and have only 
 an historical interest. 
 
 637. Double - Acting Engine. In a double- 
 acting steam-engine, the steam is admitted to the cylinder 
 alternately above and below the' piston. This alternate 
 admission of the steam is accomplished by means of a 
 sliding-valve. The sliding-valve is placed in a steam-chest, 
 S 9 which is fastened to the side of the cylinder C. 
 
 FIG. 315. 
 
 (a. ) In the figure, the steam-chest is represented as being placed 
 tit a distance from the cylinder; this is merely for the purpose 
 of making plain the communicating passages to and from the 
 chest. Steam from the boiler enters at M, passes through A to the 
 
468 THE STEAM-ENGINE. 
 
 FIG. 316. 
 
 cylinder, where it pushes down the piston as indicated by the 
 arrows. The steam below the piston escapes by B and N. As the 
 piston nears the opening of B in the cylinder, the sliding- valve is 
 raised, by means of the rod R, to the position indicated in Fig. 
 267. Steam now enters the cylinder by B and pushes up the piston. 
 The steam above the piston escapes by A and N. As the piston 
 nears the opening of A in the cylinder, the sliding- valve is pushed 
 down by R and the process is thus repeated. The piston-rod and 
 the sliding-valve rod work through steam-tight packing -boxes. 
 (Appendix S.) 
 
 638. The Eccentric. By means of a crank or 
 similar device, illustrated in common foot-power machinery 
 like the turning-lathe, scroll-saw, or sewing-machine, the 
 alternating rectilinear motion of the piston-rod is changed 
 into a continuous rotary motion. A circular shaft is thus 
 given a revolution for every to-and-fro movement of the 
 piston. This shaft generally carries an eccentric for work- 
 ing the sliding-valve rod R. The eccentric (Fig. 317) con- 
 sists of a circular piece of metal, 0, rigidly attached to the 
 shaft of the engine 8, in such a position that the centre of 
 the piece does not coincide with the centre of the shaft, 
 
THE STEAM-ENGINE. 
 
 469 
 
 The eccentric turns within a collar, which is fastened to 
 the frame T. Every turn of the shaft moves the eccentric 
 with its collar and the frame T, backward and forward into 
 the two positions indicated by the full and dotted lines of 
 
 FIG. 317. 
 
 Fig. 317. The point a may be fastened directly to the 
 slidirig-valve rod or through the agency of the bent lever, 
 abc, as the circumstances of the case render more desirable. 
 
 639. The Governor and Fly- Wheel. The 
 
 admission of steam through M (Fig. 316) is regulated by a 
 throttle valve worked by a governor (Fig. 318). A vertical 
 shaft is given a rotary motion by the machinery. To the 
 top of this rod are hinged two arms carrying heavy balls, fib. 
 From these arms, supports extend to a 
 collar, c, surrounding the vertical rod. 
 This collar is connected with a valve con- 
 trolling the admission of steam to the 
 valve-chest in such a way that when the 
 collar rises the valve closes. As the 
 machinery increases its speed, the balls 
 revolve more rapidly about the vertical 
 axis and tend to fly further apart ( 74). 
 In doing so, they raise the collar and partly close the valve, 
 diminishing the supply of steam. The machinery is thus 
 made to slacken its speed, the balls fall, and the valve opens. 
 The rapidity of motion can therefore be confined within 
 
 FIG. 318. 
 
470 
 
 THE STEAM-ENGTNE. 
 
 FIG. 319. 
 
 the limits due to closing the throttle-valve and throwing 
 it wide open. Further than this, smoothness of motion is 
 secured by attaching a heavy fly-wheel to the shaft of the 
 engine. A little reflection will show that the fly-wheel 
 also acts as an accumulator of energy. 
 
 O4O. The Safety- Valve. The safety-valve is a 
 necessary part of every steam-boiler. It consists of a 
 valve, V, held down over an opening in the top of the 
 boiler by means of a spring or a 
 loaded lever of the second class. 
 The force with which the valve 
 is held down is to be less than 
 the strength of the boiler, i. e., 
 the force must be such that the 
 valve will open before the tension 
 
 of the steam becomes dangerous. On steamboats, the 
 weight, W, is generally locked in position by a Government 
 officer. 
 
 641. Non-Condensing Engines. When the 
 
 steam is forced out at N (Fig. 316), it has to overcome an 
 atmospheric pressure of 15 pounds to the square inch. 
 This must be deducted from the total tension of the steam 
 to find the available power of the engine. Such an engine 
 is known as a non-condensing engine. It may be recog- 
 nized by the escape of steam in puffs. It is generally a 
 high-pressure engine. The railway locomotive is a high- 
 pressure, non-condensing engine. 
 
 (a.) Only a small part of the heat developed by the combustion of 
 the fuel can be converted into mechanical energy by the engine. 
 Most of it passes off in the exhaust steam, still existing as lieat 
 which is wasted, so far as useful effect is concerned. The ratio 
 between the heat delivered to the engine and the heat converted for 
 
THE STEAM-ENGINE. 471 
 
 doing the work is called the efficiency of the engine. "It is not 
 possible, even with a perfect engine, to convert into work more than 
 15 per cent, of the heat used." 
 
 642. Condensing Engines. The steam may be 
 conducted from the exhaust pipe, N (Fig. 316), to a chamber 
 called a condenser. Steam from the cylinder and a jet of 
 cold water being admitted at the same time, a vacuum is 
 formed and the loss of energy due to atmospheric pressure 
 is avoided. Such an engine is known as a condensing, or 
 low-pressure engine. 
 
 (a.) Low-pressure engines are always condensing engines. A low- 
 pressure engine will do more work with a given amount of fuel 
 than a high-pressure, non-condensing engine will, is less liable to 
 explosion, and causes less wear and tear to the machinery. But it 
 must be larger, more complicated, more costly and less portable. 
 
 643. Heat and Work of Steam-Engines. - 
 
 More heat is carried to the cylinder of a steam-engine than 
 is carried from it. The piston does work at every stroke 
 and this work comes from the heat that disappears. Every 
 stroke of the piston annihilates heat. Careful experiments 
 show that the heat destroyed and the work performed are 
 in strict agreement with Joule's equivalent. With a given 
 supply of fuel, the engine will give out less heat when it 
 is made to work hard than when it runs without doing 
 
 much work. 
 
 EXERCISES. 
 
 1. The mechanical equivalent of heat is 1,390 foot-pounds. What 
 is it in kilogrammeters ? 
 
 2. Find the weight of water that may be warmed 15 C. by burn- 
 ing 1 ounce of sulphur in oxygen. Ans. 148 oz. 
 
 3. What weight of water would be heated from C. to 1 C. by 
 the combustion of one gram of phosphorus ? Ans. 5,747 g. 
 
 4. One gram of hydrogen is burned in oxygen. To what tempera- 
 ture would a kilogram of water at C. be raised by the combustion V 
 
 5. From what height must a block of ice at C. fall that the heat 
 generated by its collision with the earth shall be just able to melt it 7 
 
472 THERMODYNAMICS. 
 
 6. From what height must it fall that the heat generated may be 
 sufficient to vaporize it ? Am. 996,630 ft. in vacuo. 
 
 7. To what height could a ton weight be raised by utilizing all the 
 heat produced by burning 5 Ib. of pure carbon ? Am. 28,078 ft. 
 
 8. Find the height to which it could be raised if the coal had the 
 following percentage composition : 
 
 C = 88.42 ; H = 5.61 ; = 5.97. 
 
 9. To what temperature would a cannon-ball weighing 150 Ib. 
 and moving 1,920 feet per sec., warm 2,000 Ib. of water at 32 F., if 
 its motion were suddenly converted into heat ? Am. 37 F. 
 
 10. (a.) How many pounds of water can be evaporated by 80 Ib. 
 of pure carbon ? (6.) If applied to iron, how many pounds could be 
 heated from F. to 2,000 F, ? Ans. (a.) Not more than 1,203.72 Ib. 
 
 11. With what velocity must a 10-ton locomotive move to give 
 a mechanical energy equivalent to the heat necessary to convert 
 48 pounds of ice at C. to steam at 100 C.? Ans. 392 ft. 
 
 12. An 8-lb. ball is shot vertically upward in a vacuum with a 
 velocity of 2,000 feet. How many pounds of water may be raised 
 from the freezing to the boiling point by the heat generated when 
 it strikes the earth on its descent ? Ans. 3.57 Ib. 
 
 13. (a.) From what height must water fall in order to raise its 
 own temperature 1 C. by the destruction of the velocity acquired, 
 supposing no other body to receive any of the heat thus generated? 
 (Answer to be given in meters.) (&.) How far must mercury fall to 
 produce the same effect? (Specific heat of mercury = .0333.) 
 
 14. With a velocity of how many cm. per second must a leaden 
 bullet strike a target that its temperature may be raised 100 C. by 
 the collision, supposing all the energy of the motion to be spent in 
 heating the bullet ? (Specific heat of lead=.0314; ^=980 cm. % 127.) 
 
 15. A steam-engine raises a ton weight 386 ft. How many calories 
 are thus expended ? 
 
 16. A 64-pound cannon-ball strikes a target with a velocity of 
 1,400 feet per second. Supposing all the heat generated to be given 
 to 60 pounds of water, how many centigrade degrees would the 
 temperature of the water be raised ? Ans. 23.3. 
 
 17. A cannon ball weighing 7 pounds strikes an iron target with a 
 velocity of 1,000 feet per second. Suppose the whole of the motion 
 to be converted into heat and the heat uniformly distributed through 
 70 pounds of the target, determine the change of temperature thus 
 produced. (Specific heat of iron = .1138.) Ans. 17.7 F. 
 
 18. 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 melt- 
 ing point, 442 F., and to melt it. Ans. 136,217.856 foot-pounds. 
 
REVIEW. 473 
 
 Recapitulation. In this section we have considered 
 the definition of Thermodynamics ; the Corre- 
 lation of Heat and Mechanical Energy ; 
 heat from Percussion ; from Friction ; First 
 Law of thermodynamics; Joule's Equivalent 
 and its Use ; Chemical Affinity and the Heat- 
 ing Powers of various substances ; the Single and 
 Double-acting Steam-engines ; the Eccen- 
 tric, Governor and Safety-valve ; Condens- 
 ing and Non-condensing Engines ; the relation 
 between Heat and Work in the steam-engine. 
 
 REVIEW QUESTIONS AND EXEKCISES. 
 
 1. Lead melts at 326 C. In melting it absorbs about as much 
 heat as would warm 5.37 times its weight of water 1C. What 
 numbers will replade the 326 and 5.37 when the Fahrenheit scale is 
 used? 
 
 2. What is the difference between the temperatures 40 C. and 
 -40 F. ? 
 
 3. A quantity of gas at 100 C. and under a pressure of 750 mm. of 
 mercury measures 4500 cu. cm. What will be its volume at 200 C. 
 and under a pressure of 76 cm. of mercury ? Ans. 5,631 cu. cm. 
 
 4. Over how high a ridge can you carry water in a siphon, where 
 the minimum range of the barometer is 27 inches ? Explain. 
 
 5. (.) What is Specific Gravity ? (6.) How do you find that of solids 
 heavier than water ? (c.) What principle is involved in your method ? 
 
 6. (a.) Of what physical force is lightning a manifestation ? (6.) 
 Give some plain directions for the construction of lightning-rods, 
 with reasons for your directions. 
 
 7. Give the fundamental principle of mechanics, and illustrate its 
 application by one of the mechanical powers. 
 
 8. (a.) What are the essential properties of matter? (&.) What is a 
 pendulum ; (c.) to what use is it principally applied, and (d.) what 
 are the laws by which it is governed ? 
 
 9. (a.) In what ways may two musical tones differ? (&.) What ia 
 the physical cause of the diffe^nce in each case ? 
 
 10. (a.) Convert -3 F. and 77 F. into G- readings ; (6.) 18 C 
 and 20 C. to F. readings. 
 
474 
 
 11. (a.) To what temperature should a liter of oxygen at C. be 
 raised in order to double its volume, the pressure remaining con- 
 stant? (b.) Give reasons for your answer. Ans. 273 C. 
 
 12. (a.) What is meant by the boiling point of a liquid ? (&.) State 
 some circumstances that cause it to vary. 
 
 13. A kilogram each of water, iron and antimony, at C. are 
 heated ten minutes by the same source of heat, and are then found 
 to be 1 C., 9 C. and 20 C. respectively. Kequired the specific heat 
 of each. 
 
 14. (a.) Define latent heat. (&.) Describe a method of determining 
 the latent heat of water, (c.) Describe the cooling and freezing of 
 a lake. 
 
 15. (a.) If 2 kilograms of water should be suddenly stopped after 
 falling 212 metres, how much heat would be generated? (6.) 
 Describe the essential parts of a steam-engine. 
 
 16. (a.} How many cubic feet of water will be displaced by a boat 
 weighing two tons ? (&.) How many of salt water of sp. gr. 1.09 ? 
 (c.) How does a noise differ from a musical sound ? 
 
 17. The sp. gr. of alcohol is .8 ; that of mercury 13.6. When a 
 mercury barometer indicates a pressure of 30 inches, what will be 
 the height of an alcohol barometer column ? Ans. 510 in. 
 
 18. (a.) Describe the ordinary force-pump ; (&.) explain the use of 
 its essential parts. 
 
 19. (.) Give the formulas for changing thermometric readings 
 from F. to C., and vice versa. (&.) Explain the graduation of two 
 kinds of thermometers, (c.) Define increment of velocity. 
 
 20. (a.) What is distillation, and upon what fact does the process 
 depend? (&.) What is latent heat? (c.) Illustrate the conversion 
 of sensible into latent heat, (d.) On what does the pitch of sound 
 depend ? 
 
 21. (a.) Define boiling and boiling-point. (6.) What is the rate of 
 expansion for gases ? (c.) Will water boil at a lower temperature 
 at the sea level or on the top of a mountain ? Why ? (d.} What 
 constitutes the timbre of a sound ? (e.) Give the formulas for the 
 wheel and axle. 
 
 22. (a.) If the pressure remain the same, how much will 546 cu. cm. 
 of hydrogen expand when heated from C. to 10 C. ? (&.) How 
 much work may be performed by a ball weighing 64.32 lb., moving 
 with a velocity of 50 ft. per second? (c.) When has water the 
 greatest density ? Ans. (a.) 20 cu. cm. (&.) 2,500 foot -pounds. 
 
 23. Show that to raise the temperature of a pound of iron from 
 C. to 100 C. requires more energy than to raise seven tons of iron 
 a foot high. 
 
IX. 
 
 LIGHT. 
 
 ECTJON I. 
 
 THE NATURE, VELOCITY AND INTENSITY 
 OF LIGHT. 
 
 644. What is Light? Light is that mode of 
 motion which is capable of affecting the optic 
 nerve. The only physical difference between light 
 and radiant heat is one of wave length. 
 
 (a.) We have seen that the vibrations of air particles in a sound 
 wave are to and fro in the line of propagation. In the case of 
 radiant heat and light, the ether particles vibrate to and fro across 
 the line of propagation. Vibrations in a sound wave are longitudi- 
 nal ; those of a heat or light wave are transversal. 
 
 645. Luminous and Non-Luminous Bodies. 
 
 Bodies that emit light of their own generating, as the 
 sun or a candle, are called luminous. Bodies that merely 
 diffuse the light that they receive from other bodies are 
 said to be non-luminous or illuminated. Trees and plants 
 are non-luminous. 
 
 (a.) Visible bodies may be luminous or illuminated, but in either 
 case they send light in every direction from every point in their 
 surfaces. In Fig. 320 we see represented a few of the infinite 
 number of lines of light starting from A, B and C, three of the 
 
476 THE NATURE OF LIGHT. 
 
 infinite number of points in the surface of a visible object. If the 
 
 infinite number of lines were drawn from each of the infinite number 
 of points, there would be no vacant spaces in 
 the figure ; the rays really intersect at every 
 point from which the object is visible. 
 
 646. Transparent, Translu- 
 cent and Opaque Bodies. Bodies 
 are transparent, translucent or opaque 
 according to the degree of freedom which 
 
 they afford to the passage of the luminiferous waves. 
 Transparent bodies allow objects to be seen distinctly 
 through them, e. (/., air, glass and water. Translucent 
 bodies transmit light, but do not allow bodies to be seen 
 distinctly through them, e. g., ground glass and oiled paper. 
 Opaque bodies cut off the light entirely and prevent 
 objects from being seen through them at all. The light 
 is either reflected or absorbed. So much of the radiant 
 energy as is neither reflected nor transmitted is changed 
 to absorbed heat. 
 
 647. Luminous Rays. A single line of light is 
 called a ray. The ray of light is perpendicular to the 
 wave of ether. The ray may, without considerable error, 
 be deemed the path of the wave. 
 
 648. Luminous Beams and Pencils. A col- 
 lection of parallel rays constitutes a beam ; a cone of rays 
 constitutes a pencil. The pencil may be converging or 
 diverging. If a beam or pencil should dwindle in thick- 
 ness to a line, it would become a ray. 
 
 649. Rectilinear Motion of Light. A medium 
 is homogeneous when it has an uniform composition and 
 density. In # homogeneous medium, light travels 
 
TffE NATURE OF LIGHT. 477 
 
 in straight lines. This is a fact of incalculable scien- 
 tific and otherwise practical importance. 
 
 (a.) The familiar experiment of "taking sight" depends upon 
 this fact, for we see objects by the light which they send to the eye. 
 We cannot see around a corner or through a crooked tube. A beam 
 of light that enters a darkened room by a small aperture, marks an 
 illuminated course that is perfectly straight. 
 
 (&.) This fact may be illustrated by providing two or three per- 
 forated screens and arranging them as shown in Fig. 321, so that 
 the holes and a candle flame shall be in the same straight line. 
 
 FIG. 321. 
 
 When the eye is placed in this line behind the screens, light passes 
 from the flame to the eye ; the flame is visible. A slight displace- 
 ment upward, downward or sidewise of the eye, the flame or any 
 screen, cuts off the light and renders the flame invisible. 
 
 (c.) Prepare a piece of wood, 1| x 2| x 18 inches, taking care that 
 the edges are square. Saw it into six pieces, each three inches long. 
 Prepare three pieces of wood, 3 x 4 x ^ inches. Place three postal 
 cards one over the other on a board, and pierce them with a fine 
 awl or stout needle, | inch from the end and 1* inch from either 
 side of the card. With a sharp knife pare off the rough edges of 
 the holes, and pass the needle through each hole to make the edges 
 smooth and even. Over the ^ x 3 inch surface of one of the blocks 
 place the unperforated end of one of the postal cards, and over this 
 place one of the 3x4 inch pieces, so that their lower edges shall be 
 
478 THE NATURE OF LIGHT. 
 
 even. Tack them in this position. Make thus two more similar 
 screens. The three screens, with a bit of candle three inches long, 
 placed upon one of the remaining blocks, furnishes the material 
 for the experiment above. Save the screens and three blocks for 
 future use. (See Fig. 329.) 
 
 65O. Inverted Images. If light from a highly- 
 illuminated body be 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 upon 
 
 FIG. 322. 
 
 the screen. Every visible point of the illuminated object 
 sends a ray of light to the screen. Each ray brings the 
 color of the point which sends it and prints the color upon 
 the screen. As the rays are straight lines, they cross at 
 the aperture; hence, the inversion of the image. The 
 image will be distorted unless the screen be perpendicular 
 to the rays. The darkened room constitutes a camera 
 obscura. The image of the school playground at recess is 
 very interesting and easily produced. 
 
 (a.) Place a lighted candle about a meter from a white screen in 
 a darkened room. (The wall of the room will answer for the screen.) 
 Pierce a large pin-hole in a card and hold it between the flame and 
 the screen. An inverted image of the flame will be found upon the 
 screen. 
 
 (6.) Bore an inch hole in one side of a wooden box ; cover thii 
 
THE NATURE OF LIGHT. 479 
 
 opening with tin-foil and prick the tin-foil with a needle. Place a 
 lighted candle within the box ; close the box with a lid or a shawJ 
 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 
 size of the object is to the size of the image as the distance from 
 the aperture to the object is to the distance from the aperture to the 
 image. 
 
 (c.) Cover one end of a tube, 10 or 12 cm.^ong, with tin-foil ; the 
 other end with oiled paper. Prick a pin-hole in the tin-foil and turn 
 it toward a candle flame. The inverted image may be seen upon 
 the oiled paper. The size of the image will depend upon the dis- 
 tance of the flame from the aperture. The apparatus rudely repre- 
 sents the eye, the pin-hole corresponding to the pupil and the oiled 
 paper to the retina. (Almost any housekeeper will give you an 
 empty tin can. Place it upon a hot stove just long enough to melt 
 off one end, thrust a stout nail through the centre of the other 
 end, cover the nail-hole with tin-foil, and you will have the greater 
 part of the apparatus.) 
 
 651. Shadows. Since rays of light are straight, 
 opaque bodies cast shadows. A shadow is the dark- 
 
 FIG. 323. 
 
 ened space behind an opaque body from which all 
 rays of light are cut off. It is sometimes called the 
 perfect shadow or the umbra. If the source of light be a 
 point, the shadow will be well defined ; if it be a surface, 
 the shadow will be surrounded by an imperfect shadow 
 called a penumbra. The penumbra is the darkened space 
 
4&0 THE NATURE OF LlGIfT. 
 
 behind an opaque body from which some of the rays (the 
 rays from a part of the luminous surface) are cut off. 
 
 (a.) Hold a lead pencil between the flame of an ordinary lamp 
 and a sheet of paper held about two feet (61 cm.) from the lamp ; 
 (1.) When the edge of the flame is toward the pencil; (2.) When 
 the side of the flame is. to ward the pencil. 
 
 652. Visual Angle. The angle included be- 
 tween two rays of light coming from the extrem- 
 ities of an object to the centre of the eye is called 
 the visual angle. This angle measures the apparent 
 length of the line that subtends it. Any cause that 
 increases the visual angle of an object increases its appa- 
 rent size. Hence the effect of magnifying-glasses. From 
 
 FTG. 324. 
 
 Fig. 324 we see that equal lines may subtend different 
 visual angles, or that different lines may subtend the same 
 angle. 
 
 65.3. Velocity of Light. Light traverses the ether 
 with a velocity of about 186,000 miles or about 298 mil- 
 lion meters per second. This was first determined about 
 200 years ago by Roemer, a Danish astronomer. 
 
 (a.) At equal intervals of 42h. 28m. 36s., 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 intervals if light 
 traveled instantaneously from planet to planet. Roemer found 
 that when the earth was farthest from Jupiter the eclipse was seen 
 16 min. 36 sec. later than when the earth was nearest Jupiter. Bui 
 Jupiter and the earth are nearest each other when they are on the* 
 
NATURE OP LIGHT. 481 
 
 same side of the sun and in a straight line with the sun (conjunc- 
 tion), and farthest from each other when they are on opposite 
 aides of the sun and in a straight line with that luminary (opposi- 
 
 FIG. 325. 
 
 tion). Hence, Roemer argued that it requires 16 min. 36 sec. for 
 light to pass over the diameter of the earth's orbit, from Eto E'. 
 This distance being approximately known, the velocity of light is 
 easily computed. 
 
 (6.) The velocity of light has been measured by other means, 
 giving results that agree substantially with the result above given. 
 When astronomers accurately determine the mean distance of the 
 earth from the sun, the velocity of light will be accurately known. 
 
 (c.) It would require more than 17 years for a cannon-ball to pass 
 over the distance between the sun and the earth ; light makes the 
 journey in 8 min. 18 sec. For the swiftest bird to pass around the 
 earth would require three weeks of continual flight ; light goes as 
 far in less than one seventh of a second. For terrestrial distances, 
 the passage of light is practically instantaneous ( 487). 
 
 654. Effect of Distance upon Intensity. 
 
 The intensity of light received by an illuminated 
 body varies inversely as the square of its distance 
 from the source of light. 
 
 (a.} Let a candle at 8 be the source of light ; A, a screen one foot 
 square and a yard from 8 ; B, a screen two feet square two yards 
 from 8; 0, a screen three feet square three yards from S. It 
 will easily be seen that A will cut off all the light from B and (7. 
 If now A be removed, the quantity of light which it received, no 
 more and no less, will fall upon B. If now B be removed, the 
 quantity of light which previously illuminated A and B will fall 
 upon C. We thus see the same number of rays successively illu 
 
8 'THE ft AZURE OP LICF&T. 
 
 trfnating, one, four and nine square feet. One square foot at B will 
 
 receive one-fourth, and one 
 square foot at C will receive 
 one-ninth as many rays as 
 one square foot at A. The 
 light being diffused over a 
 greater surface is corres- 
 pondingly diminished in in- 
 tensity. 
 
 (6.) The experiment may 
 be tried by placing the large 
 screen at A and tracing the 
 outline of the shadow with 
 a pencil, then placing the 
 
 FIG. 326. screen successively at B and 
 
 C, tracing the shadow each. 
 
 time. The experiment will be more satisfactory if a perforated 
 screen be placed at 8. (See First Prin. Nat. Phil., 428.) 
 
 EXERCISES. 
 
 1. A coin is held 5 feet from a wall and parallel to it. A lumi 
 nous 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 ? 
 
 2. (a.) What is the velocity of light ? (&.) How was it determined ? 
 
 3. (a.) How are the intensities of two lights compared ? (6.) De- 
 fine light, (c.) Give your idea of the carrier of radiant heat and light. 
 
 4. (a.) Define luminous, transparent, opaque, beam and pencil. 
 (6.) How could you show that light ordinarily moves in straight 
 lines ? (c.) Explain the formation of inverted images in a dark room. 
 
 5. A " standard " candle (burning 120 grains of sperm per hour) is 2 
 feet from a wall, a lamp is 6 feet from the wall. They cast shadows of 
 equal intensity on the wall. What is the " candle power " of the lamp ? 
 
 Recapitulation. In this section we have considered 
 the Nature of Light; Luminous, Illuminated, 
 Transparent, Translucent and Opaque bodies ; 
 Rays, Beams and Pencils of light; that Light 
 Moves in Straight Lines; Inverted Images 
 and Shadows ; the Visual Angle ; the Veloc- 
 ity and Intensity of light. 
 
THE NATURE OF L1GHI. 48.') 
 
 ECTION II. 
 
 REFLECTION OF LIGHT. 
 
 Note. The heliostat, or porte-lumtire, is composed of one oi 
 more mirrors, by means of which a beam of light may be thrown 
 in any desired direction. The instrument may be had of apparatus 
 manufacturers at prices ranging from $12 upward. Directions for 
 making one may be found in Mayer & Barnard's little book on 
 " Light," published by D. Appleton & Co. It is very desirable that 
 the instrument be secured in some way. 
 
 655. Reflection. If a sunbeam enter a darkened 
 room by a hole in the shutter, as at A, and fall upon a 
 
 FIG. 327. 
 
 polished plane surface, as at B, it will be continued in a 
 different direction, as toward C. AB is called the incident 
 beam and EC the reflected beam ( 97). The incident 
 and the reflected beams are in the same medium, the air. 
 A change in the direction of light mithout a change 
 in its medium is called reflection of light. 
 
 656. Laws of Reflection. The reflection of light 
 
484 REFLECTION OF LIGHT. 
 
 from polished surfaces is m accordance with the following 
 laws: 
 
 (1.) The angle of incidence is equal to the angle 
 of reflection. 
 
 (2.) The incident and reflected rays are both in 
 the same plane, which is perpendicular to the 
 reflecting surface. 
 
 (a.) Fill a basin to the brim with mercury or with water blackened 
 with a little ink. In this liquid suspend by a thread a small 
 weight of greater specific gravity than the liquid used ( 253). The 
 plumb-line will be perpendicular to the liquid mirror. Let the 
 plumb-line hang from the middle of a horizontal meter or yard- 
 
 FIG. 328. 
 
 stick. Place the tip of a candle flame opposite one of the divisions 
 of the stick, and place the eye in such a position that the image of 
 the top of the flame will be seen in the direction of the foot of 
 the plumb-line. Mark the point where the line of vision (i. e., the 
 reflected rays) crosses the meter- stick. It will be found that this 
 point and the tip of the flame are equally distant from the middle 
 of the stick. From this it follows (Olney's Geometry, Art. 342) 
 that the angles of incidence and of reflection are equal. 
 
 (&.) Fig. 328 represents a vertical semiaircle graduated to degrees, 
 with a background of black velvet. A mirror at the centre is 
 furnished with an index set perpendicular to its plane ; both mirror 
 and index can be turned in any direction desired. A ray of light 
 from any brilliant source is allowed to enter the tube at the base, 
 in the direction of the centre. By means of a little smoke from 
 brown paper, the paths of the incident and reflected rays are easily 
 shown to a large claws. 
 
REFLECTION OF LIGHT. 485 
 
 (c.) Place two of the screens and the three extra blocks men- 
 tioned in 649 in position, as shown in Fig. 329. At the middle 
 of the middle block place a bit of window glass, 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 mir- 
 ror on the middle block. Place a candle flame near the hole in one 
 of the screens, as shown in the figure. 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 the exact spot in the mirror with a 
 needle held in place by a bit of wax. Place a piece of stiff writing 
 paper upright upon m and n, mark the position of B and of m, 
 and draw on the paper a straight line joining these two points. 
 The angle between this line and tho lower edge of the paper 
 coincides with the angle Bmn. Reverse the paper, placing it upon 
 
 FIG. 329. 
 
 m and o. It will be found that the same angle coincides with 
 Amo. Amo and Bmn being thus equal, the angle of incidence 
 equals the angle of reflection. 
 
 657. Diffused Light. Light falling upon an 
 opaque body is generally divided into three parts : the 
 first is regularly reflected in obedience to the laws above ; 
 the second is irregularly reflected or diffused ; the third is 
 absorbed. The irregular reflection is due to the fact that 
 the bodies are not perfectly smooth, but present little pro- 
 tuberances that scatter the light in all directions, and thus 
 render them visible from any position. Light regularly 
 reflected gives an image of the body from which it came 
 before reflection ; light irregularly reflected gives an image 
 
486 REFLECTION OF LIGHT. 
 
 of the body that diffuses it. A perfect mirror would be 
 invisible. Luminous bodies are visible on account 
 of the light that they emit; non-luminous bodies 
 are visible on account of the light that they dif- 
 fuse. 
 
