LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
 
 Class 
 
THE ELECTRON THEORY 
 
DR. G. JOHNSTONS STONEY 
 From a photograph by Elliott <& Fry. 
 
 Frontispiece. 
 
THE 
 
 ELECTRON THEORY 
 
 A POPULAR INTRODUCTION TO THE 
 
 NEW THEORY OF ELECTRICITY 
 
 AND MAGNETISM 
 
 BY 
 
 E. E. FOURNIER n'ALBE 
 
 \\ 
 
 B.Sc. (LOND.), A.R.C.Sc. 
 
 COMPILER OF "CONTEMPORARY ELECTRICAL SCIENCE" 
 
 WITH A PREFACE 
 
 BY 
 
 G. JOHNSTONE STONEY 
 
 'ith Frontispiece, and Diagrams in Text 
 
 LONGMANS, GREEN, A*ND CO. 
 
 39 PATERNOSTER ROW, LONDON 
 
 NEW YORK AND BOMBAY 
 
 1906 
 
 All rights reserved 
 
SP 
 
 PREFACE 
 
 IN 1811 nearly a hundred years ago Avogadro 
 promulgated the important law which bears his 
 name, and which gives expression to the fact that 
 all the more perfect gases, when reduced to the 
 same pressure and temperature, will contain within 
 a given volume the same number of gaseous mole- 
 cules. The fact was established: but the reason 
 why it is so was not then understood, nor till long 
 afterwards, when in the forties and fifties of the 
 last century some of the activities that go on within 
 gases became gradually known. Until these later 
 dates it was erroneously supposed, even by careful 
 students of nature, that natural objects which to 
 our senses appear at rest such as stones, coins, 
 books, air which has been left for a long time 
 undisturbed within a room are in reality devoid 
 of any internal motion. As to gases, one of the 
 illustrations made use of in those . days to help 
 students to picture what they were supposed to be 
 like, was that the molecules of a gas may perhaps 
 resemble the stationary bubbles of a froth, which 
 by expanding when warmed, contracting when 
 
 102823 
 
vi PREFACE 
 
 cooled, and by pressing against one another and 
 against the walls of a containing vessel, behave 
 in these respects very much like a gas. Under 
 this view, Avogadro's Law was expressed by saying 
 that the bubbles, or quasi-bubbles, are all of the 
 same size whatever the gas may be, provided that 
 they are compared with one another when at the 
 same temperature and pressure. 
 
 It was about sixty years ago when there 
 appeared the first glimmerings of the knowledge 
 which has since ripened into that which we now 
 possess, that neither the molecules of any natural 
 object nor the parts of which those molecules 
 consist are ever at rest; that, on the contrary, 
 swift and orderly movements are ever in progress 
 among them and within them; and that where 
 bodies appear to us to be stationary, it is only be- 
 cause this great internal activity is on too small a 
 scale, the parts moving too tiny, and the motions 
 subject to too rapid changes of direction for 
 senses like ours even when assisted by the micro- 
 scope to obtain any suggestion that all this activity 
 is going forwards. Accordingly, until other means 
 than direct observation of arriving at the truth 
 were discovered, every one remained under the 
 delusion that the objects about us on the earth 
 could be " brought to rest" i.e. absolutely freed 
 from every motion except the celestial motion, 
 which is consequent upon their being on a planet 
 
PREFACE Vll 
 
 which rotates upon an axis, revolves in an orbit 
 round the sun, and accompanies the solar system 
 in its peregrinations through space. 
 
 There was one man an Englishman who above 
 sixty years ago perceived that this view of nature 
 was a mistake, at least with reference to matter 
 in the gaseous state. J. J. Waterston, in 1845 
 submitted a memoir to the Royal Society, in 
 which he showed that the recognised properties 
 of the more perfect gases indicate with emphasis 
 that instead of consisting of stationary molecules 
 pressing against one another, they are in reality 
 swarms of much smaller bodies, so small that they 
 leave much of the space unoccupied, in which 
 they dart about amongst one another with extra- 
 ordinary activity, and produce gaseous pressure by 
 encountering one another or where turned back 
 by the walls of a containing vessel. Waterston's 
 contention led to results at variance with the views 
 entertained by scientific men at the time, and his 
 great discovery with the arguments in favour of it, 
 were withheld from publication until long after- 
 wards; so that this great advance in knowledge 
 did not become generally known until, shortly after- 
 wards, Professor Clausius of Geneva rediscovered 
 the kinetic constitution of gases. His announce- 
 ment of it was received with much scepticism. 
 However, Clausius persisted, and in a masterly 
 series of papers published in the later forties and 
 
viil PREFACE 
 
 in the fifties of the nineteenth century he met 
 objections, and piled proof upon proof, until the 
 evidence could no longer be resisted. In the later 
 developments of the theory he was assisted by 
 other scientific men, among whom J. Clerk Maxwell 
 was pre-eminent. 
 
 Until some information can be acquired respect- 
 ing the magnitudes with which we are dealing 
 when investigating any branch of nature's opera- 
 tions, we continue to be unable to form a satis- 
 factorily clear notion of those operations. In the 
 domain of Molecular Physics the first magnitude 
 that was ascertained was when Clausius succeeded 
 in estimating the speeds with which molecules in 
 a gas are travelling about. At any one instant 
 the individual molecules are darting about with 
 very different speeds, but at each temperature 
 there is a certain mean speed towards which the 
 encounters which prevail within a gas tend to 
 bring any speeds which too much differ from it, 
 and round which the innumerable speeds tend 
 to group themselves. The mean speed so defined 
 is not the arithmetic mean of the values of v, 
 but the square-root of the arithmetic mean of the 
 values of v 2 . This mean speed Clausius succeeded 
 in finding to be about 
 
 485 /^ metres per second . . . 1 (a) 
 
PREFACE ix 
 
 Where T is the absolute temperature of the gas 
 estimated in centigrade degrees, and p the relative 
 specific gravity of the gas compared with air. Ex- 
 pressed in miles per hour this mean speed is 
 
 / =^ miles per hour 
 \/ 273*p 
 
 1085 
 
 The arithmetic mean of the various speeds that 
 prevail among the molecules is a different mean 
 from that given above. It is somewhat less, and 
 to obtain it we multiply the above value by 0*92132. 
 Thus the arithmetic mean is 
 
 447 A / 97^7- metres P er second. 
 
 Again, the temperature of our laboratories when 
 experiments are being made in them may be taken 
 to be about 16 C., which is the same as r=289. 
 Introducing this value for r, we find that the arith- 
 metic mean of the speeds at this temperature is 
 
 460 /- metres per second . . . 2 (a) 
 V P 
 
 which is the same as 
 
 1022 /- miles per hour . . . . 2 (b) 
 
 so that, in the air about us, and at the tempera- 
 tures to which we are most accustomed, the mole- 
 cules of its principal gases are travelling with 
 
X PREFACE 
 
 speeds of which the arithmetic mean is more than 
 1000 miles per hour. In order to get the arith- 
 metic mean for each gaseous constituent of our 
 atmosphere we must insert in the last expression 
 the value of p for each gas. We thus find what 
 it is in nitrogen, oxygen, argon, aqueous vapour, 
 and the rest. 
 
 The next important molecular magnitude to be 
 discovered was when Professor Maxwell In 1859 and 
 1860 deduced from observations on the viscosity 
 of gases, and also from the rate of diffusion of 
 olefiant gas into air, the mean length of the little 
 straight path along which a molecule of air darts 
 between consecutive encounters. It is, at the 
 temperature of 15 C. and at the pressure of an 
 atmosphere, about 
 
 7'6 eighthet-metres ... 3 
 
 which is the mean of three determinations made by 
 Maxwell. By an eighthet is to be understood the 
 fraction represented by a unit in the eighth place 
 of decimals, or by the symbol 10~ 8 ; and eighthet- 
 metre is a convenient abbreviation for eighthet of a 
 metre in like manner as a quarter-inch means the 
 quarter of an inch. 
 
 It is worth taking notice, here, that the mean 
 length of the free paths of the molecules be- 
 tween their encounters, although a giant among 
 molecular magnitudes, falls short of the smallest 
 
PREFACE XI 
 
 interval which the microscope can detect. Two 
 minute specks on the stage of a microscope, even 
 if separated by twice this interval, would never- 
 theless be blurred together into the appearance 
 of a single object, when viewed under the most 
 favourable conditions, through the best of micro- 
 scopes handled with the utmost skill. 
 
 By comparing this small measure with the aver- 
 age total distance which the molecule travels in 
 a second, which we have found to be 460 metres 
 (see equ. 2 (a)), we learn that the path pursued 
 by the molecule within one second is a zigzag 
 course, divided on the average into 6,000,000,000 
 little straight free paths between the encounters 
 that it meets with. 
 
 When Maxwell had determined the average 
 length of the free path, it was easy to form a 
 preliminary estimate of the number of molecules 
 that are present; and, accordingly, this was at- 
 tempted by the present writer in 1860, immediately 
 after the publication of Maxwell's papers. What 
 was sought in this preliminary effort was to deter- 
 mine which power of 1000 is nearest in the geo- 
 metric series to the number of molecules in a 
 cubic millimetre of gas. This v a s found to be 
 the sixth power, which is 10 18 ; from which it 
 followed that the actual number of molecules is 
 to be looked for within the group of numbers that 
 intervenes between 10 18 -f x/1000 and 10 18 x A/1000, 
 
xii PREFACE 
 
 i.e. it is a number greater than 3*16 x 10 16 and less 
 than 3*16 x 10 19 . Other determinations of this im- 
 portant physical constant have since been made, 
 and some from data admitting of much closer 
 approximation. From these we learn that we may 
 now accept 4 x 10 16 as a trustworthy and reasonably 
 close approximation to the number of gaseous mole- 
 cules within a volume which is not far from being 
 one cubic millimetre the gas, or mixture of gases, 
 being at or near standard temperature and pressure. 
 To this number of molecules within each cubic 
 millimetre of dry air the principal constituents of 
 the earth's atmosphere contribute nearly in the 
 following proportions : 
 
 Nitrogen .... 
 Oxygen .... 
 Argon 
 
 4 x 7810 000000 000000 molecules 
 4x2090000000000000 
 4 x 100 000000 000000 
 4 x 4 000000 000000 
 4 x 100000 000000 
 / 10000 000000) 
 \ or 5000 000000 j " 
 
 of N 2 
 2 
 A 
 C0 2 
 
 Ne 
 
 He 
 
 Carbon dioxide 
 Neon (about) .. * 
 
 Helium (perhaps) . 
 
 Minor constituents are also present, but in smaller 
 numbers. These are krypton, xenon, and hydrogen, 
 with probably a few molecules of ammonia and 
 some of the oxides of nitrogen ; and of course there 
 will be a variable amount of aqueous vapour present, 
 if the air has not been completely dried. 
 
 These various determinations enable us to con- 
 struct our first picture of what each cubic milli- 
 
PREFACE xiii 
 
 metre of the air about us really is. We are to 
 imagine these enormous swarms of little missiles 
 dashing about in every conceivable direction, each 
 of the missiles successively encountering and 
 occasionally grappling with about six thousand 
 millions of its neighbours every second, and dart- 
 ing along the free paths between these encounters 
 with various speeds, but speeds that are so high 
 that they average more than a speed of 1000 miles 
 per hour. Wonderful as this picture is, we shall 
 presently find that it falls almost infinitely short 
 of the far more astonishing reality. We are 
 enabled to see that this is so, by being already 
 in a position to advance one step nearer to the 
 reality, and by the prospect that then opens before 
 us of further extensions into the still more deeply 
 seated operations which are being carried on by 
 nature. In fact 
 
 While the investigations which revealed to us 
 the kinetic constitution of gases, were in progress 
 in the last century, another line of inquiry was 
 being simultaneously pushed forward which touched 
 upon deeper mysteries of nature. As an introduc- 
 tion into this new region of exploration it will be 
 convenient to recall one of the facts already referred 
 to, that while the free paths of the molecules have 
 very various periods, their average duration is 
 about the six thousand millionth of a second. Let 
 us then compare this brief duration with the vastly 
 
XIV PREFACE 
 
 smaller periodic times of the alternating event 
 which we call light. When this is done it 
 is found that while a molecule of air has been 
 travelling between one encounter and the next, 
 60,000 double vibrations of red light have on the 
 average taken place, and twice that number of the 
 extreme violet ray; and as the periods of all the 
 motions within a molecule which give rise to 
 visible spectral rays must lie between these limits, 
 we are forced to admit that either that im- 
 mense number of orbital motions have been on 
 the average executed within the molecule during 
 each of its flights, or else that periodic motion of 
 some kind has been going on of so complex a 
 kind that when resolved it furnishes that im- 
 mense number of constituents. It is now no 
 longer surprising that the temporary perturbation 
 caused while two molecules have been grappling 
 with one another has in most instances abun- 
 dant time to pass away early in the interval 
 between two encounters, so as to leave the 
 greater part of the motions within the molecule 
 to be executed in the undisturbed manner which 
 the definiteness of the lines of a gaseous spectrum 
 attests to us. 
 
 The chemical elements are some of them gases 
 in the state in which they usually present them- 
 selves to us. A few of the others can be vapourised 
 in a Bunsen's burner; and the rest can be vapourised 
 
PREFACE XV* 
 
 and rendered incandescent in the arc-light, or, at 
 all events, brought into a condition, when an 
 electric spark passes between electrodes of the 
 element, such that molecules will detach them- 
 selves and travel along free paths as in a gas. In 
 all these cases each element furnishes its charac- 
 teristic spectrum of defined lines, each of which 
 is a ray of light with its own definite period of 
 undulation. These spectra make manifest the 
 marvellous regularity of the motions that go on 
 within the molecules of each element, when its 
 molecules are freed from being interfered with by 
 neighbouring molecules; and at the same time the 
 complexity of that motion; with other information 
 of the most instructive kind as regards the rela- 
 tions in which the elements stand to one another. 
 But the greatest achievement of all, and one to 
 which we may reasonably look forward, has not 
 yet been effected. No one has yet succeeded in 
 tracing back from the periodicities, the intensities, 
 and the other properties of the lines of the 
 spectrum of an element, what that motion of the 
 electrons within the molecules must have been 
 to have been able to produce these precise effects. 
 The information is given to us by nature in the 
 spectrum exhibited to us. It is written there ; but 
 in a language which has not yet been deciphered. 
 Let us hope that this great discovery, which 
 has thrown its shadow so plainly before us, 
 
XVI PREFACE 
 
 will have been made before long. The ground has 
 been prepared by many notable investigations 
 Rydberg's, and Kayser and Runge's, on the series 
 of lines which exist in the spectra of the elements, 
 and the relationships which these investigations 
 have brought to light ; the study of the Zeeman's 
 effect, which we may hope will be within a 
 moderate time made much more complete than 
 it now is; and the many facts with reference to 
 corpuscles, each of which either is or contains one 
 electron, that have been elicited with great skill 
 by Professor J. J. Thomson all these are, as it 
 were, so many letters of the writing which has 
 to be deciphered. Along with these we have the 
 dynamical data that the spectrum as we see it, is 
 caused by motions given to the electrons, or more 
 probably to some one or two amongst them, by 
 the general shaking up of a molecule when it has 
 left off grappling with another molecule, and when 
 its motions have settled down into that natural 
 permanent state which is consequent upon whatever 
 is the natural periodic swing within the molecule 
 as modified by the fact that energy is escaping from 
 the electrons into the surrounding aether. 
 
 If the gas is condensed into a liquid or becomes a 
 solid, the free space about its molecules disappears, 
 or at least so much shrinks, that the perturbations 
 caused by an encounter have not time to have passed 
 away during any part of the transit of a molecule 
 
PREFACE XVll 
 
 between one encounter and the next. Accordingly 
 the spectrum of this object is no longer due to the 
 natural swing of the motions within molecules 
 freed from outside interference. When a gas is 
 being condensed the motions within a molecule 
 which have been perturbed during an encounter 
 continue to be confused motions during an in- 
 creasing proportion of the shortened flight of the 
 molecule. Accordingly the lines of its spectrum 
 become less sharply defined : as the condensation 
 of the gas progresses its spectral lines widen, and 
 ultimately they run together and present the 
 appearance which is called a continuous spectrum, 
 which sometimes occupies part, in other cases 
 occupies the whole extent of the spectrum. Of 
 this kind are the spectra of most solid and liquid 
 elements when rendered incandescent by heat, or 
 when the electrons that lie near the surface of 
 the body have been set in motion by incident 
 light falling upon them; which latter is the state 
 of things most familiar to us. In all cases we 
 may take it that objects become visible when 
 the negative electrons and the mass of positive 
 electricity within each chemical atom have been 
 displaced in regard to one another, and set swinging 
 in the way that can excite luminous undulations 
 in the surrounding aether. 
 
 In olden times the best conception that men 
 could form of a gas was that it was somewhat 
 
xviii PREFACE 
 
 like a froth of bubbles in which the molecules 
 of the gas are represented by the bubbles of the 
 froth. In those days even scientific men were not 
 aware that any activities whatever were going on 
 within calm air. Afterwards, when the kinetic 
 constitution of gas became understood, the earlier 
 crude conception was exchanged for a better one 
 in which the molecules were represented as missiles 
 travelling about with marvellous energy, whose 
 numbers it was possible to estimate, as well as 
 the average speed with which they dash about, 
 and the average length of their little journeys. 
 Another conception of nature, both truer and more 
 recondite, was attained when it became under- 
 stood that the molecules are far more than merely 
 missiles, that while they are travelling about subtile 
 events are all the time going on within each of 
 them, involving rapidly alternating displacements 
 of the electricity with which they are charged, and 
 as a consequence the transmission of alternating 
 electro-magnetic stresses in the form of waves 
 through the surrounding aether. We thus are 
 introduced to smaller entities than the missiles, 
 to the negative electrons of which the number 
 in each chemical atom seems, from a remarkable 
 investigation by Professor J. J. Thomson, to be 
 about the same as the number of times by 
 which its atomic weight exceeds that of hydrogen ; 
 with corresponding positive charges in each atom, 
 
PREFACE XIX 
 
 equal in amount to the sum of its negative 
 electrons, but not like the negative electricity 
 split up into separate electrons. Here, then, the 
 electron is introduced to us as a new entity. Is 
 not it, too, a complex system within which in- 
 ternal events are ever taking place ? And when 
 this question can be answered shall we not be 
 in the presence of the inter-active parts of an 
 electron? And do not the same questions arise 
 with respect to these? for there is no appearance 
 of there being any limit to the minuteness of the 
 scale upon which nature works. Nothing in 
 nature seems to be too small to have parts in- 
 cessantly active among themselves. 
 
 Our present position is one which has been 
 reached by slow steps, and we may reasonably 
 hope that our successors will be able to continue 
 to advance, as there is no visible limit. The 
 inquirer who is now entering upon this depart- 
 ment of the study of nature will find it much to 
 his advantage to take as his starting-point the 
 picture of nature, which has taken form in the 
 mind of a thoughtful student of the present state 
 of our knowledge, such as is presented in the fol- 
 lowing pages. This, however, he shbuld entertain, 
 not like a stereotype plate which must remain 
 as it is, but rather like well and firmly set 
 movable type, susceptible with ease of any im- 
 provements the future may bring with it, while 
 
XX PKEFACE 
 
 before and after each correction it is so firmly 
 fixed in its frame that the most effectual use can 
 be made of it. 
 