 (a.) If a beam of light fall upon a sheet of drawing paper, it 
 will be scattered and illuminate a room. If it fall upon a mirror, 
 nearly all of it will be reflected in a definite direction, and intensely 
 illuminate a part of the room. Place side by side upon a board 
 a piece of black cloth (not glossy), a piece of drawing paper and a 
 piece of looking-glass. In a darkened room, allow a beam of sun- 
 light to fall upon the cloth and notice the absorption. Let it fall 
 upon the paper, and notice the diffusion of the light and its effects. 
 Let it fall upon the looking-glass, and notice the regular reflection 
 and its effects. Move the board so that the cloth, paper and glass 
 ghall pass through the beam in quick succession, and notice the 
 effects. 
 
 (6.) In the darkened room place a tumbler of water upon a table ; 
 with a hand-mirror reflect a sunbeam down into the water ; the 
 tumbler will be visible. Stir a teaspoonful of milk into the water, 
 and again reflect the sunbeam into the liquid ; the whole room will 
 be illuminated by the diffused light, the tumbler of milky water 
 acting like a luminous body. 
 
 658. Invisibility of Light. Rays of light that 
 do not enter the eye are invisible. A sunbeam 
 entering a darkened room is visible because the floating 
 dust reflects some of the rays to the eye. If the reflecting 
 particles of dust were absent the beam would be invisible. 
 
 (a.) Take any convenient box, about 60 cm. (2ft.) on each edge, 
 provide for it a glass front, and, at each end, a glass window about 
 10cm. (4 inches) square. Place it on a table in a darkened room, 
 and, with the heliostat, send a solar beam through the windows. 
 Standing before the glass front of the box, this beam may be 
 traced from the heliostat to the box, through the box and beyond 
 it. Open the box, smear the inner surfaces of its top, back and 
 bottom with glycerine, and close the box air-tight. Allow it to 
 remain quiet a few days ; the dust in the box will be caught by 
 the glycerine and the confined air thus freed from particles capablf? 
 
REFLECTION OF LIGHT. 487 
 
 of reflecting light. Then send another solar beam from the helio- 
 stat through the two windows of the box. Standing as before, 
 the beam may be traced to the box and beyond it, but within th 
 box all is darkness. 
 
 659. Apparent Direction of Bodies. Ever} 
 
 point of a visible object sends a cone of rays to the eye. 
 The pupil of the eye is the base of the cone. The point 
 always appears at the place where these rays seem 
 to intersect (i. e. 9 at the real or apparent apex of the cone). 
 If the rays pass in straight lines from the point to the eye, 
 the apparent position of the point is its real position. If 
 these rays bo, bent by reflection, or in any other manner, 
 the point will appear to be in the direction of 
 the rays as they enter the eye. No matter how 
 devious the path of the rays in coming from the point to 
 the eye, this important rule holds good. 
 
 660. Plane Mirrors; Virtual Images. If an 
 
 object be placed before a mirror, an image of it appears 
 
 behind the mirror. In- 
 asmuch as the rays of 
 the cone mentioned in 
 659 do not actually con- 
 verge back of the mirror, 
 there can be no real image 
 there. As there really is 
 no image behind the mir- 
 ror, we call it a virtual 
 image. All virtual images 
 are optical illusions, and 
 
 are to be clearly distinguished from the real images to be 
 studied soon. Each point of this image will seem 
 to be as far behind the mirror as the correspond/ 
 
488 REFLECTION OF LIGHT. 
 
 ing point of the object is in front of the mirror, 
 Hence, images seen in still, clear water are inverted. 
 
 (a.) In Fig. 330, let A represent a luminous point ; MM, a mirror ; 
 A A' and BG, lines perpendicular to the mirror. Rays from A enter 
 the eye at DD'. The angle ABC = the angle CBD (656). The 
 angle ABC = the angle BAA (Olney's Geometry, Art. 150). There 
 fore the angle CBD = the angle BAA ' . The angle CBD = the angle 
 BA'A (Olney, 152). Therefore the angle BAA = the angle BAA. 
 Hence AM A' M (Olney, 287). In other words, A' is as far behind 
 the mirror as A is in front of it. 
 
 (&.) Place a jar of water 10 or 15 cm. back of a pane of glass placed 
 upright on 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 of the candle 
 wi; 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. 
 
 661. Reflection of Rays from Plane Mir- 
 rors. If the incident rays be parallel, the reflected rays 
 will be parallel. If the incident rays be diverging, the 
 reflected rays will be diverging ; they will seem to diverge 
 from a point as fur behind the reflecting surface as their 
 source is in front of that surface (See Fig. 330). If the 
 incident rays be converging, the reflected rays will be con- 
 verging ; they will converge at a point as far in front of 
 the mirror as the point at which they were tending to 
 converge is behind the mirror. 
 
 662. Construction for the Image of a 
 Plane Mirror. The position of the image of an object 
 may be determined by locating the images of several well- 
 chosen points in the object and connecting these images. 
 
 (a.} In Fig. 331, let AB represent an arrow ; MN, the reflecting 
 gurface of a plane mirror, and E the eye of the observer. Froio 
 
REFLECTION OF LIGHT. 
 
 489 
 
 FIG. 331- 
 
 , draw Aa perpendicular to MN and make ad equal to Ad. Then 
 will a indicate the position of the image 
 of A. From B, draw Bb perpendicular 
 to MN and make be equal to Be. Then 
 E will b indicate the position of the image 
 of B. By connecting a and b we locate 
 the image of AB. Draw aE, bE, Ao 
 and Bi. AoE represents one ray of the 
 cone of rays from A that enters the eye ; 
 BiE represents one ray of a similar cone 
 from B. Draw a similar figure on a 
 larger scale, representing the eye at G. 
 Test your figure by seeing if the angle of incidence is equal to the 
 angle of reflection. In all such constructions, represent the direction 
 of the rays by arrow-heads, as shown in Fig. 331. 
 
 663. Multiple Images. By placing two mirrors 
 facing each other, we may produce multiple images of 
 an object placed between them. Each image acts 
 tt,s a material object with respect to the other 
 'mirror, in which we see an image of the first 
 image. "When the mirrors are placed so as to form an 
 angle with each other, the number of images becomes 
 limited, being one less than the number of times that the 
 included angle is contained in four 
 
 right angles. The mirrors will give 
 three images when placed at an angle 
 of 90; five at 60; seven at 45. 
 
 (a.} 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, a' and a". 
 
 664. Concave Mirrors. A spherical concave 
 mirror may be considered as a small part of a spherical 
 shell with its inner surface highly polished. Let MN (Fig. 
 333) represent the section of such a concave spherical mir- 
 
490 REFLECTION OF LIGHT. 
 
 ror, and C the centre of the corresponding sphere. C is called 
 the centre of curvature ; A is the centre of the mirror. A 
 straight line of indefinite length drawn from A through 
 (7, as A CX, is called the principal axis of the mirror. A 
 straight line drawn from any other point of the mirror 
 through C, as 
 JCd, is called a 
 secondary axis. 
 The point F, 
 midway between 
 
 A and (7, is 
 
 11 j ^ FlG - 333 ' 
 
 called the prin- 
 cipal focus. The distance AF is the focal distance of the 
 mirror ; the focal distance is, therefore, one-half the radius 
 of curvature. The angle MCN is called the aperture of 
 the mirror. 
 
 (a.) A curved surface may be considered as made up of an infinite 
 number of small plane surfaces. Thus, a ray of light reflected from 
 any point on a curved mirror may be considered as reflected from a 
 plane tangent to the curved surface at the point of reflection. This 
 reflection then takes place in accordance with the principles laid 
 down in 656. It should be borne in mind that the radii drawn 
 from C to points in the mirror as / and J are perpendicular to the 
 mirror at these points. Thus, the angles of incidence and reflection 
 for any ray may be easily determined. 
 
 665. Effect of Concave Mirrors. The ten- 
 clency of ou concave jnirror is to increase the con- 
 vergence or to decrease the divergence of incident 
 rays. 
 
 (a.) If the divergence be that of rays issuing from the principal 
 focus, the mirror will exactly overcome it and reflect them as par- 
 allel rays. If the divergence be greater than this, viz., that of rays 
 issuing from a point nearer the mirror than the principal focus, the 
 mirror cannot wholly overcome the divergence, but will diminish it 
 
REFLECTION OF LIGHT 491 
 
 The reflected rays will still diverge, but not so rapidly as the incident 
 rays. If the divergence be less than that first mentioned, viz., that 
 of rays issuing from a point further from the mirror than the prin- 
 cipal focus, the divergence will be changed to convergence and a 
 peal focus will be formed. 
 
 666. The Principal Focus. The focus of a con- 
 cave mirror is the point toward which the reflected rays 
 converge. All incident rays parallel to the principal axis 
 will, after reflection, converge at the principal focus. The 
 principal' focus is the focus of rays parallel to the 
 principal axis. The rays will be practically parallel 
 when their source is at a very great distance, e. g., the sun's 
 rays. Solar rays coming to the human eye do not diverge 
 a thousandth of an inch in a thousand miles. 
 
 (a.) Above we stated that parallel rays would be made to converge 
 at the principal focus of a spherical concave mirror. This is only 
 approximately true; it is strictly true in the case of a parabolic 
 mirror. In order that the difference between the spherical and the 
 parabolic mirror may be reduced to a minimum, the aperture of a 
 spherical mirror must be small. The case is somewhat analogous 
 to the coincidence of a circular arc of small amplitude with the 
 cycloidal curve ( 144, a). A source of light placed at the focus of 
 a parabolic mirror will have its rays reflected in truly parallel lines. 
 The head lights of railway locomotives are thus constructed. Para- 
 bolic mirrors would be more common if it were not so difficult to 
 make them accurately. 
 
 667. Conjugate Foci. Rays diverging from a 
 luminous point in front of a concave spherical mirror and 
 at a distance from the mirrcr greater than its focal distance, 
 will converge, after reflection, at another point. The focus 
 thus formed will be in a line drawn through the luminous 
 point and the centre of curvature. In other words, if the 
 luminous point lie in thr principal axis, the focus will also ; 
 if the luminous point lie in any secondary axis, the focus 
 will lie in the same secondary axis. The distinction be- 
 
492 
 
 REFLECTION OF LIGHT. 
 
 fcween principal and secondary axes is almost wholly one 
 of convenience. Rays diverging from B will form a focus 
 at b. The angle of incidence being necessarily equal to the 
 
 FIG. 334. 
 
 angle of reflection, it is evident that rays diverging from b 
 would form a focus at B. On account of this relation 
 between two such points, they are called conjugate foci. 
 Therefore, conjugate foci are two points so related 
 that each forms the image of the other. 
 
 668, Construction for Conjugate Foci. In the case 
 of concave mirrors, to locate the conjugate focus of a luminous 
 point, it is necessary to find the point at which at least two reflected 
 rays really or apparently intersect. The method may be illustrated 
 as follows : 
 
 Fin. 335- 
 
 (1.) Let 8 (Fig. 335) represent the luminous point whose con- 
 jugate focus is to be located. It may or may not lie in the principal 
 axis. Draw the axis for the point S, *.., a line from S through C\ 
 17 
 
REFLECTION OF LIGHT. 493 
 
 the centre of curvature, to the mirror. This line represents one ol 
 the infinite number of rays sent from 8 to the mirror. As this 
 incident ray is perpendicular to the mirror, the reflected ray will 
 coincide with it. (Angles of incidence and of reflection = 0.) The 
 conjugate focus must therefore lie in a line drawn through 8 and 0. 
 Draw a line representing some other ray, as Si. From i, the point 
 of incidence, draw the dotted perpendicular iC. Construct the 
 angle Cis equal to the angle CiS. Then will is represent the direc- 
 tion of the reflected ray. The focus must also lie in this line. The 
 intersection of this line with the line drawn through 8C marks the 
 position of 8, the conjugate focus of 8. 
 
 (2.) If the reflected rays be parallel, of course no focus can be 
 formed. If they be divergent, produce them back of the mirror as 
 dotted lines (Fig. 336) until they intersect. In this case the focus 
 will be virtual, because the rays only seem to meet. In the other 
 cases the focus was real, because the rays actually did meet. 
 
 FIG. 336. 
 
 (3.) With a radius of cm., describe ten arcs of small aperture to 
 represent the sections of spherical concave mirrors. Mark the 
 centres of curvature and principal foci, and draw the principal 
 axes. Find the conjugate foci for points in the principal axis 
 designated as follows : (1.) At a distance of 1 cm. from the mirror, 
 (2 ) Two cm. from the mirror. (3.) Three cm. from the mirror. 
 (4.) Four cm. from the mirror. (5.) Six 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. 
 
 669. Formation of Images. Concave mirrors 
 give rise to two kinds of images, real and virtual. After 
 
494 REFLECTION OF LIGHT. 
 
 learning what has been said concerning conjugate, real and 
 virtual foci, the formation of these images will be easily 
 understood. The image of an object is determined by 
 finding the images of a number of points in the object. 
 
 67 O. Construction for Real Images Formed by 
 Concave Mirrors. (1.) The method may be illustrated as 
 follows : Let AB represent an object in front of a concave mirror, 
 at a distance greater than the radius of curvature. Draw Ax, the 
 secondary axis for the point A. The conjugate focus of A will lie 
 in this line ( 668 [1]). From the infinite number of rays sent 
 from A to the mirror, select, as the second, the one that is 
 parallel to the principal axis. This ray, after reflection at t, will 
 pass through the principal focus ( 666). The reflected rays, t^and 
 xA (secondary axis for A), will intersect at , which is the con- 
 
 FIG. 337- 
 
 jugate focus for A In similar manner, b, the conjugate focus for 
 B, may be found. Points between A and B will have their con- 
 jugate foci between a and b. 
 
 (2.) If the eye of the observer be placed far enough back of the 
 image thus formed for all of the image to lie between the eye and 
 the mirror, it will receive the same impression from the reflected 
 rays as if the image were a real object. All of the rays from any 
 point in the object, as A, that fall upon the mirror, intersect after 
 reflection at a, the conjugate focus. These reflected rays, after 
 intersecting at a, form a divergent pencil. A cone of these rays 
 thus diverging from a enters the eye. They originally diverged 
 
REFLECTION OF LIGHT. 
 
 495 
 
 from A, but as they enter the eye, they diverge from a. Hence the 
 effect produced ( 659). 
 
 (3.) From the similar triangles, ABC and dbC, it is evident that 
 the linear dimensions of the object and of its image are directly 
 proportional to their distances from the centre of curvature. It 
 may also be proved that the length of the object is to the length of 
 the image as the distance of t^ie object from the principal focus is 
 to the focal distance of the mirror. 
 
 (4.) Since the lines that join corresponding points of object and 
 image cross at the centre of curvature, the real images formed by 
 concave mirrors are always inverted. 
 
 FIG. 338. 
 
 671. Projection of Real Images by Con- 
 cave Mirrors. The real image formed by a concave 
 mirror may be rendered visible even when the eye of the 
 observer is not in the position mentioned in the last article, 
 by projecting it upon a screen. In a darkened room, let a 
 candle flame be placed in front of a concave mirror, at a 
 distance from it greater than the focal distance. Incline 
 the mirror so that the flame shall not be on the principal 
 axis. Place a paper screen at the conjugate focus of any 
 
496 REFLECTION OF LIGHT. 
 
 point in the luminous object. The proper position for the 
 screen may easily be found by trial. Shield the screen from 
 the direct rays of the flame by a card painted black. The 
 inverted image may be seen by a large class. If the image 
 fall between the mirror and the candle, the screen should 
 be quite small. (See First Principles, Fig. 205.) 
 
 672. Description of Real Images Formed 
 by Concave Mirrors. (1.) If the object be at the 
 principal focus there will be no image. Why ? (You can 
 find out by trying a construction for the image ( 670). 
 (2.) If the object be between the principal focus and the 
 centre of curvature, the image will be beyond the centre, 
 inverted and enlarged. The nearer the object is to the prin- 
 cipal focus, the larger and the further removed the image 
 will be. (3.) When the object is at the centre, the image 
 is inverted, of the same size as the object and at the same 
 distance from the mirror. (4.) When the object is not 
 very far beyond the centre of curvature, the image will 
 be inverted, smaller than the object, and between the 
 centre and the principal focus. (5.) When the object is 
 at a very great distance, all of the rays will be practically 
 parallel ; there will be but one focus, and consequently no 
 image. 
 
 (a.) For each of these five cases construct the images. The third 
 case may be prettily illustrated as follows : In front of the mirror, 
 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 eye of the observer 
 is to be in the position mentioned in 670 (2). By giving the mirror 
 a certain inclination, easily determined by trial, an image of the 
 invisible bouquet will be seen just above the box. A glass vase 
 may be placed upon the box so that it may seem to hold the imaged 
 flowers. 
 
REFLECTION OF LIGHT. 497 
 
 673. Construction for Virtual Images formed by 
 Concave Mirrors. Let AB represent an object in front of a 
 concave mirror at a distance from it less than the focal distance. 
 Draw the secondary axes for the points A and B, and produce them 
 back of the mirror as dotted lines. From A and B, draw the inci- 
 dent rays Ao and Bi, parallel to the principal axis. After reflection 
 they will pass through the principal focus ( 666). Produce these 
 rays back of the mirror as dotted lines until they intersect tl 3 
 prolongations of the secondary axes at a and b, which will be tha 
 virtual conjugate foci for A and B. The conjugate foci for other 
 points in AB will be between a and b. Therefore, if the object be 
 between the principal focus and the mirror, the image will be 
 virtual, erect and enlarged. 
 
 FIG. 339- 
 
 674. Images of the Observer formed by a 
 Concave Mirror. A person at a considerable distance 
 before a concave mirror, sees his image, real, inverted and 
 smaller than the object. As he approaches the centre of 
 curvature, the image increases in size. As the observer 
 moves from the centre to the principal focus, the image is 
 formed back of him and is, therefore, invisible to him. As 
 he moves from the principal focus toward the mirror, the 
 image becomes virtual, erect and magnified, but gradually 
 growing smaller. The eye will not always recognize real 
 images as being in front of the mirror. It may some- 
 
498 . REFLECTION OF LIGHT. 
 
 times be aided in this respect by extending the outspread 
 fingers between the image and the mirror. 
 
 675. Convex Mirrors. In convex mirrors, the 
 foci are all virtual; the images are virtual, erect and 
 smaller than their objects. The foci may be found and 
 the images determined by the means already set forth. 
 The construction is made sufficiently plain by Fig. 340. 
 
 FIG. 340. 
 
 Note. In constructions for curved mirrors, we have chosen two 
 particular rays for each focus sought ; one perpendicular to the 
 mirror, the other parallel to the principal axis. This was only for 
 the sake of convenience. Any two or more incident rays might 
 have been taken and the direction of the reflected rays determined 
 by making the angle of reflection equal to the angle of incidence. 
 
 EXERCISES. 
 
 1. What must be the angle of incidence that the angle between 
 jhe incident and the reflected rays shall be a right angle ? 
 
 2. The radius of a concave mirror is 18 inches. Determine the 
 conjugate focus for a point on the principal axis, 12 inches from 
 the mirror. 
 
 3. (a.} Illustrate by a diagram the image of an object placed at the 
 principal focus of a concave mirror; (&.) of one placed between 
 that focus and the mirror ; (c.) of one placed between tjie focus and 
 the centre of the inirrpr. 
 
REFLECTION OF LIGHT. 499 
 
 4. (a.) What kind of mirror always makes the image smaller than 
 the object? (6.) What kind of a mirror may make it larger or 
 smaller, and according to what circumstances ? 
 
 5. Rays parallel to the principal axis fall upon a convex mirror. 
 Draw a diagram to show the course of the reflected rays. 
 
 6. (a.) Why do images formed by a body of water, appear in- 
 verted? (6.) What is the general effect of concave mirrors upon 
 incident rays ? 
 
 7. A person, placed at a considerable distance before a concave 
 mirror, sees his image, (a.) How does it appear to him ? He ap 
 preaches the mirror and the image changes. (&.) Describe the 
 changes that take place until he sees a virtual image of himself. 
 
 8. A man stands before an upright plane mirror and notices that 
 he cannot see a complete image of himself. (.) Could he see a 
 complete image by going nearer the mirror? Why ? (6.) By going 
 further from it ? Why ? 
 
 9. When the sun is 30 above the horizon, its image is seen in a 
 tranquil pool. What is the angle of reflection ? 
 
 10. 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. 
 
 11. 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. 
 
 Recapitulation. In this section we have considered 
 the Nature and Laws of Reflection; Dif- 
 fused and Invisible light; the Apparent Direc- 
 tion of bodies; Images formed in Plane Mirrors 
 and their Construction ; Concave Mirrors, 
 their Effects, Principal and Conjugate Foci ; 
 Images formed by them with their Construction, 
 Projection and Description; foci and images for 
 Convex Mirrors, 
 
500 
 
 REFRACTION OF LIGHT. 
 
 HI. 
 
 REFRACTI ON OF LIGHT 
 
 (>76. Preparatory. So far, we have considered only 
 that part of the incident beam that is turned back from 
 the reflecting surface. As a general thing, a part of the 
 beam enters the reflecting substance, being rapidly absorbed 
 when the substance is opaque and freely transmitted when 
 the substance is transparent. We have now to consider 
 those rays that enter a transparent substance. 
 
 (a.) Procure a clear glass bottle with flat sides, about 4 inches 
 (10 cm.} broad. On one side paste a piece of paper, in which a circu- 
 lar hole has been cut. On 
 this clear circular space, 
 draw two ink-marks at 
 right angles to each 
 other, as shown in Fig. 
 341. Fill the bottle with 
 clear water up to the 
 level of the horizontal 
 ink-mark. Hold it so 
 that a horizontal sun- 
 beam from the heliostat 
 may pass through the 
 clear sides of the bottle 
 above the water, and no- 
 tice that the beam passes 
 through the bottle in a 
 straight line. Raise the 
 bottle so that the beam 
 shall pass through the 
 water, 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 
 
 Fia 34 
 
REFRACTION OF L1G8T. 
 
 501 
 
 shall fall upon the surface of the water at i, the intersection of the 
 two ink-marks. Notice that the reflected beam is straight until it 
 reaches the water, but that it is bent as it obliquely enters the 
 water. 
 
 677. Refraction. Refraction of light is the 
 bending of cu luminous ray when it passes from 
 ^ne medium to another. 
 
 678. Index of Refraction. If a ray of light from 
 L (Fig. 342) fall upon the surface of water at A, it will be 
 refracted as shown in the figure. The angle LAS is the 
 angle of incidence and KAC the angle of refraction, BC 
 being perpendicular to the water's surface. From A as a 
 
 centre, with a radius equal to unity, 
 describe a circle. From the points m 
 and p, where this circle cuts the inci- 
 dent and refracted rays, draw mn and 
 pq perpendicular to BC. Then will 
 mn be the sine of the angle of incidence 
 SLudipq the sine of the angle of refrac- 
 tion. The quotient arising from 
 dividing the sine of the angle of 
 incidence by the sine of the angle of refraction is 
 called, the index of refraction for the two media. 
 It is evident that the greater the refractive power of the 
 substance, the less the value of the divisor pq, and the 
 greater the value of the quotient, the index of refrac- 
 tion. 
 
 (a.) The following table gives the indices of refraction when light 
 passes from a vacuum into any of the substances named : 
 
 Flint glass 1.575 
 
 FIG 342. 
 
 Mr 1.000294 
 
 Water 1.336 
 
 Alcohol 1374 
 
 Crown glass 1.534 
 
 Carbon bisulphide 1.678 
 
 Diamond 2.439 
 
 Lead chromate .2.974 
 
502 
 
 REFRACTION OF LIGHT. 
 
 The index of refraction for any two media may be found by divid- 
 ing the absolute index of one, as given above, by the absolute index 
 of the other. 
 
 679. Laws of Refraction of Light. (1.) 
 
 When light passes perpendicularly from one me* 
 dium to another it is not refracted. 
 
 (2.) When light passes obliquely from a rarer to 
 a denser medium it is refracted toward a line drawn, at 
 the point of incidence, perpendicular to the refracting 
 surface, or, more briefly, it is refracted toward the 
 perpendicular. 
 
 (3.) W^^en light passes obliquely from a denser 
 to a rarer medium, it is refracted from the per- 
 pendicular. 
 
 (4.) The incident and refracted rays are in the same 
 plane which is perpendicular to the refracting surface. 
 
 (5.) The index of refraction is constant for the same two 
 media. 
 
 680. Illustrations of Refraction. Put a small coin into 
 a tin cup and place the 
 
 cup so that its edge just 
 
 intercepts the view of 
 
 the coin. A ray of light 
 
 coming from the coin 
 
 toward the observer 
 
 must pass above his eye 
 
 and thus be lost to 
 
 sight. If, now, water be 
 
 gradually poured into 
 
 the cup, the coin will 
 
 become visible. The 
 
 rays are bent down as 
 
 they emerge from the 
 
 water and some of them FIG. 343. 
 
 enter the eye. For the 
 
 same reason, an oar or other stick half immersed in water seems 
 
 bent at the water's surface, while rivers and ponds whose bottoms 
 
REFRACTION OF LIGHT. 
 
 503 
 
 are visible are generally deeper than they seem to be. (Fig. 343.) 
 As air expands, its index of refraction becomes less. Hence the 
 indistinctness and apparent unsteadiness of objects seen through 
 air rising from the surface of a hot stove. Light is refracted as it 
 enters the earth's atmosphere. Hence the heavenly bodies appear 
 to be further above the horizon than they really are except when 
 they are overhead. 
 
 681. Total Reflection. When a ray of light 
 passes from a rarer into a denser medium, it may always 
 approach the perpendicular so as to make the angle of re- 
 fraction less than the angle of incidence ( 679 [2]). But 
 when a ray of light attempts to pass from a denser into a 
 rarer medium there are conditions 
 under which the angle of refraction 
 cannot be greater than the angle of 
 incidence. Under such circum- 
 stances the ray cannot emerge 
 from the denser medium, but 
 will be wholly reflected at the 
 point of incidence. Fig. 344 represents luminous rays 
 emitted from A, under water, and seeking a passage into 
 air. Passing from the perpendicular, the angle of refrac- 
 tion increases more rapidly than the angle of incidence 
 until one ray is found that emerges and grazes the surface 
 of the water. Eays beyond 
 this cannot emerge at all. 
 
 683. The Critical An- 
 gle. Imagine a spherical 
 (Florence) flask half filled 
 with water. A ray of light 
 from L will be refracted at A 
 in the direction of R. If the 
 angle of incidence, GAL, be 
 
 FIG. 344 
 
 FIG. 345. 
 
504 REF&AC'HOX OF LIG&T. 
 
 gradually increased the angle of refraction will be gradually 
 increased until it becomes 90, when the ray will graze the 
 surface of the water AM. If the source of light be still 
 further removed from (7, as to I, the ray will be reflected 
 to r ( 656). For all media there is an incident angle of 
 this kind, called the critical or limiting angle, beyond 
 which total internal reflection will take the place of refrac- 
 tion. The reflection is called total because all of the 
 incident light is reflected, which is never the case in 
 ordinary reflection. Hence, a surface at which total re- 
 flection takes place constitutes the most perfect mirror 
 possible. The critical angle (with reference to air) is 
 48 35' for water; 40 49' for glass; 23 43' for diamond. 
 
 (a.) From this it follows, as may be seen by referring to Fig. 344, 
 that to an eye placed under water, all visible objects above the 
 water would appear within an angle of 97 10', or twice the critical 
 angle for water. 
 
 (&.) The phenomena of total reflection may be produced by placing 
 the bottle shown in Fig. 341 upon several books resting upon a table, 
 and inverting the card so that a beam of light reflected obliquely 
 upward from a mirror on the table may enter through the slit near 
 the bottom of the bottle, taking a direction through the water simi- 
 lar to the line I A of Fig. 345. When one looks into an aquarium in 
 a direction similar to rA, images of fish or turtles near the surface 
 of the water are often seen. 
 
 (c.) Place a strip of printed paper in a test-tube ; hold it ob- 
 liquely in a tumbler of water and look downward at the printing 
 which will be plainly visible. Change the tube gradually to a 
 vertical position, and soon the part of the tube in the water takes a 
 silvered appearance and the printing becomes invisible. Show that, 
 in this case, the disappearance of the 
 reading is due to total reflection. By 
 dissolving a small bit of potassium di- 
 chromate in the water, the tube will 
 have a golden instead of a silver-like 
 appearance. 
 
 (d.) Fig. 346 represents a glass vessel 
 partly filled with water. Mirrors are FIG. 346. 
 
REFRACTION OF LIGHT. 
 
 505 
 
 placed at m and n. 
 and refracted at i. 
 
 In this way a ray may be reflected at m, n and 0, 
 
 (e.) Fig. 347 represents a glass jar with an opening, from which 
 
 a stream of water issues under a 
 head ( 254 []) kept constant. 
 Through a lens placed opposite 
 this orifice, a concentrated beam 
 of light from the heliostat is 
 thrown into the stream of water 
 as it issues. Internal reflection 
 keeps most of it there, a prisoner. 
 The stream of water is full of 
 light and appears a stream of 
 melted metal. Thrust a finger 
 into the stream and notice the 
 effect. Place a piece of red gluss 
 between the heliostat and the 
 lens ; the water looks like blood. 
 
 FIG. 347. 
 
 Thrust the finger into the stream again. Repeat the experiment 
 with pieces of glass of other colors in place of the red. 
 
 683. Refraction Explained. To understand the 
 way in which a ray of light is refracted, let us consider its 
 passage through a glass prism, ABC. It must be under- 
 stood that the velocity of light is 
 less in glass than in air, and 
 that the direction in which a 
 ivave moves is perpendicular to 
 its wave front. A wave in the 
 ether approaches the surface of the 
 prism AB. When at a, the lower end of the wave front 
 first strikes the glass and enters it. The progress of this 
 end of the wave front, being slower than that of the other 
 which is still in the air, is continually retarded until the 
 whole front has entered the glass. The wave front thus 
 assumes the position shown at c. But the path of the 
 wave being perpendicular to the front of the wave, this 
 
 FIG. 348. 
 
R&F&ACTION OP 
 
 change of front causes a change in the direction of the ray 
 which is thus refracted toward a perpendicular. The wave 
 now moves forward in a straight line until the top of the 
 wave front strikes A C, the surface of the prism, as shown 
 at m. The upper end of the wave front emerging first 
 into the air gains upon the other end of the front which is 
 still moving more slowly in the glass. When the lower 
 end emerges from the glass, the wave has the position 
 shown at n. This second change of front involves another 
 change in the direction of the ray which is now refracted, 
 from the perpendicular. (See First Principle*, 443, a. ) 
 
 684. Three Kinds of Refractors. When a ray 
 
 of light passes through a refracting medium, three cases 
 may arise : 
 
 (1.) When the refractor is bounded by planes, the re- 
 fracting surfaces being parallel. 
 
 (2.) When the refractor is bounded by planes, the re- 
 fracting surfaces being not parallel. The refractor is then 
 called a prism. 
 
 (3.) When the refractor is bounded by two surfaces of 
 which at least one is 
 curved. The refractor 
 is then called a lens. 
 
 685. Parallel 
 Plates. When a ray 
 passes through a me- 
 
 dium bounded by paral- 
 
 FIG. 349. 
 lei planes the refractions 
 
 at the two surfaces are equal and contrary in direction, 
 The direction of the ray after passing through the plate is 
 
OP LIGHT. 50? 
 
 parallel to its direction before entering; the ray merely 
 suffers lateral aberration. Objects seen obliquely through 
 such plates appear slightly displaced from their true position. 
 
 686. Prisms. A prism produces two simultaneous 
 effects upon light passing through it ; a change of direc- 
 tion and decomposition. The second of these effects will 
 be considered under the head of dispersion ( 701). 
 
 (a.) Let mno represent a section formed by cutting a prism by a 
 plane perpendicular to its edges. A ray of light from L being re- 
 fracted at a and & en 
 ters the eye in the di- 
 rection be. The object 
 being seen in the direc- 
 tion of the ray as it 
 enters the eye ( 659), 
 appears to be at r. An 
 object seen through a 
 prism seems to be 
 moved in the direction 
 of the edge that sepa- 
 rates the refracting 
 surfaces. The rays FIG. 350. 
 
 themselves are bent 
 
 toward the side that separates the refracting surfaces, or toward 
 the thickest part of the prism. 
 
 (&.) Prisms are generally made of glass, their principal sections 
 being equilateral triangles. In order to give a 
 liquid the form of a prism, it is placed in a 
 vessel (Fig. 351) in which at least two sides 
 are glass plates not parallel. Bottles are made 
 for this purpose. 
 
 (c.) In Fig. 352, ABC is the principal section 
 of a right-angled isosceles, glass 
 FIG. 351. prism, right-angled at G. A ray 
 
 of light falling perpendicularly 
 npon either of the cathetal (cathetus) surfaces, as AC, 
 will not be refracted. With AB, it will make an 
 angle of 45 which exceeds the critical angle for 
 glass ( 682). It will therefore be totally reflected ' IG ' 352 ' 
 and pass without refraction from the cathetal surface BC. Such 
 prisms are often used in optics instead of mirrors. 
 
508 
 
 REFRACTION OF LIGHT. 
 
 687. Lenses. 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. "With respect to their 
 shape, lenses are of six kinds : 
 123 
 
 Thinner at the middle than 
 at the edges. 
 
 FIG. 353- 
 
 (1.) Double-convex, | Thicker at the middle 
 
 (2.) Plano-convex, at the edges. 
 
 (3.) Concavo-convex, or meniscus, J 
 
 The double-convex may be taken as the type of these. 
 
 (4.) Double-concave, "| 
 
 (5.) Plano-concave, 
 (6.) Convex-concave, or diverging j 
 meniscus, J 
 
 The double-concave may be taken as the type of these. 
 (a.) The effect of convex lenses may be considered as produced by 
 two prisms with their bases in contact ; that of concave lenses, by 
 two prisms with their edges in contact. 
 
 688. Centre of Curvature ; Principal Axis ; 
 Optical Centre. A double-convey lens may be de- 
 scribed as the part common to two spheres which intersect 
 each other. The centres of these spheres are the centres 
 of curvature of the lens. The straight line passing 
 through the centres of curvature is the principal axis of 
 the lens. In every lens there is a point on the principal 
 axis called the optical centre. When the lens is bounded 
 by spherical surfaces of equal curvature, as is generally the 
 case, the optical centre is at equal distances from the two 
 
REFRACTION OF LIGHT. 509 
 
 faces of the lens. Any straight line, other than the prin- 
 cipal axis, passing through the optical centre is a second- 
 ary axis. (See First Principles, Fig. 216.) 
 
 (a.) If a ray of light passing through the optical centre be re- 
 fracted at all, the two refractions will be equal and opposite in direc 
 tion. The slight lateral aberration thus produced may be disregarded, 
 
 689. Principal Focus. Ml rays parallel to 
 the principal axis will, after two refractions, con- 
 verge at a point called the principal focus. This 
 point may lie on either side of the lens, according to the 
 direction in which the light moves ; it is a real focus. The 
 greater the refracting power of the substance of which the 
 
 FIG. 354- 
 
 lens is made, the nearer the principal focus will be to the 
 Jens. In a double-convex lens of crown glass, the principal 
 focal distance is equal to the radius of curvature; in a 
 plano-convex lens of the same material, it is twice as great. 
 
 (a.) The position of the principal focus of a lens is easily deter- 
 mined. Hold the lens facing the sun. The parallel solar rays 
 incident upon the lens will converge at the principal focus. Find 
 this point by moving a sheet of paper back and forth behind the 
 lens until the bright spot formed upon the paper is brightest and 
 smallest. (See First Prin. Nat. Phil., Exp. 228.) 
 
 (b.) It is also true that rays diverging from a point at twice the 
 principal focal distance from the lens will converge at a point just 
 as far distant on the other side of the lens. Rays diverging from 
 / will converge at /', these two points being at twice the focal dis- 
 tance from the lens. By experimenting with a lens and candle- 
 flame until the flame and its image are at equal distances from the 
 lens, we are able, in a second way, to determine the principal focal 
 distance of the lens. The conjugate foci situated at twice the prin- 
 cipal focal distance aye called secondary foci. 
 
510 REFRACTION OF LIGHT. 
 
 69O. Conjugate Foci. Kays diverging from a 
 luminous point in the principal axis at a small distance 
 beyond the principal focus on either side of the lens will 
 form a focus on the principal axis beyond the other prin- 
 cipal focus. Thus, rays from L will converge at /; con- 
 versely, rays from / will converge at L ( 667). If the 
 luminous point be in a secondary axis, the rays will con- 
 verge to a point in the same secondary axis. Two 
 
 FIG. 355- 
 
 points thus related to each other are called con- 
 jugate foci; the line joining them always passes 
 through the optic-al centre. 
 
 (a.) If the luminous point be more than twice the focal distance 
 from the lens, the conjugate focus will lie on the other side of the 
 lens at a distance greater than the focal distance, but less than twice 
 the focal distance. If the luminous point be moved toward the 
 lens, the focus will recede from the lens. When the luminous 
 point is at one secondary focus, the rays will converge at the other 
 secondary focus. When the luminous point is between the second- 
 ary and principal foci, the rays will converge beyond the secondary 
 focus on the other side of the lens. When the luminous point is at 
 the focal distance, the emergent rays will be parallel and no focus 
 will be formed. When the luminous point is at less than the focal 
 distance, the emergent rays will still diverge as if from a point on 
 the same $ide pf the lens, more distant than the principal focus 
 
REFRACTION OF LIGHT. 
 
 511 
 
 FIG. 356. 
 
 This focus will be virtual. Conversely, converging rays falling 
 upon a convex lens will form a focus nearer the lens than the 
 principal focus. (See Fig. 356.) 
 
 691. Conjugate Foci of Concave Lens. 
 
 Rays from a luminous point at any distance whatever will 
 be made more divergent by passing through a concave lens. 
 
 FIG. 357. 
 
 Rays parallel to the principal axis will diverge after refrac- 
 tion as if they proceeded from the principal focus. In 
 any case, the focus will be virtual, and nearer the lens thai) 
 the luminous point. 
 
 692. Images Formed by Convex Lenses. 
 
 The analogies between the convex lens and the concave 
 
512 REFRACTION OF LIGHT. 
 
 mirror cannot have escaped the notice of the thoughtful 
 pupil. Others will appear. If secondary axes be nearly 
 parallel to the principal axis, well-defined foci may be 
 formed upon them, as well as upon the principal axis. A 
 number of these foci may determine the position of an 
 image formed by a lens. 
 
 (a.) The linear dimensions of object and image are directly as 
 their respective distances from the centre of the lens ; they will be 
 virtual or real, erect or inverted, according as they are on the same 
 side of the lens or on opposite sides. 
 
 693. Construction for Real Images. To determine 
 the position of the image of the object AB (Fig. 358), draw from 
 any point, as A, a line parallel to the principal axis. After refrac- 
 
 FIG. 358. 
 
 tion, the ray represented by this line will pass through F, the prm- 
 cipal focus. Draw the secondary axis for the point A. The inter- 
 section of these two lines at a determines the position of the con- 
 jugate focus of A. In similar manner, the conjugate focus of S is 
 found to be at &. Joining these points, the line ah is the image of 
 the line AB. 
 
 694. Diminished Real Image. If the object 
 be more than twice the focal distance from the convex 
 lens, its image will be real, smaller than the object and 
 inverted (Fig. 359). Construct the image as indicated in 
 the last paragraph. 
 
REFRACTION OF LIGHT. 
 
 513 
 
 FIG. 359. 
 
 695. Magnified Real Image. If the object be 
 further from the lens than the principal focus, but at a 
 
 FIG. 360. 
 
 distance less than twice the focal distance, the image will 
 be real, magnified and inverted. (Fig. 360.) Construct 
 the image. 
 
514; REFRACTION OF LIGHT. 
 
 696. Virtual Image. If the object be placed 
 nearer the lens than the principal focus, the image will be 
 virtual, magnified and erect. (Fig. 361.) This explains 
 the familiar magnifying effects of convex lenses. Con- 
 struct the image. 
 
 697. Image of Concave Lens. Images formed 
 by a concave lens are virtual, smaller than the object and 
 erect. The construction of the image is shown in Fig. 
 362. 
 
 FIG. 362. 
 
 * 
 
 Note. The power of the convex lens to form real and diminished 
 images of distant objects and magnified images of near objects, is 
 of frequent application in such optical instruments as the micro- 
 scope, telescope, magic lantern, lighthouse lamps, etc. Owing to 
 the identity between heat and luminous rays, a convex lens is also 
 a " burning-glass." 
 
 698. Spherical Aberration. The rays that pass 
 through a spherical lens near its edge are more refracted 
 than those that pass nearer the centre. They, therefore, 
 converge nearer the lens. A spherical lens cannot refract 
 all of the incident rays to the same point. Hence 
 "spherical aberration" and its annoying consequences in 
 the construction and use of optical apparatus. 
 
REFRACTION OF LIGHT. 515 
 
 EXERCISES. 
 
 1. (a.) What is refraction of light ? (&.) State the laws governing 
 the same, and (c.) give an illustrative diagram. 
 
 2. (a.) Name and illustrate by diagram the different classes of 
 lenses. (&.) Explain, with diagram, the action of the burning-glass 
 
 3. (a.) Explain the cause of total reflection. (&.) Show, with 
 diagram, how the secondary axes of a lens mark the limits of the 
 image. 
 
 4. (a.) Using a convex lens, what must be the position of an 
 object in order that its image shall be real, magnified, and inverted 1 
 (6.) Same, using a concave lens ? 
 
 5. (a.) Show how a ray of light may be bent at a right angle by 
 a glass prism. (&.) The focal distance of a convex lens being 6 
 inches, determine the position of the conjugate focus of a point 
 12 inches from the lens, (c.) 18 inches from the lens. 
 
 6. (a.) The focal distance of a convex lens is 30 cm. Find the 
 eonjugate focus for a point 15 cm. from the lens. (6.) How may the 
 focal length of a lens be determined experimentally? 
 
 7. If an object be placed at twice the focal distance of a convex 
 lens, how will the length of the image compare with the length of 
 the object ? 
 
 8. A small object is 12 inches from a lens ; the image is 24 inches 
 from the lens and on the opposite side. Determine (by construction) 
 the focal distance of the lens. 
 
 9. 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? 
 
 Recapitulation. In this section we have considered 
 the Definition, Index, Laws and Explanation 
 of refraction ; Internal Reflection ; Plates, 
 Prisms and Lenses ; principal and conjugate Foci 
 of lenses ; Construction for conjugate foci and 
 images; Spherical Aberration. 
 
516 
 
 CHROMATICS SPECTRA. 
 
 IV. 
 
 CHROMATICS. SPECTRA. 
 
 699. Other Results of Refraction. In our previous 
 <nsideration of luminous rays we have studied the effect of refiec 
 tion and refraction upon the direction of rays ; in fact, we have 
 dealt with only those properties which are common to all luminous 
 rays. But the properties of light and the phenomena of refraction 
 are not so simple as we might thus be led to suppose. Most 
 luminous objects emit light of several kinds blended together. We 
 must not be satisfied with our knowledge of light until we are able 
 to sift these varieties one from the other, and to deal with any one 
 kind by itself. 
 
 FIG. 363. 
 
 7OO. Solar Spectrum. Admit a sunbeam through 
 a very small opening in the shutter of a darkened room. 
 The opening may be prepared by cutting a slit an inch 
 (25 mm.} long and ^ of an inch (1 mm.) wide in a card. 
 See that the edges of the slit are smooth. Tack the 
 card over an opening in the shutter. If we look at the 
 aperture from E we shall see the sun beyond. The path 
 of the beam from 8 to E is made visible by the floating 
 
CHROMATICS SPECTRA. 517 
 
 dust. If a prism be placed in the path of the beam, as 
 shown in Fig. 363, the sides of the slit and edges of the 
 prism being horizontal, the beam will be refracted upward^ 
 If the refracted beam be caught upon a screen, it will 
 appear as a band of differently colored light, passing by 
 imperceptible gradations from red at the bottom, through 
 orange, yellow, green, blue and indigo to violet at the 
 upper end of the beautifully colored band. This colored 
 band is called the solar spectrum. 
 
 (a.) The different colors do not occupy equal space in the spectrum, 
 orange having the least and violet the most. The initials of these 
 colors form the meaningless word VIBGYOR, which may aid the 
 memory in remembering these prismatic colors in their proper 
 order. By placing the slit in a vertical position, and standing the 
 prism on its end so that its edges will be parallel with the sides of 
 the slit, the spectrum will be projected as a horizontal band. 
 
 701. Dispersion. By looking at Fig. 363, it will 
 be seen that the red rays have been refracted the least and 
 the violet the most of all the luminous rays. This sepa- 
 ration of the differently colored rays by the prism 
 is called the dispersion of light ; it depends upon the 
 fact that rays of different colors are refracted in different 
 degrees. 
 
 702. Pure Spectrum. The spectrum above de- 
 scribed is composed of overlapping and differently-colored 
 images of the slit. In a pure spectrum these images must 
 not overlap. The first requisite in preventing this over- 
 lapping is that the slit be very narrow. 
 
 (a.) The most simple way of producing a pure spectrum is to look 
 jhrough. a prism at a very narrow slit in the shutter of a darkened 
 room. The edges of the prism should be parallel to the slit ; the 
 prism should be at least five feet (1| m.) from the slit ; the prism 
 should be Burned until the colored image of the slit is at the least 
 
518 CHS OMA TICS SPECTRA. 
 
 angular distance from the slit itself. A pure spectrum is also 
 obtained by passing the beam through several prisms in succession, 
 thus increasing the dispersion. 
 
 7O3. Fraunhofer's Lines. A pure solar spectrum 
 is not continuous, but is crossed by numerous dark lines, 
 many hundreds of which have been counted and accu- 
 rately mapped. The more conspicuous of these dark lines 
 are distinguished by letters of the alphabet, as shown in 
 Fig. 364. Each of these dark lines indicates that a par- 
 ticular kind of ray is wanting in solar light. 
 
 AaBCD EftP G HH' 
 
 BOY G B I V 
 
 FIG. 364. 
 
 (a.) The spectra of incandescent solids are continuous, from the 
 extreme red to a limit depending upon the temperature. The 
 spectra of incandescent gases (not containing solid particles in 
 suspension) are non -continuous, consisting of a number of definite 
 bright lines. A candle or gas flame gives a continuous spectrum 
 because it is chiefly due to the incandescence of solid carbon 
 particles. 
 
 (6.) The spectroscope is an instrument for producing and observing 
 pure spectra. It has proved to be one of the most powerful aids 
 to modern science. It affords the most delicate means of chemical 
 analysis ; by its aid several elements have been discovered ; the 
 presence of ^j^^^-y of a grain of sodium has been detected by 
 " spectrum analysis." It is of incalculable importance to the 
 astronomer. For definite information, the pupil is necessarily 
 referred to some of the excellent manuals upon the subject recently 
 published. 
 
 Experiment I. Let the rays that have been dispersed by a 
 prism fall upon a convex lens as shown in Fig. 365. They mil be 
 refracted to a focus and recombined to form white light. A concave 
 mirror may be used to reflect the rays to a focus instead of using 
 the lens as above described. 
 
CHROMATICS. 
 
 FIG. 365. 
 
 Experiment 2. Make a "Newton's disc" of cardboard painted 
 with the prismatic colors in proper proportion as indicated by Fig. 
 366. It is better to divide the surface given to each color into 
 smaller sectors arranged alternately as shown in Fig. 367. You 
 
 FIG. 366. 
 
 FIG. 367. 
 
 may paste sectors of properly colored paper upon the cardboard 
 instead of painting them. Cause this disc to revolve rapidly by 
 means of the whirling table or by fastening it to a large top. Notice 
 that the colors are blended and that the disc appears grayish white. 
 
 Experiment 3. Hold a second prism near one that is used to 
 produce a solar spectrum, the position of the second being inverted 
 with reference to the first. If the dispersing prism be held as shown 
 in Fig. 365, the second should be held with the refracting edge 
 uppermost, the facing surfaces being parallel. The dispersed rays 
 emerging from the first prism will pass through the second. The 
 rays separated by the first will be again blended by the second and 
 appear an while light. 
 
 Experiment 4. Hold a hand mirror near the dispersing prism 
 so as to reflect the refracted rays to a distant wall or ceiling. Give 
 
520 CHROMATICS. 
 
 to the mirror a rapid, angular motion so that the spectrum is made 
 to move 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. The effect is due to what is known as the "Persistence 
 of Vision," familiarly illustrated by the experiment of producing 
 a ring of light by whirling a firebrand around a circle. 
 
 704. The Composition of White Light. We 
 
 have now shown, by both the processes of analysis and 
 synthesis, that white light is composed of the seven 
 prismatic colors. We have decomposed white light 
 into its seven constituents and recombined these constit- 
 uents into white light. 
 
 Experiment 5. 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 
 cardboard. 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 6. 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 al- 
 cohol 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 7. In a clear tumbler or large beaker glass of 
 water, dissolve a little soap (white castile is desirable) 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 screen behind the vessel and 
 examine the liquid by reflected sunlight. Notice that it appears 
 blue. 
 
 705. Color of Bodies. The color of a body is its 
 property of reflecting or transmitting to the eye light of 
 
THE RAINBOW. 521 
 
 that particular color, the other rays being absorbed. This 
 power may be described as selective absorption. 
 
 (a.) Properly speaking, color is not a property of matter, but of 
 light. A ribbon is called red, but the redness belongs to the light, 
 not to the ribbon. There would be more propriety in saying that 
 the ribbon has all the other colors of the rainbow, because it absorbs 
 the others and reflects the red. If the red ribbon be placed in the 
 green or blue of the spectrum it will appear black because it 
 receives no red rays to reflect. Colored substances decompose the 
 incident light, absorbing some rays and assuming the hue of those 
 they reflect or transmit to the eye. A body that absorbs very few 
 of the rays is white ; one that absorbs nearly all is black. There- 
 fore, black is not a color but its absence. 
 
 (6.) If the rays that form the spectrum be divided into any two 
 parts and the rays in each part be mixed, it is evident that each 
 resultant color will contain what the other needs to make white 
 light. Such are called complementary colors ; either is said to be 
 complementary to the other. The mixture of colors is a very 
 different thing from the mixture of pigments. 
 
 (c.) Some bodies transmit one kind of rays and reflect another. 
 Thus, gold leaf reflects yellow rays and transmits green rays. The 
 beautiful blue of the summer sky, the terrible black of the storm 
 cloud and the matchless sunset hues are effects due to the reflec- 
 tion, absorption and transmission of sunlight by particles suspended 
 in the atmosphere. An observer placed at a very high elevation, 
 above most of the reflecting particles and looking into outer space, 
 sees no blue canopy but only an inky darkness, illumined here and 
 there by some gleaming planet or twinkling star. 
 
 7O6. The Rainbow. The rainbow is due to re- 
 fraction, reflection and dispersion of sunlight by water- 
 drops. The necessary conditions are : 
 
 (1.) A shower during sunshine. 
 
 (2.) That the observer shall stand with his back to the 
 sun, between the falling drops and the sun. 
 
 (a.) The centre of the circle of which the rainbow forms a part 
 is in the prolongation of a line drawn from the sun through thu 
 eye of the observer. This line is called the axis of the bow. 
 
523 THE RAINBOW. 
 
 7O7. Dispersion by a Raindrop. Suppose the 
 
 circle whose centre is at (Fig. 368) to represent the section 
 
 FIG. 368. 
 
 of a raindrop. A ray of sunlight, as Sm, falling upon the 
 raindrop would be refracted at m, reflected at n, and again 
 refracted at m'. In passing thus through the drop, the 
 light is also decomposed. If m'E represent the path of 
 a red ray, the violet ray will traverse a path above, because 
 violet is refracted more than red. The path of this violet 
 ray may be represented by m'B. If the raindrop be in the 
 exact position for the red ray, m'E, to enter the eye of the 
 observer, the violet and other colored rays will pass over- 
 head and not be seen. This drop will appear red. 
 
 7O8. Successive Colors of the Rainbow. In order 
 that a violet ray may enter the eye at E, it must proceed from a drop 
 situated below the one that sends the red ray. This drop will appear 
 violet. Intervening drops will give the intervening colors of the 
 solar spectrum in their proper order as is shown in Fig. 369. Owing 
 to the distance of the sun, all of the incident rays are parallel with 
 the axis, EO, drawn from the sun through E, the eye of the ob- 
 server, to 0, the centre of the circle of which the bow forms a part. 
 The angle between the incident and the emergent ray, SHE, and 
 
THE KAINBO 
 
 OW. 
 
 523 
 
 consequently the angle, REO, is, for the red ray, about 43. The 
 angles 8' F^and VEO are, for the violet ray, about 40. The other 
 
 FIG. 369. 
 
 colors lying between these, it will be seen that the angular width of 
 the rainbow is about two degrees. 
 
 7O9. Form and Extent of the Rainbow. 
 
 From Fig. 370, it will be seen that every drop in the arc of 
 a circumference drawn, with as 
 a centre and with V as radius, 
 being opposite the sun and hav- 
 ing the same angular distance 
 from OE, viz., 40, will send 
 violet colored rays to the eye at E, 
 and the violet colored part of 
 the bow will be a circular arch. FlG - 3?o- 
 
 For the same reason, the red of the bow is a circular arch 
 lying without the violet and at an angular distance of two 
 degrees therefrom ; the other colors will form circular 
 
524: THE RAINBOW. 
 
 arches lying between these two. If the sun he at the 
 horizon, EO will be horizontal and the arches will be 
 semicircles. If the sun be above the horizon, will be de- 
 pressed below the horizon and less than semicircles will be 
 seen. If the observer be on a mountain-top or up in u 
 balloon, he may see more than a semicircle. 
 
 71O. The Secondary Bow. Sometimes two col- 
 ored arches are seen, one within the other. The inner 
 which we have just considered is called the primary bow ; 
 the outer, the secondary bow. 
 
 (a.) In explaining the primary bow, we traced a ray of light fall- 
 ing upon the top of the raindrop ; to explain the secondary bow, wo 
 trace a ray falling upon its lower part. Such a ray, as Sm, will be 
 refracted at m, reflected at n and n' ' , and again refracted at m', 
 coming to the eye at E. If the ray which thus comes to the eye at 
 E be a red ray, the violet will follow m 1 F, and thus, passing below 
 the eye because of its greater refrangibility, be lost to sight. The 
 drop that sends a violet ray to the eye at 7must be placed above 
 instead of below the drop that sends the red ray. (Fig. 371.) 
 
 FIG. 371. 
 
 (6.) In the secondary bow, the red arch will be on the inside, with 
 an angular distance from the axis, EO, of about 51, while the violet 
 
CHROMATICS SPECTRA. 525 
 
 will be on the outside at an angular distance of about 54. In the 
 case of either bow, some light is lost at each reflection ; therefore, 
 since there are more reflections in the secondary bow, this will 
 appear fainter. 
 
 711. Chromatic Aberration. It is impossible, 
 by means of a single spherical convex lens, to bring all of 
 the incident rays to a common focus. The blue and violet 
 rays being refracted more than 
 the red rays will converge at 
 points nearer the lens. In con- 
 sequence of this, when an image 
 is projected upon a screen, the 
 image is surrounded with a col- 
 ored border, the color depending upon the distance of the 
 screen from the lens. This inability of a single lens 
 to bring differently colored rays to the same focus 
 is called chromatic aberration. 
 
 Achromatic Lens. A convex lens of crown 
 glass, by combination with a concave lens of flint glass, may 
 have its dispersive power neutralized without completely 
 neutralizing its refraction. As the converging effect of the 
 compound lens is not destroyed, images may be formed ; 
 as the dispersive effect is destroyed, the colored fringe is 
 avoided. Jl combination of lenses by which disper- 
 sion is avoided and refraction secured is called an 
 achromatic lens. 
 
 Experiment 8. In any convenient clamp, firmly press together 
 two pieces of clean, thick, plate glass. A beautiful play of colors 
 will be seen in the glass. 
 
 713. Interference of Light. If a plano-convex 
 lens of very small curvature be pressed down upon a flat 
 plate of glass and looked at from above, colored rings 
 
526 Ctttt OMA TICS SPECT&A. 
 
 (known as Newton's rings) may be seen around the centre 
 of the lens. If the light be homogeneous (i. e. } composed 
 of one kind of rays, as red) instead of white, the rings will 
 be separated by dark spaces. The dark rings are due to 
 the interference of the ether waves reflected from the 
 lower surface of the lens and from the upper surface of the 
 plate respectively. Whenever the distance between the 
 two reflecting surfaces is such that the two sets of waves 
 unite in opposite phases, a dark ring will appear. Two 
 luminous waves, as well as two sound waves ( 515), may 
 unite so as to destroy each other. When white light is 
 used, the color in any given ring is complementary to the 
 color that is destroyed by interference. Similar colors are 
 often seen in soap bubbles, in small quantities of oil that 
 have been spread over large sheets of water, in mica, seli- 
 nite and other crystals that easily cleave into thin plates, 
 etc., and are due to the interference of light reflected from 
 two surfaces very near each other. 
 
 Experiment 9. Cover one side of a pane of glass with India ink, 
 being sure that it is made opaque. Scratch 20 parallel lines about 
 2 mm. apart, upon the glass, so that the light may pass through. 
 Standing about 6 or 7 meters from a lamp, with one eye shut and 
 the other shaded from the sunlight, look through the lines ruled on 
 the glass at the flame. Slowly moving the glass toward and from 
 the eye, such a position may be found for it that many spectra of 
 the flame may be seen separated by dark spaces. 
 
 Experiment 10. Throw a sunbeam through a very small open- 
 ing in the shutter of a darkened room. Receive the beam upon a 
 
 FIG. 373. 
 
 convex lens of short focal length, placing a piece of red glass be- 
 tween the aperture and the lens. Place an opaque screen with a 
 
CHROMATICS SPECTRA. 52? 
 
 sharp edge beyond the focal distance of the lens, as at e, so as to 
 cut off the lower part of the luminous cone and project the upper 
 part thereof upon a screen at b. A faint light is seen on the screen 
 below the level of b and, therefore, within the geometrical shadow. 
 Jhe part of the screen immediately above the level of b contains a 
 series of dark and light bands as shown at B, which is a front view 
 of the screen at b. 
 
 714. Diffraction. The pupil may have noticed that 
 when water waves strike a rock or other obstacle a little 
 ways from the shore, 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 centre. 
 The original wave, which we may call the primary, passes 
 directly onward while the other waves, which we may call 
 secondary, wind around behind the obstacle. In similar 
 manner, luminous waves are modified when they pass the 
 edge of an opaque body, as in going through a narrow 
 slit, in consequence of which the rays seem to be bent 
 and to penetrate into the shadow. Such an apparent 
 bending of the luminous rays is called diffraction. 
 As the primary and secondary waves cut each other, they 
 will unite at some points, crest with crest and, at other 
 points, crest with trough. At the latter points, we shall 
 have interference of light and the effects of colors pro- 
 duced 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 eyelashes at a distant source of brilliant light are 
 also due to diffraction. 
 
 Experiment II. Look carefully at the black and the white circles 
 given in Fig. 374 and determine which seems to be the larger. 
 Then carefully measure their diameters and see which is the larger. 
 
528 CHROMATICS SPECTRA. 
 
 715. Irradiation..^ white or very bright object 
 seen against a black ground appears larger than it 
 
 FIG. 374. 
 
 really is ; a black object on a ivhite ground appears 
 smaller than it really is. This effect is called irra- 
 diation. It arises from the fact that the impression 
 produced by a bright object on the retina extends beyond 
 the outline of the image. 
 
 (a.) The effect of irradiation is very perceptible in the apparent 
 magnitude of stars which are thus made to appear much larger than 
 they otherwise would ; also in the appearence of the new moon, the 
 illuminated crescent seeming to extend beyond the darker portion, 
 the new, thus, holding the old moon in its arms. 
 
 716. Properties of the Sunbeam. We have seen that 
 we may decompose a sunbeam by availing ourselves of the varying 
 refrangibility of the different kinds of rays of which it is composed. 
 We have been able in this manner to produce the seven prismatic 
 colors from white light. But our analytic investigations must go 
 still further. Beyond the limits of the visible spectrum, in both 
 directions, there are rays that do not excite the optic nerve, the ex- 
 istence of which, however, may be easily proved. The sunbeam 
 has three properties which we must consider in detail : luminous, 
 thermal and actinic. 
 