 Before concluding this preface, I should wish to 
 invite the attention of mathematical physicists to 
 the remarkable table of dimensions which Mr. 
 Fournier has given in his last chapter, in which 
 the obscure uncertainties of ' the usual tables 
 are avoided by the natural expedient of adopt- 
 ing four fundamental units viz. units of mass, 
 electricity, length, and time. Compare this simple 
 system with those unsatisfactory systems into 
 which specific inductive capacity and magnetic 
 permeability have to be admitted without dimen- 
 sions that can be assigned. 
 
 G. JOHJSTSTONE STONEY. 
 
 September 1906. 
 
CONTENTS 
 
 CHAPTER PAGE 
 
 I. INTRODUCTION 1 
 
 II. THE ORIGIN AND DEVELOPMENT OF THE 
 
 ELECTRON THEORY 7 
 
 III. THE ELECTRON AT REST 
 
 1. Properties of the Electron . . 23 
 
 2. Electrons and Matter ... 25 
 
 3. Distribution of Free Charges . . 35 
 
 4. Energy of Position : Potential . . 39 
 
 5. Condensers ..... 52 
 
 6. Specific Inductive Capacity : . 62 
 
 7. Electrostatic Machines . . .65 
 
 IV. THE ELECTRIC DISCHARGE 
 
 1. Discharge in General ... 69 
 
 2. Discharge through Insulators . . 72 
 
 3. Discharge through Gases . . 75 
 
 4. Discharge through Solid Conductors . 83 
 
 5. Discharge through Liquids . . 98 
 
 6. Discharge through a Vacuum . .114 
 
 ^ 
 
 V. THERMO-ELECTRICITY . . . . .121 
 
 VI. VOLTAIC ELECTRICITY . . . .134 
 
 VII. ELECTRO- DYNAMICS . . . . .146 
 
 xxl 
 
XXll CONTENTS 
 
 CHAPTER PAGE 
 
 VIII. MAGNETISM . . . . . . .159 
 
 IX. INDUCED CURRENTS . . . . . 176 
 
 X. RADIATION . , . . . . . 190 
 
 XI. MEASUREMENTS CONCERNING ELECTRONS . 206 
 
 XII. ELECTRICITY AND LIGHT / . . . 222 
 
 Refraction Dispersion and Colour 
 Absorption and Reflection 
 Polarisation Double Refraction 
 Optical Rotation. 
 
 XIII. MAGNETO-OPTIC PHENOMENA . . . 237 
 
 Zeeman Effect Faraday Effect 
 Kerr Effect Macaluso-Cor- 
 bino Effect. 
 
 XIV. ELECTRICITY, HEAT, AND MAGNETISM . 252 
 
 Hall, Leduc, Nernst and v. Ettings- 
 hausen Effects Longitudinal 
 Effects. 
 
 XV. RADIO-ACTIVITY . ;Y. ; * . . , 264 
 
 XVI. CONSTITUTION OF THE ELECTRON . . .280 
 
 XVII. DIMENSIONS OF ELECTRICAL QUANTITIES . 291 
 
 REFERENCES 305 
 
 INDEX . 309 
 
LIST OF DIAGRAMS 
 
 Dr. G. JOHNSTONE STONEY Frontispiece 
 
 PIG. PAGE 
 
 1. Matter and Electricity Compared 
 
 2. Measurement of Electric Force 27 
 
 3. Equipotential Surfaces . 42 
 
 4. Proof of Law of Potential 43 
 
 5. Electric Images 50 
 
 6. Force Exerted by Charged Plane . . . * . 53 
 
 7. 54 
 
 8. Elementary Condenser 56 
 
 9. Leyden Jar . 57 
 
 10. Specific Inductive Capacity ...... 62 
 
 11. Point Discharge 78 
 
 12. Glow Discharge 80 
 
 13. Discharge through Copper 87 
 
 14. Successive Conductors 93 
 
 15. Length of Conductor 93 
 
 16. Elementary Circuit 96 
 
 17. Liquid Conductor 101 
 
 18. Thermo-electric Junction 124 
 
 19. Thomson Effect 132 
 
 20. Electrons passing along a Wire ..... 149 
 
 21. Magnetic Force of Electrons 152 
 
 22. Attraction of Two Circuits 154 
 
 23. Attraction of Current Elements 157 
 
 24. Constitution of a Magnet 162 
 
 25. Coaxial Solenoids 170 
 
 26. Explanation of Polarity 171 
 
 27. Magnetism of the Earth 188 
 
 28. Electric Waves in Wires . . .' * V- -< 197 
 
 29. Perrin's Experiment . . . . , . . . 208 
 
 30. Thomson's Deflection Experiment ..... 209 
 
 31. Zeeman Effect . . . .... . 245 
 
 32. Thermo-magnetic Phenomena 253 
 
 33. Transverse Effects 255 
 
 34. Longitudinal Effects 259 
 
 35. A Combination Diagram 261 
 
 xxiii 
 
'Do Cutn 
 
 T)e 
 
THE ELECTRON THEORY 
 
 CHAPTER I 
 
 INTRODUCTION 
 
 THE object of this work is to place before the reader 
 a concise and connected account of the new theory 
 of electricity and magnetism, which, though, gene- 
 rally accepted, has as yet hardly found its way into 
 the elementary textbooks. The new theory gives us 
 a grip of electrical and magnetic phenomena which 
 was quite unattainable so long as we knew nothing 
 about the real nature of electricity. We now know 
 that electricity is a kind of subtle fluid consisting 
 of electrons, or very small corpuscles, some thirty 
 thousand times smaller than the atoms of ordinary 
 matter. The electron theory is that theory which " 
 reduces all electric and magnetic phenomena to the 
 distribution and motion of these electrons. To gain 
 a clear grasp of the nature and properties of the 
 electron is, therefore, henceforth the first step in 
 the knowledge of electricity. In presenting it to 
 the reader, my first objects will be simplicity and 
 
 A 
 
2 THE ELECTRON THEORY 
 
 lucidity, and I hope to enable those readers whose 
 mathematical attainments have not transcended the 
 elementary rules of algebra to master the essential 
 principles of the science, so as to be able to apply 
 them to practical problems. 
 
 A theory has two functions one is to register a 
 large number of isolated facts in due order, and the 
 other is to give us an insight into their connection 
 with each other, so as to be able to deduce one from 
 the other and to predict new facts and produce 
 effects hitherto unknown. The electron theory 
 fulfils both these functions in a manner which 
 no previous theory of electrical phenomena has 
 been able, even remotely, to approach. 
 
 In no branch of human knowledge have greater 
 difficulties been encountered in framing an adequate 
 theory than in the science of electricity. The be- 
 wildering variety of the phenomena, the constant 
 stream of new facts and discoveries, the revolutionary 
 character of many of them, and the intangible nature 
 of the agent itself, combined to render the formula- 
 tion of an all-embracing theory difficult. But the 
 reward of arduous work has been correspondingly 
 great. To-day we know more about the atom of 
 electricity than we do about the atom of ponderable 
 matter. We can contemplate it as a centre of force 
 producing the old phenomena of the pith ball and 
 the gold leaf and the rubbed glass rod. We see it 
 in swift motion in the vacuum tube, and in slow 
 
INTKODUCTION 3 
 
 motion along the current-bearing wire, now no 
 longer the inscrutable mystery it was ten years ago. 
 We observe its surgings to and fro in the alternating 
 current, and follow the waves it emits across space 
 into the wireless receiver. We imagine its orbital 
 motion round the^-atqm it clings to, and the vista of 
 magnetic phenomena flashes into view. We watch 
 it dragging along that same atom through the 
 electrolytic cell, and gain an insight into the secrets 
 of chemistry such as seems likely to remodel that 
 whole vast science. Not content with having an- 
 nexed practically the whole of physics and chemistry, 
 our new conception launches out into unexplored 
 fields. It hints at the transmutation of the elements, 
 the constitution and destruction of matter, the 
 explanation of inertia, and an electrical theory of 
 mechanics as an answer to the all-pervading influ- 
 ence hitherto exercised by mechanical conceptions. 
 The electron theory, this latest and widest of 
 scientific generalisations, is the fitting reward of 150 
 years of laborious research. A somewhat unusual 
 circumstance attending its victory lies in the fact 
 that it supplements rather than displaces the older 
 theories. It has something of Franklin's one-fluid 
 theory about it, inasmuch as it links all electric 
 phenomena with the distribution and motion of a 
 kind of gas possessing a pressure and an atomic 
 structure. It supplements the analytical specu- 
 lations of Ampere and Weber by providing the 
 
4 THE ELECTRON THEORY 
 
 necessary material substratum, and fits itself, lastly, 
 into the ether theories of Maxwell and Hertz by 
 telling us what is at the ends of the lines and tubes 
 of force whose distribution and motion have played 
 such a useful and almost exclusive role in the 
 electromagnetic theory of yesterday. 
 
 This may partly account for the almost ominous 
 silence with which the new theory has made its 
 appearance in the electrical world. It has not been 
 heralded by a flourish of trumpets, nor has it been 
 received with violent opposition from the older 
 schools. No one man can claim the authorship of 
 it. The electron dropped, so to speak, into the 
 supersaturated solution of electrical facts and specu- 
 lations, and furnished the condensation nucleus 
 required for crystallisation. One after another 
 the molecules the facts of electricity fell into 
 line, and one department of electrical science after 
 another, crystal on crystal, clicked into its place, 
 dispersion first, then electrolysis, then gas discharges, 
 then radium rays, then metallic conduction, and," 
 lastly, magnetism. 
 
 Nor is the crystal fully shaped yet. The electron 
 theory has to absorb every detail, to assimilate the 
 vast store of accumulated facts, to find a place in the 
 edifice for every loose brick, to strengthen every 
 weak place, and there are still many, though they 
 diminish daily in number and importance. 
 
 Our textbooks, always shy of innovations, must 
 
INTRODUCTION 5 
 
 gradually be brought round to the newer views. 
 They must be given courage to speak about " elec- 
 tricity " a word they have lately been chary of 
 using, as it conveyed no meaning! The scientific 
 electrician had become accustomed to deal with 
 " electrification " or "electric quantity" as the only 
 thing he knew, and to leave the use (and misuse) of 
 the word "electricity" to the layman. The electrical 
 theorist found a refuge in differential equations 
 involving pure quantities, and dealt with them by 
 mathematical rules, alias generalisations from the 
 results of experiments in counting. The practician, 
 having no such vast experience in processes of count- 
 ing, but having instead a close familiarity with the 
 behaviour of bodies and substances, also derived from 
 vast experience, found that the habits of thought 
 thus acquired did not assist him towards an intimate 
 knowledge of the nature of electricity. He did his 
 best by annexing Faraday's semi-material "lines of 
 force," and applying them to problems of induction 
 with truly astonishing industrial results. What he 
 will do when he gets a grip of the electron we can 
 only faintly guess. 
 
 Will the electron theory be final, or will it in turn 
 be superseded by another theory? This is a very 
 pertinent question, but more pertinent for the text- 
 books and professors than for the research worker or 
 the practician. In one sense, no theory is final. A 
 final theory is the death of science. When a man 
 
6 THE ELECTRON THEORY 
 
 frames a theory he is delighted to find it confirmed 
 everywhere. When he comes across a case where it 
 fails, he should be equally delighted, for he has 
 found a really new truth, a truth not contained 
 implicitly in his theory. But a theory may be final 
 in the sense that Newton's gravitational theory is 
 final. That theory applies to all ponderable matter 
 at distances beyond molecular range. The electron 
 theory applies to all electrified and magnetised 
 matter, and has even been made to include gravita- 
 tion as a special case. If it can bring the whole of 
 electrical and magnetic phenomena into one well- 
 ordered system, not to speak of chemistry and 
 mechanics, it will be of permanent and incalculable 
 value. If it succeeds in analysing the chemical 
 atom, it will abolish one of those puzzling complexi- 
 ties of which the human intellect is so persistently 
 impatient the variety of the chemical elements. 
 Progress in this direction will tend to unify physical 
 science, and leave the road free for advance into 
 those realms of infinitely greater complexity which 
 harbour the phenomena of life. 
 
CHAPTER II 
 
 THE ORIGIN AND DEVELOPMENT OF THE 
 ELECTRON THEORY 
 
 THE first serious attempt to formulate a theory of 
 electricity as distinct from a vague guess or a pro- 
 visional hypothesis was made by Benjamin Franklin, 
 who announced his one-fluid theory in 1750 in his 
 letters to Collinson. He supposed that a subtle 
 fluid or "electric fire" was distributed throughout 
 the world, that it was attracted by ordinary matter, 
 but that its' particles repelled each other. The fluid 
 can penetrate metals, but not insulators. Being, 
 however, attracted by insulators, like glass, it ac- 
 cumulates at the surface only. To explain why a 
 glass rod should be electrified by friction, Franklin 
 made the fantastic assumption that the glass, being 
 expanded by the heat, takes up more than its 
 ordinary share of the fluid, and seeks to give it up 
 again on cooling. This explanation seems forced; 
 but it should be remembered that frictional electri- 
 fication is, up to the present day, the least explained 
 of all electric phenomena. 
 
 Franklin's theory, in order to be consistent, had 
 
 7 
 
8 THE ELECTRON THEORY 
 
 to assume that atoms of ordinary matter repel each 
 other, and this was at once perceived to be at 
 variance with the facts of gravitation and cohesion. 
 But how close the agreement is between Franklin's 
 one-fluid theory and the electron theory may be 
 seen by putting the latter into Franklin's language 
 as follows : 
 
 " Through all corporeal nature one subtle matter 
 is distributed, which contains the reason and cause 
 of all electric phenomena. The particles of this 
 fluid repel each other. All matter in its normal 
 state contains a fixed quantity of this fluid. If 
 any portion of matter is deprived of some of this 
 fixed quantity, it attracts the fluid with a force 
 proportional to the amount it has lost, and repels 
 another portion of matter that has suffered a similar 
 loss. All electric phenomena are due to the dis- 
 tribution and motion of the particles of the fluid." 
 
 Franklin's theory failed on the question of con- 
 ductors v. insulators. He supposed that conductors 
 could take up any amount of the fluid and store 
 it throughout their substance, while insulators could 
 only store it on their surfaces. The modern version 
 is that conductors take up an additional amount 
 of the fluid, within limits depending upon circum- 
 stances, and store it on their surfaces only. On 
 the other hand, they cannot be deprived of more 
 than the " fixed quantity" mentioned above. But 
 the fundamental difference between the old and 
 
ORIGIN AND DEVELOPMENT 9 
 
 the new views lies in the use of the words " posi- 
 tive" and " negative." In an evil hour the elec- 
 tricity derived from rubbed glass was called positive 
 electricity, and the electricity derived from amber 
 was called negative. The fact that the two elec- 
 tricities neutralised each other made the terms 
 justifiable : but there was nothing to indicate which 
 kind was the real and only fluid. It was assumed, 
 at haphazard, that the glassy electricity was the 
 fluid, and for 150 years all algebraic signs continued 
 to be placed in accordance with that idea, and they 
 continue so to the present day. Thus we speak 
 of the " positive pole " of a battery as the pole 
 from which the glassy electricity appears to flow, 
 whereas we know now that if there is a flow at all it 
 is towards that same pole, the flow in the reverse 
 direction being insignificant in comparison. This 
 fundamental difference is not apparent in our Frank- 
 linian version of the electron theory above ; but it 
 makes a very radical difference, and places a serious 
 obstacle in the way of popularising a logical ter- 
 minology. We have to learn that the " negative" 
 electricity is the electricity, and the negative current 
 the current. In the present period of transition, 
 great care must be exercised to prevent confusion, 
 and a way of doing so will be indicated later on. 
 
 The one-fluid theory, as we have seen, did not 
 succeed very well in explaining frictional electri- 
 fication. Hence, when, in 1759, Symmer brought 
 
10 THE ELECTRON THEORY 
 
 out his two-fluid theory, it met with a wide accept- 
 ance, and continued in active possession until the 
 phenomena in vacuum tubes began to exhibit an 
 essential difference between positive and negative 
 electrification. 
 
 The fluid theories were marvellously ingenious, 
 considering the poverty of the materials upon which 
 they were based. In the whirl of subsequent dis- 
 coveries, they were like guiding stars faintly visible 
 through a mist. Sometimes they were almost lost 
 sight of in the crowd of new facts and speculations ; 
 but other forces were at work to bring order into 
 the chaos. The greatest force was the advance in 
 measurement. Lane's unit jar in 1781 was the 
 true beginning of electrical science, if we accept the 
 dictum that " Science is measurement." Coulomb's 
 torsion-balance (1784-1788) gave us two new inverse- 
 square laws in addition to the Newtonian one of 
 gravitation. The mathematicians had begun to 
 handle these new laws with fruitful results when 
 the scientific world was startled with Galvani's 
 frog in 1791, and kept in a state of agitation by 
 the long controversy between Volta and Galvani 
 concerning a third fluid, which the latter persisted 
 in calling " animal electricity." Volta's pile in 
 1799, followed by Cruikshank's and Davy's electro- 
 chemical work, closed the eighteenth century, which 
 left the theory of electricity in wild confusion, and 
 its devotees torn by endless dissension. 
 
ORIGIN AND DEVELOPMENT II 
 
 This state of things, coinciding with the Napoleonic 
 wars, accounts for the temporary collapse of electrical 
 research in the new century. There is hardly any- 
 thing to chronicle between 1800 and 1820, except 
 perhaps young Grotthus's hypothesis (1805) and 
 Poisson's mathematical treatment of electric and 
 magnetic potential (1811), based upon Coulomb's 
 laws. In revenge, the next twenty years brought 
 forth a flood of discovery such as has rarely been 
 crowded into so short a time, and remained un- 
 equalled until the revolution of 1896. Ampere, 
 Oerstedt, Biot, Savart, Seebeck, Ohm, Peltier, Fara- 
 day, Weber, and Joule, all fall within this period. 
 Truly a galaxy of genius and phalanx of philosophy. 
 
 Oerstedt, in 1820, threw the first bridge between 
 electricity and magnetism. Seebeck connected elec- 
 tricity with heat, and Faraday linked the phenomena 
 of electricity and motion, and laid the foundation of 
 the two great modern theories of electricity and 
 magnetism : Maxwell's ether theory and the electron 
 theory. The latter foundation he laid, however, 
 unwittingly, being personally disposed to consider 
 rather what happened in the medium between 
 bodies than what happened in the bodies them- 
 selves. * 
 
 It is interesting, in the light of the modern 
 electron theory, to read some passages from Weber's 
 Werke, where he foreshadows the atomic theory 
 of electricity. Thus in vol. iv. p. 279, we read : 
 
12 THE ELECTRON THEORY 
 
 " Considering the general distribution of electricity, 
 we may assume that an electric atom is attached 
 to every ponderable atom." And again, p. 281 : 
 " Let e be the positive electric particle ; let the 
 negative one be equal and opposite, and let it be 
 denoted by e. Let only the latter have a pon- 
 derable atom attached to it, and let its mass be 
 thereby increased to such an extent that the mass 
 of the positive particle vanishes in comparison. 
 We may then regard the particle e as stationary, 
 and only the +e as revolving round e." [I have 
 italicised the words which show that Weber's con- 
 ception is exactly the reverse of the modern one.] 
 He proceeds : " The two dissimilar particles, being 
 in the molecular state of aggregation described, 
 then represent an Amperian molecular current, for 
 it can be shown that they fulfil the assumptions 
 made by Ampere concerning his molecular cur- 
 rents." Finally, on p. 292 : " The vis viva (leben- 
 dige kraft) of all the molecular currents contained 
 in the conductor increases, while the current passes 
 through in proportion to the resistance and to the 
 square of the current intensity." 
 