 717. Luminous Kays. The difference in color be- 
 tween the rays found in different parts of the spectrum is 
 merely one of rate of vibration or wave-length. In respect 
 
CHROMATICS SPECTRA. 529 
 
 to the visible spectrum, it may be said that color is to 
 light what pitch is to sound. The length of an ether- 
 wave that can awaken the sensation of redness is about 
 Tsoiro f an i ncn ; f one ^ nat can awaken the sensation of 
 violet, about -^\-Q-Q. The waves corresponding to the 
 intermediate colors have intermediate lengths. The 
 visibility or invisibility of certain rays depends on the 
 construction of the eye rather than on any peculiarity of 
 the rays. It is quite possible that the eyes of some 
 animals are so constructed that ultra-red rays may excite 
 vision, and that the eyes of other animals are so con- 
 structed that ultra-violet rays may excite vision. 
 
 718. Thermal Rays. If a very delicate ther- 
 mometer or thermopile be successively placed in various 
 parts of the spectrum it will be found that the tempera- 
 ture is scarcely affected in the violet, but that there is a 
 continual increase in temperature as the thermometer is 
 moved toward the other end of the spectrum, it being 
 quite marked in the red and even beyond the red, wholly 
 outside the visible spectrum. We thus detect ultra-red 
 rays constituting a heat spectrum. Their position 
 indicates their low refrangibility and increased wave- 
 length. Because of its diathermancy, a rock-salt prism is 
 desirable for this experiment ; glass absorbs most of the 
 ultra-red rays. 
 
 (.) The oxy-hydrogen flame (Chemistry, 41) develops little 
 light but an intense heat. Most of its rays are obscure heat rays. 
 If a small cylinder of lime be held in this flame, it emits a most 
 brilliant light. This change of obscure heat rays into luminous rays 
 is called color escence. 
 
 719. Actinic Rays. The actinic or chemical effects 
 
530 CHROMATtOS SPECTRA. 
 
 of sunlight are, in a general way, familiar to all. For 
 example, plants absorb carbon from the atmosphere only 
 during the day time. Silver chloride is very sensitive to 
 this action of sunlight. The sensitive paper of the photog- 
 rapher will remain unchanged in the dark ; it will be 
 quickly blackened in the light. If a piece of paper freshly 
 washed in a solution of sulphate of quinine, or some other 
 fluorescent substance, be held in the ultra-violet rays, it 
 will become visible. Such a slip of paper may be used as 
 a test for the presence of actinic rays. By placing it 
 successively in the different parts of the visible spectrum, 
 it will be affected least in the red and most in the violet. 
 Actinic effects will be found even beyond the violet, wholly 
 outside the visible spectrum. > We thus detect ultra- 
 violet rays constituting an actinic spectrum. Their 
 position indicates their high ref rangibility ; that their 
 wave-length is less than that of the violet rays. A quartz 
 prism is desirable for this experiment as glass quenches 
 most of the actinic rays. The change of obscure, actinic 
 rays into luminous rays is called. fluorescence. -jL 
 
 72O. The Electric Light. The electric light is 
 particularly rich in these invisible rays. The dark heat 
 rays may be sifted from the beam of light by passing it 
 through a transparent solution of alum; only the lumi- 
 nous rays will be allowed to pass. The luminous rays may 
 be sifted out by sending the beam through an opaque solu- 
 tion of iodine in carbon di-sulphide. If these solutions 
 be placed in spherical flasks, they will constitute lenses 
 that will refract the transmitted rays to well-defined foci. 
 The focus of the transparent solution will be brilliantly 
 illuminated, but will have little heating power; that of 
 
CHROMATICS SPECTRA. 531 
 
 the opaque solution will be invisible, while gun-cotton 
 placed there may be instantly exploded. Platinum-foil 
 has been raised to a red heat at one of these dark foci. 
 Photographs are now frequently taken by the electric light. 
 
 721. Selective Radiation and Absorption. 
 
 Radiation of light or heat consists in giving motion to 
 the ether; absorption consists in taking motion from the 
 ether. Molecules of one kind are able to vibrate at one 
 rate ; those of another kind may be obliged to vibrate at 
 a different rate. The first set of molecules may be able to 
 give to the ether, or take from it, a rate of vibration which, 
 in the ether, constitutes obscure heat. These molecules 
 can absorb or radiate obscure heat. They may be unable 
 to vibrate at the higher rate which will enable them to ab- 
 sorb or radiate light. They must either transmit or reflect 
 light that falls upon them. In other words, a body absorbs 
 with special energy the kind of rays itself can radiate, 
 both the absorption and the radiation depending upon the 
 possible rate of vibration of the molecules of the body. 
 
 (a.) In the case of gases, the period of molecular vibration is 
 sharply defined. Gaseous molecules, like musical strings, can 
 vibrate at only definite rates. Liquid and solid molecules, like 
 sounding-boards, are able to vibrate at different rates lying between 
 certain fixed limits. These limits depend largely upon the tempera- 
 ture. This principle underlies solar, spectrum analysis. 
 
 722. Relation between Radiation and Ab- 
 sorption. Transparent bodies are transparent because 
 the ether-waves which produce or constitute light pass be- 
 tween the molecules of such bodies without having their 
 wave-motion transferred to the molecules. Diathermanous 
 bodies transmit heat freely because the ether-waves which 
 produce or constitute heat pass between the molecules of 
 
532 
 
 CHR OMA TICS SPECTRA. 
 
 such bodies without having their peculiar wave-motion 
 transferred to the molecules of the body through which 
 they pass. When a ray of light or heat, in passing through 
 a substance, gives its energy to the molecules between 
 which it is passing in the ether,, the ray is absorbed. It 
 no longer exists as radiant energy; it has become absorbed 
 heat and warms the body. It is no longer a motion of 
 the ether; it has become a motion of ordinary matter. 
 As in the case of radiant heat, so with light; the best 
 absorbents are the best radiators. A piece of transparent, 
 colorless glass will absorb very little 
 fight ; heat it intensely and it will 
 radiate very little light. On the 
 other hand, a piece of opaque glass 
 will absorb a great deal of light ; 
 when heated intensely, it will radi- 
 ate a great deal of light. See 625. 
 
 (.) If an intensely heated pot of melted FlG - 375- 
 
 lead, tin or plumber's solder be carried into a dark place and the dross 
 
 skimmed aside by a red-hot 
 iron ladle, the liquid metal 
 (which in sunlight would 
 reflect rather than absorb 
 the light) will appear less 
 bright than the surround- 
 ing dross. If a piece of 
 platinum-foil bearing an 
 ink-mark be heated to in- 
 candescence and viewed in 
 a dark room, the ink-mark 
 will radiate more light 
 than the metal. Exposed 
 to sunlight, the ink-mark 
 will absorb more light than 
 the metal. If a chalk-mark 
 be made on a black poker, 
 FIG. 376. the poker heated red-hot 
 
EXERCISES. 
 
 533 
 
 and viewed in a dark room, the chalk will be less luminous than the 
 iron. If a piece of stone- ware of black and white pattern (Fig. 375? 
 be heated to redness and viewed in a dark room, the black will shine 
 more brightly than the white, the pattern being reversed as shown 
 in Fig. 376. 
 
 EXEKCISES. 
 
 1. Give the best reason you can think of, why the rainbow is a 
 circular arc and not a straight line or of some other shape. 
 
 2. Taking the velocity of light to be 188,000 miles per second and 
 the wave-length for green light to be .00002 of an inch, how many 
 waves per second beat upon the retina of an eye exposed to green 
 light? 
 
 3. How may spherical and chromatic aberration caused by a lens 
 be corrected ? 
 
 4. Describe Fraunhofer's lines and tell how they may be produced. 
 Why not through a circular orifice ? 
 
 5. Describe in full what is meant by dispersion and the dispersive 
 power of a medium. 
 
 Recapitulation. To be amplified by the pupil for 
 review. 
 
 r DISPERSION. 
 
 COMPLEXITY OF 
 SUNBEAM.. 
 
 CO 
 
 u 
 
 ANALYSIS.. 
 
 By Prisms. 
 
 * SPECTRA. . 
 
 SYNTHESIS. -I 
 
 By Water Drops. 
 
 Solar. 
 
 Luminous. 
 
 Thermal. 
 I Actinic. 
 BY LENSES. 
 BY MIRRORS. 
 BY PRISMS. 
 BY PERSISTENCE OF VISION, 
 
 U 
 
 (CAUSE OF. 
 COMPLEMENTARY. 
 SKY. 
 
 INTERFERENCE. 
 
 DIFFRACTION. 
 
 IRRADIATION. 
 
 RADIATION AND ABSORPTION RELATED, 
 
534 OPTICAL INSTRUMENTS. 
 
 ECTFON V. 
 
 OPTICAL INSTRUMENTS. POLARIZATION. 
 
 723. Photographers' Camera. The photogra^ 
 pher's camera is nearly the same as the camera-obscura 
 described in 650. Instead of the darkened room we have 
 a darkened box, DE; instead of the simple hole in the 
 shutter, we have an achromatic convex lens, placed in a 
 sliding tube at A. 
 
 (a.) Sometimes, one part of the box slides within the other part 
 with a movement like that of a telescope tube. Sometimes the front 
 and the back of the box are joined by flexible sides, as shown in 
 Fig. 377, so that the distance between A and E may be varied. 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. (See 694.) This 
 adjustment, or "focussing," 
 is completed by moving the 
 lens and its tube by the 
 toothed wheel at D. When 
 the " focussing " is satis- 
 factory, A is covered with 
 a black cloth, the ground- 
 
 glass plate re P laced b ^ a 
 chemically- prepared sensi- 
 tive plate, the cloth removed and the image projected thereon. The 
 light works certain chemical changes where it falls upon this plate 
 and thus a more lasting image is produced. The preliminary and 
 subsequent processes necessarily involved in photography cannot be 
 considered here ; they belong rather to chemistry. 
 
 724. The Human Eye. This most admirable of 
 all optical instruments is a nearly spherical ball, capable of 
 
OPTICAL INSTRUMENTS. 535 
 
 being turned considerably in its socket. The outer coat, S, 
 is firm and, excepting in front, is opaque. It is called 
 the "white of the eye," or the sclerotic coat. Its trans- 
 parent part in front, (7, is called the cornea. The cornea 
 is more convex than the 
 rest of the eyeball. The 
 cornea fits into the coat, S, 
 as a watch crystal does into 
 its case. Behind the cornea, 
 is a curtain, /, called the 
 iris. It is colored and 
 opaque; the circular window 
 in its centre is called the 
 pupil. The color of the FlG - 378. 
 
 iris constitutes the color of the eye. Back of the pnpil is 
 the crystalline lens, L, built of concentric shells of varying 
 density. Its shape is shown in the figure. This lens 
 divides the eye into two chambers, the anterior chamber 
 containing a limpid liquid called the aqueous humor ; the 
 posterior chamber containing a transparent jelly, V, called 
 the vitreous humor. The viteous humor is enclosed in a 
 transparent sack, H, called the hyaloid membrane. The 
 cornea, aqueous humor, crystalline lens and vitreous 
 humor are refracting media. Back of the hyaloid mem- 
 brane is the retina, R, an expansion of the optic nerve. 
 At the centre of the back of the eye is a slight depression 
 called the yellow spot. This is the most sensitive part of 
 the retina. The point at which the optic nerve enters the 
 eye is called the blind spot. It is at one side of the yellow 
 spot, nearer the nose. Between the retina and the 
 sclerotic coat is JV ? the choroid coat, intensely black and 
 opaque, 
 
536 OPTICAL INSTRUMENTS. 
 
 The eye, optically considered, is simply an arrangement 
 for projecting inverted real images of visible objects upon 
 a screen made of nerve filaments. The image thus 
 formed is the origin of the sensation of vision. ( 650 c.) 
 
 Experiment P. Stick two needles into a book-cover or board 
 about 6 inches apart. Close one eye and hold the book so that the 
 needles shall be nearly in range with the open eye and about 6 and 12 
 inches respectively 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. (See Fig. 
 354.) 
 
 Experiment 2. Close the left eye, look steadily at the cross be- 
 low, 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 towards the face. When the image of 
 the dot falls on the blind spot of the eye, the dot will disappear. 
 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. 
 
 Experiment 3. 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 
 be green, the image afterward seen will be of a reddish (comple- 
 mentary) color. 
 
 725. The Action of the Eye. The iris acts as a 
 self-regulating diaphragm, dilating the pupil and thus 
 admitting more light when the illumination is weak ; con- 
 tracting the pupil and cutting off more light when the 
 illumination is strong. The adjustment for distance 
 (necessary to throw the foci on the retina) is effected by 
 
OPTICAL INSTRUMENTS. 537 
 
 changing the convexity of the anterior surface of the 
 crystalline lens. (See Experiment 2.) 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 per- 
 sistence of vision. If the impressions are repeated within 
 the interval of the persistence of vision, they appear con- 
 tinuous. (Compare 490.) 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. The 
 sensibility of the retina is easily exhausted, as though the 
 terminal cones of the optic nerve became tired of vibrat- 
 ing at a given'rate and thus became insensible to certain 
 impulses of light corresponding to a certain color. (See 
 Experiment 3.) The retinas of some eyes seem to be 
 affected similarly by rays of different colors. The owners 
 of such eyes are said to be color blind. Serious railway 
 accidents caused by mistaking the color of signal lights, 
 have led to examinations for color blindness. Such ex- 
 aminations have shown that this optical defect is much 
 more common than is generally supposed, many persons 
 being color blind without knowing it. 
 
 Estimates of Size and Distance. We 
 
 estimate the size of visible objects (by instinct or by ex- 
 perience) from the visual angle and the supposed distance 
 of the object and by comparison with objects of known 
 size. If we are mistaken in the distance of the object, we 
 are often mistaken in our estimate of its size. We estimate 
 the distance of an object by the distinctness with which 
 we see it, by comparison with objects of known distance 
 
538 OPTICAL INSTRUMENTS. 
 
 and by the muscular effort we make in turning the eyes 
 inward so as to direct them upon the object. The axes of 
 the eyes intersect at the object. The angle between the 
 axes is called the optical angle. The greater the optical 
 angle, the less the distance. 
 
 (a.) The more obscure an object, the more distant (and, conse- 
 quently, the larger) it seems to be. Hence, the apparent enormous 
 size of objects seen in a fog. When the moon appears on the hori- 
 zon, we see that she is beyond all terrestrial objects in that direction 
 and she seems farther off (and, consequently, larger) than when she 
 is overhead, there being then no intervening objects for comparison. 
 But the moon is actually nearer us when she is in the zenith than 
 when in the horizon and the visual angle is, consequently, greater. 
 
 727. Distinct Vision. That vision may be 
 distinct, the image formed on the retina must be 
 clearly defined, well illuminated and of sufficient 
 size. 
 
 (a.) The power of the eye to adjust itself for distance is limited. 
 When a book is held close to the eyes, the rays from the letters are 
 50 divergent that the eye cannot focus them upon the retina. The 
 jear 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 
 T,O the small size of the pupil, rays from a point 20 inches or more 
 distant are practically parallel. 
 
 (&.) The near point of some eyes is less than 3^ inches, while the 
 far point is only 8 or 10 inches. The owners of such eyes are near- 
 sighted. In such eyes, the retina is too far back, the eyeball being 
 elongated in the direction of its axis. The remedy is in concave 
 glasses. 
 
 (c.) The near point of some eyes is about 12 inches and the far 
 point is infinitely distant. The owners of such eyes are far-sighted. 
 In such eyes the retina is too far forward, the eyeball being flat- 
 tened in the direction of its axis. The remedy is in convex glasses. 
 
 (d.) The eye loses its power of adjustment with age, the crystal- 
 line lens losing its elasticity. The cause of the difficulty is different 
 from that of far sightedness, but the remedy is the same. 
 
OPTICAL INSTRUMENTS. 
 
 539 
 
 728. Magnifying Glasses. A magnifying glass, 
 or simple microscope, is a convex lens, generally double- 
 convex. The object is placed between the lens and its 
 principal focus. The image is virtual, erect and magni- 
 fied (Fig. 361.) The visual angle subtended by the image 
 is greater than that subtended by the object. 
 
 729. Compound Microscope. The compound 
 microscope consists of two or 
 
 more convex lenses placed in 
 a tube. One of these, o, 
 called the object glass or ob- 
 jective, is of short focus. The 
 object, ab, being placed slightly 
 beyond the principal focus, a 
 real image, cd, magnified and 
 inverted, is formed within the 
 tube ( 695). The other lens, 
 E, called the eyeglass, is so 
 placed that the image formed 
 by the objective lies between 
 the eyeglass and its focus. A 
 magnified virtual image, AB, 
 of the real image is formed 
 by the eyeglass ( 696) and 
 seen by the observer. (See 
 Fig. 379.) 
 
 FIG. 379. 
 
 (a.) Compound microscopes are usually provided with several 
 objectives of different focal distances, so that a selection may be 
 made according to the magnifying power required. The powers 
 generally used range from 50 to 350 diameters (i. e., they multiply 
 linear dimensions so many times). The object generally needs to 
 be intensely illuminated by a concave mirror or convex lens. 
 
540 
 
 OP TIC A L INSTR UMENTS. 
 
 73O. Galilean Telescope; Opera Glass. In 
 the telescope attributed to Galileo, the objective is a double 
 
 FIG. 380. 
 
 convex and the eye-piece is a double concave lens. The 
 concave lens intercepts the rays before they have reached 
 the focus of the objective ; were it not for this eye-piece, a 
 real, inverted image would be formed back of the position 
 of the concave lens. The rays from A, converging after 
 refraction by 0, are rendered diverging by (7; they seem to 
 diverge from a. In like manner, the image of B is formed 
 at b. The image, ab, is erect and very near. An opera- 
 glass consists of two Galilean telescopes placed side by 
 side. In a good instrument, both lenses are achromatic. 
 
 731. Astronomical Telescope; Refractor. 
 
 Astronomical telescopes are of two kinds refractors and 
 
 FIG. 381. 
 
 reflectors. Fig. 381 represents the arrangement of the 
 lenses and the direction of the rays in the refracting 
 telescope. The object-glass is of large diameter that it 
 may collect many rays for the better illumination of the 
 image. The inverted, real image formed by the objective, 
 
OPTICAL INSTRUMENTS. 541 
 
 0, is magnified by the eye-piece, as in the case of the 
 compound microscope. The visible image, cd, is a virtual 
 image of ab, the real image of AB. 
 
 (a.) The telescope now building for the Lick Observatory (on the 
 summit of Mt. Hamilton, California, 4,400 ft. above the level of the 
 sea) will be the largest refractor in the world. The objective is 38j 
 inches in diameter. The telescope will be 60 ft. in length. The 
 two glasses will cost $51,000 ; the mounting will cost as much more ; 
 the dome of the Observatory will cost $50,000. 
 
 732. Reflecting Telescopes. A reflecting tele- 
 scope consists of a tube closed at one end by a concave 
 
 FIG. 382. 
 
 mirror, so placed that the image thus formed may be mag- 
 nified by a convex lens used as an eye-piece. Sometimes 
 the eye-piece consists of a series of convex lenses placed 
 in a horizontal tube, as shown in Fig. 382. The rays 
 from the mirror may be reflected by a cathetal prism, mn 
 ( 686 [c]), and a real image formed at ab. This image is 
 magnified by the glasses of the eye-piece and a virtual 
 image formed at cd. The Earl of Rosse built a telescope 
 with a mirror six feet in diameter and having a focal dis- 
 tance of fifty-four feet. (Appendix T.) 
 
 733. Terrestrial Telescope. The inversion of 
 the image in an astronomical telescope is inconvenient 
 when viewing terrestrial objects. This inconvenience is 
 
542 
 
 OPTICAL INSTRUMENTS. 
 
 obviated in the terrestrial telescope by the interposition of 
 two double convex lenses, m and n, between the objective 
 
 FIG. 383. 
 
 and the eye-piece. The rays, diverging from the inverted 
 image at J, cross between rti and n and form an erect, 
 magnified, virtual image at ab. 
 
 Experiment 4. 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. 384), or 
 
 FIG. 384. 
 
 written your autograph. 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 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 th 3 foci of the lens. If a screen, 88, be held at the positions of 
 these foci, a and 6, the image will appear clearly cut and bright. If 
 the screen be held nearer the lens or further from it, as at 8' or S", 
 the picture will be blurred. 
 
 734. Magic Lantern. In the magic lantern, a 
 lamp is placed at the common focus of a convex lens in 
 front of it and of a concave mirror behind it. The light 
 is thus concentrated upon ab, a transparent picture, called 
 the "slide." A system of lenses, m, is placed at a little 
 
OPTICAL INSTRUMENTS. 
 
 543 
 
 more than its focal distance beyond the slide. A real, 
 inverted, magnified image of the picture is thus pro- 
 
 FIG. 385. 
 
 jected upon the screen, 8. The tube carrying m is adjust- 
 able, so that the foci may be made to fall upon the screen 
 and thus render the image distinct. By inverting the 
 slide, the image is 
 seen right side up. 
 The solar and elec- 
 tric microscopes act 
 in nearly the same 
 way, the chief differ- 
 ence being in the 
 source of light. 
 
 FIG. 386. 
 
 (a.) Directions for 
 making a simple magic 
 lantern may be found 
 on page 84 of Mayer and 
 Barnard's little book on Light. Fig. 386 represents a very compact 
 and efficient lantern, known as Marcy's Sciopticon, and furnished by 
 James W. Queen & Co. of Philadelphia. 
 
 735. Stereoscopic Pictures. Close the left eye 
 and hold the right hand so that the forefinger shall hide 
 
544 
 
 OPTICAL INSTRUMENTS. 
 
 FIG. 387. 
 
 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. 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. 387. 
 
 Looking at it with only the 
 right eye, it appears as shown 
 at B. From this we see that 
 when we look at a solid, the 
 images upon the retinas of 
 the two eyes are different. 
 
 If, in any way, we combine two drawings, so as to produce 
 images upon the retinas of the two eyes like those produced 
 by the solid object, we obtain the idea of solidity. 
 
 736. The Stereoscope. To blend these two pic- 
 tures is the office of the stereoscope. Its action will be 
 readily understood from Fig. 388. The 
 diaphragm, D, prevents either eye from 
 seeing both pictures at the same time. 
 Rays of light from B are refracted by 
 the half -lens E' so that they seem to 
 come from C. 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 successfully blended ; 
 the picture "stands out," or has the 
 appearance of solidity. If the two 
 pictures of a stereoscopic view were exactly alike, this 
 impression of solidity would not be produced. 
 
 FIG. 
 
P OLA RIZA TION. 545 
 
 737. Polarization. If a horizontal string, tightly 
 drawn, be hit a vertical blow, a wave will be formed with 
 vibrations in a vertical plane. If the string be hit a 
 horizontal blow, a wave will be formed with vibrations in 
 a horizontal plane. Thus a transversal wave is capable of 
 assuming a particular side or direction while a longitudinal 
 wave is not. This is expressed by saying that a transversal 
 wave is capable of polarization. Polarization of light 
 may be produced in three ways by absorption, by reflec- 
 tion and by double refraction. 
 
 (a.) Polarized light presents, to the naked eye, the same appear- 
 ance as common light. In polarization experiments, two pieces of 
 apparatus must generally be employed ; one to produce polariza- 
 tion ; the other to show it. The former is called the polarizer; the 
 latter, the analyzer. Apparatus that serves for either of these pur- 
 poses will also serve for the other. 
 
 738. Planes of Vibration in Sunbeam. If 
 
 we imagine a sunbeam to be cut by a plane perpendicular 
 to the direction of the beam, we may sup- 
 pose the section to consist of vibrations 
 moving in every possible plane, as repre- 
 sented by Fig. 389. It is not to be sup- 
 posed that all of these planes will intersect 
 at the same point. There will be many rays 
 whose planes of vibration are vertical, many whose planes 
 of vibration are horizontal, etc. 
 
 739. Polarization by Absorp- 
 tion. If a sunbeam fall upon a substance 
 whose molecular structure allows vibrations 
 in only a particular plane, say vertical, the 
 substance may be compared to a frame with 
 FIG. 390. vertical bars, as represented by Fig. 390, 
 
546 P OLARIZA TION. 
 
 Such a frame or such a substance will absorb the rays 
 whose vibrations lie in a plane that is horizontal or nearly 
 so, convert them into absorbed heat and transmit, as 
 polarized light, those rays whose vibrations lie in a plane 
 that is vertical or nearly so. A plate cut 
 in a certain way from a crystal of tour- 
 maline acts in such a way ; it is called a 
 tourmaline analyzer. If the sunbeam fall 
 upon a substance that allows vibrations 
 
 in only a horizontal plane, the substance 
 FIG. 39 r. 
 
 may be compared to a frame with hori- 
 zontal bars, as represented in Fig. 391. Such a body will 
 quench all the rays whose vibrations lie in a plane that is 
 vertical or nearly so and transmit, as polarized light, those 
 rays whose vibrations lie in a plane that is horizontal or 
 nearly so. The tourmaline analyzer previously used acts 
 in this way when turned a quarter way around. 
 
 74O. Tourmaline Tongs. If these two frames, or 
 two tourmaline analyzers, be placed one over the other in 
 such a way that the bars of the second shall be perpen- 
 dicular to those of the 
 first, it will be seen that 
 the first will quench or 
 
 absorb part of the rays, 
 
 J ' FIG. 392. 
 
 while the rays trans- 
 mitted by the first as polarized light will be quenched by 
 the second. But if the bars of the second be parallel to 
 those of the first, the polarized light transmitted by the 
 first will also be transmitted by the second. This partial 
 or total absorption of luminous rays is shown easily with 
 the " tourmaline tongs," which consist of two tourmaline 
 
POLARIZATION. 
 
 547 
 
 FIG. 393- 
 
 plates set in movable discs (Fig. 392). Light transmitted 
 by either plate is polarized (and colored by the accidental 
 tint of the tourmaline). When the plates are superposed, 
 polarized light may be transmitted by both, or all of the 
 incident light may be absorbed according to their relative 
 positions as above stated. 
 
 741. Polarization by Reflection. Light is 
 polarized when the rays whose 
 vibrations lie in a particular 
 plane are alone allowed to pass. 
 This effect may be produced by 
 causing a beam of light to be 
 reflected by a non-metallic mirror 
 at a certain angle which depends 
 upon the nature of the reflecting 
 substance. For glass, the ray 
 must make with the reflecting surface an angle of 35 25' 
 (angle of incidence = 54 35'). 
 
 742. Malus's Po- 
 lariscope. This in- 
 strument has two reflec- 
 tors made of bundles of 
 glass plates. (An ordi- 
 nary looking-glass is a 
 metallic mirror.) Of 
 these, A is called the 
 polarizer and B the 
 analyzer. Both reflec- 
 tors turn upon horizon- 
 tal axes; B also turns 
 vertical axis by means of the horizontal circles, (7(7, 
 
 FIG. 395. 
 
548 P OLARIZA TION. 
 
 When A and B are placed at the polarizing angle with 
 the vertical axis, a beam of light is made to fall upon the 
 polarizer in such a direction that the reflected light will 
 pass vertically upward to B. This reflected light will be 
 polarized. The polarized light will be reflected by B 
 when the second reflector is parallel to the first (Fig. 395); 
 it will be absorbed or transmitted when B is perpendicular 
 to A (Fig. 394). 
 
 (a.) Place B as shown in Fig. 395. Throw a beam of light upon 
 A, the room being darkened. The light reflected from B will form 
 a white spot upon the side of the room. Turn the collar, C, slowly 
 around. The spot of light will move around the sides of the 
 room, gradually growing fainter. When G has been turned a 
 quarter way around (Fig. 394), the spot has wholly disappeared. 
 Beyond this it grows brighter until G has been turned half way 
 around, when it is as bright as at the beginning. When C has 
 been turned three-quarters around, the spot again disappears, 
 again reappearing as G and B are brought to their original 
 positions. 
 
 743. Double Refraction. A crystal of Iceland 
 spar shows a very important effect upon an incident 
 
 beam. The retarda- 
 tion of the vibrations 
 whose plane is paral- 
 lel to the axis (the 
 line joining the two 
 obtuse angles of the 
 crystal) is different 
 
 FIG , from the retardation 
 
 of the vibrations 
 
 whose plane is perpendicular to the axis. This differ- 
 ence in change of velocity produces a difference in the 
 refraction of the two sets of rays. A beam of light, 
 
OPTICAL INSTRUMENTS. 549 
 
 therefore, falling upon a crystal of Iceland spar will be 
 generally split into two, producing the effect known as 
 double refraction. 
 
 (a.) A small object, as a dot or line, viewed through a crystal of 
 Iceland spar, will generally show two images formed by light oppo- 
 sitely polarized. If the eye be placed directly above the dot and 
 the crystal be slowly turned around, one image known as the ordinary 
 image will remain stationary, while the other known as the extra- 
 ordinary image will revolve about it at a varying distance. The 
 ordinary ray has a constant and the extraordinary ray a variable 
 index of refraction. 
 
 (6.) On looking, through a tourmaline or any other analyzer, at 
 the two images formed by double refraction, it will be found that 
 there is a marked difference in the brightness of the two images. 
 As the analyzer is turned around, one image grows brighter and the 
 other fainter, the greatest brightness of one being simultaneous 
 with the extinction of the other. 
 
 744. Nicol's Prism. One of the most valuable 
 pieces of polarizing apparatus is Nicol's prism. A crystal 
 
 FIG. 397. 
 
 of Iceland spar is bisected in a plane, AB, passing through 
 its two obtuse angles, as shown in the figure. The two 
 halves are then cemented in their original position with 
 Canada balsam. The refractive power of the balsam is 
 such that the extraordinary ray passes through it at E, 
 while the ordinary ray, striking the balsam at an angle 
 greater than its critical angle, is reflected at N, passes out 
 
550 
 
 OPTICAL INSTRUMENTS. 
 
 of the crystal and is then absorbed by the surrounding 
 frame of the prism. Since the " Nicol " allows only the 
 extraordinary ray to pass, it may be used, like a tourmaline, 
 as an analyzer or as a polarizer. 
 
 (a.) When the light of the blue sky is looked at through a Nicol 
 or other analyzer (at an angular distance of 90 from the sun), a dif- 
 ference of brightness is seen as the analyzer is turned. The degree 
 of difference between the maximum and the minimum of light thus 
 observed measures the degree in which such light is polarized. 
 
 FIG. 398. 
 
 745. A Simple Polariscope. In the accompany- 
 ing figure, B is a pile of six or eight glass plates about 
 
 15 cm. square, serving as 
 a polarizer. A Nicol at 
 E serves as an analyzer. 
 The Nicol is supported, 
 as shown in the figure, so 
 as to view the centre of 
 the polarizer at the polar- 
 izing angle of glass. The 
 prism should be mounted 
 so that it may be turned on its axis in its support. G is 
 a piece of ground glass for cutting off the images of 
 outside objects. The object to be examined is placed on 
 the glass table or shelf, T. The instrument is placed with 
 G facing a window and covered with a cloth to cut off 
 unpolarized light. 
 
 (a.) Place a thin plate (film) of mica or selenite on the table, T, 
 and look through the Nicol while you turn it about on its axis. A 
 beautiful display of colors is seen, each reaching its maximum brill- 
 iancy, fading away and changing to its complementary color as the 
 analyzer is turned. The colors and changes of color are due to 
 the interference of polarized rays. 
 
RECAPITVLA TlOtf. 
 
 551 
 
 Recapitulation. To be amplified by tbe pupil for 
 review. 
 
 f OBSCURA. 
 
 CAMERA J 
 
 I PHOTOGRAPHER'S. 
 
 HUMAN EYE AND ITS ACTION. 
 
 r SIMPLE. 
 
 en 
 
 MICROSCOPES 
 
 TELESCOPES 
 
 
 COMPOUND. 
 REFLECTORS. 
 
 REFRACTORS 
 
 GALILEAN. 
 OPERA GLASS. 
 ASTRONOMICAL 
 TERRESTRIAL, 
 
 
 
 MAGIC LANTERN. 
 STEREOSCOPE. 
 
 POLARIZATION 
 
 BY ABSORPTION. 
 
 BY REFLECTION. 
 
 BY DOUBLE REFRACTION. 
 
 POLARISCOPES. 
 
552 ENERGY. 
 
 CONCLUSION. 
 
 ENERGY. 
 
 746. Solar Energy. The work performed by men 
 and other animals is due to the transformed energy of food. 
 " This food is of vegetable origin and owes its energy to 
 the solar rays. The energy of men and animals is, there- 
 fore, the transformed energy of the sun. Excepting the 
 energy of the tides, the sun's rays are the source of all the 
 forms of energy practically available. It has been esti- 
 mated that the heat received by the earth from the sun 
 each year would melt a layer of ice over the entire globe 
 a hundred feet in thickness. This represents energy 
 equal to one horse-power for each fifty square feet of 
 surface." 
 
 747. Dissipation of Energy. "It has been seen 
 that only a fraction of the energy of heat is available for 
 transformation into other forms of energy and that such 
 transformation is possible only when a difference of tem- 
 perature exists. Every conversion of other forms of 
 energy into heat puts it in a form from which it can be 
 only partially recovered. Every transfer of heat from one 
 body to another, or from one part to another of the same 
 body, tends to equalize temperatures and diminish the 
 proportion of energy available for transformation. Such 
 transfers of heat are continually taking place ; and, as far 
 as our present knowledge goes, there is a tendency toward 
 an equality of temperature, or, in other words, a uniform 
 
ENERGY. 553 
 
 molecular motion, throughout the universe. If this con- 
 dition of things were reached, although the total amount 
 of energy existing in the universe would remain un- 
 changed, the possibility of transformation would be at an 
 end and all activity and change would cease. This is the 
 doctrine of the dissipation of energy to which our limited 
 knowledge of the operations of nature leads us; but it 
 must be remembered that our knowledge is very limited 
 and that there may be in nature the means of restoring 
 the differences upon which all activity depends." Anthony 
 and Braclcett. 
 
 748. Varieties of Energy. Like matter, energy 
 is indestructible. We have already seen that energy may 
 oe visible or invisible (i. e., mechanical or molecular), 
 kinetic or potential. "We have at our control at least 
 eight varieties of energy. 
 
 (a.) Mechanical energy of position (visible, potential). 
 (&.) Mechanical energy of motion (visible, kinetic). 
 (e.) Latent heat (molecular, potential). 
 (d.) Sensible heat (molecular, kinetic). 
 (e.) Chemical separation (molecular or atomic ; potential). 
 (/.) Electric separation (probably molecular, potential). 
 (g.) Electricity in motion (probably molecular, kinetic). 
 (h.) Radiant energy, thermal, luminous or actinic (molecular, 
 kinetic). 
 
 749. Conservation of Energy. The doctrine 
 that; considering the universe as a whole, the sum of ah 
 these forces is a constant quantity, is known as the Con- 
 servation of Energy. 
 
 a + b + c + d + e+f + g + h = & constant quantity. 
 
 This does not mean that the value of a is invariable ; we 
 have seen it changed to other varieties as b or d. " We have 
 
554 ENtittQY. 
 
 seen heat changed to electricity and vice versa, and eithef 
 or both changed to mechanical energy. It does not mean 
 that the sum of these eight variable quantities in the earth 
 is constant, for we have seen that energy may pass from 
 sun to earth, from star to star. But it does mean that the 
 sum of all these energies in all the worlds that constitute 
 the universe is a quantity fixed, invariable. 
 
 750. Correlation of Energy. The expression 
 Correlation of Energy refers to the convertibility of one 
 form of energy into another. Our ideas ought, by this 
 time, to be clear in regard to this convertibility. One im- 
 portant feature remains to be noticed. Eadiant energy can 
 be converted into other forms, or other forms into radiant 
 energy only through the intermediate state of absorbed 
 beat. 
 
 751. A Prose Poem." A river, in descending from an 
 elevation of 7720 feet, generates an amount of heat competent to 
 augment its own temperature 10 F., and this amount of heat was 
 abstracted from the sun, in order to lift the matter of the river to 
 the elevation from which it falls. As long as the river continues 
 on the heights, whether in the solid form as a glacier, or in the 
 liquid form as a lake, the heat expended by the sun in lifting it 
 has disappeared from the universe. It has been consumed in the 
 act of lifting. But, at the moment that the river starts upon its 
 downward course, and encounters the resistance of its bed, the heat 
 expended in its elevation begins to be restored. The mental eye, 
 indeed, can follow the emission from its source through the ether, 
 as vibratory motion, to the ocean, where it ceases to be vibration, 
 and takes the potential form among the molecules of aqueous vapor ; 
 to the mountain top, where the heat absorbed in vaporization is given 
 out in condensation, while that expended by the sun in lifting the 
 water to its present elevation is still unrestored. This we find paid 
 back to the last unit by the friction along the river's bed ; at the 
 bottom of the cascade, where the plunge of the torrent is suddenly 
 arrested ; in the warmth of the machinery turned by the river ; in 
 the spark from the millstone ; beneath the crusher of the miner ; ia 
 
555 
 
 the Alpine saw-mill ; in the milk-churn of the chalet ; in the sup- 
 ports of the cradle in which the mountaineer, by water-power, rocks 
 his baby to sleep. All the forms of mechanical motion here indi- 
 cated are simply the parcelling out of an amount of calorific motion 
 derived originally from the sun ; and, at each point at which the 
 mechanical motion is destroyed or diminished, it is the sun's heat 
 ,vhich is restored." TyndalL 
 
 o 
 
 w 
 
 Recapitul ation . 
 
 f VISIBLE OR MECHANICAL. 
 
 SOURCE. 
 DISSIPATION. 
 
 J OF POSITION, e. g., Hanging Ap- 
 Potential. pie, Head of 
 
 INVISIBLE OR 
 MOLECULAR. 
 
 HEAT. 
 
 
 LIGHT 
 
 ELECTRICITY... 4 
 
 Water. 
 
 OF MOTION, e. g., Falling Apple, 
 ^ Kinetic. Flowing Water. 
 
 OF POSITION, e. g., Latent Heat. 
 Potential. 
 
 OF MOTION, e. g., Sensible Heat. 
 Kinetic. 
 
 OF MOTION, or 
 Kinetic. 
 
 OF POSITION, e. g., Charged Ley* 
 Potential. den jar, Batter j 
 
 with circuit bro- 
 k,n. 
 
 OF MOTION, e. g., Ley den jar dis- 
 Kinetic. charging: Bat- 
 
 tery with cir- 
 cuit closed. 
 
 GENERAL REVIEW. 
 
 1. (a.) Define science, matter, mass, molecule and atom. (&.) How 
 do physical and chemical changes differ ? (c.) Define physics. 
 
 2. (a.) What are chemical and physical properties of matter? 
 (&.) Define and illustrate two universal and one characteristic 
 properties of matter. 
 
 3. (a.) Define meter, liter and gram. (&.) What is a solid, a 
 liquid, and a gas ? (c.) Define dynamics and force. 
 
 4. (a.} Name and define three units of force. (&.) Give Newton's 
 Laws of Motion, (c.) Give the law of reflected motion. 
 
,5-56 REVIEW. 
 
 5. (a.) Explain the parallelogram of forces, and (6.) the polygon 
 of forces. 
 
 6. (a.) Define gravitation and give its laws. (6.) Give the law of 
 weight, (c.) What is the centre of gravity, and how may it be 
 found ? 
 
 7. (a.) Describe Att wood's machine. (6.) Give the rules and 
 formulas for falling bodies, (c.) How far will a body fall in three 
 seconds ? 
 
 8. (a.) What is a pendulum ? (&.) Give the laws of the pendulum. 
 (c.) How long must a pendulum be to vibrate 10 times a minute ? 
 
 9. (a.) Define energy, foot-pound, dyne, erg, and horse-power. 
 (b.) Deduce the formula for measuring kinetic energy when weight 
 and velocity are given. 
 
 10. (.) Define each of the six traditional simple machines. (&.) 
 Give the law for each, (c.) What is the office of a machine ? (d.\ 
 Discuss the subject of friction. 
 
 11. (a.) Give Pascal's law, and the rule for determining lateral 
 liquid pressure. (&.) Describe the hydrostatic press, and state the 
 general principle upon which its action depends. 
 
 12. (a.) State Archimedes' principle. (6.) What is specific gravity ? 
 (c.) Explain the determination of the sp. gr. of a solid lighter than 
 water, (d.) Explain the use of the specific gravity bulb, (e.) 
 Describe Nicholson's hydrometer and explain its use. 
 
 13. (a.) A 1000 gr. bottle having in it 928 grs. of water, has the 
 remaining space filled with metallic sand and then weighs 1126.75. 
 What is the sp. gr. of the sand ? (6.) Through which of the three 
 kinds of levers can the greatest power be gained ? (c.) Through 
 which can none be gained ? (d.) Why do we use it ? (e.) Give an 
 example. 
 
 14. A ball projected vertically upward, returns in 15 seconds to 
 the place of projection. How far did it ascend ? 
 
 15. (a.) A floating solid displaces how much liquid? (&.) An 
 immersed solid displaces how much liquid ? (c.) A floating solid 
 loses how much weight ? (d.) An immersed solid loses how much 
 weight ? 
 
 16. What is the energy of a rifle-ball weighing 32 grains, having 
 a velocity of 213 meters per second, and striking in the centre of a 
 pendulum of wood weighing 23 kilograms ? 
 
 17. (#.) What is meant by the increment of velocity or gravity ? 
 (6.) How far will a body fall in 6| seconds? (c.) How far in the 
 9th second ? (d.) If a freely-falling body have a velocity of 448 ft. 
 per second, how long has it been falling ? 
 
 18. (a.) Deduce, from the laws of falling bodies, the formula for 
 
REVIEW. 557 
 
 the velocity of spouting liquids (t> = 8.02 /y/A). (&.) Why must the 
 unit of measure used with this formula be feet? (c.) Deduce a 
 similar formula in which the meter is involved as the unit. 
 
 19. Name four kinds of water-wheels, and describe the most 
 efficient of them. 
 
 20. (a.} Explain the action of the mercury barometer. (6.) Give 
 Mariotte's law. (c.) Describe the piston of Sprengel's air-pump. 
 (d.) Describe the ordinary air-pump, (e.) Explain the action of the 
 siphon. 
 
 21. (a.) How would you illustrate the law of magnetic attraction 
 and repulsion? (&.) Give the theory of magnetism, (c.) Explain 
 the action of the electrophorus ; what do you think of its accuracy 
 and value ? (d.) Explain terrestrial induction. 
 
 22. If the capacity of the barrel of an air-pump be \ that of the 
 receiver, how much air would remain in the receiver at the end of 
 the fourth stroke of the piston, and what would be its tension 
 compared with that of the external air ? 
 
 23. What is the pressure on the side of a reservoir 150 feet long, 
 and filled with water to the height of twenty feet ? 
 
 24. (a.) Why is a reservoir usually built in connection with 
 water- works ? (&.) Why are fire-engines provided with an air- 
 chamber? (c.) Why should the nozzle be smaller than the 
 hose? 
 
 25. (a.) Why can you not raise water 50 feet with a common 
 pump ? (6.) What change would it be necessary to make in the 
 pump in order to raise water to that height ? (c.) Illustrate by a 
 diagram. 
 
 26. (a.) Give the law of electrical attraction and repulsion, and 
 illustrate by pith-ball electroscope. (6.) Define conductors and non- 
 conductors, electrics and non-electrics, (c.) Illustrate by an example 
 of each. 
 
 27. (a.) Give and illustrate each of the laws of motion. (6.) 
 Explain composition and resolution of forces with illustrative 
 figures. 
 
 28. (a.) Give the facts of gravity and the law of weight. (6.) 
 If a body weigh 120 Ibs. 2500 miles below the surface of the earth, 
 at what distance above the surface will it weigh 80 Ibs. ? 
 
 29. Explain and illustrate electric induction fully. 
 
 30. (a.) Explain the construction and action of the electrophorus. 
 What kind of electricity is discharged from it ? (&.) Describe the 
 Leyden jar and explain its action, (c.) Explain the action of the 
 plate electric machine, (d.) In what way do lightning-rods protect 
 buildings ? 
 
558 REVIEW. 
 
 31. (a.) Discuss carefully the resistance of a Galvanic cell. (b.\ 
 Describe the Voltaic arc. 
 
 32. (a.) State the difference between a magnet and an electro 
 magnet. (5.) Give the principles on which the telegraph operates, 
 (c.) What is meant by an " electro negative substance ? " 
 
 33. (a.) Describe Ruhmkorff s coil, and (&.) explain its action. 
 
 34. Describe the thermo-electric pile, and explain its use. 
 
 35. (a.) Give Prof. Tyndall's illustration of the propagation of 
 sound. (6.) What is the velocity of sound in air ? (c.) How is it 
 affected by temperature ? 
 
 36. (a.) Explain the difference between noise and music, (fc.) 
 Name the three elements of a musical sound, and state the physical 
 cause of each. 
 
 37. (a.) Describe and explain the telephone. (6.) The phono- 
 graph. 
 
 38. (a.) Explain interference of sound. (6.) Give the laws of 
 vibration of musical strings, (c.) Give the relative numbers of 
 vibration for the tones of the major diatonic scale. 
 
 39. (a.) If 18 seconds intervene between the flash and report of a 
 gun, what is its distance, temperature being 82 F. ? (6.) If a 
 musical sound be due to 144 vibrations per second, how many 
 vibrations correspond to its 3d, 5th, and octave ? 
 
 40. The bottom of a tank is 100 centimeters on one side, and a 
 meter on the adjoining side. The tank has a depth of 50 centi- 
 meters of water, (a.} What is the pressure on the bottom ? (&.) 
 On either one of the vertical sides ? 
 
 41. (a.) What is a horse-power? (6.) How many horse-powers 
 are there in a machine that will raise 8250 Ibs. 176 ft. in 4 minutes ? 
 (c.) State the modes of diminishing friction. 
 
 42. What will be the kinetic energy of a 25-pound ball that has 
 fallen a mile ? (Reject small remainders ) 
 
 43. Two bodies are attracting a third with forces as 441 to 576, 
 the first, weighing 25 Ibs., at a distance from the third of 20 feet, 
 and the second at a distance of 30 feet ; what is the weight of the 
 second ? 
 
 44 How far will a body fall in the first second on Saturn, the 
 density of Saturn being .12 that of the earth, and its diameter being 
 72000 miles? 
 
 45. (a.) What is temperature ? (6.) Discuss the expansion of 
 water by heat, (c.) What is the rate of gaseous expansion by heat ? 
 
 46. (a.) What is the difference between evaporation and boiling ''. 
 \b.) What is the boiling point ? (c ) What is distillation, and 
 
 is it performed. ? 
 
REVIEW. 559 
 
 47. (a.) Define latent, sensible and specific heat, ft.) What is the 
 latent heat of water and of steam ? 
 
 48. (a.) Explain the several modes of diffusing heat, showing 
 how they differ. (b.) State and explain the relation between the 
 absorbing and radiating powers of any given substance. 
 
 49. (a.) What is thermodynamics ? (b.) State the first law of 
 thermodynamics, (c.) What is the mechanical equivalent of hea v 
 in kilogrammeters ? (d.) What does your answer mean ? 
 
 50. (d.) Draw a figure showing the position of the parts of thf 
 cylinder and steam-chest when the piston is going up. 
 
 51. (a.) To what temperature would a cannon-ball weighing 
 150 Ibs. and moving 1920 feet a second, raise 2000 Ibs. of water 
 from 32 F., if its motion were suddenly converted into heat ? (&.) 
 Explain the origin and propagation of sound waves. 
 
 52. (a.) Express a temperature of 50 F. in degrees centigrade. 
 (b.) Name and describe the essential parts of a steam-engine in their 
 proper order, (c.} Point out the changes in form of energy from 
 the furnace fire, through a high-pressure engine to the heated axles 
 set in motion thereby. 
 
 53. The mechanical equivalent of heat being 1390 foot-grams, 
 the foot being equal to 30.48cm., and the increment of velocity on 
 the earth being 980 cm. , find the mechanical equivalent in ergs. 
 
 Am. 41519856. 
 
 54. (a.) What is the difference between waves of sound and 
 waves of light ? (6.) What is the difference between an atherma- 
 nous and an opaque substance ? (c.) What determines the apparent 
 size of a visible object ? 
 
 55. (a.) If the gun-cotton mentioned in 620 (a.) be rubbed with 
 a little lamp-black, will it be ignited with more or less difficulty ? 
 Why? (b.) What is reflection of light? (c.) How does it differ 
 from refraction of light ? 
 
 56. (.) How could you show that light is invisible unless it en- 
 ters the eye? (&.) What determines the apparent position of an 
 object? (c.) What is the distinction between real and virtual 
 
 57. (a.) Describe and illustrate a construction for conjugate foci 
 in the case of a concave mirror. (6.) In the case of a convex lens. 
 (c.) What is meant by the index of refraction ? (d.) Give the laws 
 for refraction of light. 
 
 58. (.) Explain total internal reflection, (b.} What is meant by 
 dispersion of light? (c.) What is pure spectrum and how may it 
 be produced ? (d.) What are Fraunhofer's Lines and what do they 
 indicate? (e.) Name the prismatic colors in order. 
 
560 REVIEW. 
 
 59. (a.) Why does a certain piece of glass look red when it ia 
 held between a lamp and the eye? (b.) Why does it look red when 
 the lamp is between the glass and the eye ? (c.) Explain the suc- 
 cession of colors in the rainbow, (d.) What three classes of rays in 
 a sunbeam ? 
 
 60. (a.) Describe the human eye as an optical instrument. (&.) The 
 3pera-glass. (c. ) The terrestrial telescope, (d.) The stereoscope. 
 
 61. (a.) Explain polarization of light by absorption, (&.) By 
 reflection. 
 
 62. (a.) Explain the action of the siphon. (&.) Find the volume 
 of a balloon filled with hydrogen that has a lifting power of 440 Ibs. 
 (sp. gr. of air = 14.42. One liter of hydrogen weighs .0896 g.) 
 
 63. (.) The barrel of an air-pump is $ that of the receiver ; find 
 the tension of the air in the receiver after 8 strokes of the piston, call- 
 ing the normal pressure 15 Ibs. and disregarding the capacity of the 
 connecting pipes. (&.) A stone let fall from the top of a cliff was 
 seen to strike the bottom in 6| seconds ; how high was the cliff ? 
 
 64. (a.) A ship passing from the sea into a river, discharges 44800 
 Ibs. of cargo, and is found to sink in the river to the same mark as 
 in the sea. The sp. gr. of sea-water being 1.028, find the weight of the 
 ship and cargo. (&.) A body weighing 12 Ibs. (sp. gr. = ^,)is fastened 
 to the bottom of a vessel by a cord. Water being poured in until 
 the body is covered, find the tension of the cord. 
 
 65. (a.) A current of 9 amperes worked an arc electric light. 
 ( 467.) The difference of potential between the carbon tips was 
 measured by an electrometer and found to be 140 volts. What 
 horse-power was absorbed ou the arc? (&.) Find the maximum 
 weight that can be supported by a hydraulic elevator connected 
 with a reservoir, the area of the piston being 24 sq. in. and the 
 reservoir being 170 ft. above the cylinder, (c.) The difference be- 
 tween the fundamental tones of two organ -pipes of the same length, 
 one of which is closed at the top, is an octave. Explain why. 
 
 66. If the force of gravity be taken as 980 dynes, and the 
 mechanical equivalent of heat be 424 grammeters, what will be the 
 value of a lesser calorie in ergs? Ans. 41,552,000 ergs. 
 
iir 
 
 j 
 
 APPENDIX A. 
 
 Mathematical Formulas. 
 
 TT 3.14159. I Circumference of circle = TT D. 
 
 Area of a circle = TT R 2 . | Surface of a sphere = 4 TT R 2 = TT D*. 
 
 Volume of a sphere = ^ TT R 3 = 1 TT D*. 
 
 APPENDIX B. 
 
 Soldering. The teacher or pupil will often find it very con- 
 venient to be able to solder together two pieces of metal. The pro- 
 cess here described is very simple and will answer in most cases. 
 A bit of soft solder, the size of a hazlenut, may be had gratis of any 
 good natured tinsmith or plumber. Cut this into bits the size of a 
 grain of wheat and keep on hand. Dissolve a teaspoonful of zinc 
 chloride (muriate of zinc) in water and bottle it. It may be labelled 
 "soldering fluid." If you have not a spirit-lamp obtain one, or 
 make one. A small bottle (such as those in which school-inks are 
 commonly sold) will answer your purpose. Get a loosely fitting cork 
 and through it pass a metal tube about an inch long and the size of 
 an ordinary lead pencil. Through this tube, pass a bit of candle 
 wicking. Fill the bottle with alcohol, insert the cork, with tube 
 and wick, and in a few minutes the lamp is ready. Having novf 
 the necessary materials you are ready for work. For example, sup- 
 pose that you are to solder a bit of wire to a piece of tinned ware. 
 If the wire be rusty, scrape or file it clean at the place of joining. 
 By pincers or in any convenient way hold the wire and tin together. 
 Put a few drops of " soldering fluid" on the joint, hold the tin in 
 the flame so that the wire shall be on the upper side, place a bit of 
 solder on the joint and hold in position until the solder melts. Re- 
 move from the flame holding the tin and wire together until the 
 solder has cooled. The work is done. If you have a "soldering- 
 iron," you can do a wider range of work, as many pieces of work 
 cannot be held in the lamp flame. 
 
 In soldering electric wires, do not use the " soldering fluid " above 
 mentioned. Twist the wires together, heat the joint in the lamp flame, 
 dip it into powdered rosin and then into coarse filings of solder, and 
 hold it in the flame again until the adhering solder melts and " runs," 
 
562 APPENDIX. 
 
 APPENDIX C. 
 
 A copy of the lecture of Prof. Crookes on " Radiant Matter " 
 ( 59 6.) may be obtained of JAMES W. QUEEN & Co., Philadelphia, 
 for 25 cents. Teacher and pupils should secure one or more copies. 
 The theory and experiments are alike beautiful, interesting and 
 instructive. In concluding the lecture, Prof. Crookes said : 
 
 ' ' In studying this Fourth State of Matter, we seem at last to 
 have within our grasp and obedient to our control the little indi- 
 visible particles which, with good warrant, are supposed to consti- 
 tute the physical basis of the universe. We have seen that, in some 
 of its properties, Radiant Matter is as material as this table, whilst 
 in other properties it almost assumes the character of Radiant 
 Energy. We have actually touched the border land where Matter 
 and Force seem to merge into one another, the shadowy realm 
 between Known and Unknown." 
 
 APPENDIX D. 
 
 Prince Rupert Drops. A neat illustration of the trans- 
 mission of pressure by liquids ( 216), may be given by filling a 
 small bottle with water, holding a Prince Rupert drop in its mouth, 
 and breaking off the tapering end. 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 ; they may be obtained from James W. 
 Queen & Co., 924 Chestnut street, Philadelphia. 
 
 APPENDIX E. 
 
 Difference between Theory and Practice. The re- 
 sults mentioned in 256 are never fully attained in practice. Only 
 the particles near the centre of the jet attain the theoretical velocity. 
 Further than this, if we carefully examine the stream we shall 
 notice that at a little distance from the orifice the stream is not more 
 than two-thirds or three-fourths the size of the orifice. This is duo 
 to the fact that the liquid particles come from all sides of the 
 opening and thus flow in different directions, forming cross currents, 
 which may be seen if there are solid particles floating in the water. 
 These cross currents impede the free flow and diminish the volume 
 of liquid discharged. Short cylindrical or funnel-shaped tubes in- 
 crease the actual flow. In a cylindrical tube, this narrowing of the 
 jet could not take place without forming a vacuum around the nar- 
 
APPENDIX. 563 
 
 row neck (called the vena contracta). The pressure of the atmos- 
 phere, tending to prevent this formation of such a vacuum, increases 
 the velocity and the volume of the discharge. The funnel-shaped 
 tube prevents the formation of cross currents by leading the liquid 
 more gradually to the point of exit. 
 
 APPENDIX P. 
 
 Barker's Mill. A working model of this apparatus ( 264) 
 may be easily made by any wide-awake pupil. Select a long, sound 
 lamp-chimney and a fine-grained cork that snugly fits the lower end. 
 Take a piece of glass tubing, the size of a lead pencil, heat it intensely 
 in an alcohol or gas flame until you melt off a piece a little shorter 
 than the lamp chimney. By reheating the end thus closed by 
 fusion, you may give it a neat, rounded finish. Prepare four pieces 
 of glass tubing, each 12 cm. long. These pieces would better be 
 made of tubing smaller than that just used. To cut the tube to the 
 desired length, scratch the glass at the proper point with a tri- 
 angular file, hold the tube in both hands, one hand on each side of 
 the mark just made, knuckles uppermost and thumb-nails touching 
 each other at a point on the tube directly opposite the file-scratch, 
 push with the thumbs and at the same time pull with the fingers. 
 The tube will break squarely off Smooth the sharp edges by soft- 
 ening in the alcohol flame. Bend each of these four pieces at right 
 angles, 2 cm. from each end, in such a way that one of the short 
 arms may be in a horizontal plane while the other short arm of the 
 same piece is in a vertical plane. The tubes may be easily bent 
 when heated red-hot at the proper points in the alcohol or gas flame. 
 See that the four pieces are bent alike. In the middle of the cork, 
 cut. a neat hole a little smaller than the tube first prepared. Near 
 the edge of the cork, at equal distances, cut four holes a little 
 smaller than the four pieces of bent tubing. Push the open end of 
 the straight tube through the middle hole. From the other side of 
 the cork, enter one end of each bent tube into one of the four holes. 
 Place the cork with its five tubes into the end of the chimney, see- 
 ing to it that the straight tube lies along the axis of the chimney, 
 i. e., that it is parallel with the sides of the chimney. The closed end 
 of the central tube should be near the open end of the lamp-chimney. 
 In pushing the tubes into the cork, grasp the tube (previously dip- 
 ped in soap and water) near the cork, and screw it in with a slow, 
 rotary, onward motion. See that the bent tubes are at right-angles to 
 each other, like those shown in Fig. 91. For a support, take a piece 
 of stout wire, small enough to turn easily in the central tube, and, a 
 
564 APPENDIX. 
 
 little longer than the chimney. Place one end in the middle of a tin 
 pepper-box and fill the box with melted lead. This makes a firm 
 base. File the other end of the wire to a sharp point. For a few 
 cents, such a wire with an iron base may be had ready made at the 
 stationer's. Pass the straight tube of the apparatus over this wire 
 until the closed end of the tube rests upon the sharpened point. The 
 chimney, with its four horizontal arms, is now delicately suspended, 
 free to revolve in stable equilibrium. Place the apparatus in the 
 middle of a tub and pour water into the open end of the chimney. 
 Tour wheel will work as well as Queen's. The satisfaction of seeing 
 the machine work and knowing that you made it will amply repay 
 the cost, leaving the instruction and added skill for clear profit. 
 
 APPENDIX G. 
 
 Weight of Air. (See 272.) A little thought concerning the 
 full meaning of Archimedes' Principle will show that if a body weighs 
 less than its own bulk of air it will rise in the air. Thus, soap- 
 bubbles filled with hydrogen or other light gas will ascend. If the 
 bubble be made from hot water and filled with warm air it will 
 rise ; if it be made from cold water and filled with cold air it will 
 fall. (Explain why.) The same principle applies to balloons. A 
 balloon will support a weight equal to the difference between the weight 
 of the balloon with the contained gas and the weight of the air dis- 
 placed. A liter of hydrogen weighs 0.0896 g. ; a liter of coal gas, 
 from 0.45 g. to 0.85 g. ; a liter of air heated to 200 Centigrade, about 
 0.8 g. On June 5th, 1783, at Annonay, about 40 miles from Lyons, 
 France, the Montgolfier Bros, inflated a linen globe 105 feet in diam- 
 eter with heated air. When released, it rose to a great height and 
 descended in 10 minutes at a distance of 1^ miles. This was the dis- 
 covery of the balloon. During the siege of Paris in 1870, the 
 Parisians communicated with the outer world by means of balloons 
 about 50 feet in diameter, having a capacity of about 70,600 cu. ft. 
 These balloons, with net and car, weighed about 1,000 pounds each 
 and had a carrying ability of about 2,000 pounds. Balloons have 
 been made about 100 feet in diameter, having a capacity of about 
 half a million cubic feet. In 1861-, an ascent was made to a height 
 of seven miles. 
 