 Substitute " electrons " for " molecular currents," 
 and you have nearly the modern view of metallic 
 conduction. 
 
 The most important dates in Faraday's career 
 were 1831 and 1833. In the former year he dis- 
 covered electromagnetic induction, and did for a 
 
ORIGIN AND DEVELOPMENT 13 
 
 varying current what Oerstedt had done for a steady 
 one viz. established the link between electricity 
 and magnetism. This discovery naturally predis- 
 posed him to devote his attention to the happenings 
 in the dielectric medium rather than the conducting 
 substance. And yet he made, two years after, a 
 discovery of transcendent importance which was 
 bound sooner or later to lead up to an atomic 
 theory of electricity. It was that whenever two 
 metals or other elements of the same valency are 
 deposited or evolved in the electrolytic cell, the 
 amounts of electricity consumed, as measured by 
 Lane's unit jar or other instrument, are inversely 
 proportional to the atomic weights of the elements. 
 Or, in other words, that the electricity attached to 
 every atom of a given valency is the same, and 
 that if a metal is divalent its atom is associated 
 with twice the usual atomic quantity of electricity. 
 
 Commenting upon this discovery in his Faraday 
 lecture, Helmholtz said : " If we accept the hypo- 
 thesis that elementary substances are composed of 
 atoms, we cannot avoid the conclusion that elec- 
 tricity, positive as well as negative, is divided into 
 definite elementary portions which behave like 
 atoms of electricity." 
 
 James Clerk Maxwell, who, following in Faraday's 
 footsteps, worked out a beautiful and successful 
 theory based upon the properties of the medium, 
 also saw the force of this conclusion, without, how- 
 
14 THE ELECTRON THEORY 
 
 ever, being able to follow it up owing to tlie lack 
 of experimental data. In the first edition of his 
 "Electricity and Magnetism," published in 1873, 
 he says (p. 312): "Suppose, however, that we leap 
 over this difficulty by simply asserting the fact of the 
 constant value of the molecular charge, and that we 
 call this constant molecular charge, for convenience 
 of description, one atom of electricity." Later on, 
 however, he adds : " It is extremely improbable that 
 when we come to understand the true nature of 
 electrolysis we shall retain in any form the theory 
 of molecular charges, for then we shall have ob- 
 tained a clear basis on which to form a true 
 theory of electric currents, and so become inde- 
 pendent " of these provisional theories." 
 
 Maxwell's vision here was clouded, for the theory 
 "of molecular charges" now holds the field in 
 undisputed possession, after decisive victories in 
 four different quarters where its attacks were little 
 dreamt of in 1873. 
 
 The very next year an Irish physicist, G. John- 
 stone Stoney, at the Belfast meeting of the British 
 Association, drew attention to this "atom of elec- 
 tricity" as one of the three fundamental physical 
 units of nature (the others being the velocity of 
 light and the constant of gravitation), and gave 
 an approximate calculation of its value. He said : 1 
 
 1 See Scientific Proceedings of the Royal Dublin Society, Feb. 
 1881, p. 54. Philos. Mag., May 1881, pp. 385, 386. 
 
ORIGIN AND DEVELOPMENT 1$ 
 
 " Finally, Nature presents us in the phenomena of 
 electrolysis with a single definite quantity of elec- 
 tricity, which is independent of the particular 
 bodies acted on. To make this clear I shall ex- 
 press ' Faraday's Law ' in the following terms which, 
 as I shall show, will give it precision viz. for each 
 chemical bond which is ruptured within an electro- 
 lyte, a certain quantity of electricity traverses the 
 electrolyte which is the same in all cases. This 
 definite quantity of electricity I shall call Ej." 
 
 He calculates the actual charge by dividing the 
 quantity of electricity required for the electrolysis 
 of 1 c. cm. of hydrogen by the number of hydrogen 
 atoms in 1 c. cm. as given by Loschmidt, and finds 
 1Q- 20 " amperes " (now called absolute electromagnetic 
 units of quantity). This figure compares well with 
 the latest value for the electron viz. 1-1 x 10~ 20 E.M. 
 units. 
 
 In 1879 followed Crookes's epoch-making experi- 
 ments on the mechanical properties of those mys- 
 terious vacuum discharges called cathode rays by 
 Goldstein, and studied by Plticker and Hittorf 
 since 1859. Crookes, pushing the vacuum to the 
 furthest attainable point, and leaving in the tube 
 only one-millionth of the air originally contained 
 in it, obtained what he called " radiant matter " in 
 a fourth state, superior in dilution to the gaseous 
 state, and marked by a still further disappearance 
 of differentiating qualities such as is observed in 
 
1 6 THE ELECTKON THEORY 
 
 passing from solid to liquid and from liquid to gas. 
 He actually constructed a little windmill driven by 
 a torrent of electrons, of the real "electric fluid" 
 as we now know it, without, however, quite realising 
 the tremendous feat he had accomplished. His 
 opinions and theories were smiled at as being too 
 " grossly material," and the discoverer had to wait 
 twenty years before they were brilliantly confirmed. 
 
 The same year that witnessed Crookes's demon- 
 strations before the Koyal Society saw the realisa- 
 tion of the long-cherished dream of deflecting a 
 current in a conductor by means of a magnetic 
 field. Crookes had deflected his "radiant matter" 
 by a magnet, and so what more natural than to 
 expect that a magnet should deflect the same matter 
 when picking its way through the substance of a 
 metal! This was accomplished at last by Hall of 
 Baltimore, by bringing a very thin film of gold into 
 a strong magnetic field, and finding that the elec- 
 tricity tended to make its way out by the sides 
 when the current was turned on. If this discovery 
 had been followed up with any spirit, the true 
 import of the negative current as the real current 
 would have been realised seventeen years earlier 
 than it was. Hall himself observes: 1 
 
 "If we regard the electric current as a stream 
 flowing from the negative to the positive pole, the 
 phenomena observed indicate that two currents 
 
 1 American Journal of Mathematics, vol. ii. p. 287, 1879. 
 
ORIGIN AND DEVELOPMENT 17 
 
 parallel and in the same direction tend to attract 
 each other. . . . Whether this fact, taken in con- 
 nection with what has been said above, has any 
 bearing upon the question of the absolute direction 
 of the electric current, it is perhaps too early to 
 decide." 
 
 In the following year Von Ettinghausen actually 
 claimed to prove that the current proceeded from the 
 negative pole with a velocity of a few millimetres per 
 second. This result was, as we shall see, not far 
 from the truth. 
 
 Taken in conjunction with the effect produced 
 on light by reflecting it from a magnetised surface, 
 discovered by Kerr in 1875, the Hall effect might 
 have led very close to the modern electron theory, 
 but for the difficulty of distinguishing between forces 
 on electricity and forces - on conductors. Without 
 any idea of the density or inertia of the particles of 
 electricity, all quantitative deductions necessarily re- 
 mained as vague as Franklin's original " electric fire." 
 
 That avenue being barred, electric research took 
 other directions. One of the most fruitful of these 
 was electrochemical research, which, since Faraday's 
 fundamental discovery, had occupied a school by 
 itself, cultivating but little intercourse with the rest 
 of the electrical world. Hittorf, Clausius, and Kohl- 
 rausch had, with infinite patience, traced the migra- 
 tion of the ions through the liquid in the electrolytic 
 
 cell, discovered their mutual independence, and 
 
 B 
 
1 8 THE ELECTRON THEORY 
 
 formulated the theory of ionisation, culminating in 
 the memorable announcement by Arrhenius in 1884 
 that at infinite dilution all molecules of the electro- 
 lyte would be dissociated and free to obey electric 
 forces. This discovery, together with van't HofFs 
 work on osmotic pressure, formed the foundation 
 on which Ostwald and Nernst have since been able 
 to raise the imposing edifice of the chemistry of 
 ionisation. 
 
 Meanwhile, Maxwell's electromagnetic theory was 
 radiating out from Cambridge, and gradually attract- 
 ing to itself the leading thinkers of the Continent, 
 who felt the inadequacy of the mathematical theories 
 of Weber, Clausius, and Riemann, based upon action 
 at a distance between charged points. Maxwell's 
 successor at Cambridge, J. J. Thomson, took his 
 first step towards the modern corpuscular theory 
 of electricity in the light of Maxwell's views of 
 electromagnetic energy by calculating, in 1881, the 
 " quasi-inertia " possessed by a charged body in virtue 
 of its charge alone. 
 
 But the doubts engendered by the two main lines 
 of thought were removed with dramatic suddenness 
 by a few simple experiments made by Hertz, at 
 Bonn, in 1888. He proved that electric force has 
 a finite rate of propagation, and that, if a body is 
 charged, the field of force around it does not per- 
 vade all space instantly, but takes a certain time 
 very short, but still measurable to reach a distant 
 
ORIGIN AND DEVELOPMENT 1 9 
 
 point. The speed was found to be the same as 
 that of light viz. 186,000 miles per second. 
 
 This momentous discovery turned the tables com- 
 pletely on the theories of instantaneous action at 
 a distance, and enthroned Maxwell's theory in every 
 Chair in Europe and America. For half a genera- 
 tion after those experiments men were feverishly 
 engaged in testing dielectrics, and making them 
 convey waves of electromagnetic force, the wave of 
 research itself culminating in the triumphs of wire- 
 less telegraphy. 
 
 In the struggle for the mastery of the dielectric, 
 the harmless necessary conductor was in sore danger 
 of being lost sight of altogether. But already there 
 were indications of the dawn of a new light pro- 
 ceeding from the vacuum tube a piece of apparatus 
 which, owing to its many vagaries, had acquired an 
 evil reputation as a kind of theory-trap, and had 
 for some time been shunned by all but the most 
 reckless or courageous pioneers. Arthur Schuster 
 was the first to break distinctly new ground, by 
 calculating, with the aid of the magnetic deflection, 
 the ratio of the charge to the inertia possessed by 
 what he, rather unfashionably, called the cathode- 
 ray particles. This ratio came out. very high, in- 
 dicating that either the charge must be high or 
 the mass very small. Every one thought there was 
 something wrong about this measurement, especially 
 when, in 1893, Lenard succeeded in persuading the 
 
2O THE ELECTRON THEORY 
 
 rays to pass out through an aluminium " window'' 
 into the open air, and proclaimed them, on the 
 strength of their absorption, to be composed of 
 ether waves. We now know that Schuster was 
 right and Lenard wrong; but it took five years 
 of controversy before Lenard gave way before an 
 avalanche of new facts, and finally surrendered. 
 
 Towards the end of 1895 the world was startled 
 by the announcement that a professor in Wiirzburg 
 had discovered rays which could penetrate the 
 human body and show up the bones . as shadows. 
 This discovery, made by Rontgen by means of a 
 vacuum tube, converted the latter from being 
 the most despised into being the' most universally 
 popular of scientific instruments. 
 
 In the nineteenth century four epochs stand out 
 as of transcendent importance in the life-history 
 of the science of electricity. They are 1820, 1833, 
 1888, and 1896. In 1820, with Oerstedt, Ampere, 
 Biot, and Savart, the twin sciences of magneto- 
 electricity and electro-dynamics started into being. 
 In 1833 Faraday linked them with chemistry. In 
 1888 Hertz annexed the ether and enthroned Max- 
 well's theory; and finally, in 1896, the electron 
 theory was enthroned above all others as their 
 culmination and fulfilment, with almost equal 
 suddenness and with much less opposition than 
 that which Maxwell's theory had encountered. 
 
 In that year, Zeeman, of Leyden, discovered that 
 
ORIGIN AND DEVELOPMENT 21 
 
 the spectrum of the light from a sodium flame could 
 be modified by a powerful electromagnet, the lines 
 being doubled when seen in one direction and 
 trebled when seen in another. This phenomenon, 
 mysterious at first sight, was found to be fully 
 explained by a theory formulated by H. A. Lorentz 
 sixteen years before a theory which reduced the 
 action of matter on light to the presence of minute 
 charged corpuscles revolving round the atoms. 
 
 The same year also saw the discovery of uranium 
 radiation by H. Becquerel. The vast significance 
 of these discoveries was perceived in the following 
 year, when J. J. Thomson succeeded in determining 
 the ratio of the charge to the mass of the cathode- 
 ray particles, and, to his great surprise, found this 
 ratio to be identical with that of the Lorentz 
 corpuscles. 
 
 Discoveries now followed in rapid succession. 
 Rutherford extended the corpuscular theory to 
 atmospheric electricity. The Curies discovered 
 radium and its radiation of electrons, and then 
 proved that radium emits heat and charged particles 
 without cessation. Everywhere, and sometimes in 
 the most unexpected quarters, the same electron 
 the same fundamental quantity of " ; negative" elec- 
 tricity was rediscovered. Schuster-, Simon, Kauf- 
 mann, Townsend, Wilson, Riecke, t)rude, and a 
 host of others busied themselves with investigating 
 its properties; and one realm of electrical science 
 
22 THE ELECTRON THEORY 
 
 after another was annexed to the all-embracing 
 electron theory. Abraham, Sommerfeld, Bucherer, 
 Wien, Larnior, Langevin, and Lodge extended the 
 theory, both mathematically and experimentally, 
 and reconciled it with the fundamental equations 
 of Maxwell and Hertz. Nor is the work yet com- 
 pleted. Every day brings new material and new 
 conquests. A fresh zest has been given to research 
 in all branches of electricity, and hosts of workers 
 are engaged in pushing the new conceptions to their 
 logical conclusion. When they have reached the 
 engineers and practical men, new discoveries and 
 inventions of far-reaching import may be confidently 
 anticipated. 
 
CHAPTER III 
 
 THE ELECTRON AT REST 
 
 &J 
 
 1. Properties of the Electron. The electron is 
 the--smallest--^leatrified body c arable.. j>__ .separate 
 existence. Its inass is approximately 0*61 xlO~ 27 
 grammes. Its radius is roughly estimated at 
 10~ 13 cm. Its charge consists of what has hitherto 
 been called " negative " electricity i.e. the electricity 
 possessed by a stick of sealing-wax when rubbed 
 with wool. 
 
 The fundamental property of the electron which 
 distinguishes it from ordinary matter is that it 
 repels another electron, instead of attracting it, as 
 two pieces of matter would do. When one electron 
 is placed at a distance of 1 cm. in a vacuum from 
 another electron, it repels it with a force of 1*16 x 
 10-19 dynes, a force which is something like a quad- 
 rillionth of a pound. This force may appear 
 excessively small, but, as a matter of fact, it is 
 enormous. It is more than a trilKon trillion times 
 (more precisely, 10 43 times) greater than gravita- 
 tional attraction, which accounts for the weight of 
 
 bodies on the earth's surface and the motion of 
 
 23 
 
24 THE ELECTRON THEORY 
 
 the heavenly bodies. How enormous it is may be 
 
 realised by the following imaginary experiment. 
 
 Let two masses, M M x (Fig. 1), say of lead, weighing 
 
 1 gramme each, be placed 1 cm. apart. They 
 
 will attract each other with a force of 6*6 x 10~ 8 
 
 ^ ^ dynes, a force quite too small to be 
 
 measured by any known instrument. 
 
 But now let 2 grammes of pure 
 
 negative electricity, E E x , made up 
 
 of electrons, be placed side by side 
 
 ^ /9\ at ^6 same distance. They will 
 
 ^ repel each other with a force of 
 
 E| 314 x 10 34 dynes, or 320 quadrillion 
 
 WO - L tons! 
 
 Even if they were placed, one at the North Pole 
 of the earth, and the other at the South Pole, they 
 would still repel each other with a force of 192 
 million tons, and that in spite of the fact that the 
 force decreases with the square of the distance. 
 That force would be capable of imparting to each 
 of these grammes of pure electricity a velocity equal 
 to that of light in less than a millionth of a second, 
 and would only fail to do so owing to the fact 
 that the inertia of each electron becomes infinite, 
 or nearly so, as it approaches the velocity of light. 
 In any case, it is obvious that the experiment must 
 remain purely imaginary. 
 
 We obtain somewhat less appalling figures if 
 we suppose there to be only 1 gramme of pure 
 
THE ELECTRON AT REST 25 
 
 electricity, and a single electron placed at 1 cm. 
 from it. The force is still 194 million dynes; but 
 >if we separate the two bodies, as before, by the 
 distance of the earth's axis, the force reduces itself 
 to the inappreciable amount of l'2xlO~ 10 dynes. 
 Small as this force is, it must be remembered that 
 the mass at one end of its line of action has been 
 reduced in the same proportion, so that the single 
 electron will be projected just as before with the 
 same explosive velocity. We should have to remove 
 it as far as the sun to reduce the acceleration to 
 something like manageable proportions, and even 
 at that enormous distance ( = l*53x!0 13 cm.), the 
 force exerted by 1 gramme of pure electricity on 
 earth upon all the free electrons in the sun would 
 suffice to impart to them a velocity equal to that 
 of light in 20 seconds. 
 
 It is quite evident from the above considerations 
 that in all ordinary electrical phenomena, we are 
 dealing with a very minute quantity of free elec- 
 tricity. Let us attempt to arrive at some idea of 
 its amount. 
 
 2. Electrons and Matter. We deduce from the 
 laws of electrolysis that every atom of matter 
 is capable of temporarily uniting with a definite 
 quantity of electricity, which is exactly proportional 
 to its chemical valency, but is otherwise indepen- 
 dent of the nature of the element. Thus in the 
 electrolysis of hydrochloric acid every atom of 
 
26 THE ELECTRON THEORY 
 
 chlorine brings to the anode a definite quantity 
 of negative electricity, a quantity which we can 
 measure with a galvanometer. Knowing the weight 
 of the chlorine evolved and the weight of the atom 
 of chlorine (as we do), we can find by a simple 
 calculation that the quantity transported by each 
 atom is, as nearly as we can make it out, just one 
 electron. We therefore conclude that every atom 
 of chlorine in the electrolytic cell has one electron 
 somehow associated with it, but associated in such 
 a manner that it is ready to be detached when a 
 finite force is brought to bear upon it. In the 
 normal state the chlorine atom does not carry this 
 electron with it, and it is therefore uncharged. 
 
 Other elements such as hydrogen and the metals 
 are also uncharged in the normal state. Each 
 atom contains a number of electrons, but their 
 electrical action is compensated by some force 
 within the atom which, for lack of a better term, 
 we may call "positive electricity"; but each of 
 their atoms, when placed in an electrolytic cell and 
 subjected to electric force, is liable to temporarily 
 lose an electron or two electrons if the element 
 is divalent and thereby become " positively " 
 charged. 
 