 Air in motion constitutes a wind and has energy by virtue of its 
 weight and velocity. Winds are utilized for moving ships, for 
 driving windmills, etc. They arise from atmospheric disturbances 
 caused by solar heat. The energy of wind-power like that of water 
 r>ower (8 260, 746) is, therefore, traceable to the sun as its source. 
 
APPENDIX. 
 
 565 
 
 APPENDIX H. 
 
 Atmospheric Pressure. (See 275.) Into a bent glass 
 tube, ACS, pour mercury to a height of about 20 inches, or 50 cm. 
 The mercury will, of course, stand at exactly the same level, ac, in 
 the two branches. If equal pressures of any kind be exerted upon 
 the surfaces of the mercury at a and c, this level will not be dis- 
 turbed, while any difference of pressure would be 
 promptly shown by the movement of the mercury 
 and a consequent difference in the heights of the 
 two mercury columns. The atmosphere presses 
 upon both mercurial surfaces, at a and c, but it 
 presses upon them equally and, therefore, does not 
 change the common level. Into the arm, A, push 
 an air-tight piston, p, which has a valve opening 
 upward but not downward. As this piston is pushed 
 downward, the air in A escapes through this valve 
 and p finally rests upon the surface of the mercury 
 at a. When the piston, p, is subsequently lifted to 
 A, the atmospheric pressure is wholly removed from 
 the surface of the mercury in that arm of the tube, 
 while it acts with unchanged intensity upon the sur- 
 face at c. The consequence is that the mercury fol- 
 lows the piston until there is a difference of about 
 760 mm. or 30 inches between the levels of the mer- 
 cury in the two arms of the tube. If the tube have 
 a sectional area of one square inch, the mercury thus 
 supported would weigh about 15 pounds, and would 
 exactly equal the weight of an air column of the 
 
 FIG. 399. 
 
 same sectional area, reaching from the apparatus to the upper sur- 
 face of the atmosphere. 
 
 APPENDIX I. 
 
 Copper Wire. Copper wire is usually designated by its 
 gauge. Unfortunately there are several gauges in common use, of 
 which the most important two are the English or Birmingham wire 
 gauge (B. W. G.} and the American or Brown and Sharpe (B. & 8.} 
 gauge. For corresponding numbers, the B. W. G. is a little larger 
 than the B. & 8. The following table of some of the more common 
 sizes will be convenient for reference ; 
 
566 
 
 APPENDIX. 
 
 AMERICAN WIRE GAUGE (B & S.). 
 
 
 DIAMETER IN 
 
 
 
 
 DIAMETER IN 
 
 
 No. 
 
 
 CIRCULAR 
 
 OHMS 
 
 PER 
 
 No. 
 
 
 CIRCULAR 
 
 OHMS 
 
 PER 
 
 
 
 
 
 
 MILS, 
 
 MILLIM 
 
 MILS. 
 
 1000 FT. 
 
 
 MILS. 
 
 MILLIM, 
 
 MILS, 1000 B-T. 
 
 
 
 
 
 .051 
 
 19 
 
 
 
 
 
 0000 
 
 460.00 
 
 11.684 
 
 211600.0 
 
 35.39 
 
 .899 
 
 1252.4 
 
 8.617 
 
 000 
 
 409.64 
 
 10.405 167805.0 
 
 .064 
 
 20 
 
 31.96 
 
 .812 
 
 1021.5 10.566 
 
 00 
 
 364.80 
 
 9.266 133079.4 
 
 .081 
 
 21 
 
 28.46 
 
 .723 
 
 810.1 13.323 
 
 
 
 324.95 
 
 8.254 105592.5 
 
 .102 
 
 22 
 
 25.35 
 
 .644 
 
 642.7 16.799 
 
 1 
 
 289.30 
 
 7.348 83694.2 
 
 .129 
 
 23 
 
 22.57 
 
 .573 
 
 509.5 21.185 
 
 | 257.63 
 
 6.544 66373.0 
 
 .163 
 
 | 24 
 
 20.10 
 
 .511 
 
 404 26.713 
 
 3 
 
 229.42 
 
 5.827 52634.0 
 
 .205 
 
 1 25 
 
 17.90 
 
 .455 
 
 320.4 33.684 
 
 4 
 
 204.31 
 
 5.189 41742.0 
 
 .259 
 
 26 
 
 15.94 
 
 .405 
 
 254.0 42.477 
 
 5 
 
 181.94 
 
 4.621 33102.0 
 
 .326 
 
 i 27 
 
 14.19 
 
 .361 
 
 201.5 53.503 
 
 6 162.02 
 
 4.115 26250.5 
 
 .411 
 
 28 
 
 12.64 
 
 .321 
 
 159.8 67.542 
 
 7 144.28 
 
 3.665 20816.0 
 
 .519 
 
 29 
 
 11.26 
 
 .286 
 
 126.7 
 
 85.170 
 
 8 128.49 
 
 3.264 
 
 16509.0 
 
 .654 
 
 30 
 
 10.03 
 
 .255 
 
 100.5 
 
 107.391 
 
 9 114.43 
 
 2.907 
 
 13094.0 
 
 .824 
 
 31 
 
 8.93 
 
 .227 
 
 79.7 
 
 135.402 
 
 10 101.89 
 
 2.588 
 
 10381.0 
 
 1.040 
 
 32 
 
 7.95 
 
 .202 
 
 63.2 
 
 170.765 
 
 11 90.74 
 
 2.305 
 
 8234.0 1.311 
 
 33 
 
 7.08 
 
 .180 
 
 50.1 
 
 215.312 
 
 12 80.81 
 
 2.053 
 
 6529.9 1.653 
 
 34 
 
 6.30 
 
 .160 
 
 39.7 
 
 271.583 
 
 13 71.96 
 
 1.828 
 
 5178.4 
 
 2.084 
 
 35 
 
 5.61 
 
 .143 
 
 31.5 
 
 342.443 
 
 14 04.01 
 
 1.628 
 
 4106.8 
 
 2.628 
 
 36 
 
 5.00 
 
 .127 
 
 25.0 
 
 431.712 
 
 15, 67.07 
 
 1.450 
 
 3256.7 
 
 3.314 
 
 37 
 
 4.45 
 
 .113 
 
 19.8 
 
 544.287 
 
 16 1 50.83 
 
 1.291 
 
 2582.9 
 
 4.179 
 
 88 
 
 3.96 
 
 .101 
 
 15.7 
 
 686.511 
 
 17j 45.26 
 
 1.150 
 
 2048.2 
 
 5.269 
 
 39 
 
 3.53 
 
 .090 
 
 12.5 
 
 865.046 
 
 18 40.30 
 
 1.024 
 
 1624.3 
 
 6.645 
 
 40 
 
 3.14 
 
 .080 
 
 9.9 
 
 1091.865 
 
 Note. The second column gives the diameters in thousandths of an inch ; the 
 third column, in millimeters. The fourth column gives the equivalent number of 
 wires each one mil in diameter. The numbers therein given are the squares of the 
 diameters in mils. By multiplying the numbers in the fifth column by 5.28, the 
 resistances per mile may be found. The resistance for any other metal than cop- 
 per may be found by multiplying the resistance given in the table by the ratio 
 between the specific resistance of copper and the specific resistance of the given 
 metal. (See table of specific resistances in Appendix K [2]). The resistances 
 given in the table are for pure copper wire at a temperature of 75 U F. or 24 C. 
 Ordinary commercial copper wire has a conductivity of about 95 or 96 per cent. 
 that of pure copper. Consequently, the resistances of such wires will be about 5 
 per cent, greater than those given in the table. 
 
 STUBS' OR BIRMINGHAM WIRE GAUGE (B. W. G.). 
 
 
 DlAl 
 
 IETER IN 
 
 Wll 
 
 DIAJ 
 
 UETER IN 
 
 
 DIAJ 
 
 IETER IN 
 
 
 MILS. 
 
 MILLIM. 
 
 
 MILS. 
 
 MILLIM. 
 
 
 MILS. 
 
 MILLIM. 
 
 too 
 
 ><) 
 1 
 
 4 
 
 6 
 
 454 
 380 
 300 
 238 
 203 
 
 11.53 
 9.65 
 7.62 
 6.04 
 5.16 
 
 8 
 
 is 
 
 14 
 
 16 
 
 165 
 134 
 109 
 
 OQ 
 
 65 
 
 4.19 
 3.40 
 2.77 
 2.11 
 1.65 
 
 18 
 20 
 24 
 30 
 36 
 
 49 
 35 
 22 
 12 
 4 
 
 1.24 
 0.89 
 0.55 
 0.81 
 0.10 
 
 The catalogue of electrical wires (furnished gratis by Holmes, Booth & Haydens, 
 22 Murray street, New York City, or by The Electrical Supply Co., 17 Dey street), 
 contains many valuable tables and other information. 
 
APPENDIX. 567 
 
 APPENDIX J. 
 
 The Ijeycleii Jar. The following is extracted (as much other 
 information in this volume has been) from Silvanus Thompson's 
 " Elementarj Lessons in Electricity and Magnetism": 
 
 The existence of a residual charge ( 356) can be explained either 
 on the supposition that the dielectric is composed of heterogeneous 
 particles which have unequal conducting powers or on the hypothesis 
 that the molecules are actually subjected to a strain from which, 
 especially if the stress be long continued, they do not recover all at 
 once. There is an analogy between this phenomenon and that of 
 the " elastic recovery " of solid bodies after being subjected to a bend- 
 ing or a twisting strain. A fibre of glass, for example, twisted by a 
 certain force, flies back when released to almost its original position, 
 a slight sub-permanent set remains from which, however, it slowly 
 recovers itself, the rate of its recovery depending on the amount and 
 duration of the original twisting strain. It is possible to superpose 
 several residual charges, even charges of opposite signs, which 
 apparently " soak out " as the strained material gradually recovers 
 itself. 
 
 As to the precise nature of the molecular or mechanical operations 
 in the dielectric when thus subjected to the stress of electrostatic 
 induction, nothing is known. One pregnant experiment of Faraday 
 is of great importance, by showing that induction is, as he expressed 
 it, "an action of contiguous particles." In a glass trough, T (Fig. 
 400), is placed some oil 
 of turpentine, in which 
 
 are put some fibres of dry T~~~**fij7^ j j 
 
 silk cut into small bits. 
 Two wires pass into the 
 liquid, one of which is 
 joined to earth, the other 
 
 being put into connection with 0, the prime conductor of an elec- 
 trical machine. The bits of silk come from all parts of the liquid and 
 .form a chain of particles from wire to wire, p to p'. On touching 
 them with a glass rod they resist being pushed aside, though they 
 at once disperse if the supply of electricity is stopped. Faraday 
 regarded this as typical of the internal actions in every case of in- 
 duction across a dielectric, the particles of which he supposed to be 
 41 polarized," that is, to be turned into definite positions, each particle 
 having a positive and a negative end. The student will perceive an 
 obvious analogy, therefore, between the condition of the particles of 
 
568 
 
 APPENDIX. 
 
 a dielectric across which electrostatic induction is taking place, and 
 the molecules of a piece of iron or steel when subjected to magnetic 
 induction. 
 
 Siemens has shown that the glass of a Leyden jar is sensibly 
 warmed after being several times rapidly charged arid discharged. 
 This obviously implies that molecular movement accompanies the 
 changes of dielectric stress. 
 
 The internal volume of a Leyden jar is increased when it is 
 charged, as though the attraction between the two charged surfaces 
 compressed the glass and caused it to expand laterally. 
 
 APPENDIX K. 
 
 (1.) Electrical Resistance. The idea implied in resistance 
 is that of a force opposing the E. M. F. which maintains the current. 
 It is analogous to friction in mechanics. The resistances of a circuit 
 are of two kinds, viz., the resistances of the conductors themselves 
 and the resistances due to imperfect contact. The latter kind is 
 affected by pressure, which brings the surfaces into more intimate 
 contact. The contact resistance of two wire conductors may vary 
 from infinity to the small fraction of an ohm. Hence, great care 
 should be exercised in splicing two such wires, by seeing that the 
 contact surfaces are clean and that the wires are tightly twisted to- 
 gether. In many cases, it is desirable to solder the spliced wires. 
 
 (2.) Specific Resistance. The specific resistance of a sub- 
 stance is best stated as the resistance in absolute units (i. e., in 
 billionths of an ohm) of a cubic centimeter of the substance. 
 
 TABLE OF SPECIFIC EESI8TANCES AND KELATIVE CONDUCTIVITIES. 
 
 SUBSTANCE. 
 
 SPECIFIC RESISTANCE. 
 
 RELATIVE CONDUCTIVITY. 
 
 Metals. 
 Silver, 
 
 gsr 
 
 Platinum, 
 Iron (soft), 
 Lead, 
 German Silver, 
 Mercury (liquid). 
 Selenium (annealed), 
 
 1,609 
 1,642 
 2,154 
 8,939 
 9,827 
 19,847 
 21,170 
 96,146 
 6 x 10 1S 
 
 100 ;.- 
 
 98 
 74 
 18 
 16 
 8 
 7'5 
 1-6 
 
 47To66 OOO"O(>5 
 
 Lif/ttifiK. 
 Pure Water at 22 C. 
 Dilute Sulphuric Acid ) 
 (ft acid), f 
 Dilute H a SO (; acid) 
 
 7-18 x 10 10 
 332 x 10 1 " 
 126 x 10' 
 
 Less than one millionth 
 part. 
 
 Insulators. 
 Glass (at 200 C), 
 Gutta-percha (at 20" C) 
 
 2-27 x 10 18 
 8'5 x 10 23 
 
 Less than one millionth 
 of a millionth part. 
 
APPENDIX. 569 
 
 If the poles of 100 Daniell cells be connected with tin-foil sheets 
 1 m. square pasted on opposite faces of a plate of gutta-percha 1 cm. 
 thick, less than 10 coulombs would pass through this circuit of very 
 high resistance in a whole century. 
 
 Those substances that possess a high conducting power for elec- 
 tricity are the best conductors of heat ( 604 [6.]). Liquids are worse 
 conductors than the metals and gases are perfect non-conductors, 
 3xcept when so rarefied as to admit of discharge by convection 
 through them. 
 
 (3.) Effects of Heat on Resistance. The resistance of a 
 conductor is constant as long as the molecular condition of the con- 
 ductor is unchanged. But it is changed by heat, strain, tempering, 
 magnetization and, in some cases, by light. The resistance of metals 
 increases considerably as the temperature is raised. On the other 
 hand, the resistance of carbon appears to diminish on heating. 
 German- silver and other alloys do not show so much change, hence 
 they are used in making standard resistance-coils. Liquids that 
 conduct only by being electrolyzed conduct better as the tempera- 
 ture rises. Vide, Encyclopaedia Britannica, vol. viii, p. 52 (Ninth 
 edition}. 
 
 (4.) Effect of Light on Resistance. Ordinary fused or 
 vitreous selenium (Chemistry, 160) is a very bad conductor ; its 
 resistance being nearly 3.8xl0 10 times as great as that of copper. 
 When carefully annealed (by keeping for some hours at a tempera- 
 ture of about 220 C., just below its fusing point, and subsequently 
 cooling slowly), it assumes a crystalline condition, in which its electric 
 resistance is considerably reduced. In the latter condition, especially, 
 its resistance is considerably and instantly lessened by exposure to 
 light. Greenish-yellow rays are the most effective. Prof. Graham 
 Bell and Mr. Sumner Tainter have devised forms of " selenium cells," 
 in which the selenium is formed into narrow strips between the 
 edges of broad conducting plates of brass, thus securing both a re- 
 duction of the transverse resistance and a large amount of surface- 
 exposure to light. The resistance of such a cell in the dark was 
 300 ohms; when exposed to sunlight, it had a resistance of but 150 
 ohms. This property of selenium has been applied in the construc- 
 tion of the Photophone, an instrument which transmits sounds to a 
 distance by means of a beam of light. The light is reflected to the dis- 
 tant station by a thin mirror thrown into vibrations by the voice ; the 
 beam falling, consequently, with varying intensity upon a receiver of 
 selenium connected in circuit with a small battery and a Bell telephone. 
 The sounds are thus reproduced by the variations of the current, 
 
570 
 
 APPENDIX. 
 
 Similar properties are possessed, to a smaller degree, by tellurium 
 (Chemistry, 161). 
 
 APPENDIX L. 
 
 (1.) The Tangent Galvanometer. it is not possible to 
 make a galvanometer in which the strength of current shall be pro- 
 portional to the angle of deflection through its whole range. But a 
 simple galvanometer may be made in which the strength of the 
 current shall be proportional to the tangent of the angle of deflec- 
 tion. The tangent gal- 
 vanometer, one form of 
 which is shown in Fig. 
 401, is such an instrument. 
 A horizontal needle ( 439a) 
 not more than an inch 
 long is delicately suspend- 
 ed at the centre of a stout 
 copper wire hoop about 
 fifteen inches in diameter. 
 The single coil or hoop 
 being placed in the mag- 
 netic meridian, a current 
 flowing through the coil will 
 deflect the needle through 
 such an angle that the 
 tangent of the angle of 
 deflection is proportional to 
 the strength of the current. 
 For example, suppose that 
 
 a certain battery gives a deflection of 15 and a second battery gives 
 a deflection of 30. The numbers of amperes are not in the ratio of 
 15 : 30 but in the ratio of tan 15 : tan 30. The values of such 
 tangents must be obtained from a Table of Natural Tangents (see 
 below), from which it will be found that the strengths of the currents 
 are in the ratio of 
 
 0.268 : 0.577, or about 10 : 22. 
 
 If a known current, (7, gives a deflection of m degrees and an 
 unknown current, c, gives a deflection of n degrees, the value of c 
 may be found (with the help of the table below) from the proportion 
 C : c :: tan m : tan n. 
 
 A delicate, stiff pointer or index of aluminum (Chemistry, 346) 
 Is usually fastened to the short, stout needle of the tangent gal- 
 vanometer. But, at the best, this instrument is not very sensitive. 
 
APPENDIX. 
 
 571 
 
 TABLE OF NATURAL TANGENTS. 
 
 ABC. 
 
 TANGENT. 
 
 ABC. 
 
 TANGENT. 
 
 ABC. 
 
 TANGENT. 
 
 ABC. 
 
 TANGENT. 
 
 1 
 
 .017 
 
 24 
 
 .445 
 
 47 
 
 1.07 
 
 70 
 
 2.75 
 
 2 
 
 .035 
 
 25 
 
 .466 
 
 48 
 
 1.11 
 
 71 
 
 2.90 
 
 3 
 
 .052 
 
 26 
 
 .488 
 
 49 
 
 1.15 
 
 72 
 
 3.08 
 
 4 
 
 .070 
 
 27 
 
 .510 
 
 50 
 
 1.19 
 
 73 
 
 3.27 
 
 5 
 
 .087 
 
 28 
 
 .532 
 
 51 
 
 1.23 
 
 74 
 
 3.49 
 
 6 
 
 .105 
 
 29 
 
 .554 
 
 52 
 
 1.28 
 
 75 
 
 3.73 
 
 7 
 
 .123 
 
 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 
 
 3t 
 
 .675 
 
 57 
 
 1.54 
 
 80 
 
 5.67 
 
 12 
 
 .213 
 
 35 
 
 .700 
 
 58 
 
 1.60 
 
 81 
 
 6.31 
 
 13 
 
 .231 
 
 36 
 
 .727 
 
 59 
 
 1.66 
 
 82 
 
 7.12 
 
 14 
 
 ,249 
 
 37 
 
 .754 
 
 60 
 
 1.73 
 
 83 
 
 8.14 
 
 15 
 
 .268 
 
 38 
 
 .781 
 
 61 
 
 1.80 
 
 84 
 
 9.51 
 
 16 
 
 .287 
 
 39 
 
 .810 
 
 62 
 
 1.88 
 
 85 
 
 11.43 
 
 17 
 
 .306 
 
 40 
 
 .839 
 
 63 
 
 1.96 
 
 86 
 
 14.30 
 
 18 
 
 .325 
 
 41 
 
 .869 
 
 64 
 
 2.05 
 
 87 
 
 19.08 
 
 19 
 
 .344 
 
 42 
 
 .900 
 
 65 
 
 2.14 
 
 88 
 
 28.64 
 
 20 
 
 .364 
 
 43 
 
 .933 
 
 66 
 
 2.25 
 
 89 
 
 57.29 
 
 21 
 
 .384 
 
 44 
 
 .966 
 
 67 
 
 2.36 
 
 90 
 
 Infinite. 
 
 22 
 
 .404 
 
 45 
 
 1.000 
 
 68 
 
 2.48 
 
 
 
 23 
 
 .424 
 
 46 
 
 1.036 
 
 69 
 
 2.61 
 
 
 
 (2.) The Sine Galvanometer. 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 central axis, may be used as a Sine Galvanometer. 
 The coils are set parallel to the needle (i. e., in the magnetic merid- 
 ian). The current is then sent through the coils, deflecting the 
 needle. The coil is then turned until it overtakes the needle which 
 once more lies parallel to the coil. Two forces are now acting on 
 xhe 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 pro- 
 portional to the ' sine of the angle through which the coil has been 
 turned. The values of the sines must be obtained from a Table of 
 Natural Sines. 
 
 TABLE OP NATURAL SINES. 
 
 ABC. 
 
 SINE. 
 
 ABC. 
 
 SINE. 
 
 ABC. 
 
 SINE. 
 
 ABC. 
 
 SINE. 
 
 
 
 .000 
 
 9 
 
 .156 
 
 50 U 
 
 .766 
 
 83 
 
 998 
 
 1 
 
 .017 
 
 10 
 
 .174 
 
 55 
 
 .819 
 
 84 
 
 995 
 
 2 
 
 .035 
 
 15 
 
 .259 
 
 60 
 
 .866 
 
 85 
 
 996 
 
 3 
 
 .052 
 
 20 
 
 .342 
 
 65 
 
 .906 
 
 86 
 
 998 
 
 4 
 
 .070 
 
 25 
 
 .423 
 
 70 
 
 .940 
 
 87 
 
 999 
 
 5 
 
 087 
 
 30 
 
 .500 
 
 75- 
 
 .966 
 
 88 
 
 999 
 
 6 
 
 1 
 
 .105 
 .122 
 .139 
 
 35 
 40 
 45 
 
 .574 
 .643 
 .707 
 
 80 
 81 
 82 
 
 .985 
 .988 
 .990 
 
 89 
 90 
 
 999 
 1000 
 
572 
 
 APPENDIX. 
 
 (3.) The Mirror Galvanometer. In this instrument, a 
 very light mirror of silvered glass is fastened to the needle so that a 
 ueam of light may be reflected upon a graduated scale. The 
 slightest motion of the needle is thus magnified and made apparent. 
 Fig. 402 shows the mirror galvanometer devised by Sir W. Thomson 
 
 FIG. 402. 
 
 for signalling through submarine cables. The magnet consists of 
 one or more pieces of steel watch spring fastened to the back of a 
 small concave mirror which is hung by a single fibre of cocoon silk 
 within the coil. A curved magnet, carried on a vertical support 
 above the coil, serves to counteract the earth's magnetism and to 
 direct the needle within the coil. A beam of light from the lamp 
 passes through a small opening under the scale, falls upon the 
 mirror and is reflected back upon the scale. The curved magnet 
 above the coil enables the operator to bring the spot of reflected 
 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 apparatus i? 
 wondrously 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. 
 
 (4.) The Differential Galvanometer, In this instm 
 
APPENDIX. 
 
 573 
 
 ment, the coil is made of two separate 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 "nil" methods of measurements. 
 [See App. M (3).J 
 
 APPENDIX M. 
 
 Electrical Measurements. The wonderful advance made 
 by electrical science within the last few years is largely due to the 
 adoption of a system of exact measurements. In September, 1881, 
 the Paris Electrical Congress, composed of representative electricians 
 of all countries, established a system of new (C. G. S.) electrical units 
 which are now generally accepted and used. 
 
 (1.) Resistance Coils. Wires of standard resistance are now 
 sold by instrument makers under the name of Resistance Coils. 
 They consist of coils of german- 
 silver (or sometimes silver-iridium 
 alloy), wound with great care and 
 adjusted to such a length as to 
 have resistances of a definite num- 
 ber of ohms. In order to avoid 
 self-induction and the consequent 
 sparks at the opening or closing of 
 the circuit, they are wound in the 
 peculiar manner indicated in Fig. 
 403, each wire (covered with silk or 
 
 paraffined- cotton) being doubled on itself before being coiled up. Each 
 end of a coil is soldered to a solid brass piece, as coil 1 to A and B, 
 coil 2 to B and C; the brass pieces being themselves fixed to a block 
 
 of ebonite (forming 
 the top of the " resist- 
 ance box "), with suf- 
 ficient room between 
 them to admit of the 
 insertion of stout, 
 well-fitting plugs of 
 brass. Fig. 404 shows 
 a complete resistance- 
 box, as fitted up for 
 electrical testing, 
 FIG. 404. with the plugs in 
 
 FIG. 403. 
 
574 APPENDIX. 
 
 their places. So long as the plugs remain in, the current flows 
 through the solid brass pieces and plugs without encountering any 
 serious resistance ; but when any plug is removed, the current can 
 pass from the one brass piece to the other only by traversing the 
 coil thus thrown into circuit. The series of coils chosen is usually 
 of the following numbers of ohms' resistance 1, 2, 2, 5 ; 10, 20, 20*, 
 
 50 ; 100, 200, 200, 500 ; up to 10,000 ohms. By pulling 
 
 out one plug any one of these can be thrown into the circuit and 
 any desired whole number, up to 20,000, can be made up by pulling 
 out more plugs ; thus a resistance of 263 ohms will be made up as 
 200 + 50 + 10 + 2 + 1. 
 
 (2.) Measuring- External Resistances. (a.) Suppose that 
 
 we have a standard battery of a few 
 Daniell's cells, joined up in circuit 
 with R, a wire of unknown resist- 
 ance, and with a galvanometer, that 
 indicates a current of a certain 
 strength, as shown in Fig. 405. If 
 we remove the wire, R, and, in its 
 place in the circuit, substitute wires 
 FIG. 405. whose resistances we know, we may, 
 
 by trying, find one which, when 
 
 interposed in the path of the current, gives the same deflection of 
 t.ie galvanometer needle. Hence, we shall know that this wire and 
 the one we called R offer equal resistances to the current. 
 
 (6.) A rheostat is a long thin wire coiled upon a wooden cylinder, 
 so that any desired length of the wire may be thrown into the 
 circuit by unwinding the proper number of turns of wire off the 
 cylinder, or by making contact at a point at any desired distance 
 from the end of the wire. The rheostat has been superseded by the 
 resistance coils mentioned above. 
 
 (c.) The method explained above may be used with any galva- 
 nometer of sufficient sensitiveness, but if a tangent galvanometer is 
 available the process may be shortened. Suppose the tangent 
 galvanometer and an unknown resistance, R, to be included in the 
 circuit, as in Fig. 405, and that the current is strong enough to pro- 
 duce a deflection of a degrees. Substitute for R any known 
 resistance, r, which will alter the deflection to b degrees ; then 
 (provided the other resistances of the circuit be negligibly small) it 
 is clear that since the strengths of the currents are proportional to 
 tan a and tan b respectively, the resistance, R, may be calculated by 
 the inverse proportion : 
 
 tan a : tan b = r : R. 
 
APPENDIX. 
 
 575 
 
 (d.) With a differential galvanometer and a set of standard resist- 
 ance coils, it is easy to measure the resistance of a conductor. Let 
 the circuit of a battery divide into two branches, so that part of the 
 current flows through the given resistance and round one set of coils 
 of the galvanometer, the other part of the current being made to flow 
 through known resistances and then round the other set of coils in 
 the opposing direction. When we have succeeded in matching the 
 imknown resistance by one equal to it from the known resistances, 
 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. 
 
 Or we may vary the resistance of the second circuit until it balances 
 the given resistance ; remove the given resistance and put known 
 resistances in its place until the galvanometer again shows no deflec- 
 tion. This is the better way, as it gives good results even if the two 
 coils of the galvanometer are not exactly symmetrical. (Compare 
 177.) 
 
 FIG. 406. 
 
 (e.) The best of all the ways of measuring resistances is, however, 
 with a set of standard resistance coils and the important instrument 
 known as Wheatstone's Bridge. This instrument is represented by 
 the diagram shown in Fig. 406. The circuit of a constant battery 
 is made to branch at P into two parts which reunite at Q, so that 
 part of the current flows through the point M, the other through the 
 point N. The four conductors, A, B, C and D, are called the arms 
 of the bridge. The resistance of any three of these arms being 
 known, that of the remaining one may be calculated. When the 
 current that starts from the battery arrives at P, the potential will 
 have fallen to a certain value. The potential of the current in the 
 
576 
 
 APPENDIX. 
 
 upper branch falls again to M and continues to fall to Q. The po- 
 tential of the lower branch falls to JV and continues to fall until, at 
 <2, it is of the same value as that of the upper branch at the same 
 point. If the ratio of the resistance of G to the resistance of D is 
 the same as the ratio of the resistance of A to the resistance of B, 
 then will M and N be at equal potentials. If a sensitive galvanom- 
 eter, placed in the branch wire between M and N, shows no deflec- 
 tion, we may know that M and JVare at equal potentials and that 
 the resistances of the four arms "balance" by being in proportion, 
 thus : 
 
 A:C = B:D. 
 
 For example, if the resistances, A and G, are (as indicated in Fig. 
 407) 10 ohms and 100 ohms respectively and the resistance of G is 15 
 ohms, the resistance of D will be 150 ohms. 
 
 FIG. 407. 
 
 It is usual to construct Wheatstone's bridges with some resistance 
 coils in the arms, A and C, as well as with a complete set in the 
 arm, B. The advantage of this arrangement is that by adjusting A 
 and G we determine the ratio between the resistances of B and D 
 and can, in certain cases, measure to fractions of an ohm. Fig. 407 
 shows a more complete scheme, in which resistances of 10, 100 and 
 1,000 ohms are included in the arms, A and C. 
 
 For example, suppose that we have a wire, the resistance of which 
 we know to be between 46 and 47 ohms and wish to measure the 
 fraction of an ohm. Insert the wire at D. Make the resistance of A, 
 100 ohms and that of C, 10 ohms. In this case, D must be balanced 
 
APPENDIX. 577 
 
 by a resistance in B, 10 times as great as that of D. If, on trial, 
 this is found to be 464 ohms, we know that the resistance of D is 
 (464 x 10 -*- 100 =) 46.4 ohms. 
 
 In practice, the bridge is not made in the diamond shape of the 
 diagrams. The resistance box shown in Fig. 404 is a complete 
 bridge, the appropriate connections being made by screws at various 
 points. In using the bridge, the battery circuit should always be 
 made by depressing the key, k, before K, the key of the galvanometer 
 branch is depressed. This avoids the sudden " throw" of the galva- 
 nometer needle, in consequence of the self-induction, when the cir- 
 cuit is closed ( 458). 
 
 Vide, Encyclopaedia Britannica (9th edition), vol. viii, pp. 43 to 46. 
 
 (3.) Measuring Internal Resistance. The best way of 
 determining the internal resistance of a voltaic cell is to join two 
 similar cells in opposition to one another, so that they send no cur- 
 rent of their own. Then measure their united resistance (as if it 
 were the resistance of a wire) as just described. The resistance of 
 one cell will be half that of the two. 
 
 (4.) Measuring- Electromotive Forces. The usual 
 method of measuring E. M. F. is by comparison with the E. M. F. 
 of a Daniell cell (= 1.079 volts). 
 
 (a.) Represent the E. M. F. of the standard cell or battery by E 
 and that of the given cell or battery by X. Join cell X with the 
 galvanometer and note the number of degrees of deflection that it 
 produces through the resistances of the circuit. Represent this de- 
 flection by a. Then add enough resistance, R, to bring the deflec- 
 tion down to b degrees (c. g. , 10 degrees less than before). Then 
 substitute the standard for the given battery in the circuit and adjust 
 the resistances of the circuit until the galvanometer shows a deflec- 
 tion 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 will produce an equal reduction of cur- 
 rent will be proportional to the electromotive forces. 
 
 (&.) If the poles of a standard battery are joined by a long, thin 
 wire, the potential will fall uniformly from the + to the pole. 
 Hence, by making contacts at one pole and at a point any desired 
 distance along the wire, any desired proportional part of the whole 
 electromotive force may be taken. This proportional part may be 
 
578 APPENDIX. 
 
 balanced against the electromotive force of any other battery, or 
 used to compare the difference between the electromotive forces of 
 two different cells. 
 
 (c.) A galvanometer having a coil resistance of several thousand 
 ohms (in comparison with which the internal resistance of a battery 
 or dynamo is insignificant) may be used to measure E. M. F., for, by 
 Ohm's law, the strength of current that such a battery or dynamo 
 can send through it will depend only on the E. M. F. (or difference 
 of potential) between the ends of the coil. Such a galvanometer, 
 properly graduated, is called a voltmeter or a potential galvanometer. 
 It may be used to determine the difference of potential between any 
 two points of a circuit by placing the galvanometer in a shunt circuit 
 between those two points. 
 
 (d.) The following method was devised by Dr. C. F. Brush for 
 determining the difference of potential between the terminals of a 
 standard Brush arc lamp : A battery of 48 small Daniell cells had its 
 + electrode connected to the + terminal of the lamp (which was in 
 the dynamo circuit) and its electrode connected to the terminal 
 of the lamp, a very sensitive galvanometer being placed in the bat- 
 tery circuit which was thus completed through the lamp. It is evi- 
 dent that if the difference of potential between the ends of the bat- 
 tery is greater than that between the terminals of the lamp, the 
 current will circulate in its normal direction through the battery 
 and will be indicated by the galvanometer; but if this potential is 
 less than that of the lamp, the current will flow through the battery 
 but in a reverse direction and will be so indicated by the galvanom- 
 eter; while, if the difference of potential is the same in both, no 
 current will pass in either direction through the battery and the 
 galvanometer will show no deflection. 
 
 The E. M. F. of the battery exceeding the difference of potential 
 between the terminals of the lamp, cells were gradually removed 
 until the galvanometer indicated no current or currents fluctuating 
 from zero equally in both directions. The large number of observa- 
 tions made sufficiently eliminated the error due to the fact that no 
 fraction of a single cell of the battery could be used in the experi- 
 ments. This method of measuring the difference of potential be- 
 tween the terminals of the lamp proved to be extremely satisfactory 
 and certain in its operation, the addition or subtraction of a single 
 cell of battery being sufficient to deflect the galvanometer needle 
 strongly to the right or left, By finding the average result of all 
 the observations, it was found that the difference of potential be- 
 tween the terminals of the average lamp was equal to that of 42.46 
 cells of the battery, or 45.8 volts. 
 
APPENDIX. 579 
 
 The resistance of the lamp being measured was found to be 4.56 
 ohms. Therefore, the current passing in the dynamo circuit was 
 (45.8 -T- 4.56 =) 10.04 amperes. 
 
 (5.) Measuring Capacity. The capacity of a condenser is 
 generally measured by comparing it with the capacity of a standard 
 condenser. Fig. 408 represents a ^ micro- 
 farad condenser. The two brass pieces 
 upon the ebonite top are connected respect- 
 ively with the two series of alternate sheets 
 of tin-foil. The plug between them serves 
 to keep the condenser discharged v.-hen not 
 in use. 
 
 (a.) Charge the given condenser to a cer- 
 tain potential and make it share its charge Fir T 8 
 with a condenser of known capacity. 
 Measure the potential to which the charge sinks. Calculate the 
 original capacity, which will bear the same ratio to the total capacity 
 of the two condensers that the final potential bears to the original 
 l>otential. 
 
 (6.) Charge the two condensers simultaneously from one pole of 
 the same battery, interposing high resistances in each branch and 
 adjusted so that the potential rises at an equal rate in both ; then 
 the capacities are inversely proportional to the resistances through 
 which they are respectively being charged. 
 
 (c.) The following method requires no condenser : Allow the 
 given condenser to discharge itself slowly through a wire of very 
 high resistance. The time taken for the potential to fall to any 
 given fraction of its original value is proportional to the resistance, 
 to the capacity and to the logarithm of the given fraction. 
 
 (d.) The capacity of a condenser, like that of a simple conductor, 
 is measured by the quantity of electricity required to produce unit 
 rise of potential. 
 
 APPENDIX N. 
 
 Field of Force." A field of force is a region such that a 
 paiticle constituting a part of a mutually interacting system, placed 
 at any point in the region, will be acted on by a force and will move, 
 if free to do so, in the direction of the force. The particle so mov- 
 ing would, if it had no inertia, describe what ifl called a line of 
 force, the tangent to which, at any point, is the direction of the 
 force at that point. The strength of the field at a point is measured 
 by the force developed by unit quantity at that point and is ex- 
 
580 APPENDIX. 
 
 pressible, in terms of lines of force, by the convention that each line 
 represents a unit of force and that the force acting on unit quantity 
 at any point varies as the number of lines of force which pass per- 
 pendicularly through unit area at that point. Each line, therefore, 
 represents the direction of the force and the number of lines in unit 
 area, the strength of field. An assemblage of such lines of force, 
 considered with reference to their bounding-surface, is called a tube 
 of force," Anthony and Brackett. 
 
 APPENDIX 0. 
 
 The Telephone . (See 506.) The theory that the diaphragm 
 of the receiving telephone is made to vibrate to and fro hy the vary- 
 ing intensity of the magnetic attraction of the iron core has lately 
 been questioned. Many experiments go to show that the variations 
 in the magnetic intensity of the iron core are too feeble to produce 
 such mechanical effects. It also appears that paper and other sub- 
 stances may replace the iron of the diaphragm in the receiving tele- 
 phone, without destroying the sounds, and that the diaphragm may 
 even be removed and the sounds still produced and transmitted to 
 the ear. These facts are believed to show that the reproduced sound 
 is due to movements of the molecules of the iron core, such molecular 
 motions being due to the electric currents from the " transmitter " (or 
 telephone spoken to), and that the diaphragm is valuable for the 
 purposes of strengthening the sound ( 510) and transmitting it to 
 the ear of the listener. The scientific paper, Nature, says that care- 
 ful investigation leads to the conclusion that, at the sending station, 
 the evidence of molecular action, though suggestive, is by no means 
 conclusive, whereas, at the receiving station, the existence of molec- 
 ular as well as mechanical action amounts to demonstration and is 
 shown to be considerable in amount. 
 
 " The infinite varieties of sound arc duo to the subtile capacity for 
 complex motion possessed by air particles. If we could see the dance 
 of the air particles when music is executed, it would be a picture of 
 mathematical exactness and infinite complication that has no analogy 
 in anything we observe. It has always been regarded as one of the 
 mysterious miracles of vital structure that the drum of the human 
 ear can take up so perfectly this rapid stream of intricate motions in 
 the air, thousands of tympanums being affected alike, while the 
 nerves transmit the thrills to the brain, awakening the same musical 
 sensations in the consciousness of as many persons as can be brought 
 within hearing. The chain of effects is wonderful indeed, but the 
 diaphragm of the telephone is as sensitive as the living tympanum 
 
APPENDIX. 
 
 581 
 
 to all the delicate refinements of sound. Let a word be pronounced 
 for a person to repeat; the telephone will hear and speak it a hun- 
 dred miles away in a tenth part of the time that the listener would 
 need to utter it." 
 
 APPENDIX P. 
 
 The Phonograph. (See 508.) The appearance of this 
 instrument is shown in the accompanying cut, in which F represents 
 
 FIG. 409. 
 
 the mouthpiece ; C, the cylinder covered with tin -foil ; E, the axis 
 with a thread working in A, one of the two supports. The mouth- 
 piece, with its diaphragm and style, may be moved toward the 
 cylinder or from it, by means of the supporting lever, HG, which 
 turns in a horizontal plane about the pin, I. 
 
 APPENDIX Q. 
 
 The Sonometer. (See 519.) The sonometer box may be 
 made by any carpenter. It is about fifty-nine inches long, 4f inches 
 wide and 4f inches deep. The ends are made of inch oak boards, 
 the sides of | inch oak boards and the top of | inch pine board. The 
 top should be glued on ; no bottom is needed ; the box may sit 
 directly on the table. Three or four one-inch holes may well be 
 bored in each side-piece. The two bridges, shown at A and B (Fig, 
 268), should be of very hard wood and glued to the cover just 47 J 
 inches (120 centimeters) apart, measured from centre to centre. The 
 strings may be such as are used on bass-viols ; they should be alike. 
 Two similar pieces of piano-forte wire (large size) may be used. The 
 strings may be stretched by weights as shown in the figure or by 
 
582 APPENDIX. 
 
 two piano string pegs turned with a wrench or a piano tuner's key. 
 The familiar screw arrangement of the bass-viol may be used for the 
 purpose. If piano wires are used for strings, the ends must be 
 annealed by heating them red hot and cooling them slowly, so that 
 they may remain fixed when wound around their fastenings. Lines 
 should be drawn across the top of the box, exactly dividing the dis- 
 tance between the middle of the bridges (at which points the strings 
 are supported) into halves, thirds and quarters. Provide a block 
 of wood, about two inches wide, 4| inches long and just thick 
 enough to slip between the strings and the top of the box. (See Fig. 
 279.) 
 
 APPENDIX R. 
 
 Differential Thermometer. (See 547.) Prepare two 
 boards, each 5x7 inches and an inch thick. Place them upon end 
 parallel to each other, 7 inches apart. Connect the boards by 
 nailing to their tops two thin strips, each an inch wide and 9 inches 
 long. The strips will be 3 inches apart. This is our stand. For 
 the two bulbs, use two tin oyster cans with flat sides. To the centre 
 of one end of each, solder a tin tube, 1| inches long and f of an 
 inch in diameter. Take a 30-inch piece of glass tubing that will 
 slide easily within the tin tubes. Bend it at right angles, 12 inches 
 from each end, like the tube shown iii Fig. 289. Color a little 
 alcohol with red aniline, and pour into the bent tube enough to fill 
 an inch or two above each bend. Over each arm of the bent tube, 
 pass an inch of snugly-fitting rubber-tubing and slide it down 
 about 8 inches. Pass the arms of the glass tube up through the 
 tin tubes of the inverted cans as far as they will go. Slide the 
 rubber-tubing upward to make air-tight joints between the glass 
 and the tin tubes. Place the cans upon the horizontal strips of the 
 frame already made, allowing the glass tube to hang between the 
 boards. The level of the liquid in either arm may be marked by a 
 thread or rubber band that may be moved up or down. 
 
 APPENDIX S. 
 
 Cut-off Engines. With a plain sliding valve, like that 
 described in 637^ the steam pressure is evidently the same at the 
 end as at the beginning of the stroke of the piston. But the greatest 
 economy of operation is attained when the steam is so used that, 
 when the piston has reached the end of its stroke and the exhaust 
 valve is opened, the steam pressure is but little if any above that of 
 
APPENDIX. 583 
 
 the atmosphere. To secure this economy, the Cut-off Engine has 
 been devised. Here, the steam is not admitted to the cylinder during 
 the full travel of the piston, but is cut off at an earlier or later 
 point of the stroke, the steam already admitted expanding with 
 decreasing pressure to the end of the stroke. The engine may be 
 built so as to cut off at a certain fraction of the stroke, as three- 
 fourths, obtaining the benefit of the expansion of the steam for the 
 remaining one-fourth. 'This arrangement is called a fixed cut-off. 
 
 But in many cases, the power required is frequently varying with 
 the nature of the work, and the point of cut-off best adapted to one 
 load is unfitted to another. Hence, the desirability of being able to 
 shift the point of cut-off to an earlier or later part of the stroke. 
 Many devices have been brought forth to secure this object. If the 
 shifting be done by hand, the arrangement is called an adjustable 
 cut-off; if it be done by the governor, the arrangement is called an 
 automatic cut-off. 
 
 APPENDIX T. 
 
 Telescopes. (See 731 and 732.) In estimating the efficiency 
 of a telescope, the illuminating power must be considered as well 
 as the magnifying power. The brilliancy of the image depends 
 largely upon the diameter of the object-glass or reflector. It is 
 evident that of two telescopes having equal magnifying power, the 
 one that has the larger " aperture " will receive and transmit more 
 luminous rays and, hence, cause the image to be better illuminated 
 and more distinct. 
 
NUMBERS REFER TO PARAGRAPHS, UNLESS OTHERWISE 
 INDICATED. 
 
 Aberration, Chromatic, 711. 
 
 Spherical, 698. [ 39 8. 
 
 Abreast method of joining voltaic cells, 
 
 Absolute electric units, -320. 
 
 magnetic " 450, 451. 
 pitch of sound, 523. 
 " units, 68, 154, 450, 451. 
 zero of temperature, 558. 
 
 Absorption and radiation of heat and 
 light, 721, 722 ; Absorption of heat,6i8. 
 
 Accordeon, 535 (a). 
 
 Achromatic lens, 712, 
 
 Acoustic tubes, 495. 
 
 Actinic rays, 719. 
 
 Adhesion defined, 46. 
 
 Aerial ocean, 271. 
 
 Aeriform body denned, 57, 61. 
 
 Aether, 608. 
 
 Affinity, Chemical, 633. 
 
 Air-chamber, 297. 
 
 Air-pump, 288-293. 
 
 Air, Weight of, 272. 
 
 Alphabet, Morse's, 445. 
 
 Amalgam, 302 (a). 
 
 Amalgamating battery zincs, 388. 
 
 American wire gauge, App. I. 
 
 Ampere, 385. 
 
 Ampere-volt, 475. 
 
 Amplitude of vibration, 140, 481, 493. 
 
 Analysis of light, 700-703. 
 
 " sounds. Exp. 16, p. 404 ; 529. 
 
 Analyzer of polariscope, 737 (). 
 Aneroid barometer, 280. 
 Angle of incidence, 97. 
 Anion, 411. . 
 Annunciators, 444. 
 
 Anode, 411. 
 
 Apparent direction of bodies, 659. 
 
 Archimedes' principle, 238-239. 
 
 Arc lamps, 467. 
 
 Armatures for magnets, 424, 449, 464. 
 
 Arrangement of voltaic cells, Best, 40* 
 
 Artificial magnet, 310, 424. 
 
 Ascending bodies, 132. 
 
 Astatic galvanometer, 418. 
 
 " needle, 439 (a). 
 Astronomical telescope, 731, 732. 
 Athermanous, 617. 
 Atlantic cable, 359, 360. 
 Atmospheric electricity, 365-370. 
 
 pressure, 273, 275, 277. 
 Atom denned, 6. 
 Attraction, Capillary, 235. 
 
 Electric, 303, 321 (). 
 
 Forms of, 7. 
 
 " Magnetic, 427-449. 
 
 Attwood, 122. 
 Aurora borealis, 370. 
 Australis, The Aurora, 370. 
 
 Balance, 175. 
 
 " False, 176. 
 Balloons, App. G. 
 Barker's mill, 264, App. F. 
 Bar magnet, 424. 
 Barometer, 274, 278-280. 
 Baroscope, 281. 
 Battery, Best arrangemement of, 400. 
 
 " Brush, 415 (</). 
 
 " Faure, 415 (a). 
 
 " Galvanic. (See Voltaic.) 
 
 " Intensity, 400 (). 
 
INDEX. 
 
 585 
 
 Numbers refer to paragraphs, unless other-wise indicated. 
 
 Battery, Leyden, 358. 
 
 " of high resistance, 399. 
 
 u of low resistance, 400. 
 Quantity, 400 (6). 
 
 " Requisites of a good, 401. 
 
 " Secondary, 415. 
 
 " Voltaic, 398-402. 
 
 44 zincs, Amalgamating, 388. 
 Beam of light, 648. 
 Beats, 516, 517 
 Beaume's hydrometer, 252. 
 Bell, Electric, 447. 
 Bellows, Hydrostatic, 222. 
 Bent levers, 173. 
 
 Best arrangement of voltaic cells, 402. 
 Bi-chromate of potassium cell or bat- 
 tery, 392. 
 
 Biot's hemispheres, Exp. 28, p. 212. 
 Birmingham wire gauge (B. W.G.) Ap. I. 
 Blake transmitter, 507. 
 Blind spot of eye, 724. 
 Boiling-point, 544, 566-575. 
 Borealis, The Aurora, 370. 
 Bramah's press, 223. 
 Breast wheel, 262. 
 Brittleness defined, 49. 
 Broken magnets, 430. 
 Brown & Sharpe wire gauge, App. I. 
 Brush, battery, 415 (d). 
 ' ; dynamo, 465. 
 " laoips, 467. 
 Bunsen's air-pump, 291. 
 
 " cell or battery. 397. 
 Burglar alarms, Electric, 444. 
 B. W. G., App. I. 
 
 Callaud cell or battery, 395. 
 Calorie, 471, 579. 
 Calorescence, 718 (a). 
 Calorific powers, 634. 
 Calorimeter, 596 (a). 
 Camera obscura, 650. 
 
 " The photographer's, 723. 
 Candle, Standard, Ex. 5, p. 482. 
 Capacity, Dielectric, 352 (S). 
 
 " Electric, 330. 
 
 " How measured, App. 
 
 M( 5 ). 
 Capillary attraction, 235. 
 
 " phenomena, 236. 
 Cathetal prism, 686 (c). 
 Cathion, 411. 
 Cathode, 411. 
 
 Cells, Voltaic, Best arrangement of, 402, 
 
 " Varieties, 39-397- 
 Centrifugal force, 74, 77. 
 C. G. S. units, 69, 154, 450, 451. 
 Changes, Chemical, u. 
 
 " of condition of matter, 59. 
 
 l> Physical, 10. 
 Characteristic properties, 19, 21. 
 Characteristics of magnets, 428. 
 Charge, Residual, 356 ; App. J. 
 Charging with electricity by conduc- 
 tion, 331. 
 Charging with electricity by contact, 
 
 33i- 
 Charging with electricity by induction, 
 
 332-335- 
 
 Chemical affinity, 633. 
 " changes, u. 
 " effects of electric current, 
 
 410. 
 
 " properties, 15. 
 44 unit of matter, 6. 
 Chromatic aberration, 711. 
 Chromatics, 699. 
 Circuit, Electric, 305. 
 Clarionet, 535 (a), 536. 
 Clouds, Electrified, 365-368. 
 Coercive force, 425. 
 Cohesion defined, 46. 
 Coils, Induction, 457-460. 
 44 Primary, 457. 
 " Resistance, App. M (i). 
 " Ruhmkorff, 459. 
 " Secondary, 457. 
 Coincident waves, 511. 
 Color blindness, 725. 
 44 of bodies, 705. 
 Colors, by polarized light, 745 (a). 
 44 Complementary, 705 (6). 
 " of the sky, 705 (<:). 
 " Prismatic, 700. 
 Combs, 344. 
 Commercial efficiency of dynamo. Ex. 
 
 4, p. 366. 
 
 Communicating vessels, 234. 
 Commutator, 459 (</), 465. 
 Compass, 309, 439 (a). 
 Compensating pendulum, 149. 
 Complementary colors, 705 (). 
 Composition of forces, 80, 88. 
 
 14 " white light, 704. 
 
 Compound machines, 211. 
 
 44 tones, 529. 
 Compressibility defined, 43. 
 
586 
 
 INDEX. 
 
 Numbers refer to paragraphs^ unless otherwise indicated. 
 
 Concave lens, 687, 691, 697. 
 Condensation of electricity, 350. 
 Condensers, 292, 351, 360; App. M (5). 
 Conditions of matter, 53. 
 
 " " " Changes of, 59. 
 
 Conduction of electricity, 324. 
 
 " heat, 603. 
 
 Conductive discharge, 364. 
 Conductors of electricity, 324, 476. 
 Conjugate foci, 503, 667, 690, 691. 
 Conservation of energy, 749. [693. 
 
 Construction for images, 662, 670, 673, 
 Continuous sounds, 490. 
 Convection of heat, 606. 
 Convective discharge, 363. 
 Convertibility of energy, 159, 470-475, 
 
 581,582, 746. 
 
 Convex lens, 687-690, 692-696. 
 Copper plating, Exp. 78, p. 285. 
 
 " voltameter, Exp. 78, p. 285. 
 
 " wire, App. I. 
 Correlation of energy, 627, 750. 
 Coulomb, 387. 
 Coulomb's law, 319 (2). 
 Critical angle, 682. 
 Crooke's tubes, Exp. 71, p. 250. 
 Current, Electric, 314, 374, 377, 405 -418, 
 
 456-465, 468, 469-476- 
 Current, Electric, Effects of, 405-418. 
 
 " " Unit of, 385. 
 
 " electricity, 306, 374, 377. 
 
 " Extra, 458. 
 Curves, Magnetic, 433. 
 Cut-off engines (steam), App. S. 
 Cycloidal pendulum, 144. 
 
 Daniell's cell or battery, 394. 
 Dark Foci, 720. 
 Declination, Magnetic, 441. 
 Deflection of magnetic needle, 417. 
 Delany's telegraph, 446. 
 Density, Electric, 342. 
 Diamagnetic substances, 431. 
 Diathermancy, 617. 
 
 Dichromate of potassium cell or bat- 
 tery, 392. 
 Dielectric capacity, 352. 
 
 " machine, 346, 347. 
 Dielectrics, 352, App. J. 
 Differences of potential, 328, 329. 
 Differential galvanometer, App. L (4). 
 
 thermometer, 547, App. R, 
 
 Diffraction, 714. 
 Diffused light, 657. 
 Diffusion of heat, 602. 
 Dip, Magnetic, 440. 
 Dipping needle, 439, 440. 
 Direction, Line of, 65, 114. 
 
 " of bodies, Apparent, 659. 
 Discharge, Modes of electric, 361-364. 
 Discharger for electricity, 355, 358 
 
 Exp. 56, p. 244. 
 Dispersion of light, 701. 
 Disruptive discharge, 362. 
 Dissipation of energy, 747. 
 Distance, How estimated, 726. 
 Distillation, 576-578. 
 Distribution of electricity, 342. 
 " magnetism, 426. 
 Divided electric circuits, 404. 
 Divisibility defined, 41. 
 Divisions of matter, 3. 
 Double refraction, 743. 
 " weighing, 177. 
 Downward pressure, 225, 226. 
 Ductility defined, 51. 
 Duplex telegraph, 446. 
 Duration of electric spark, 368. 
 Duty of dynamo, Ex. 3, p. 366. 
 Dynamics defined, 63. 
 Dynamo electric machine, 465. 
 Dynamos, 465. 
 
 " Commercial efficiency of, 
 
 Ex. 4 , P. 366. 
 Duty of, Ex. 3, p. 366. 
 Dyne defined, 69. 
 
 Ear, Range of, 517. 
 Earth a magnet, 437. 
 Ebullition, 566-575. 
 Eccentric, 638. 
 Echo, 504. 
 
 Edison's electric lamp, 466 (a). 
 " meter ,-41 1 (). 
 Effects of electricity, 405-418, 470-476. 
 Efficiency of dynamo, Commercial, 
 
 Ex. 4, p. 366. 
 
 Efficiency of steam engine, 641 (a). 
 Egg-shell conductor, 332 (6). 
 Elasticity, 45. 
 Electric action, Law of, 319. 
 
 " attraction, 303, 321 (a), 
 
 " battery, 358. 
 
 " bell, 447. 
 
INDEX. 
 
 587 
 
 Numbers refer to paragraphs, unless otherwise indicated. 
 
 Electric bomb, Exp. 53, p. 243. 
 
 " brush, 362 ; Exp. 35, p. 23^. 
 " capacity, 330. 
 
 Unit of, 359. 
 " charge, 314, 341. 
 " chime, Exp. 41, p. 240. 
 " circuit, 305, 377. 
 " . condensers, 351. 
 " conductors, 324, 476. 
 " current, 314, 374, 377, 405-418, 
 
 456-465, 468, 469-476. 
 " density, 342. 
 " discharge, 361-364. 
 
 effects, 405-418, 470-476. 
 glow, 362 ; Exp. 35, p. 233. 
 " induction,- 332-335. 
 " kite, Exp. 45, p. 241. 
 lamps, 466, 467. 
 light, 465-467. 
 
 44 machines, 343-349, 465. 
 u manifestations, 314. 
 ' 4 measurements, App. M. 
 44 motors, 465 (<:), 473. 
 44 orrery, Exp. 49, p. 242. 
 pendulum, 304, 323 (a). 
 44 portrait, Exp. 57, p. 244. 
 44 potential, 326-330, 384. 
 " quantity, 387. 
 44 repulsion, 304, 321 (a). 
 44 resistance, 379, App. K, App. 
 
 M (1-3). 
 
 44 resistance, Unit of, 380. 
 " separation, 316, 332. 
 4 ' series, 318. 
 14 shock, 409. 
 
 44 spark, 362; Exp. 35, p. 233 ; 460. 
 44 swing, Exp. 43, p. 241. 
 
 telegraph, 444-446. 
 44 tension, 326. 
 44 testing, App. M (i). 
 41 transmission of power, 474. 
 44 trembler, 447. 
 44 units, 320, 321, 329, 330, 359. 
 44 whirl, Exp. 48, p. 241. 
 Electricity and energy, 340, 372, 376, 
 
 470-475. 
 
 44 and heat, 470-472, 476. 
 44 Atmospheric, 365-370. 
 44 Condensation of, 350. 
 * 4 Condensers of, 351. 
 44 Conductors of, 324. 
 44 Current, 306, 314, 374, 377. 
 44 44 Unit of, 385. 
 
 Electricity, Distribution of, 341, 342. 
 44 Effects of, 405-418, 470-476. 
 Frictional, 302-304, 314-370. 
 
 Laws of, 319. 
 44 Galvanic, see voltaic. 
 
 Induced, 311, 374, 456-469. 
 Nature of, 313. 
 Static, see frictional. 
 44 Tests for, 322. 
 Theory of, 337. 
 Thermo-, 311, 374, 419-422. 
 Two kinds of, 315, 317. 
 " Voltaic, 305, 306, 373-418 
 Electrics, 325. 
 Electrodes, 378, 411. 
 Electrolysis, 410-415. 
 Electrolyte, 410. 
 Electrophorus, 338-340. 
 Electro-chemical series, 413. 
 44 gilding, 412. 
 44 magnet, 307, 442-449- 
 44 magnetic engines, 473. 
 
 ' 4 units, 320, 451. 
 44 metallurgy, 412. 
 44 motive force, see E. M. F. 
 negative, 413. 
 plating, 412. 
 44 positive, 413, 
 Electro -static distribution, 342. 
 
 44 induction, 332-335, App. J 
 4i units, 320, 321, 329. 330. 
 Electrotyping, 412. 
 
 Electroscope, 323, 338 (b) Ex. n. p. 223. 
 E. M. F. (electromotive force), 327, 382. 
 E. M. F., How measured, App. M (4). 
 E. M. F. of battery, 399 (a), 400 (). 
 E. M. F. of polarization, 414. 
 E. M. F., Relation to conductors, 476. 
 E. M. F., Unit of, 382. 
 Endless screw, 210. 
 Energy a constant quantity, 160. 
 
 and electricity, 340. 372, 376, 
 
 470-475- 
 
 14 and magnetism, 455. 
 14 Conservation or, 749. 
 44 Convertibility of, 159, 470-475 
 
 581, 582, 746. 
 
 " Correlation of, 627, 750. 
 14 defined, 151. 
 44 Dissipation of, 747. 
 44 Formulas for kinetic, 157. 
 " Indestructibility of, 163. 
 Solar, 74 6. 
 
588 
 
 INDEX. 
 
 Numbers refer to paragraphs, unless other-wise indicated. 
 
 Energy, Types of, 158. 
 
 Varieties of, 748. 
 Engine, The steam, 635-643. 
 English measures, 23. 
 Equator, Magnetic, 426. 
 Equilibrant,' 86. 
 
 Equilibrium, 110-113; of liquids, 233. 
 Equipotential surface, 329 (a). 
 Erg defined, 154. 
 Ether, 608. 
 
 Evaporation, 564, 565. 
 Expansibility defined, 44. 
 Expansion by heat, 548-557. 
 Extension defined, 22. 
 Extra current, 458. 
 Eye, The human, 724-727. 
 
 Fahrenheit's hydrometer, 251. 
 
 " thermometer, 545. 
 
 Falling bodies, 119. 
 