 We have, therefore, reason to suppose that in 
 any uncharged lump of a divalent metal say a 
 ball of copper there are at least twice as many 
 electrons as there are atoms. Since the connection 
 
THE ELECTRON AT BEST 27 
 
 between the atoms and these electrons is not rigid, 
 we may suppose that this proportion is liable to 
 variations. When the electrons are in excess of the 
 usual number, we find that the ball is negatively 
 charged; when there is a deficiency, the ball is 
 positively charged. Having seen above what enor- 
 mous forces the electrons are capable of exerting 
 upon each other, we have no difficulty in conceiving 
 adequate causes for such variations. 
 
 Now, when the balls are thus charged, it is found 
 that the electrons, or the positively charged 
 atoms, in spite of their mutual repulsion, do 
 not shoot out of the metal into the sur- 
 rounding air. They traverse the metal with 
 very little friction, but experience a great 
 resistance at the boundary between metal 
 and air. They therefore take up a position 
 of equilibrium on the surface itself, and stay 
 there, leaving the interior of the metal 
 uncharged. 
 
 Next, suppose that two small copper balls, 
 A and B, are suspended side by side by in- 
 sulating fibres 1 m. long (Fig. 2). Let them 
 be negatively charged, so as to repel each A B 
 other, and remain 1 cm. apart. Then the 
 force between them is easily proved to be -zfafh 
 part of their weight. If their radii are 1 mm. each, 
 what number of free electrons will suffice to produce 
 the necessary repulsion ? 
 
28 THE ELECTRON THEORY 
 
 The following data are easily calculated : 
 
 Volume of each ball . . . 4*2 x 10~ 3 cm. 
 Weight (density 8'93) . . 3'75 x 10~ 2 gr. 
 Force of repulsion . . . 1*87 x 10~ 4 gr. 
 
 = 0*184 dynes. 
 
 This is the force that would be exerted by 1260 
 million electrons upon an equal number placed at a 
 distance of 1 cm. in air. This is, then, the number 
 of free electrons in each ball. 
 
 The number seems exceedingly high, but we shall 
 soon see that it is but an insignificant fraction of the 
 total available electrons present. 
 
 According to the most trustworthy estimates, the 
 total number of atoms contained in a cubic centi- 
 metre of solid copper is about one quadrillion, or 
 1*23 x 10 24 . Now each of our balls having a volume of 
 4-2 x 10- 3 c. cm., would contain (1-23 x 10 24 ) (4-2 x 10~ 3 ) 
 atoms, and double that quantity of detachable elec- 
 trons, or 10,300 trillion. The ratio of detachable 
 electrons to extra electrons is therefore 
 
 10,300 trillion ^ g 
 1,260 million 
 
 Hence if, for every eight billion combined electrons 
 in the copper, we add one extra electron, we obtain 
 the necessary force of repulsion. Since a neutral 
 atom deprived of an electron repels another such 
 atom with the same force as that which exists be- 
 tween two electrons, we may also produce the same 
 
THE ELECTRON AT REST 29 
 
 repulsion by removing from each ball one electron 
 out of every eight billion that are in it ; they then 
 repel each other by virtue of their positive charges. 
 
 On account of the intensity of the forces called 
 into play, it is found practically impossible to remove 
 more than about one-billionth of the detachable elec- 
 trons, or add more than that proportion to those 
 already there. This explains why the charging or 
 discharging of a body produces no perceptible differ- 
 ence in its weight. If, however, by some special 
 contrivance, electrons or positive atoms are continu- 
 ally discharged from a body, the body is gradually 
 disintegrated. This happens to the cathode in a 
 vacuum tube and to the positive carbon in the arc 
 lamp. 
 
 We may now formulate the forces between electrons 
 and positively charged atoms a little more precisely 
 as follows: (a) Every electron placed at a distance 
 of 1 cm. from another electron repels it with a force 
 of 1/16 x 10~ 19 dynes. (6) Every neutral atom from 
 which one electron is removed repels any similar 
 atom placed at a distance of 1 cm. with the same 
 force viz. 1*16 x 10~ 19 dynes. And, on the other 
 hand, (c) every electron attracts every neutral atom 
 from which one electron is removed, when placed at 
 a distance of 1 cm. from it, with the same force 
 viz. 1-16 X 10~ 19 dynes, or if two, three, &c., electrons 
 have been removed, with a force two, three, &c., 
 times that amount, (d) All these forces vary in- 
 
30 THE ELECTRON THEORY 
 
 versely as the square of the distance, unless that 
 distance is so small as to become comparable with 
 the dimensions of the atom (i.e. 10~ 8 cm.). 1 
 
 It follows from the law of attraction that an elec- 
 tron cannot be removed from a neutral atom without 
 a very great force as compared with its mass. The 
 attraction between them is the strongest cohesive 
 force we know, and if it accounts for cohesion to any 
 perceptible extent, the force required will at least be 
 that necessary to rupture the metal or other sub- 
 stance. If the law of attraction holds good down 
 to molecular dimensions, which are of the order of 
 10~ 8 cm., we can calculate the force between an elec- 
 tron and the atom it is being induced to leave. We 
 need only divide the attraction at 1 cm. by the square 
 of the distance, or 10~ 16 . The force then becomes 
 
 116 1 Q-L Q ~ 19 > orl>16xlQ " 3 d y nes - 
 
 This force, acting upon an electron for one second, 
 
 1 According to the electron theory of gravitation (W. Sutherland, 
 Phil. Mag., Dec. 1904), the attraction between opposite charges is 
 greater than the repulsion of similar charges in the ratio of 
 (1 + 10" 43 ) : 1, thus accounting for a very small resultant attraction. 
 In the electron theory the attractions and repulsions are, like 
 gravitational force, independent of the manner in which the inter- 
 vening space is filled up. Matter free from electrons would have 
 no electrical effect whatever, and can be theoretically replaced by 
 pure ether in all electrical problems. The effects hitherto ascribed 
 to the " specific inductive capacity " or dielectric constant of the 
 medium are accounted for by the charges which that medium 
 contains. 
 
THE ELECTRON AT REST 31 
 
 would give it a speed measured by the ratio of 
 the force to the mass, or 
 
 1-16 x lO- 3 , A24 cm. 
 
 0-61x10- ==19xl 4 sec: 
 
 This result shows that any electron coming within 
 the radius of molecular action would be instantly 
 captured and absorbed by a positively charged atom. 
 Since the number of free electrons in the universe 
 is by all accounts strictly equal to the number of 
 positively charged atoms, or, rather, valencies of 
 such atoms, it is difficult to conceive how it is pos- 
 sible for any electrons to have remained free at 
 all. Were they all to become absorbed, as they 
 some day will be most likely, there would be no 
 electric action of any kind, and, we suspect, no 
 chemical action either, and two sciences would 
 become superfluous. 
 
 To understand why we have escaped that fate, we 
 may take an analogy on a very large scale. The 
 force exerted by the sun on the earth is some four 
 trillion tons. Yet the earth does not fall into the 
 sun, on account of the centrifugal force generated by 
 its own velocity. Let us see what velocity would be 
 required to keep the electron from being absorbed 
 by the atom. The force to be counterbalanced is, 
 as we have seen, 1*16 x 10~ 3 dynes. The centrifugal 
 force of a body of mass m describing an orbit of 
 
 radius R with a velocity v is ~ . Substituting for 
 
32 THE ELECTRON THEORY 
 
 m the mass of the electron (0-61 x 10~ 27 gramme), 
 and for R its distance from the centre of the atom 
 (10~ 8 cm.), we get 
 
 which gives v = 1*38 xlO 8 cm. per second. This 
 orbital velocity of the electron, though large, is quite 
 conceivable, inasmuch as it is still less than -^ih 
 the velocity of light (the utmost attainable speed). 
 Knowing the size of the orbit, we can calculate the 
 number of revolutions it makes per second. This is 
 2-2 x 10 15 or 2200 billion. As we shall see below, 
 the revolving electron sends out ether-waves into 
 space with the velocity of light (3 x 10 10 cm. per 
 second). Hence the length of these waves is 
 
 3 X 1Q1< L r 136 x 10- 6 mm. 
 2-2 x 10 16 ' 
 
 This wave-length is about one-third of that of the 
 shortest visible light-waves. The waves emitted by 
 the electron are thus waves of ultra-violet light. 
 Now, by Kepler's law we can easily find what dis- 
 tance between electron and atom would give us any 
 required wave-length. By that law the squares of 
 the periods of revolution are in the same ratio as the 
 cubes of the distances. If, therefore, we make the 
 distance 10~ 7 cm. instead of 10~ 8 , we increase the 
 distance ten times, and the cube of it 1000 times. 
 The wave-length will, therefore, be increased in the 
 
THE ELECTRON AT REST 33 
 
 ratio of VlOOO : *Jl 9 or 31-6 times. This gives for the 
 wave-length of the light emitted by the electron in 
 its new orbit the value 4300 x 10" 6 mm. This light 
 is also invisible, being about six times longer in wave 
 than the most extreme red light of the spectrum. It 
 is " infra-red." An intermediate value of the distance 
 will give visible light. The yellow light of sodium 
 would require a distance of 2-66 x 10~ 8 cm. between 
 the electron and the atom. 
 
 Of course, the electrons in a solid metal have 
 widely varying velocities, and hence they give a 
 continuous spectrum when the average velocity is 
 high enough i.e. when the body is hot enough ; 
 otherwise they radiate heat-waves of great length 
 and small energy, in accordance with the law of 
 exchanges. 
 
 The above considerations show that we must con- 
 ceive a metal to be composed of a mass of metallic 
 atoms pretty closely packed, so that the electrons, in 
 their constant vibration due to a finite temperature, 
 are often and easily exchanged between them. They 
 therefore pass from one atom to another with com- 
 paratively little frictional loss of energy. The metals 
 are called " good conductors of electricity " on account 
 of this property. 
 
 In other bodies, such as glass, ebonite, shellac, 
 quartz, oil, indiarubber, and porcelain, there are only 
 very few electrons sufficiently free to pass from one 
 atom to another. If they surround a metal, they 
 
 c 
 
34 THE ELECTRON THEORY 
 
 prevent the electrons escaping from it even under 
 the influence of a considerable force. Hence they 
 are called " insulators." 
 
 That they do contain their due ratio of electrons 
 to atoms is shown by the strain to which an electric 
 force subjects them, and by the influence they exert 
 upon light which passes through them. 
 
 A vacuum, offering, as it does, no resistance to 
 the motion of an electron, is, in that sense, a perfect 
 conductor ; but not in the accepted electrical sense. 
 To conduct electricity, a body must be able to pro- 
 vide carriers for its connection. These carriers are 
 the electrons and positive atoms, with or without 
 extra matter attached to them. The vacuum, con- 
 taining no such carriers, is a perfect insulator. This 
 conflict of characteristics warns us that our definition 
 of a good conductor is not complete. To conduct 
 electricity well, a body must contain free electric 
 charges, and offer but a slight resistance to their 
 motion in the direction of the electric force. These 
 free electric charges are either single electrons or 
 portions of neutral matter associated with positive or 
 negative charges. A good conductor is one which con- 
 tains a large number of free electric charges (called 
 "ions"), and offers but slight resistance to their 
 motion. The " conductivity " of any material is de- 
 fined, in accordance with the electron theory, as the 
 number of ions in unit of volume multiplied by the 
 steady speed acquired by them under the influence 
 
THE ELECTEON AT REST 35 
 
 of unit electro-motive force. In accordance with 
 this definition, we must declare the ether to be a 
 perfect insulator. 
 
 3. Distribution of Free Charges. We have seen 
 that a metal consists of a vast number of atoms 
 (about one quadrillion per cubic centimetre), and 
 about double that number of electrons. These are 
 in rapid motion, and the ether waves they emit in 
 consequence of that motion constitute their radiant 
 heat. Every body radiates heat, unless it is at the 
 absolute zero of temperature ( 273 C.), and it is 
 enabled to do so by the heat it receives in exchange 
 from its surroundings. 
 
 In an insulator, the electrons are incapable of 
 moving outside the range of the atoms to which they 
 are attached. An electric force displaces them 
 slightly; but when the force is withdrawn, they 
 return more or less rapidly to their former position 
 of equilibrium. 
 
 In a conductor matters are different. The 
 motion of both atoms and electrons is much more 
 violent, and electrons are constantly running free, 
 colliding with atoms and with each other, whirling 
 round atoms, locked up with them, liberated by 
 collision with other electrons or atoms, and starting 
 on the same round over again. * This difference 
 between dielectrics and conductors is not as yet fully 
 explained, but several circumstances shed light upon 
 it. In the first place, conductors are usually heavier 
 
36 THE ELECTRON THEORY 
 
 than dielectrics. Therefore the atoms are heavier or 
 more closely packed, and the electron is claimed by 
 a greater number of neighbouring atoms. Secondly, 
 conductors, mostly metals, have a low specific heat, 
 which means that a comparatively small amount of 
 heat suffices to give them the molecular velocity 
 corresponding to a given temperature. Hence they 
 radiate and absorb heat-waves readily, and the 
 " exchange " above referred to is more lively in 
 conductors than in dielectrics. 
 
 We shall for the present confine our attention to 
 conductors, and more particularly to metals, or to 
 copper as a particularly good conductor. 
 
 In this metal it has been roughly estimated that 
 every electron combines with an atom, and is 
 liberated again about a hundred million times per 
 second. For every 5000 seconds which it spends 
 locked in the embrace of an atom it roams free for 
 one second. It is these roaming electrons which 
 produce all the phenomena of conductivity. We 
 may suppose that they constitute TO Voth of the 
 total number of electrons in the copper; but this 
 number is very uncertain, and must vary with the 
 temperature and the quality of the metal. The roam- 
 ing electrons do not constitute an electric charge, 
 since they are balanced by an equal number of 
 positively charged atoms contained in the conductor. 
 
 What will happen if a mass of free electricity, 
 such as we have contemplated above, but containing 
 
THE ELECTION AT REST 37 
 
 a smaller and more manageable number of electrons, 
 is brought near a lump of metal containing neither 
 an excess nor a deficiency of electrons ? 
 
 Obviously, the free electrons in the lump of metal 
 will be repelled, and will make their way as far as 
 they can in the opposite direction. The charged 
 atoms left behind will be attracted, and will crowd 
 towards the mass of electricity. When equili- 
 brium has been attained, the point of the conductor 
 nearest the store of electrons will be found to be 
 positively charged, and the point farthest away will 
 be found negatively charged, with a more or less 
 gradual transition at intermediate points, according 
 to the shape of the conductor. This is the well- 
 known phenomenon of "charge by influence," dis- 
 covered 150 years ago by Jipinus in St. Petersburg. 
 
 To keep in touch with reality, it will be well to 
 obtain some quantitative idea of this charge, and to 
 do so we must deal with a larger quantity of elec- 
 tricity than that of a single electron. The most 
 natural procedure would be to make our unit consist 
 of a certain large number of electrons, say a multiple 
 of ten. But this is barred by the uncertainty which 
 still surrounds the precise charge of the electron. 
 J. J. Thomson's latest estimate is 34 x 10~ 10 " electro- 
 static units," and this is the value we have assumed 
 throughout our calculations. But in practical 
 measurements the unit is defined as that quantity 
 which, when placed in a vacuum at a distance of 
 
38 THE ELECTRON THEORY 
 
 1 cm. from an equal quantity of the same sign, 
 repels it with a force of 1 dyne ( = | T gramme). 
 
 Now since one electron or positive atom repels 
 another at 1 cm. with a force of 1-16 X 10" 19 dynes, 1 
 and the force varies with both masses, the repulsive 
 force of 1 dyne would be produced by 2*93 xlO 9 
 electrons, or 2930 million. 
 
 This quantity of 2930 million electrons (more 
 or less) is what is called the ''electrostatic unity 
 of quantity," being derived from measurements of 
 electrostatic force. For the purposes of this work, in 
 which the reader is to be constantly reminded that 
 electricity has an atomic structure, we shall prefer to 
 call the 2930 million electrons (the equivalent of 
 one "electrostatic unit" of negative electricity) a 
 " company " of electrons, and the same number of 
 charged atoms (or any other objects) a "company" 
 of such atoms or objects. The number 2930 million 
 is for the present assumed to be correct, but it may 
 have to be slightly modified in course of time. 
 
 We may now re-state our laws of repulsion as 
 follows : 
 
 (a) One company of electrons repels another 
 company placed at 1 cm. from it with a force of 
 1 dyne. 
 
 (6) One company of neutral atoms deprived of one 
 
 1 The dyne is the force which, acting for one second on a mass of 
 one gramme, produces in it a speed of 1 cm. per second. It is the 
 981st part of a gramme. 
 
THE ELECTRON AT REST 39 
 
 electron each repels another such company at 1 cm. 
 with a force of 1 dyne. 
 
 (c) One company of electrons attracts a company 
 of neutral atoms deprived of one electron each with 
 the force of 1 dyne. 
 
 (d) These forces vary inversely as the square of 
 the distance (the distance being large as compared 
 with that between the individual electrons or 
 atoms). 
 
 4. Energy of Position : Potential. When motion 
 takes place in spite of a resistance, work is being 
 done. When the motion is steady the force produc- 
 ing it is equal to the force resisting it, and the work 
 is measured by the distance covered. If the resist- 
 ance encountered between two points is due to con- 
 tact with intervening matter, the amount of work 
 done in passing from one point to another depends 
 upon the path. Thus, in driving from one town to 
 another, the work is less over a good road than a bad 
 one. If, however, one road is twice as good as 
 another and also twice as long, the total work is the 
 same. The badness of a road is measured by the 
 resistance it offers to the vehicle, and the work is 
 measured by the product of the distance and resist- 
 ance, so that if the work along two routes is the 
 same, the length of each route must be inversely as 
 its " badness " (resistance). 
 
 When the resistance is due, not to intervening 
 matter, but to the repulsion of a distant body, the 
 
4O THE ELECTRON THEORY 
 
 work done simply depends upon the distance from 
 that body, and is quite independent of the path 
 traversed. Ignorance of this fact has inspired most 
 of the unsuccessful seekers after perpetual motion. 
 
 If the repelling distant body is a point or very 
 small sphere, and a series of concentric spheres are 
 constructed round it, work has to be done on the 
 repelled body to make it pass from one sphere to the 
 next ; but no work is required to move it along the 
 surface of any given sphere, since all points on that 
 surface are at the same distance from the repellent 
 body. In passing from one sphere to the next inner 
 one, a certain amount of work must be done. When 
 the repelled body returns to its first sphere, that 
 work is given up again, and can be used to overcome 
 some other resistance. A body thus capable of per- 
 forming work owing to its position, is said to possess 
 " potential energy," in other words, a potentiality 
 of work. Clearly, the potential energy will be the 
 greater the nearer the body is to the repellent body. 
 But how can the actual amount of the total potential 
 energy be measured? The problem presents one 
 obvious difficulty the repulsive force extends into 
 infinite space, so that the potential energy would 
 appear to be infinite; that is to say, the repelled 
 body can be made to do work to an infinite extent, 
 for however great the distance to which it may have 
 been repelled, there is still some remainder of 
 repulsion ready to act upon it and make it work. 
 
THE ELECTRON AT REST 41 
 
 This argument, though plausible, is vitiated by 
 the fact that the sum of an infinite number of 
 infinitesimal quantities is not infinite, but limited. 
 That this must be so may be illustrated by a few 
 familiar examples. One of them is the old Greek 
 dilemma about Achilles and the tortoise. A tortoise 
 is a mile ahead of Achilles, who starts in pursuit. 
 Achilles runs 100 times as fast as the tortoise, so 
 that when he has run the mile, the tortoise is T ^j- 
 mile ahead. When Achilles runs that distance, the 
 tortoise is I0 ooo mile ahead, and so on. So that 
 Achilles will always get nearer the tortoise, but 
 never quite up to it. The solution is that the sum 
 of these quantities 
 
 1 + loo + 10,000 + 1,000,000' &c< 
 
 is a finite number, as is evident when written as a 
 decimal fraction 
 
 1-0101010101 
 
 a number which is certainly smaller than 1*0102, 
 and is exactly equal to - 1 //-. The tortoise will 
 therefore have gone exactly ^ of a mile when 
 Achilles overtakes it. 
 
 Another example is this. If you stand on a 
 bridge over two parallel lines of railway, the rails 
 seem to meet on the horizon. If you stand over one 
 line, the rails, if running straight along an infinite 
 plane, will meet in a point on a level with your eyes. 
 
THE ELECTRON THEORY 
 
 If a train is travelling out along the other line of 
 rails, it will approach the first line as the distance 
 increases. It can never cross it, as the rails are all 
 supposed to be parallel. If the train, therefore, 
 moves on for infinite time it will always be 
 approaching that point on the horizon, but never 
 reaching it. We see, then, that infinities and 
 infinitesimals may often be combined into finite 
 quantities subject to ordinary arithmetic. This may 
 encourage us to tackle the problem of the total 
 potential energy of a repelled body. 
 
 For this purpose we will surround the repelling 
 body E with a series of concentric spheres (Fig. 3). 
 
 The surfaces of these 
 spheres are called 
 " equipotential sur- 
 faces," since the re- 
 pelled body has the 
 same potential energy 
 while it remains in 
 the same surface. We 
 will not draw these 
 spheres at random, but 
 make their successive 
 diameters so that the same amount of work is done 
 in passing from any sphere to the next. Since the 
 force of repulsion varies inversely as the square of 
 the radius, the distance between two successive 
 spheres must vary directly as the square of their 
 
 FIG. 3. 
 
THE ELECTRON AT BEST 
 
 43 
 
 mean radius. At twice the distance, therefore, the 
 equipotential surfaces will be four times as far apart. 
 
 Now place a small negatively electrified body, say, 
 a "company" (1 E.S. unit) of electrons, at E and 
 another at a point P. The problem is to find its 
 total potential energy at P i.e. the work that has 
 been done on it to bring it up to P from an infinite 
 distance, or the work that it is capable of doing in 
 retiring to an infinite distance. 
 
 To simplify matters, describe a special sphere 
 passing through P, and others with radii twice, 
 four times, eight times, &c., as large, passing through 
 Q, R, S, &c. (Fig. 4). In passing from P to Q, the 
 company cuts a cer- 
 tain number of equi- 
 potential surfaces, and 
 this number measures 
 the work done upon it. 
 Let this work be de- 
 noted by W. In pass- 
 ing from Q to R, its 
 experience will be pre- 
 cisely similar, except 
 that, the distance be- 
 tween successive surfaces being four times what 
 it was before, the rate of work will be one- 
 fourth. Since, however, the distance traversed 
 is twice as great, the actual work done between 
 Q and R will be one-half that done between 
 
 FIG. 4. 
 
44 THE ELECTBON THEORY 
 
 P and Q. In the next compartment, the work 
 W 
 4 
 
 will be -j- instead of -5-, and the next again it will 
 
 be J. 
 
 Extending this to infinity, the total work done 
 ( = the total potential energy) is 
 
 W W W W 
 
 Now, as every one can easily try for himself, the 
 sum of 
 
 to infinity, is just = 2. 
 
 Hence the total work is 2W. This is the 
 potential energy of the company when at P. The 
 potential energy at Q will be 
 
 2W-W=W. 
 At R it is 
 
 At S it is 
 
 In other words, the potential energies at P, Q, R, S 
 are as 
 
 or 
 
THE ELECTRON AT REST 45 
 
 Since the distances are as 
 
 1:2:4:8, 
 
 we find that the potential energy at a point is 
 inversely as the distance of the point from the centre 
 of the repellent body. 
 
 To obtain the actual value of the energy in foot- 
 pounds or other units of work, we need only deter- 
 mine the work done between P and Q and double 
 the amount. If the force at P is 1 dyne, the force at 
 Q must be \ dyne. If the distance between P and 
 Q is 1 crn., the work must lie between 
 
 1 cm. x 1 dyne and 1 cm. x J dyne. 
 
 The work of overcoming or exerting a force of 
 1 dyne through 1 cm. is called "1 erg": hence the 
 work between P and Q is somewhere between 1 erg 
 and erg. By constructing a large number of equi- 
 potential surfaces between P and Q by the rule given 
 above and counting them, we find that the actual 
 work is just J erg. Hence the total potential energy 
 equal 2 x \ erg = 1 erg. 
 
 Since E P = 1 cm., and the force at P is 1 dyne, E 
 must be, by definition, just one company of electrons. 
 
 Hence we have obtained the following important 
 and fundamental result : The total work required to 
 bring up one electrostatic unit (one "company") 
 from infinity to within 1 cm. of another similar and 
 equal unit is 1 erg, and if the distance varies, the 
 total work varies inversely as the distance. 
 
46 THE ELECTRON THEORY 
 
 If we increase the repellent body, the work varies 
 as the quantity of electricity, since the effects of 
 two " companies " would be simply added up. But 
 if we double both the repelling and the repelled body, 
 the work is quadrupled. If we keep the repelled 
 body always equal to one unit or company of 
 electrons, we obtain a convenient measure for the 
 potential energy which the repelling body is capable 
 of imparting. The work performed upon one com- 
 pany or unit in bringing it up from infinity to a 
 point P against the repulsive force exercised by E is 
 called the potential function, or shortly the potential 
 at P due to E. The following theorems are imme- 
 diately evident : 
 
 (a) All points in an equipotential surface are at 
 the same potential. 
 
 (6) A charge will always tend to move from a 
 point of higher to a point of lower potential. 
 
 (c) The force at any point is proportional to the 
 rate of change of potential along the line of force 
 i.e. to the crowding together of the equipotential 
 surfaces. 
 
 (d) All points on the surface of a conductor are at 
 the same potential. For if they were not, electricity 
 would travel from the higher to the lower potentials 
 until they were levelled up. 
 
 We have supposed the repellent body E to be a 
 very small sphere. But it may be a sphere of con- 
 siderable size without disturbing our calculations, so 
 
THE ELECTRON AT REST 47 
 
 long as the electrons or positive atoms are uniformly 
 distributed over the surface. For then they act 
 outwardly as if they were all concentrated at the 
 centre. We can, therefore, find the potential at the 
 
 n 
 
 very surface of the sphere. It is -p, where E is the 
 
 number of units or " companies," and R the radius 
 in centimetres. That being so, we can calculate the 
 total work required to form the repellent body. Let 
 us build it up unit by unit. To bring the first two 
 companies within R centimetres of each other re- 
 
 quired g dynes. The next unit took double the 
 
 o t -p _ -i 
 
 work, or ^ dynes, the last unit required -^- dynes. 
 
 We get at the sum of these terms by taking the 
 average of the charges during formation. This 
 average is 
 
 E 
 
 The average potential during formation was, there- 
 
 TT 
 fore, 5, and since the total number of units to be 
 
 Z Lx 
 
 brought to that potential was E, the total energy 
 consumed in the process was 
 
 E _E 
 
 p 
 Or, if V is the final potential ^, the total energy 
 
 consumed is E V, 
 
48 THE ELECTRON THEORY 
 
 To return to our gramme of pure electricity 
 (p. 24), which we found to produce such alarm- 
 ing results even at the distance of the sun, 
 we can now calculate the energy required to 
 make it. 
 
 The gramme, as we have seen, consists of half 
 a trillion (5-6 xlO 17 ) companies. This is E. We 
 will suppose these concentrated on a sphere 1 cm. in 
 radius, so that R = l. Then the energy required to 
 build it up is 
 
 ,E 2 .(5'6xl0 17 ) 2 
 
 K ergs = y - j L = 16 x 10 34 ergs, 
 
 or a billion horse-power working for 680,000 years. 
 The same energy would, of course, be required to 
 build up the same number of charged atoms ; but if 
 only 1 gramme of charged atoms is to be built up, 
 the number of companies will be less in proportion 
 to the weight of the atom. Now the atoms are from 
 1000 to 200,000 times heavier than an electron, and 
 the number of companies per gramme 1000 to 
 200,000 times less. Hence the energy required to 
 build up a gramme of positively electrified matter 
 ranges from 16 x 10 28 ergs to 4 x 10 24 ergs, still an 
 enormous amount. 
 
 Since the potential due to a small charged body at 
 a point outside it is simply measured by its charge 
 divided by the distance of the point from its centre, 
 the potential energy, or simply potential of any other 
 charged body placed at that point, will be the product 
 
THE ELECTRON AT REST 49 
 
 of its charge by the potential at that point. If the 
 charge on the first body is E x , and on the second 
 body E 2 , and their distance R, the potential is 
 
 E E 
 
 ^~ 2 This potential is mutual, as it only depends 
 
 upon their relative position, and it does not matter 
 whether E x has been brought up to E 2 or vice versd. 
 
 If there are several bodies conferring a potential, 
 the total potential is got by simply adding up the 
 separate potentials, remembering, however, that if 
 the force is attractive instead of repulsive, the 
 
 potential is negative. The charges will have opposite 
 
 pi ., -pi 
 
 signs, say E x and E 2 , and the result * ^ 2 
 
 is a negative potential i.e. work is gained instead 
 of spent in bringing the charges together. 
 
 It follows that if the two charges E x and E 2 
 
 are equal, the total potential at any point equidistant 
 
 pi 
 from them is zero, being in one case -^ and in the 
 
 THl 
 
 other jj. Now all the points equidistant from 
 
 two other points are contained in a plane surface 
 normal to the line joining them, and bisecting that 
 line (Fig. 5), it will be noticed that we have here a 
 well-known case of optics. If E t is a luminous 
 point and AB a reflecting surface, JE 2 will be the 
 " image " of E r We might have any other such 
 points on the side of E^ and if we had equal and 
 
 opposite charges at the same distance on the other 
 
 D 
 
SO THE ELECTRON THEORY 
 
 side, the surface AB would still be an equipotential 
 surface at zero potential. Conversely, if the charges 
 on the other side were taken away, and the surface 
 were kept at zero potential throughout (as a metal 
 plate could be kept at zero potential by connecting 
 A it to earth), opposite charges 
 
 would have to be distributed over 
 the surface, so as to make up for 
 the charges taken away, and keep 
 Ea the force at every point above the 
 ~g surface the same as before. This 
 
 consideration enables one to 
 calculate the distribution of the 
 electric charge by "influence." 
 The method is a very fruitful 
 IG * ' and valuable one. It is called 
 
 the " method of electric images." 
 
 Since the surface AB is an equipotential surface, 
 no work is required to move a body along it. If 
 the distance between E x and E 2 is 2 R, the distance 
 of the plane from E x is R. Now the work required 
 to bring a company of electrons from infinity to 
 
 E 
 
 within R cm. of the charge E x was ^- while E x was 
 
 alone in space. This amount has become zero at one 
 point, owing to the presence of E 2 . This shows that 
 the potential due to one charge may be counter- 
 balanced and annulled by the potential due to 
 another. Hence, though the potential due to each 
 
THE ELECTRON AT REST 51 
 
 body by itself remains precisely the same always, the 
 net potential at any given point depends upon every 
 free charge in the whole of space, and can therefore 
 acquire any value we please. If the point in question 
 happens to be on the surface of a charged conducting 
 sphere, it follows that the " potential of that sphere " 
 is equally subject to the influence of surrounding 
 charges, being lowered by any free charge of the 
 opposite sign. In order to restore its potential to 
 the former high figure we must increase the charge 
 on it. If the potential has been halved, we must 
 double the charge, in order to restore the potential. 
 If the potential is very low, the conductor can carry 
 a great charge ; it has, so to speak, a great carrying 
 capacity. This conception of capacity is a very 
 important one, so we must define it more precisely : 
 " The capacity of a conductor is the charge required 
 to raise it to unit potential." 
 
 A sphere of radius 1 cm. has unit potential (1 dyne 
 per unit charge repelled) when it contains unit 
 charge (1 "company"). If its radius is 2 cm. its 
 potential is J, and to bring it to the same potential 
 its charge must be made 2 companies; if 3 cm., 
 3 companies, and so on. Hence we have the general 
 rule : The capacity of a sphere is proportional to its 
 radius. 
 
 If the charged sphere has an elastic surface, the 
 mutual repulsion of the charges will tend to bring 
 about an extension of the surface. This may be 
 
52 THE ELECTRON THEORY 
 
 proved by blowing a soap-bubble, and then charg- 
 ing it. The bubble expands, and its capacity 
 increases. 
 
 When two oppositely charged conductors approach 
 each other, the potential of each is lowered and the 
 capacity increased. Here again the spontaneous 
 motion leads to an increase of capacity. 
 
 When two similarly charged bodies repel each 
 other and move apart, their potential is lowered, 
 and, again, their capacity increased. 
 
 This is a general rule; If charged conductors 
 are free to move, they always move so as to make 
 their potential a minimum, and their capacity a 
 maximum. 
 
 The motion thus engendered leads, of course, to 
 a diminution of potential energy. By the law of 
 the conservation of energy, there can be no loss 
 of total energy, so what is lost in potential energy 
 is gained in energy of motion or kinetic energy. We 
 shall have to consider this kinetic energy later on 
 when dealing with the electron in motion. 
 
 5. Condensers. We have learnt that when a 
 positively charged conductor is brought near a 
 negatively charged one, the capacity of each con- 
 ductor is increased. 
 
 To simplify matters, consider an infinite plane 
 conducting surface, AB (Fig. 6), and a point, P, 
 outside it. Let the electrons be uniformly dis- 
 tributed over the surface out into infinite space, 
 
THE ELECTRON AT REST 
 
 and let P contain one company of electrons; then 
 we can prove that the repulsion between the plane 
 and P is independent of the distance of P from the 
 plane, as follows : 
 
 Draw PD, PE, two lines equally inclined to the 
 plane. Draw similar lines all round P, so as to 
 make a cone with P for 
 its apex. The base of the 
 cone will be a circle in the 
 plane surface AB, and all 
 the electrons in that circle 
 will repel P. Let their 
 total repulsion be 1000 
 dynes. Now remove P to 
 twice the distance, keeping 
 the angles between the 
 lines and the plane the 
 same as before. The lines 
 forming the sides of the 
 cone will be double their 
 previous length, and the 
 base four times its previous area. There will there- 
 fore be four times the number of electrons to exert 
 their repulsive force; but since their distance is 
 twice what it was, we must divide the force by 4 
 (the square of the distance), and the net force will 
 be the same as before. The argument will hold good 
 whatever the size of the angle at the apex, and hence 
 we may make it so large, and the cone so flat, that 
 
 B 
 
 FIG. 6. 
 
54 
 
 THE ELECTRON THEORY 
 
 the repulsion of the electrons outside the cone is 
 practically imperceptible. 1 
 
 Having thus seen that the repulsion is the same 
 at any distance, let us calculate its amount. Let 
 the point P be 100 cm. from the plane, and let 
 the plane contain 1000 companies on every sq. cm. 
 Then the repulsion between the nearest square cm., 
 ab, of the plane will be (p. 38) 
 
 1x1000 
 
 1002 
 
 = T L dyne. 
 
 Now describe round P a sphere which just touches 
 the plane. Take another square cm. in the surface, 
 say, cd. Then, if there were 1000 
 companies on cd they would repel 
 P with the same force as before 
 viz. 01 dyne. But this force 
 would not be so effective as before, 
 since it is inclined to the vertical. 
 Now produce PC and fd to Pc 1 and 
 Pd\ and let Pc 1 be = 2 PC. Then if 
 the imaginary surface c l d l had the 
 same surface density as cd its force 
 on P would be the same, since its 
 charge would be four times and its 
 distance doubled. In producing T*d l to Pe 1 , and 
 completing the intersections with the plane, we mark 
 
 1 We must add that for the above reasoning to hold good the 
 density of the electrons on the surface must be very great ; other- 
 wise the redistribution of the electrons, owing to the repulsion of 
 
 FIG. 7. 
 
THE ELECTRON AT REST 55 
 
 out a new surface, c l e l t whose size is the greater the 
 more Pc 1 slants to the surface. This slant compen- 
 sates the slant of the push of the repelling electrons 
 on c l e l , and we find that their force is O'l dyne also, 
 as before. The same argument would hold good for 
 any square cm. we choose to cut out of the hemi- 
 sphere turned towards the plane. Hence the total 
 push is as many times O'l dyne as there are square 
 centimetres on the surface of the hemisphere, viz. 
 
 2ira (radius)*, 
 or, since the radius is 100 cm., the total force is 
 
 27T x O'l x 1002 dynes 
 = 27rxlOOO dynes, 
 
 or 2?r times (6*2832 times) the number of companies 
 on each square cm. of the plane. 
 
 The companies or units per square cm. are called 
 the " surface density of electricity," and are denoted 
 by a. Hence we have 
 
 Force on 1 unit = 27ro- 
 
 at any distance from an infinite charged plane on 
 either side. 
 
 In passing through the plane only the direction 
 of the force changes, and not its amount. 
 
 P, would produce the same effect as a charge of a company of 
 positive atoms placed at the " image " of P in the plane. This 
 image would attract P, and so lessen the repulsion. If, however, 
 the surface density is great, this attraction may be left out of 
 account, as it has no perceptible influence. 
 
56 THE ELECTRON THEORY 
 
 Now let there be two infinite parallel conducting 
 planes at a distance, D, from each other (Fig. 8), 
 and let them have equal surface densities of opposite 
 sign, so that if AB contains, say, 1000 companies of 
 electrons per square centimetre, A 1 !? 1 contains 1000 
 companies of positively charged atoms per 
 square centimetre. 
 
 Then we can prove that there is no 
 electric force in the field except in the 
 space between the two planes. At a point 
 P 1 , for instance, the force due to AB is 
 27ra-, and the force due to A^ 1 is 27r<7, 
 p 1 and the sum of the two forces is zero. In 
 other words, the positive charge on A. 1 W 
 "neutralises" the negative charge on AB 
 for all infinite space outside the two 
 
 Q D | 
 
 surfaces. 
 
 FIG. 8. What is the difference of potential be- 
 tween AB and A^ 1 ? In other words, what work 
 will have to be spent on a company of electrons to 
 bring it from A*Bi to AB ? 
 