 " Laws of, 129. 
 Fall of electric potential, 384. 
 False balance, 176. 
 Farad, 359. 
 Faraday's bag, Exp. 30, p. 213. 
 
 " cage, 341 (). 
 
 Farsightedness, 727. 
 Faure battery, 415 (at). 
 Field, Magnetic, 433. 
 
 " of force, App. N. 
 Fife, 536. 
 
 Fire alarms, Electric, 444. 
 Floating bodies, 240. 
 Flow of liquids, 254-259. 
 Fluid defined, 60, 61. 
 
 " displaced by immersed solid, 237. 
 Fluorescence, 719. 
 Flute, 536. 
 Fly-wheel, 639. 
 Focus, Dark, 720. 
 
 " of heat, 620, 6? i. 
 
 " " light, 664, 666-668, 689-691 
 
 " " sound, 501. 
 Foot-pound defined, 153. 
 Foot-pound-second unit, 68. 
 Force, Absolute unit of, 68. 
 
 " Centrifugal, 74, 77. 
 
 " C. G. S., unit of, 69. 
 
 " Constant, 118. 
 
 " defined, 64. 
 
 ' Elements of a, 65. 
 
 " Field of, App. N, 
 
 Force, F. P. S. unit of, 68. 
 " Gravity unit of, 67. 
 " Kinetic unit of, 68. 
 " Measurement of, 66. 
 " of gravity resolved, 199. 
 " pump, 297. 
 ' Tube of, App. N. 
 Forces, Composition of, 80. . 
 
 " Graphic representation of, 81. 
 " Moments of, 171. 
 *' Parallogram of, 82. 
 " Parallelepiped of, 90. 
 " Polygon of, 89. 
 tl Resolution of, 91. 
 " Triangle of, 87. 
 Forms of attraction, 7. 
 
 " " motion, 8. 
 
 Formulas, Mathematical, App. A. 
 F. P. S. unit of force, 68. 
 Fraunhofer's lines, 703. 
 Freezing mixtures, 586. 
 
 " point, 543. 
 Friction, 212-214. 
 
 " develops heat, 629. 
 Frictional electricity, 302-304, 314-370. 
 Fuel, 641 (a). 
 
 Fundamental tones, 524, 525. 
 Fusion of ice, Heat equivalent of, 593. 
 Fusing point, 562. 
 
 G 
 
 Galileo, 121, 730. 
 Galvanic, see voltaic. 
 Galvani's experiment, 408. 
 Galvanometer, Astatic, 418. 
 
 " Differential, App. L (4). 
 
 " Mirror, App. L (3). 
 
 " Potential, App. M (4*:). 
 
 " Sine, App. L (i). 
 
 M Tangent, App. L (2). 
 
 Gamut, 521. 
 Gas defined, 58. 
 Gases, Kinetic theory of, 62, 
 " Specific gravity of, 248. 
 " Tension of, 62, 269, 282-287, 559- 
 " Type of, 270. 
 Gauges, Wire, App. I. 
 Geissler's tubes, Exp. 70, p. 249. 
 Gold leaf electroscope, 323. 
 Gore's railway, Exp. 74, p. 279. 
 Governor for steam engines, 639. 
 Graduation of thermometers, 542. 
 Gram defined, 36. 
 Graphic representation of forces, 81. 
 
INDEX. 
 
 589 
 
 Numbers refer to paragraphs, unless otherwise indicated. 
 
 Gravitation defined, 98 ; Laws of, 100. 
 Gravity cell or battery, 395. 
 
 '* Centre of, 107-110. 
 
 " defined, 102. 
 
 *' Force of, resolved, 109. 
 
 " Increment of, 127. 
 
 " Specific, 241-253. 
 
 " unit of force, 67. 
 Grenet cell, 392. 
 Grove's cell or battery, 396. 
 Guitar, 518. 
 
 H 
 
 Haloes, 714. 
 
 Hardness, 47. 
 
 Harmonics, 524. 
 
 Harp, 518. 
 
 Head of liquids, 254. 
 
 Heat, Absorption of, 721, 722. 
 
 " Conduction of, 603. 
 
 u Convection of, 606. 
 
 " defined, 538. 
 
 " Diffusion of, 602. 
 
 *' Effect on electrical resistance, 
 App. K (3). 
 
 " equivalent of chemical union, 634. 
 
 " " of fusion of ice, 593. 
 
 " " of vaporization of water, 594. 
 
 " from friction, 629. 
 
 " " percussion, 628. 
 
 ' Latent, 583-595- 
 
 " Luminous, 617. 
 
 " Mechanical equivalent of, 631. 
 
 " Obscure, 617. 
 
 " Radiation of, 607, 610, 721, 722. 
 
 '* Reflection of, 619. 
 
 " Refraction of, 621. 
 
 " Sensible, 581, 582. 
 
 ** Specific, 596-601. 
 
 " unit, 579. 
 Heating powers, 634. 
 Heliostat, 655. 
 Helix, 416 (b\ 442. 
 Helmholtz's resonators, 514, 529 (a). 
 Hollow conductors, 341. 
 Holtz electric machine, 348, 349. 
 Homogeneous light, 713. 
 Horizontal needle, 439. 
 Horse-power, 155, 475. 
 Horse-shoe magnet, 424, 443. 
 Human eye, 724-727. 
 Hydraulic motors, 384 (a). 
 Hydrokinetics, 254. 
 Hydrometer, 249-252. 
 
 Hydrostatic bellows, 222. 
 " paradox, 229. 
 
 " press, 223. 
 
 Ice, Heat equivalent of fusion of, 593. 
 
 Iceland spar, 743. 
 
 Images, Construction for, 662, 670, 673, 
 
 693- 
 
 *' Inverted, 650, 672, 674, 694, 695. 
 
 " Multiple, 663. 
 
 4i Projection of, 671, 694, 695, 734. 
 
 " Real, 669-672, 694, 695, 734. 
 
 " Virtual, 660, 673, 675, 696, 697. 
 Impenetrability defined, 31. 
 Incandescence lamp, 466. 
 Incidence, Angle of, 97. 
 Inclination, Magnetic, 440. 
 Inclined plane, 198-204. 
 Incompressibility of liquids, 215. 
 Increment of velocity, 127. 
 Indestructibility of energy, 162. 
 " " matter, 37. 
 
 Index of refraction, 678. 
 Induced electricity, 311, 374, 456-469. 
 Induction coils, 457-460. 
 Induction, Electro-dynamic, 456-469. 
 
 " static, 332-335, App. J. 
 " Magnetic, 435, 436. 
 Inertia defined, 38. 
 Insulators, 324. 
 
 Intensity of electric current, 385, 387 (a). 
 " light, 6 54 . 
 
 " " sound, 493, 494. 
 Interference of light 713. 
 
 " sound, 515. 
 Intermittent springs, 301. 
 Internal reflection of light, 681. 
 
 " resistance, 383, 399, 400. 
 Inverted images, 650, 672, 674, 694, 695. 
 Invisibility of light, 658. 
 Ions, 411. 
 Irradiation, 715. 
 
 J 
 
 Jar, Leyden, 353-357- 
 Joining voltaic cells, 398-402. 
 Joint resistance, Electric, 404 (). 
 Joule, The, 471. 
 Joule's equivalent, 631, 632. 
 " law, 471. 
 
 K 
 
 Kathion, 411. 
 Kathode, 411. 
 
590 
 
 INDEX. 
 
 Numbers refer to paragraphs, unless otherwise indicated. 
 
 Kinetic energy, Formula for, 157. 
 " theory of gases, 62. 
 " unit of forces, 68, 69. 
 
 Lamps, Electric, 466, 467. 
 Latent heat, 583-595. 
 Lateral pressure, 230, 231. 
 Leclanche cell or battery, 393. 
 Lenses, 687, 712. 
 Leslie's cube, 619, 623. 
 Lesser calorie, 471, 579. 
 Lever, Classes of, 169. 
 
 " Compound, 178. 
 
 u denned, 168. 
 
 " Laws of, 170. 
 Leyden battery, 358. 
 
 " Jar, 353-357; Ex - " P- 252; Ap. J. 
 
 " " and bells, Exp. 42, p. 241. 
 Lifting-pump, 294. 
 Light, Absorption of, 721, 722. 
 
 " Analysis of, 700-703. 
 
 '* Composition of white, 704. 
 
 " defined, 644. 
 
 " Diffused, 657. 
 
 " Dispersion of, 701. 
 
 " Effect on electrical resistance, 
 App. K ( 4 ). 
 
 " Electric, 720. 
 
 " Homogeneous, 713. 
 
 ' Invisibility of, 658. 
 
 " Polarization of, 737-747. 
 
 u Radiation of, 721, 722. 
 
 " Rectilinear motion of, 649. 
 
 " Reflection of, 655-675. 
 
 " Refraction of, 676-719. 
 
 " Synthesis of, 704. 
 
 " Velocity of, 653. 
 Lightning, 368 ; rods, 369. 
 Line of no variation, 441. 
 Lines of force, App. N. 
 Lines of magnetic force, 433. 
 Liquid denned, 55, 61. 
 
 " rest, Condition of, 232. 
 Liquids, Equilibrium of, 233. [259. 
 
 " flowing through pipes, 257, 
 " in communicating vessels, 234. 
 ' Incompressibilityof, 215. 
 " Spouting, 254-256. 
 Liter defined, 29. 
 Loadstone, see lodestone. 
 Local action in batteries, 388. 
 Lodestone, 310, 423. 
 
 Long coil electric instruments, 403. 
 Loudness of sound, 493. 
 Luminiferous ether, 608. 
 Luminous bodies, 645. 
 
 " effects of electric current, 
 407. 
 
 " globe, Exp. 68, p. 248. 
 
 " jar, Exp. 66, p. 247. 
 
 " pane, Exp. 67, p. 248. 
 
 " spectrum, 717. 
 
 " tube, Exp. 68, p. 248. 
 
 M 
 
 Machine cannot create energy, 164, 165. 
 " defined, 163. 
 " Laws of, 167. 
 Uses of, 166. 
 Machines, Compound, 211. 
 
 Electric, 343-349. 465- 
 Magic lantern, 734. 
 Magnet, Artificial, 310, 424. 
 " Broken, 430. 
 
 Electro-, 307, 442-449- 
 " How made, 448. 
 " Laws of, 429. 
 " Molecular changes in, 453. 
 " Natural, 310, 423. 
 " Permanent, 308. 
 " Temporary, 307. 
 Magnetic attraction, 427-449. 
 " charts, 441 (a). 
 " compass, 309, 439 (). 
 
 curves, 433. 
 " declination, 441. 
 " effects of electric current, 
 
 416. 
 " equator, 426. 
 
 field, 433. 
 
 " force, lines of, 433. 
 " inclination or dip, 440. 
 " induction, 435, 436. 
 *' meridian, 441, App. L (2). 
 " needles, 417, 439. 
 " neutral point, 426. 
 poles, 426, 438. 
 retentivity, 425. 
 screens, 432. 
 substances, 431. 
 units, 450. 
 variation, 441. 
 Magnetism, 307, 423-455- 
 
 " and energy, 455. 
 " Distribution of, 4 a6, 
 
INDEX. 
 
 591 
 
 Numbers refer to paragraphs, unless otherwise indicated. 
 
 Magnetism, Residual, 443 (a). 
 
 Terrestrial, 437, 438. 
 " Theory of, 454. 
 
 Magnetite, 423. 
 Magnetization, 434, 448. 
 Magnetized substances, 431. 
 Magneto-electric current, 462, 463. 
 Magnetos, 465 (). 
 Magnifying-glass, 728. 
 Malleability defined, 50. 
 Malus's polariscope, 742. 
 Manipulator, 415 (d). 
 Marcet's globe, 572. 
 Mariner's compass, 309, 439 (a). 
 Mariotte, 284, 285. 
 Mass defined, 4, 6. 
 Mathematical formulas, App. A. 
 Matter, Conditions of, 53. 
 
 " defined, 2. 
 
 44 Divisions of, 3. 
 
 " Properties of, 13. 
 
 44 Radiant, 59 (b) ; Exp. 71, p. 250. 
 Measurement of electric resistance, 
 
 App. M. (2 and 3). 
 
 Measurement of E. M. F., App. M (4). 
 Measures, 23-30, 34-36. 
 Mechanical effects of electric current, 
 
 405, 473-475- 
 
 Mechanical equivalent of heat, 631. 
 Megohm, 380. 
 Melting points, 562. 
 Meter defined, 25. 
 Metric measures, 24-30, 35, 36. 
 Microhm, 380. 
 Microscope, 728, 729. 
 Microvolt, 382. 
 Mil, 381 (*). 
 
 Millecalorie, see lesser calorie. 
 Milliampere, 385. 
 Mirror galvanometer, App. L (3). 
 Mirrors, Concave, 664-674. 
 
 " Convex, 675. 
 
 " Parabolic, 666 (a). 
 
 " Plane, 660-663. 
 Mobility defined, 40. 
 Molecular changes in magnets, 453. 
 
 ' velocity, 62 (a). 
 Molecules defined, 5, 6. 
 Momentary sounds, 490. 
 Moment offerees, 171, 172. 
 Momentum defined, 70. 
 Morse's alphabet, 445. 
 
 44 telegraph, 444. 
 
 Motion, Forms of, 8. 
 
 " Newton's laws of, 72, 73, 78, 93. 
 
 " of the pendulum, 139. 
 
 " Reflected, 96, 97. 
 
 " Resultant, 79. 
 Motors, Electric, 465 (c), 473. 
 
 " Hydraulic, 384 < 
 Multiple arc method of joining voltaic 
 
 cells, 398. 
 
 Multiple images, 663. 
 Multiplex telegraph, 446. 
 Music, 491. 
 Musical instruments, 530-536. 
 
 " scale, 520, 521 ; strings, 518, 519. 
 
 X 
 Natural magnet, 310, 423. 
 
 44 philosophy defined, 12, 162. 
 
 11 sines, Table of, App. L (2). 
 
 " tangents, Table of, App. L (i). 
 Nature of electricity, 313. 
 Nearsightedness, 727. 
 Needles. Magnetic, 417, 439. 
 Negative ( ) electricity, 317. 
 Neutral point, Magnetic, 426. 
 Newton's disc, Exp. 2, p. 519. 
 
 " laws of motion, 72, 73, 78, 93. 
 
 " rings, 713. 
 Nicholson's hydrometer, 250. 
 Nicol's prism, 744. 
 Nodal points or nodes, 524-527, 536. 
 Noise and music, 491. 
 Non-luminous bodies, 645. 
 
 O 
 
 Obscure heat, 617. 
 
 " rays, 617, 718, 720. 
 Ocean, The aerial, 271. 
 Oersted's apparatus, 417. 
 Ohm, 380. 
 Ohm's law, 386. 
 Opaque bodies, 646. 
 Opera-glass, 730. 
 Optical angle, 726. 
 
 " centre, 688. 
 Organ pipes, 516 (), 534. 
 Oscillation, Centre of, 141. 
 
 41 of pendulum, 140. 
 Overshot wheel, 261. 
 Overtones, 524, 526, 527. 
 
 Papin's digester, 571. 
 Paradox, Hydrostatic, 229. 
 Parallel joining of cells, 398. 
 
592 
 
 INDEX. 
 
 Numbers refer to paragraphs, unless otherwise indicated. 
 
 Parallelogram offerees, 82. 
 Parallelepiped of forces, 90. 
 Pascal, 217, 218, 221, 276. 
 Peltier effect, 422. 
 Pencil of light, 648. 
 Pendulum, Compensation, 149. 
 
 " Compound, 138. 
 
 " Cycloidal, 144. 
 
 " Electric, 304, 323 (a). 
 
 " Laws of, 143, 145, 146. 
 
 " Motion of the, 139. 
 
 " Real length of, 142. 
 Simple, 137. 
 
 " The second's, 147. 
 
 " Uses of, 148. 
 Percussion develops heat, 628. 
 Permanent magnet, 308. 
 Persistence of vision, 725. 
 Philosophy, Natural, defined, 12, 162. 
 Phonograph. 508, App. P. 
 Photographer's camera, 723. 
 Photophone, App. K (4). 
 Physical change, 10. 
 
 " properties, 14, 15. 
 " science, 9. 
 " unit of matter, 5. 
 Physics defined, 12, 162. 
 Physiological effects of electric cur- 
 rent, 409. 
 
 Piano, 518, 523 (b) ; Exp. 16, p. 404. 
 Pipes, Musical, 531-536. 
 Pitch of sound, 496-499. 
 
 " " " Absolute, 523. 
 Plane, Inclined, 198-204. 
 Plate electric machine, 344, 345. 
 Plating, Electro , 412. 
 Pneumatics defined, 268. 
 Pointed conductors of electricity, 342. 
 Polar iscope, 742, 745. 
 Polarization colors, 745 (a). 
 
 " Electric, 332, 336. 
 E. M. F. of, 4x4. 
 
 " of batteries, 389. 
 
 * of light, 737-747- 
 
 Polarizer, 737 (a). 
 Poles, Electric, 738. 
 
 * Magnetic, 426, 438. 
 Polygon of forces, 89. 
 Porosity defined, 42. 
 Porte-lumiere, 655, note. 
 Positive ( + ) electricity, 317. 
 Potassium di-chromate cell or battery, 
 392. 
 
 Potential, Electric, 326, 327-330, 384. 
 
 " galvanometer, App. M (4*:) 
 Power defined, 155. 
 
 " Electric transmission of, 474. 
 Press, Hydrostatic, 223. 
 Pressure, Atmospheric, 273, 275, 277. 
 u Downward, 225, 226. 
 " Gaseous, 62, 269, 282-287. 
 " Lateral, 230-231. 
 " of vapors, 568. 
 " Transmission of, by liquids, 
 
 216. 
 
 " Upward, 227, 228. 
 Primary coils, 457. 
 Prince Rupert drops, App. D. 
 Principal axis, 664, 688. 
 
 " focus, 664, 666, 689. 
 Prismatic colors, 700. 
 Prisms, 686, 718, 719, 744. 
 Projectiles, 133. 
 
 " Path of, 135. 
 " Time of, 136. 
 Proof-plane, 333 (a) ; Exp. 29, p. 212. 
 Propagation of sound, 484. 
 Properties, Characteristic, 19, 21. 
 " Chemical, 15. 
 '* of matter, 13. 
 " Physical, 14, 15- 
 ** Universal, 18, 20. 
 Provisional theory of electricity, 337. 
 Pulley, 192, 197. 
 Pump, Air, 288, 293. 
 " Force, 296, 297. 
 " Lifting, 294. 
 Pure spectrum, 702. 
 Q, 
 
 Quadruplex telegraph, 446. 
 Quality of sound, 528. 
 Quantity of electricity, 387. 
 Quartz prism, 719. 
 
 R. 
 
 Radiant energy, 484, 500, 607, 644. 
 " heat, 610. 
 
 " matter, 59 () ; Exp. 71, p. 250. 
 Radiation and absorption of heat and 
 
 light, 721, 722. 
 
 Radiation of sound, 484, 485, 500, 
 Rainbow, 706-710. 
 Random, 134. 
 Range, 134. 
 Rays, Actinic, 719. 
 
 " Heat, 610, 616, 718. 
 " Luminous, 717. 
 
INDEX. 
 
 593 
 
 Numbers r^fer to paragraphs, unless otherwise indicated. 
 
 Rays, Obscure, 617, 718, 719. 
 " of light, 6 47 . 
 " of sound, 500. 
 " Thermal, 718. 
 " Ultra-red, 718. 
 " Ultra-violet, 719. 
 Reaction, 72, 93, 94, 95. 
 Reed pipes, 535. 
 Reflected motion, 96, 97. 
 Reflecting telescope, 732. 
 Reflection of heat, 619, 620. 
 " light, 655-675. 
 " " sound, 502-504. 
 " Total internal, 681, 682. 
 Refracting telescope, 731. 
 Refraction, Double, 743. 
 " Index of, 678. 
 " of heat, 621. 
 " " light, 676-719. 
 " " sound, 500. 
 Refractors, Kinds of, 684. 
 Reinforcement of sound 511-514, 516, 
 
 517- 
 
 Relay, Telegraphic, 445 (V). 
 Repeater, Telegraphic, 445 (</). 
 Repulsion, Electric, 304, 321 (a). 
 Requisites of a good battery, 401. 
 Residual electric charge, 356, App. J. 
 
 " magnetism, 443 (a). 
 Resistance box and coils, App. M (i). 
 
 " Electric, 379, App. K. 
 
 " " Measurement of, 
 
 App. M. 
 
 " " Unit of, 380. 
 
 " Internal, 383, 399, 400. 
 
 * 4 Specific, App. K (2). 
 Resolution offerees, 91, 199. 
 Resonance, 513. 
 Resonators, 514, 529 (a). 
 Resultant motion, 79, 85. 
 Retentivity, 425. 
 Rheostat, App. M (zb). 
 Rivers, Flow of, 258. 
 Rock salt prism, 718. 
 RuhmkorfTs coil, 459. 
 Rupert (Prince) drops, App. D. 
 
 
 
 Safety-valve, 640. 
 Savart's bell and resonator, 513 (a). 
 Scale, Musical, 520-523. 
 Science defined, i. 
 
 " Physical, 9. 
 Screens, Magnetic, 432. 
 
 Screw defined, 208. 
 
 " Endless, 210. 
 
 *' Law of, 209. 
 Secondary axis, 664, 688. 
 " battery, 415. 
 " coils, 457. 
 " foci, 689 (). 
 Selective absorption, 618. 
 Selenium, App. K (4). 
 Sensible heat, 581. 
 Series joining of cells, 398. 
 Shadows, 651. 
 
 Short coil electric instruments, 403. 
 Shunts, 404, 
 Silver plating, 412. 
 Simple and compound tones, 529. 
 Sine galvanometer, App. L (2). 
 Sines, Natural, Table of, App. L (2). 
 Siphon, 298-300. 
 Size, How estimated, 726. 
 Smee's cell or battery, 391. 
 Solar energy, 746 ; spectrum, 700. 
 Soldering, App. B. 
 Solenoid, Exp. 101, p. 315. 
 Solid defined, 54, 61. 
 Sonometer, Fig. 268 ; 519, App. Q. 
 Sonorous tubes, 531. 
 Sound, Analysis of, Exp. 16, p. 404; 
 
 529 (a). 
 beats, 516, 517. 
 
 " Cause of, 483. 
 
 " defined, 477. 
 
 " Focus of, 501. 
 
 u Interference of, 515. 
 
 " media, 486. 
 
 " Propagation of, 484. 
 
 " Quality of, 528. 
 
 u Reflection of, 502-504. 
 
 " Refraction of, 500, 501, 516, 517. 
 
 " Reinforcement of, 511-514. 
 
 " Synthesis of, 529 (a). 
 
 " Timbre of, 528. 
 
 " Velocity of, 487-489. 
 
 " waves. 485. 
 Sounder, Telegraphic, 445 (a). 
 Sounding-board, 510. 
 Spark, Electric, 362 ; Exp. 35, p. 233; 
 
 4 6o. 
 
 Speaking-tubes, 495. 
 Specific gravity defined, 241. 
 
 " " of gases, 248. 
 
 " " " liquids, 242, 246. 
 
 " u " solids, 242 245. 
 
594 
 
 INDEX. 
 
 Numbers refer to paragraphs, unless otherwise indicated. 
 
 Specific heat, 596-601. 
 
 " inductive capacity, 352. 
 
 " inductivity, 352. 
 
 resistance (electric), App. K (2). 
 Spectroscope, 703 (b). 
 Spectrum, 700, 702, 704, 716-719. 
 Spherical aberration, 698. 
 Spouting liquids, 254-256. 
 Sprengel's air pump, 290. 
 Springs, Intermittent, 301. 
 Stability, 116. 
 
 Standard candle, Ex. 5, p. 482. 
 Static electricity, see frictional. 
 Steam, 573, 594. 
 Steam-engine, 635-643, App. S. 
 Stereoscope, 735, 736 
 Storage battery, 415. 
 Storms, Thunder, 367. [p. 252. 
 
 Striking distance of Ley den jar, Ex. n, 
 Stringed instruments, 530. 
 Strings, Musical, 518, 519. 
 Stubs' wire gauge, App. I. 
 Submarine cables, 359, 360, App. L (3). 
 Successive electric induction, 335. 
 Sunbeam analyzed, 716-719. 
 Surface electrification, 341. 
 Surveyor's compass, 439 (a). 
 Swan lamps, 466. 
 Sympathetic vibrations, 509, 625. 
 Synthesis of sound, 529 (a). 
 " " white light, 704. 
 
 Tandem joining of cells, 398. 
 Tangent galvanometer, App. L (i). 
 Tangents, Natural, Table of, App. L 
 
 0). 
 
 Tantalus's cup, 301. 
 Telegraph, 444-446. 
 Telegraphic plant, 445 (c). 
 
 " relay, 445 (6). 
 
 " repeater, 445 (d). 
 
 " sounder, 445 (a). 
 
 Telephone, 468, 469, 505-507, App. O. 
 Telephonic transmitter, 507. 
 Telescope, 7 3i-733, App. T. 
 Temperature, 539, 559- 
 Temporary magnet, 307. 
 Tenacity, 48. 
 Tension, Electric, 326. 
 
 " of gases, 62, 269, 282-287. 
 Terrestrial magnetism, 437-441. 
 " telescope, 733. 
 
 Testing, Electric, App. M (i). 
 Tests for electricity, 322, 323, 417, 418. 
 Theory of electricity, 337. 
 Thermal effects of electric currept, 406 
 " spectrum, 718. 
 " units, 579. 
 Thermodynamics, 626, 
 
 " First law of, 630. 
 
 Thermo-electricity, 311, 374, 419-422. 
 Thermo-electric pair, 420. 
 " pile, 421. 
 
 Thermometers, 541-547, Aop. R. 
 Thermometric readings, 546. 
 
 " scales, 545. 
 
 Thunder storms, 367. 
 Timbre, 528. 
 Tin tree, Exp. 77, p. 283. 
 Toepler-Holtz electric machine, Note, 
 
 p. 222. 
 Tones, Fundamental, 524, 525. 
 
 " Musical, 491. 
 Torricelli, 274. 
 
 Total internal reflection, 68 1. 
 Tourmaline tongs, 740. 
 Transferrer, 292. 
 Translucent bodies, 646. 
 Transmission of power, Electric, 474. 
 of pressure by liquids, 
 
 216. 
 
 Transmitter, Telephonic, 507. 
 Transparent bodies, 646. 
 Trembler, Electric, 447. 
 Triangle of forces, 87. 
 Tube of force, App. N. 
 Tubes, Acoustic or speaking, 495. 
 
 " Sonorous, 531. 
 Tuning-fork, 510 (^-516, 529. 
 Turbine wheel, 265. 
 
 U 
 
 Ultra-red rays, 718. 
 Ultra-violet rays, 719. 
 Undershot wheel, 263. 
 Undulations, 478. 
 Unit of electric capacity, 359. 
 " current, 385. 
 " resistance, 380. 
 " quantity, 387. 
 E. M. F., 382. 
 force, 68, 69. 
 heat, 579- 
 
 matter, Chemical, 6. 
 " Physical, 5. 
 
INDEX. 
 
 595 
 
 Numbers refer to paragraphs, unless otherwise indicated. 
 
 Unit of power, 155, 475. 
 
 " " work, 153, 154. 
 Units, Absolute (electromagnetic), 451. 
 " C. G. S., 69, 154, 450, 451- 
 " Electric, 320, 321, 329, 330, 359, 
 
 450-452. 
 
 Electromagnetic, 451. 
 " F. P. S., 68. 
 " Magnetic, 450. 
 " Practical (electromagnetic), 452. 
 Universal discharger, 358. 
 
 " properties, 18, 20. 
 Upward pressure, 227, 228. 
 
 Vacuum pan, 571 (a). 
 Vapor defined, 58. 
 
 " pressure, 568. 
 
 Vaporization of water, Heat equiva- 
 lent of, 594. 
 Variation, Line of no, 441. 
 
 " Magnetic, 441. 
 Velocity, Increment of, 127. 
 " of light, 653. 
 " of molecules, 62 (a). 
 " of sound, 487-489. 
 Vena contracta, App. E. 
 Vertical needle, 439, 440. 
 Vibration, Amplitude of, 140, 481, 493. 
 
 " of pendulum, 140. 
 Vibrations, Sympathetic, 509, 625. 
 Violin, 518, 519 (a). 
 Vision, Distinctness of, 727. 
 
 " Persistence of, 725. 
 Visual angle, 652. 
 Vocal apparatus, 535 (a). 
 Volt, 382. 
 Voltaic arc, 467. 
 
 " battery, 398-402. 
 
 " cell, 306, 375, 390-397. 
 
 *' current, 375. 
 
 " electricity, 305, 306, 373-418. 
 
 " element, see cell. 
 Volt-ampere, 475. 
 Volt-meter, App. M (4*:). 
 
 Volta's pistol, Exp. 58, p. 244. 
 " hail, Exp. 39, p. 240. 
 
 W 
 
 Water, Expansion of, 553, 554. 
 
 " Heat equivalent of vaporiza- 
 tion of, 594. 
 
 " Maximum density of, 553. 
 *' power, 260. 
 " Specific heat of, 601. 
 " voltameter, 410. 
 " wheels, 261-264. 
 Watt, 475. 
 
 Wave length, 480, 482, 499. 
 " period, 479, 482, 498. 
 Waves, Coincident, 511. 
 
 " Reflected, Exps. 8 and 9, p. 
 
 392, Exp. ii, p. 394 . 
 Wedge defined, 205. 
 
 " Use of, 206, 207. 
 Weight, 33, 103. 
 
 " Law of, 105. 
 Wheatstone's bridge, App. M (ze). 
 Wheel and axle, Advantages of 
 
 180. 
 
 defined, 179. 
 
 " " ' Forms of, 184. 
 
 " " " Formulas, 182. 
 
 " " " Law of, 183. 
 
 Wheel armature, 464. 
 Wheels, how connected, 189. 
 Wheels, Water, 261-264. 
 Wheel-work, 185-188. 
 White light, Composition of, 704. 
 Wind instruments, 530. 
 " power, App. H. 
 Wire, App. I. 
 Work defined, 150. 
 " Unit of, 153. 
 
 Yellow spot of eye, 724. 
 
 Zero of temperature, Absolute, 558 
 Zincs, Amalgamating, 388. 
 
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