 It will obviously be the product of the force into D. 
 
 Now the force on a company of electrons is a 
 repulsion by AB amounting to 27rcr, and an attrac- 
 tion by A. l E l to the same amount. These two forces 
 being in the same direction, they add up, and the 
 total force at any point between the planes is 4?rcr. 
 Hence the work on one company is 47ro-D, and that 
 is the difference of potential between AB and AB 1 . 
 
THE ELECTRON AT REST 57 
 
 A system like the above, consisting of two con- 
 ductors separated by a non-conductor, is called a 
 " condenser." The most familiar example of a 
 condenser is the Leyden jar (Fig. 9), in which 
 the conductors are made of tinfoil stuck on 1 
 the outside and inside of a glass jar, and the 
 non-conductor is the glass. (H; 
 
 The capacity of a condenser is measured 
 by the charge which must be imparted to 
 either conductor to make the difference of 
 
 potential between them one unit, so that one 
 erg of work must be spent to take a company of 
 electrons from one conductor to another. Since the 
 difference of potential between the two planes is 
 
 and this is = 1, we have 
 
 for the capacity per unit area of the condenser 
 consisting of two infinite planes. This increases 
 inversely as D, so that if we make D small enough, 
 and the plates close together, we can get a condenser 
 of any capacity we please. 
 
 The advantage of condensers of large capacity is 
 that we can store up great charges in them with 
 little work, and with little tendency to wasteful 
 discharge, as there is no force outside the coatings. 
 Hence the name " condenser." 
 
58 THE ELECTRON THEORY 
 
 If, however, the plates are connected by a wire 
 or other conductor, the mutual repulsion of the 
 electrons towards each other and the positive atoms 
 towards each other will force both into the wire, 
 where they will meet, and electrons will be absorbed 
 by the positive atoms to form neutral atoms. Their 
 potential energy will be liberated and pass first into 
 the form of motion, and then into heat. If the wire 
 is interrupted by a short gap of air, this discharge 
 will break through the air and produce a spark 
 the well-known spark from the knob of a Leyden 
 jar. 
 
 The condenser consisting of two infinite planes 
 is, of course, incapable of practical realisation, and 
 is only introduced for theoretical purposes. It 
 enables us, however, to pass to practical construc- 
 tions without sacrificing our results of calculation. 
 If the plates were, say, 1 metre square each, the 
 capacity of the condenser would be 
 
 100 2 
 
 approximately; but the distribution of the charges 
 over the plates would not be uniform, as they would 
 be crowded towards the edges. On the other hand, 
 the charges on the central portions would be practi- 
 cally uniform, and if we could separate out a single 
 square centimetre at the centre of each plate, we 
 should approach very closely to the theoretical per- 
 fection of our infinite planes, and could safely apply 
 
THE ELECTRON AT REST 59 
 
 our formulae. If we make a clean cut round the 
 small area, but connect it by a fine wire with the 
 larger area, so as to keep it at the same potential 
 as the larger area, we may regard the two small 
 areas as forming an ideal parallel-plate condenser 
 amenable to calculation. 
 
 Thus, if their areas are 1 sq. cm., and their 
 charges 1000 companies, and they are 1 mm. apart, 
 the capacity of the small condenser is 
 
 _! ___ _ _ =0-795. 
 47rx 0-1 "12-6x0-1 
 
 The charge being 1000 companies, the difference 
 of potential is 
 
 1000 
 <F795 =1260 
 
 so that it will require 1260 ergs of work to bring 
 a company of electrons from the positive to the 
 negative surface. 
 
 The attraction between the two areas is 
 
 1000x1000 
 
 = 100 million dynes, 
 
 or nearly 100 times the pressure of the atmosphere 
 upon them. If the distance were 1 cm., the attrac- 
 tion would just about balance the atmospheric pres- 
 sure, so that if there were a vacuum outside both 
 planes, the atmospheric pressure* between them 
 would not push them apart. 
 
 If we attached a spring to one of the small 
 plates, and stretched the spring till it pulled the 
 
60 THE ELECTRON THEORY 
 
 small plate back into line with the larger plate, 
 we should find that the force on the spring would 
 have to be 102 kilogrammes, or 221 Ib. If the 
 charge on each plate were double, the force would 
 be quadrupled, and would become 884 Ib. Con- 
 versely, if we know the force, we can calculate the 
 number of companies on each surface. 
 
 The rule is : " Multiply the distance between the 
 plates by the square root of the force in dynes." 
 The result is the number of companies on each 
 plate. If the force is measured in grammes, divide 
 by 981 to convert it into dynes. 
 
 The number of companies per unit area is found 
 by dividing the number found by the area of the 
 plate (in the above case, by -1). The above prin- 
 ciple is the principle on which the most accurate 
 measurements of electric quantity are made. An 
 instrument, called the Attracted-Disc Electrometer, 
 has been constructed by Lord Kelvin for the pur- 
 pose. The inventor calls the larger surrounding 
 surface the "guard-ring." 
 
 But a more widely used instrument is the Quad- 
 rant Electrometer, in which a charged flat needle 
 moves in four quadrants of a circle, two of which 
 are kept at the potential to be measured. The 
 calculation of the working of this instrument is 
 more complicated. 
 
 If two parallel planes are bent up into two con- 
 centric spheres, it is evident that there will be 
 
THE ELECTRON AT REST 6 1 
 
 nothing to disturb the even distribution of their 
 charges, and their capacity per unit area will be 
 
 j-g as before. Hence, if their average radius is r, 
 
 and D is small, the surface of both spheres will be 
 very nearly 4?rr 2 , and their total capacity will be 
 
 so that, in order to store a large amount of electricity, 
 we must make both spheres large, and their radii 
 nearly equal. If a- is the surface density, the force 
 between the surfaces will be 4m<r per unit area, as 
 in the case of the infinite planes. Now this force 
 is equal to that due to the inner sphere alone. For 
 the total charge on the inner sphere is a x surface = 
 <r x 4?rr 2 . This acts outwardly as if concentrated at 
 the centre, so its force at a distance r is 
 
 47TOT 2 
 
 -3 =47TO-. 
 
 Hence the charge on the outer sphere exerts no 
 force inside it. The electrons on each element of 
 its surface exert their forces just as usual, in accord- 
 ance with the inverse-square law; but for every 
 group on one side there is another group, more 
 distant but correspondingly larger, on the opposite 
 side of the same surface, which* counterbalances 
 its force. By an argument similar to that used 
 in the case of an infinite plane, we can extend this 
 rule to charged conductors of any shape, and for- 
 
62 
 
 THE ELECTRON THEORY 
 
 B 
 
 mulate the general rule : " The distribution of 
 charges on a closed conducting surface is always 
 such that the field of force resulting from its own 
 charges, or from forces outside it, is zero at any 
 point within the enclosure." 
 
 A conducting enclosure, even a close-meshed wire 
 cage, acts, therefore, as a perfect screen against 
 external electric forces. Such a cage is often used 
 to protect delicate measuring instruments against 
 disturbance from outside. The enclosure can be 
 charged so highly that sparks and brush discharges 
 burst forth at every corner; but the most delicate 
 indicator will fail to discover the slightest effect 
 inside. Any charge that is to exert 
 an effect must be brought inside the 
 enclosure. 
 
 6. Specific Inductive Capacity. 
 Let us return to the two infinite 
 planes, and study the effect of intro- 
 ducing between them a conducting 
 plate, RS, filling up half the space 
 between them (Fig. 10). In a con- 
 ducting substance there are always a 
 large number of electrons and posi- 
 tive atoms ready to obey electric 
 forces. The electrons will crowd to- 
 wards S, and the positive atoms towards R, until 
 the electric force inside the plate has become zero. 
 To bring this about, the surface density on R must 
 
 FIG. 10. 
 
THE ELECTRON AT REST 63 
 
 be equal and opposite to that on AA 1 , and the 
 surface density on S equal and opposite to that 
 on BB 1 . This gives us, then, practically two con- 
 densers, connected in what is called the " cascade " 
 arrangement, the potentials falling like the levels 
 in two successive waterfalls. 
 
 What difference will this make in the work re- 
 quired to take a company of electrons from BB 1 to 
 AA 1 ? The force from S to R is zero. The force 
 from BB 1 to S and from R to AA 1 is the same as 
 before, being due to the same surface density, and, 
 as we have seen, independent of the distance. But 
 the distance over which the company will struggle 
 against this force has been halved by interposing 
 
 the conductor of thickness -~. Hence the work is 
 
 4) 
 
 halved, and, therefore, also the difference of potential, 
 and the capacity doubled. The same effect would 
 
 be produced by simply reducing the distance D to -=> 
 
 without introducing the plate. 
 
 We see, therefore, that a conductor introduced 
 between two coatings of a condenser increases its 
 capacity. If, instead of a plate, a multitude of 
 small conductors were introduced, their effect would 
 depend upon their density and size, but it would 
 have the effect of increasing the capacity of the 
 condenser. 
 
 The quality whereby a substance introduced be- 
 tween the coatings of a condenser increases its 
 
64 THE ELECTRON THEORY 
 
 capacity is called the inductive capacity of the 
 substance, and its specific inductive capacity is 
 measured by the ratio by which the capacity of 
 the condenser is increased on substituting the 
 substance for air between the coatings. 
 
 The specific inductive capacity of a medium, 
 discovered and named by Faraday, is now usually 
 called its dielectric constant. 
 
 Here are a few values : Glass, 3 to 7 ; ebonite, 
 2 to 3*5 ; mica, 7 to 10 ; petroleum, 2 ; alcohol, 25 ; 
 ice, 78 ; metals, infinite. Condensers are now 
 usually made of mica, on account of its high 
 dielectric constant. 
 
 The specific inductive capacity of a medium is due 
 to the number of electrons it contains, and to the 
 extent to which these electrons are displaced out 
 of their normal positions under the influence of an 
 external electric force. In many media, notably 
 guttapercha, this displacement takes some time 
 to disappear after discharge, while in mica there is 
 very little of this remanent electrification. 
 
 The electron theory is as yet unable to state what 
 is the configuration or mobility of electrons which 
 produce the various inductive capacities of media. 
 It is known, however, from Maxwell's electromagnetic 
 theory of light, that the dielectric constant is pro- 
 portional to the square of the time required by long 
 waves of electric force to traverse the medium. 
 
 If two charges are separated, not by a vacuum, nor 
 
THE ELECTRON AT REST 65 
 
 by air (whose dielectric constant is very little higher 
 than that of a vacuum), but by a medium of dielectric 
 
 constant, K, the force between them will be, not 
 
 but -j^ 2 . This should be remembered when the 
 
 charged bodies are immersed in a medium other 
 than air. In the same way, the potential of a 
 
 TTjl 
 
 charged sphere of radius, R, becomes , and its 
 
 energy is reduced K times. 
 
 7. Electrostatic Machines. An electrostatic ma- 
 chine is a machine used for the mechanical separa- 
 tion of electrons from positive atoms. The earliest 
 machine of the kind consisted of a piece of amber 
 and a woollen cloth wherewith to rub it. This 
 was improved upon by Otto von Guericke in 1663, 
 who made a machine of a sphere of sulphur, 
 which was rotated on its axis while the hand rubbed 
 against it. The sulphur withdrew electrons from 
 the hand, and thus became negatively electrified. 
 
 This process is termed " electrification by friction/* 
 and was, for centuries, the only known way of pro- 
 ducing an electric charge. A glass rod rubbed with 
 silk is the most usual frictional apparatus for ex- 
 periments on a small scale. In this case, the silk 
 withdraws electrons from the glass, leaving the latter 
 " positively " charged. 
 
 The process whereby bodies become electrified by 
 friction is still very obscure. It is known that it 
 
66 THE ELECTRON THEORY 
 
 depends largely upon the condition of the surface, 
 and the chemical nature and structure of the bodies. 
 
 Of commonly known bodies, a catskin gives up 
 electrons most easily, and sulphur absorbs them most 
 easily, so that a machine made of those two sub- 
 stances is very effective. 
 
 We may suppose that there are at the surface of 
 every uncharged body a number of electrons ready 
 to part company with the positive atoms to which 
 they are attached. A catskin would be particularly 
 rich in those loose electrons, and sulphur particularly 
 poor. The effect of rubbing the two together is to 
 give the loose electrons an opportunity to pass from 
 the skin to the sulphur, where they are more strongly 
 held. Once we have a charged body, it is easy to 
 obtain other charged bodies by influence. We have 
 seen above (p. 37) that if a conductor is brought 
 near a negatively charged body say, a block of 
 rubbed sulphur the free electrons are pushed to the 
 end farthest from the sulphur and the positive atoms 
 are attracted towards it. If we break the conductor 
 in two, and take away the sulphur, we obtain 
 a negatively charged conductor and a positively 
 charged conductor. Or, instead of breaking the 
 conductor in two, we may make it up of two con- 
 ductors in metallic contact, and separate them while 
 still in the vicinity of the sulphur. Or we may let 
 the repelled electrons pass into the earth, and then 
 break the connection and obtain a positively charged 
 
THE ELECTRON AT REST 67 
 
 conductor only, and this process may be repeated 
 indefinitely, so that we can manufacture any number 
 of positive atoms from a single charge of electrons, 
 though not without setting free an equal number 
 of electrons. 
 
 The earliest electrostatic machines separated 
 electrons and positive atoms by friction, and then 
 used their mutual attraction for storing them in 
 condensers. This storage is closely akin to the 
 storage of water in vessels, cisterns, and reservoirs, 
 where it is held by the attraction of the earth. 
 Only the substances used are adapted to very 
 different requirements. For water, air is pervious 
 and metal impervious. Hence the water is sur- 
 rounded by metal or other solids on the side nearest 
 the earth. For electricity, on the other hand, air is 
 impervious and metal pervious. Hence the charged 
 metal must be " insulated " by means of some non- 
 conductor. 
 
 The more modern machines work by influence, and 
 are more efficient, but their efficiency is still far from 
 perfect. The ideal electrostatic machine is one in 
 which electrons can be separated from positive atoms 
 with an expenditure of work which can be entirely 
 recovered on allowing the two electricities to re- 
 combine. 
 
 A limit is set to the amount of electricity separated 
 and stored in condensers by the " dielectric strength " 
 of the medium. When the air or other dielectric 
 
68 THE ELECTRON THEORY 
 
 between the coatings of a condenser is subject to a 
 certain limiting stress, an electron breaks out from 
 the negative coating and rushes across towards the 
 positive coating. In doing so it collides with a 
 number of neutral atoms, and breaks them up into 
 " ions " of opposite signs. These ions practically re- 
 duce the distance between the coatings, and thereby 
 increase the stress. This, again, leads to a rush of 
 further electrons and positive atoms towards each 
 other, and we have a whirl and turmoil of movements, 
 collisions, separations, and recombinations. We have, 
 in fact, an electric spark ; or if it takes place on a 
 large scale in the atmosphere, we have lightning and 
 thunder. 
 
CHAPTER IV 
 
 THE ELECTRIC DISCHARGE 
 
 1. Discharge in General. Whenever an electron 
 moves from one space into another, it may be said to 
 produce a discharge from the first space into the 
 second. But an " electric discharge " is usually under- 
 stood to mean the process whereby a body loses the 
 charge that marks it off, electrically speaking, from 
 its surroundings. 
 
 These " surroundings," such as tables, walls, &c., 
 are usually connected with the earth by more or 
 less good conductors, and bodies cease to exhibit an 
 electric charge when they are at the same potential 
 as the earth. 
 
 Now what is the potential of the earth ? In other 
 words, what is the work required to bring a company 
 of electrons from infinity to the surface of the earth ? 
 The question is not easily answered, but the work 
 may perhaps be roughly estimated at a million dynes. 
 For the charge of the earth is negative. It repels 
 electrons, and attracts positive atoms. It behaves in 
 that respect like an electron, and who knows but that 
 if an electron were magnified to the size of the earth 
 it might show a marked resemblance to our own 
 
70 THE ELECTRON THEORY 
 
 planet? The resemblance is increased by the fact 
 that the sun has a large positive charge, estimated 
 by Arrhenius at 25xl0 10 " coulombs" ( = 7'5xl0 20 
 companies), which gives it a potential of 10 10 units or 
 3 billion " volts." The sun thus resembles a positive 
 atom with a number of negatively charged electrons 
 in the shape of planets revolving round it. But the 
 analogy fails when we measure the forces between 
 the sun and planets. For the electric attraction is 
 found to be quite imperceptibly small in comparison 
 with the gravitational attraction, and astronomers 
 may safely leave it out of their calculations. 
 
 Even if the negative potential of the earth is a 
 million units (300 million "volts") as supposed, its 
 action upon an electrified body near its surface will be 
 excessively small. If this potential were solely due to 
 the earth's own charge, that charge would be 6 x 10 14 
 companies, and this may be supposed to be con- 
 centrated at the centre i.e. at a distance below us of 
 6 x 10 8 cm. Consequently the repulsion exerted upon 
 one company of electrons at the surface will be 
 
 or about j^fo of the normal weight of a milligramme. 
 
 This quantity is beyond the limit of sensibility of 
 our most delicate balances. 
 
 There is, however, a constant streaming of elec- 
 tricity up and down through the air, which is greatly 
 influenced by the weather, and gives rise to the 
 
THE ELECTRIC DISCHARGE 71 
 
 phenomena of thunderstorms and atmospheric elec- 
 tricity in general. Outside the atmosphere the earth 
 behaves as a highly charged body, and discharges of 
 its negative electricity become occasionally visible 
 about the poles in the shape of the Aurora. 1 The 
 conductivity of the air, like that of any other body, 
 depends solely upon the density and mobility of the 
 ions or charged bodies contained in it. These ions 
 may be single electrons or positive atoms, or they 
 may be these associated with more or less neutral 
 matter. The presence of these ions in the air con- 
 stitutes the "ionisation" of the atmosphere. There 
 can be no discharge without ionisation. 
 
 This is a fact which has only recently come to 
 light. It has been known for a long time that every 
 charged body exposed to the air is gradually dis- 
 charged. But that was attributed to moisture or 
 particles of dust, or even to the charging of air 
 molecules. We know now that the discharge takes 
 place when both moisture and dust particles are 
 rigidly excluded, but does not take place if ionisa- 
 tion is prevented. If there is ionisation, the amount 
 of such ionisation determines the rate at which the 
 body is discharged. 
 
 Now ions may be contained in solids, liquids, or 
 gases, and discharge may therefore take place through 
 any of these, or even through a vacuum. But in the 
 case of a vacuum, the ions have to be provided by 
 
 1 See P. Villard, Comptes Rendu*, July 9, 1906. 
 
72 THE ELECTRON THEORY 
 
 the discharging body itself, since the vacuum is 
 otherwise a perfect insulator. In other cases, too, 
 the discharge has to furnish the ions as it goes 
 along. This is notably the case in the electric arc 
 lamp and the spark discharge, where the air is too 
 poor in ions to convey the whole discharge. But 
 before such a discharge can be inaugurated, it is 
 necessary, as a rule, that a few ions should exist in 
 the medium through which the discharge is to take 
 place. If no such ions exist, the medium is a perfect 
 insulator. A discharge can only be made to pass 
 through by means of a great force sufficient to pro- 
 ject ions from the charged bodies, and mechanically 
 break down the insulator. 
 
 All these various forms of discharge may be classi- 
 fied under five heads, accordingly as they take place 
 through insulators, gases, solid conductors, liquid 
 conductors, or a vacuum. 
 
 2. Discharge through Insulators. Insulators are 
 substances which contain no roaming electrons. Their 
 electrons are firmly bound up with atoms, and the 
 latter again are usually bound up together in complex 
 molecules. The substances are therefore, as a rule, 
 chemically inactive : they do not oxidise, and they 
 do not dissolve in water. Paraffin, a typical and 
 valuable insulator, is named from its lack of chemical 
 action (parum affinitatis). And chemical affinity, 
 as we shall see, is a matter of detachable electrons 
 and nothing else. 
 
THE ELECTRIC DISCHARGE 73 
 
 When the electrons of a substance are not detach- 
 able from their atoms or molecular groups, they can- 
 not easily be made to enter a metal to neutralise the 
 positive atoms which that metal may contain. And, 
 on the other hand, the positive atoms being amply 
 provided with electrons, are not prone to combine 
 with electrons from outside. 
 
 Many of the best insulators, like paraffin, beeswax, 
 gut taper cha, mica, ebonite, and amber, are highly 
 complicated carbon compounds. They have no great 
 density ; their molecules are not closely packed, and 
 their atoms are not heavy. The complex molecular 
 aggregations are well separated from each other, and 
 the electrons are effectively imprisoned in them. 
 
 If an insulator like benzene, C 6 H 6 , is bounded on one 
 side by a surface containing a large number of free 
 electrons, and on the other side by a surface contain- 
 ing a large number of free positive atoms, the electrons 
 in the benzene molecules will be wrenched to a greater 
 or less extent out of their position and pulled to- 
 wards the positive atoms; whereas the carbon and 
 hydrogen atoms, and more especially the latter, will 
 be pulled towards the surface containing the excess 
 of electrons. If there were any roaming electrons 
 in the insulator they would find their way out, and 
 would neutralise the positive atoms wherever they 
 encountered them, thus producing a discharge. But 
 a good insulator being a substance which contains 
 no such roaming electrons, no discharge will take 
 
74 THE ELECTRON THEORY 
 
 place unless the force is strong enough to pull the 
 electrons out of the benzene molecules and set them 
 a-roaming. When that happens, events will begin 
 to march rapidly: electrons will fly towards the 
 positive terminal. They will be as quickly replaced 
 by others from the negative terminal surface. These 
 double combinations will give rise to a considerable 
 commotion, which will break up further molecules 
 and impart a conductivity to the insulator by pro- 
 viding it with free electrons and free positive ions. 
 In the direct line joining the terminals a rapid 
 separation and recombination of ions will occur, 
 and will go on at an increasing rate as the conduc- 
 tivity of the insulator increases. The heat produced 
 will volatilise the liquid insulator, and through the 
 ionised gas the discharge will pass like an avalanche, 
 the ions acquiring a velocity growing with the free 
 path along which they travel under the impulse of 
 the electric force. Even when that force is spent, 
 the ions will continue to fly on, like a pendulum 
 swinging up against gravity, and like it, they will 
 return, producing a momentary current in the oppo- 
 site direction. This may be followed by several 
 minor oscillations, until at last the energy is all 
 radiated away into space, and equilibrium is re- 
 established. 
 
 Such is the process which we witness in the elec- 
 tric spark, or, on a larger scale, in the lightning- 
 flash. If the insulator is a solid, the path of the 
 
THE ELECTRIC DISCHARGE 75 
 
 discharge is marked by a perforation. Glass, mica, 
 ebonite, cardboard may be pierced in this manner. 
 
 It takes some 30,000 volts (100 electrostatic units 
 of potential) to pierce a thickness of 1 mm. of the 
 best insulators. This means that the work done 
 in passing from the negative to the positive termi- 
 nal by one company of electrons is 100 ergs. This 
 energy is sufficient to produce the necessary num- 
 ber of ions to keep a further discharge going. 
 
 If the thickness of the insulator is greater, the 
 difference of potential required is also greater, but 
 not in the same proportion. If D is the thickness 
 of dielectric, the necessary difference of potential 
 increases as UD 2 so long as the distance does not 
 exceed a few centimetres. It requires 58,000 volts 
 to pierce a plate of mica (a complex silicate of 
 aluminium and other metals). This great insulat- 
 ing power is due not only to the complexity of the 
 molecules, but to their segregation in numerous 
 successive strata. 
 
 3. Discharge through Oases. When a positively 
 charged conductor is placed near a negatively 
 charged conductor in air, the opposite charges crowd 
 towards the surface facing the other conductor. The 
 air produces no effect beyond slightly reducing the 
 effective distance between the conductors, which it 
 does by the displacement of the charges constituting 
 its neutral atoms,- the electrons straining towards the 
 positive conductor, and the positive atoms straining 
 
76 THE ELECTRON THEORY 
 
 towards the negative conductor. The superfluous 
 electrons in the metal are so much entangled with 
 the molecular aggregates of the metal that even 
 their mutual repulsion and the attraction of the 
 opposite charges in the positive terminal fail to 
 send them out into the open air. And the same 
 state of things obtains among the superfluous posi- 
 tive atoms in the positive terminal, except that 
 they are held even more firmly than the electrons. 
 For actual expulsion, some strong agency is neces- 
 sary. Radioactive substances like radium and uran- 
 ium are in such a state of unstable equilibrium that 
 an atomic catastrophe every now and then sends 
 an electron or positive atom flying out into space. 
 But ordinary substances require either a high tem- 
 perature or ultrar-violet light, or the impact of ions, 
 to enable their own ions to escape. It is only under 
 exceptional conditions that the mere pressure of 
 similar charges suffices to project some of them 
 outside the conductor. 
 
 When, however, the air is ionised, i.e. filled with 
 particles each linked with an electron or positive 
 atom, these ions beat against the terminal opposed 
 to them in sign, and shake or pull the opposite 
 charge out of the metal. 
 
 There are a number of ways of ionising air. It 
 can be done by simply heating it or illuminating it 
 with ultra-violet light, or transmitting Rontgen rays 
 or Becquerel rays through it. The energy thus 
 
THE ELECTRIC DISCHARGE 77 
 
 supplied is converted into the potential energy of 
 ionisation. But since the ions are constantly re- 
 coinbining, the ionisation must be kept up artificially. 
 
 When this is done an electric discharge can take 
 place through air, just as through a metallic con- 
 ductor a silent and steady and invisible discharge. 
 The only difference is that the fall of potential is 
 not uniformly distributed, being more rapid near 
 the terminals, where ions of the opposite sign con- 
 gregate. Such a discharge is called a " dependent 
 discharge," depending as it does upon a constant 
 supply of external energy for ionisation. 
 
 When, on the other hand, the discharge furnishes 
 its own ions as it goes along, we have an " indepen- 
 dent discharge." This is done in a variety of ways. 
 The most familiar example is the electric arc lamp, 
 where the carbon terminals give off vapour of car- 
 bon, and furnish the ultra-violet light necessary for 
 its ionisation. 
 
 Another familiar example, and the oldest known, 
 is the electric spark, and its great natural counter- 
 part, the lightning-flash. Both these are almost 
 invariably intermittent, lightning being a quick suc- 
 cession of flashes in the same direction, often pre- 
 ceded by a feeble pilot discharge wjiich passes from 
 one stray ion to another, just as it finds them, and 
 thus marks out a forked path for the main discharge 
 to traverse. 
 
 The forms of discharge which allow the greatest 
 
78 THE ELECTRON THEORY 
 
 insight into the actual processes going on are the 
 point, brush, and glow discharges, chiefly in rarefied 
 gases. 
 
 A point discharge between a metallic point and 
 a plate is the simplest form of gas-discharge known. 
 Let a sharp point, P, be placed opposite a circular 
 plate, AB, in air (Fig. 11). Let the 
 point be kept at a negative potential, 
 and AB at a positive potential. 
 x Then when the difference of poten- 
 
 ^ <= tial is sufficient, say a few hundred 
 volts, a glowing steady spark is seen 
 at the point. This spark really 
 consists of two luminous strata 
 separated by a narrow dark space. 
 A few stray positive atoms are re- 
 quired to start the discharge. They are attracted 
 to the point, near which they find an intense 
 and concentrated electric force. Their motion 
 towards the point is constantly accelerated, and 
 when they get close up to it, it is sufficiently 
 rapid to split up the gaseous molecules into ions. 
 This splitting up is facilitated by the presence of the 
 metal, which appears to exert what chemists call a 
 " catalytic " action. The region where this splitting 
 up takes place is the luminous layer immediately 
 adjoining the point. The electrons liberated by the 
 ionisation are repelled by the point, and fly out into 
 the gas. They also are accelerated until they re- 
 
 B 
 
THE ELECTRIC DISCHARGE 79 
 
 quire sufficient energy to ionise the gas, and their 
 field of action is marked by the second luminous 
 stratum. The dark space between, called the " dark 
 cathode space," is the region where both kinds of 
 ions are acquiring energy of motion, but not spend- 
 ing it, and therefore not producing any luminous 
 effects. 
 
 This double ionisation also goes on when the 
 point is positively charged, and the plate negatively. 
 Only then the dark space is still smaller. When 
 the difference of potential is very great, the electrons 
 from the negative point fly beyond the region of 
 ionisation and attack the gas further towards the 
 plate, ionising it freely. This beautiful phenomenon 
 is known as the brush discharge. Tesla's flame 
 discharges and the discharges obtained by means 
 of the Wehnelt interrupter, are varieties of it. 
 
 The form of discharge showing the greatest 
 variety of phenomena is the glow discharge, as 
 seen in vacuum tubes. It is this form of discharge, 
 indeed, which, after being a great source of per- 
 plexity, ultimately was instrumental in elucidating 
 the whole realm of electric discharges. The reduc- 
 tion of the pressure of the gas allows freer play to 
 the ions. It gives them a greater " free path " along 
 which they can follow the acceleration of the electric 
 field, and thereby acquire kinetic energy. Ionisation 
 is thus facilitated, and conductivity more rapidly 
 acquired, 
 
80 THE ELECTRON THEORY 
 
 The slow discharge in a vacuum tube consists 
 normally of five distinct parts viz. the cathode 
 layer A, the dark cathode space B, the negative 
 glow C, the intermediate space D, and the positive 
 column E (Fig. 12). The three luminous layers 
 (shown dark in the diagram) are those in which 
 ionisation is going on. They are the scenes of 
 conflict and collision, whereas the other spaces are 
 the scenes of free fall along the lines of electric 
 force. At the cathode layer A, positive atoms are 
 
 T FIG. 12. 
 
 ionising the gas next the cathode with the help of 
 the metal. As in the case of the point discharge, 
 the ions thus formed follow the electric force, the 
 positive atoms neutralising the free electrons of the 
 cathode, and the electrons traversing the dark 
 cathode space to ionise the neutral atoms in the 
 body of the gas at C. There again, both positive 
 atoms and electrons are liberated, and the latter 
 move still farther towards the anode, producing 
 further ionisation when they have acquired sufficient 
 velocity, and then we get the positive column E. 
 Sometimes it happens that all the electrons pro- 
 ceeding from C have nearly the same velocity. 
 
THE ELECTRIC DISCHARGE 8 1 
 
 They then reach ionising speed within nearly the 
 same distance, and are stopped at the beginning 
 of the positive column. Before they can acquire 
 further ionising power, they must traverse another 
 dark space, and so on alternately, the final result 
 being the " stratified " positive column, which forms 
 such a striking display when the tube is long 
 enough. If the tube is shortened, the positive 
 column is gradually " swallowed " by the anode 
 until the discharge resembles the ordinary point 
 discharge. 
 
 The above is a general outline of the main 
 phenomena in gaseous discharges. But they ex- 
 hibit an almost infinite variety, and still offer a 
 fruitful field of investigation. When the exhaustion 
 of the vacuum tube is carried to a very high point, 
 the phenomena become of profound interest to the 
 electron theory. For the electrons projected from 
 the cathode play a very prominent, and eventually 
 an almost exclusive, part. They proceed in straight 
 lines from the cathode, like rays of light, and are 
 therefore commonly called "cathode rays." It was 
 Crookes who first pronounced them to be a kind 
 of matter (" radiant matter"), and we now know 
 that they consist of particles about 200,000 times 
 smaller than the ordinary atoms viz. the electrons 
 themselves. But the positive atoms also take the 
 appearance of rays. When the cathode is per- 
 forated, such rays are seen to emerge from the 
 
 F 
 
82 THE ELECTRON THEORY 
 
 back of it. They have been called "canal rays," 
 but they simply consist of positively charged atoms, 
 or atoms or molecular aggregates deprived of 
 electrons. 
 
 A noteworthy fact with regard to gas discharges 
 is that the amount of electricity passing (the 
 " current ") is not necessarily proportional to the 
 difference of potential between the electrodes. It 
 depends upon the ionisation, and that is influenced 
 and enhanced by the passage of the discharge itself, 
 owing to collision between the ions. In the de- 
 pendent discharge, again, where the ionisation is 
 provided by an external agent, the current can 
 never exceed a certain value, fixed by the number 
 of ions supplied. When these are all engaged in 
 conveying the current, a change in the potential 
 fails to change the current. There exists, in fact, 
 a "saturation current." This, as we shall see, is 
 not the case in metals. 
 
 Discharge through flames is a special form of 
 gaseous discharge, and depends upon the natural 
 ionisation produced by a high temperature. Heat 
 also exerts an action upon the discharge from 
 metals. It is found that a hot platinum wire is 
 discharged more readily than a cold one. A nega- 
 tively charged platinum wire is easiest discharged 
 when surrounded by hydrogen ; that being a gas 
 whose atoms lose their electrons easily. They 
 surround the negative wire and pull out its elec- 
 
THE ELECTRIC DISCHARGE 83 
 
 trons. When a hot platinum cylinder is charged 
 positively and hydrogen is made to diffuse out from 
 it, the hydrogen atoms, with their positive charges, 
 rapidly free the cylinder from its positive charge 
 by conveying it into the surrounding space. 
 
 4. Discharge through Solid Conductors. In gases 
 at ordinary pressure, or in a partial vacuum, we have 
 to do with molecules possessing a certain free path, 
 which, though very small (about rannnr cm.), yet 
 gives them some little interval of undisturbed 
 motion. 
 
 In metals, on the other hand, the atoms are packed 
 close together. How closely may be found by a 
 simple calculation as follows. The mass of a copper 
 atom is 70 x 10* 24 grammes. A cubic centimetre of 
 copper weighs 8'9 grammes. That cubic centimetre 
 therefore contains 0*127 x 10 24 atoms of copper, and 
 each atom will have a volume of 7*9xlO~ 24 cc. to 
 itself. If this volume is a small cube, its side will 
 be 2 x 10~ 8 cm. This length is just the diameter of 
 a molecule of hydrogen, so that if we fill up the 
 small cubes with molecules of hydrogen, they will 
 just fit tight. How, then, will the copper atoms fit ? 
 We do not know the exact size of the atoms of 
 copper, but can make a very close guess. We may 
 take it that the diameter of a molecule of copper is 
 not more than twice the diameter of a molecule of 
 hydrogen, since we know that the mercury molecule 
 is not more than 1*7 times as thick. Therefore the 
 
84 THE ELECTRON THEORY 
 
 copper atom is just about the size of the hydrogen 
 molecule, and fits equally tight in the small cube. 
 
 The copper atoms are therefore about as closely 
 packed as they will go. Hence copper cannot be 
 perceptibly compressed. But it also explains why 
 the loose electrons attached to the copper atoms are 
 practically free to obey outside electric forces. For 
 they easily get into the neutral zone between neigh- 
 bouring positive atoms, and are then under the 
 influence of the outside force only. This happens, 
 according to J. J. Thomson, about 40 million times 
 per second to each electron. (In bismuth, at all 
 events.) As a consequence, the whole of the loose 
 electrons in a metal (I mean those electrons which 
 can enter or leave the atom without producing a 
 charge sufficient to stop the process) are every now 
 and then set free to obey external electric forces. 
 Their motion under the influence of those forces con- 
 stitutes metallic conduction. From this simple fact 
 the most important laws of metallic conduction may 
 be immediately deduced. 
 
 Schuster 1 has estimated that a metal contains 
 from one to three mobile electrons for each atom. 
 Copper contains about three mobile electrons for 
 every two atoms. We must therefore imagine these 
 electrons darting in and out among the atoms, and 
 ready to obey the pull of an electric force whenever 
 they happen to be free, which happens millions of 
 
 1 A. Schuster, Phil. Magazine, Feb. 1904. 
 
THE ELECTRIC DISCHARGE 85 
 
 times per second. The path of freedom increases as 
 the metal cools and the atoms arrange themselves 
 in larger aggregations. Hence the electrons in cold 
 metals follow the electric force more readily than in 
 hot metals. 
 
 Now it may be asked whether the atoms themselves 
 do not also obey electric forces. The answer is that 
 they do so when they are linked to either more or 
 less electrons than they contain in the neutral state. 
 If linked to more electrons, they have a negative 
 charge ; if to less, they have a positive charge. In 
 the former case they tend to go the same way as the 
 electrons, while in the latter case they tend to move 
 in the opposite direction. But, being about a hundred 
 thousand times more bulky than the electrons, they 
 make little headway, and, except in extreme cases, 
 their motion may be neglected, and we may take it 
 that the electrons alone obey the pull of the electric 
 force i.e. that it is they alone who form the " electric 
 current " in metals. But it is evident that they move 
 from the negative to the positive side, and, therefore, 
 in the direction opposite to that in which an " electric 
 current " has hitherto been supposed to flow. This 
 fact constitutes a serious difficulty in the present 
 state of transition of electrical terms. We cannot 
 hope that people will at once revise all their elec- 
 trical terms, and reverse all their previous notions. 
 The textbooks alone would prevent that. It is, there- 
 fore, imperative that we should use a term which 
 
86 THE ELECTRON THEORY 
 
 cannot possibly mislead any one. For this purpose 
 I propose to use the term " electron current" for the 
 movement of electrons. Whenever I speak of " the 
 current" pure and simple, I shall mean the move- 
 ment of electric charges without reference to their 
 direction. When the direction from positive to nega- 
 tive is to be understood, I shall speak of the " positive 
 current." 
 
 When the current is not conveyed by isolated 
 electrons, but by "ions" i.e. larger aggregates of 
 atoms containing a positive or negative charge 
 there are two real displacements in opposite direc- 
 tions, as in electrolysis. It will then be expedient 
 to talk of a " positive current," denoting the flow of 
 positively charged matter, and a " negative current/' 
 to denote the flow of negatively charged matter. 
 The total current is the sum of the two. 
 
 Having settled these important matters of termin- 
 ology, we may now proceed to unravel the mysteries 
 of the electron current in metals. 
 
 To simplify matters, we will take, as before, two 
 infinite parallel plates, AC, BD, 1 cm. apart, and 
 having a difference of potential such that it takes 
 1 " erg " of work ( = T^^V zro-<r foot-pound) to move 
 one company or electrostatic unit of electrons from 
 the positive to the negative plate. This is the elec- 
 trostatic unit of difference of potential. It can be ob- 
 tained practically by connecting the two plates with 
 the terminals of a battery of some 300 Daniell cells. 
 
THE ELECTRIC DISCHARGE 87 
 
 Now let a cube of 1 cm. side, consisting of copper, 
 be inserted between the plates, and touch both of 
 them. What will happen ? 
 
 Obviously, the two quadrillion mobile electrons 
 contained in the cubic centimetre of copper will 
 be set in motion towards the positive plate. 
 If they could fall freely along the lines of 
 force, they would arrive at the positive plate 
 with a velocity of 10 9 cm. per second, since 
 the comparatively large force of 1 dyne acts 
 through 1 cm. on the insignificant mass 
 of each company of electrons (1*78 x 10~ 18 
 grammes). Each company which falls 
 through the whole centimetre acquires 1 
 erg of energy; but as, on the average, the 
 electrons only fall through half that distance, 
 we get the energy acquired by the total electrons 
 in the copper in falling on to the positive plate 
 by multiplying the number of companies by half 
 an erg. This number of companies is 6-5 x 10 14 , so 
 that the energy acquired by them in falling on to 
 the positive plate is 325 billion ergs a quantity 
 sufficient to evaporate several hundred pounds 
 of water. Since this process would only take 
 1/9 x 10~ 9 of a second, and a further supply of elec- 
 trons from the negative plate wtfuld be ready to 
 repeat it, it may be realised what an enormous 
 evolution of energy would be going on between the 
 plates if the free path of each electron were 1 cm. 
 
88 THE ELECTRON THEORY 
 
 in other words, if the conductivity of the copper were 
 practically infinite. 
 
 But, as a matter of fact, that is not the case. 
 There are two factors which hinder a free discharge. 
 In the first place, the electrons are every now and 
 then encountering the closely packed neutral copper 
 atoms, and colliding with them. When an electron 
 is suddenly stopped like that, it cannot rebound with- 
 out loss of energy, as a perfectly elastic or a per- 
 fectly hard ball would from another. As we shall see 
 later on, the acceleration or retardation of electrons 
 is attended by radiation, and radiation means loss of 
 energy. A well-known example of such radiation 
 are the Rontgen rays, which are wave -pulses sent 
 out into the ether when a cathode particle, alias an 
 electron, strikes an obstacle. 
 
 Considering how closely the atoms are packed, we 
 may take it that an electron loses nearly the whole 
 of its energy by radiation whenever it collides with 
 a neutral atom. If it has any to spare, it will revolve 
 round the atom and radiate out its spare energy in 
 doing so. 
 
 Another factor which hinders the free discharge 
 of electrons is this binding together of a positive 
 atom and an electron until a collision sets it free. 
 It has been estimated that for every 5000 electrons 
 thus temporarily bound, there is only one electron 
 free to roam at any given instant of time. We can- 
 not therefore count upon more than ^ou^h of the 
 
THE ELECTRIC DISCHARGE 89 
 
 total number of mobile electrons to take part in 
 metallic conduction at any given instant. 
 
 We have estimated the total mobile electrons in 
 the cubic centimetre of copper at 1*9 quadrillion. 
 Of these, 380 trillion will therefore be available for 
 conduction at any given time. Since successive 
 copper atoms will be on the average 2 x 10~ 8 cm. 
 apart, we may suppose that each electron is stopped 
 every time it has gone that distance. What time 
 will it require to cover the one centimetre distance 
 between the plates ? 
 
 It can be easily shown that the time will be in- 
 creased in proportion to the square root of the 
 number of stoppages. For by a well-known law 
 of falling bodies 
 
 9 
 
 Thus, if there are four compartments, s = , and t = J, 
 so that the total time is 4 x | = 2. 
 
 Now, there are 0*5 x 10 8 such " compartments " in 
 our case, so that the time will be increased. 
 
 1 times = 0-71 x 10 4 =7100. 
 
 The time required for falling free having been 
 l*9xlO~ 9 second, the time required by the elec- 
 tron for threading its way through the copper 
 will be 
 
 7000 x 1-9 x 10~ 9 = 1-35 x 10~s second. 
 In that short time the whole of the freely moving 
 
90 THE ELECTRON THEORY 
 
 electrons, 380 trillion in number, will have passed out 
 of the copper into the positive plate, and their places 
 will have been taken by reinforcements from the 
 negative plate. In one second no less than 
 
 380 trillion 
 l-35xlO- 5 
 
 electrons will pass through any cross-section of the 
 conductor. This is the electron current. It is 
 equal in electric quantity to the ordinary or posi- 
 tive "current," but of opposite sign. In practical 
 measure it comes to about 3,000,000 amperes, a 
 current of such intensity that it would melt 
 and evaporate the copper in a fraction of a 
 second. 1 
 
 The property whereby a conductor absorbs the 
 kinetic energy of the electrons and converts it into 
 heat is called the " resistance " of the conductor. 
 
 The current, or current strength, is measured by 
 the number of electrons passing any section of the 
 conductor in unit time. 
 
 We might define unit current as the passage of 
 one company of electrons per second across any sec- 
 tion of the conductor. But such a current would be 
 exceedingly small, and could hardly be measured by 
 the ordinary instruments. It is usual to measure 
 currents by "amperes," or "coulombs" per second. 
 
 1 The current calculated from the observed resistance is 188 
 million amperes, so that the electrons are not stopped quite so 
 often as above supposed. 
 
THE ELECTRIC DISCHARGE 9! 
 
 One coulomb consists of 3 x 10 companies, or 
 8'7 x 10 18 electrons. In accordance with the prin- 
 ciple of emphasising the atomic nature of elec- 
 tricity, I shall qall the "coulomb" an "army" of 
 electrons (or positive atoms), and we shall know 
 that this army consists of 8*79 trillion men and may 
 be divided into 3000 million companies. 
 
 When one army of electrons passes across any 
 section of a conductor in one second, that conductor 
 is conveying unit current, or one " ampere." 
 
 The amount of electricity passing, every section 
 must obviously be the same. For if more electricity 
 entered by one section than what issued by the other 
 the metal between the two sections would be accumu- 
 lating electricity, and such accumulation would be 
 rapidly cleared away by the mutual repulsion of the 
 charges. 
 
 The amounts of electricity dealt with in metallic 
 conduction are much larger than those we have to 
 do with in electrostatic charges. In these, as we 
 have seen, it is not practicable to have more than 
 one-millionth of the total electricity in the shape of 
 free charges. But within the uncharged metal, every 
 free electron is compensated by a positive atom, and 
 is free to move, although it does not form an electro- 
 static charge measurable outside. 
 
 We will now proceed to consider the current under 
 various circumstances. 
 
 Suppose that in the case of the copper cube the 
 
92 THE ELECTRON THEORY 
 
 current is reduced 1000 times. That will mean that 
 only one-thousandth of the electrons will reach the 
 positive plate per second. But it will also mean 
 that the average steady velocity of each electron 
 in fact the rate at which it does its work in 
 overcoming the resistance of the conductor is 
 reduced in the same proportion. In any element 
 of volume of the conductor, the rate at which 
 energy is converted into heat will be reduced in 
 the proportion of 1 : 1000 2 , or 1 : a million. And 
 in general, the heat evolved per unit volume in 
 unit time is proportional to the square of the current. 
 (Joule's Law.) 
 
 If, on the other hand, we reduce the difference of 
 potential between the plates to r^o^th ^ ^ s f rmer 
 value, we reduce the force acting upon the electrons 
 in the same proportion, and their steady average 
 velocity and rate of work will be reduced to T oVoth. 
 For every thousand electrons which formerly passed 
 a cross-section, only one electron will pass now. The 
 current, therefore, is proportional to the difference 
 of potential at the ends of the conductor. (Ohm's 
 Law.) 
 
 Now, instead of one copper cube, let there be two. 
 Then, since the plates are supposed to be infinite, 
 and contain a supply of electrons and positive atoms 
 equal to any demand, there will be two equal currents, 
 and the total current will be twice what it was before. 
 Following up this argument, we see that the current 
 
THE ELECTRIC DISCHARGE 
 
 93 
 
 FIG. 14. 
 
 is proportional to the sectional area of the con- 
 ductor. 
 
 Next, let the two copper cubes be arranged one be- 
 hind the other (Fig. 14), so that the current 
 has to traverse both in succession, and let 
 the difference of potential be the same as 
 before. To secure this, we shall have to 
 reduce the surface density of electricity on 
 the plates to one-half, and therefore the 
 force will be halved, and also the steady 
 velocity of the electrons. Hence the 
 current itself will be half its former value, 
 and if we increased the length of con- 
 ductor n times, we should also reduce the 
 current n times. Therefore the current 
 is inversely proportional to the length of the con- 
 ductor, other circumstances being equal. A c 
 
 If, while keeping the plates the same 
 distance apart we connected them by a 
 slanting conductor (Fig. 15), we should re- 
 duce the effective force on the electrons in 
 the same proportion as we increased the 
 length of the conductor, and should, 
 therefore, also reduce the current in the 
 same proportion, so that in this ca^e also 
 the current is inversely proportional to 
 the length of the conductor. 
 
 The geometrical shape of the conductor is, how- 
 ever, not the only factor which influences the current. 
 
 FIG. 15. 
 
94 THE ELECTRON THEORY 
 
 If iron were substituted for a copper rod of the same 
 dimensions, the current would fall to one-sixth its 
 former value. The property whereby one metal 
 conducts electricity better than another is called 
 its (specific) conductivity. Its reciprocal is called 
 its " resistivity," or specific resistance. The actual 
 resistance of a metallic rod of uniform section may 
 be arrived at by multiplying its resistivity by its 
 length and dividing by its sectional area. 
 
 The resistance of a body may be measured by the 
 amount of energy transformed into heat by a current 
 of one ampere passing through it for one second. 
 A piece of iron develops six times as much heat 
 as a piece of copper. The resistance of an iron 
 wire 1 cm. long is, therefore, equivalent to that of 
 a copper wire of the same thickness, but 6 cm. 
 long. Therefore, if we have an iron wire and a 
 copper wire attached end to end, and conduct the 
 current through both, we get the same result as if 
 we passed the current through a copper wire 7 cm. 
 long. In other words, the resistance of two suc- 
 cessive conductors is equal to the sum of the 
 resistances of the conductors taken separately, and 
 the current acts accordingly. 
 
 We are now in a position to fully formulate Ohm's 
 law. If a difference of potential is maintained at the 
 ends of a conductor, or system of successive con- 
 ductors, the current through the conductor or the 
 system is proportional to the difference of potential, 
 
OF 
 
 THE ELECTRIC DISCHARGE 95 
 
 and inversely proportional to the resistance between 
 the ends. 
 
 Such a law as the above does not, of course, hold 
 good unless the number of carriers of electricity is 
 a constant quantity. In gaseous discharges, as we 
 have seen, ionisation is continually going on, and the 
 current often increases much more rapidly than the 
 difference of potential. In metals the detachable 
 electrons are all available for conduction, although 
 a large proportion of them are temporarily bound up 
 with atoms at any given instant. An increase of 
 the difference of potential does not affect the ionis- 
 ation in metals, since in them ionisation is complete 
 in the natural state. 
 
 When a current flows into a branched conductor, 
 the current flowing towards the point of division 
 must be equal to the sum of the currents flowing 
 away from it. For otherwise there would be an 
 accumulation of either electrons or positive atoms 
 at the junction. When any number of con- 
 ductors meet at the same point, the sum of the 
 currents towards the point is equal to the sum of 
 the currents from the point. This rule is known as 
 Kirchhoffs first law. 
 
 The current is seen to behave like an incompres- 
 sible fluid. As a matter of fact, electricity is a fluid, 
 and, indeed, a gas, possessing a pressure of several 
 thousand atmospheres in most metals, and having 
 the same temperature as its surroundings. What 
 
96 THE ELECTRON THEORY 
 
 distinguishes it from ordinary gases is the enormous 
 expansive force it possesses apart from its tempera- 
 ture. Ordinary gases, when deprived of all heat, are 
 at the same time deprived of all expansive force. 
 But the electric gas, made up of electrons, has an 
 enormous explosive power, even at the absolute zero 
 of temperature. Nor is electricity, regarded as a 
 fluid, really incompressible. It can be compressed 
 to the extent of about a millionth, as is done in 
 charging a conductor with a high negative charge. 
 But that is the utmost limit to which we can push 
 the compression, and in ordinary apparatus that 
 would be inappreciable. 
 
 In the imaginary experiments described above, I 
 have said nothing about the manner in which the 
 infinite plates AB and CD may 
 have been charged, because 
 that does not affect the result. 
 But any electrostatic machine 
 capable of supplying the re- 
 quired number of electrons and 
 positive atoms may take the 
 place of the infinite plates. Let 
 
 such a machine supply the 
 FIG. 16. . rr J 
 
 small plate N with sufficient 
 
 electrons to keep it at a (negative) potential of one 
 volt, and let the machine at the same time with- 
 draw a corresponding number of electrons from M, 
 so as to keep M at the potential of the earth ; then 
 
THE ELECTRIC DISCHARGE 97 
 
 the machine will be doing a certain amount of work 
 on the negative electrons to take them from M to 
 N. That work will be one erg for every " army" or, 
 "coulomb" of electrons; it is called the "electro- 
 motive force " (E.M.F.) l of the electric machine. 
 
 When the work is done without loss between M 
 and N, the E.M.F. is simply the resulting difference 
 of potential between M and N, for it represents the 
 amount of energy that can be obtained per unit of 
 electricity out of the wire in the shape of heat. But 
 when the electric machine works in such a manner 
 that not all its work is transformed into potential 
 energy, but some of it lost in overcoming a resist- 
 ance, the current is reduced in proportion to this 
 additional resistance, and the extra work is deducted 
 from the difference of potential available at the ter- 
 minals M and N. The electromotive force of the 
 machine is then no longer equal to the difference 
 of potential between the terminals M and N, but 
 larger. 
 
 Ohm's law also covers this case of what is called 
 " internal resistance." For it states that the current 
 is in all cases proportional to the total E.M.F. (whether 
 due to one machine or several in series), and inversely 
 proportional to the total resistance. 
 
 An apparatus like the above, consisting of an 
 
 1 The term electromotive force is unfortunate. It is not a force, 
 and it is not work, but work per quantity of electricity. Other 
 terms sometimes used, like tension or pressure, are equally unfor- 
 tunate. We still await a satisfactory word. 
 
98 THE ELECTRON THEORY 
 
 electric machine or other electromotive agency and 
 a conductor joining its terminals, is called an " elec- 
 tric circuit." Since electricity can neither be created 
 nor destroyed, there must in the end be a circulation 
 of electricity, and if there is a continuous flow such 
 a flow must ultimately constitute a circuit. 
 
 The current in a circuit can, by means of Ohm's 
 law, be calculated in a simple manner. The E.M.F. 
 is measured in volts, each of which is ^^ of an 
 electrostatic unit of difference of potential (1 erg per 
 company). The current is measured in amperes, or 
 coulombs per second. Resistance is measured by a 
 unit called the " ohm," which is the resistance of a 
 thread of pure mercury 1 sq. mm. in sectional area 
 and 1063 mm. long. The resistance of any other 
 conductor may be calculated from its dimensions and 
 its resistivity. That being done, we obtain the current 
 by the equation 
 
 Current in amperes = E.M.F. in volts ? 
 resistance in ohms 
 
 r lil|l-!-f . p 
 
 5. Discharge through Liquids Electrolysis. We 
 have now to consider the case where the metallic 
 circuit containing the current -yielding electric 
 machine is broken at one point, and a liquid is 
 interposed in the gap. If the circuit consists of 
 one metal only, and but one liquid is introduced, 
 two things may happen: (a) no current passes; 
 
THE ELECTRIC DISCHARGE 99 
 
 or (6) a current passes. The former alternative 
 happens when the liquid is an insulator, like oil. 
 The latter happens when the liquid contains ions. 
 
 Pure water contains practically no ions at all, 
 and is therefore a nearly perfect insulator. But 
 it has a remarkably high power of splitting up 
 the molecules of other substances into ions. Thus, 
 if it contains a drop of hydrochloric acid (HC1), it 
 splits up nearly every molecule of the acid into 
 ions; these being atoms of hydrogen and atoms 
 of chlorine respectively. To put it more precisely, 
 if water contains 0*0036 per cent, of hydrochloric 
 acid, then 99 per cent, of all the acid molecules 
 will be split up (or " dissociated " or " ionised") 
 into H and 01, and the remaining 1 per cent, will 
 be present as HC1. This hypothesis, which is 
 greatly at variance with the old chemical views 
 of the constitution of a dilute acid, is called the 
 " ionic " or " dissociation " hypothesis, and has 
 been elaborated chiefly by the celebrated Swedish 
 physicist Arrhenius. It was this hypothesis which 
 first utilised the conception of an atomic structure 
 of electricity, as suggested by Faraday's laws of 
 electrolysis. 
 
 It must not be concluded from the percentage of 
 undissociated acid that the dissociation is absolutely 
 permanent; for the ions of opposite sign attract 
 each other with a force amounting to (3*4 x 10~ 10 ) 2 
 dynes when at a distance of 1 cm. apart and it 
 
100 THE ELECTRON THEORY 
 
 must happen that they occasionally meet and 
 coalesce, in spite of the viscous resistance of the 
 intervening water, and the peculiar effectiveness of 
 the water molecules in splitting up molecules of 
 other bodies. With a solution as dilute as we 
 have above supposed, there are some 50,000 mole- 
 cules of water to every molecule of hydrochloric 
 acid, and such is the dissociating power possessed 
 by this quantity of water that only one molecule 
 HC1 out of a hundred escapes dissociation. If, there- 
 fore, two ions of the acid consisting of hydrogen 
 atoms which have lost one electron, and chlorine 
 atoms which have gained one electron, should 
 happen to meet and coalesce, they would again be 
 dissociated before long. We may suppose that all the 
 ions do meet and combine, but that for every second 
 they spend in combination they spend one minute 
 and thirty-nine seconds in separation, so that, on 
 the whole, there are always ninety-nine out of every 
 hundred of them dissociated. 
 
 This state of things is radically different from the 
 case of a metal, where, as we have seen in the case 
 of copper, each electron is combined with a positive 
 atom about 5000 times longer than the time it 
 spends flying free. From this we might at first 
 sight conclude that the conductivity of copper was 
 5000 times less than that of a dilute solution of 
 hydrochloric acid; but that conclusion would be 
 quite unjustified. In the first place, it must be 
 
THE ELECTRIC DISCHARGE 
 
 101 
 
 remembered that conduction in copper is due, not 
 to charged atoms, but to free electrons, which are 
 a hundred-thousand times smaller, and therefore 
 very much more mobile than charged atoms. Not 
 only are they smaller in size, but the mass of an 
 electron is also about a thousand times smaller than 
 that of a hydrogen atom, so that the same force 
 produces in it a thousand times more of an accelera- 
 tion than in the hydrogen atom. An E.M.F. which 
 in a metal would make the electrons move with a 
 steady velocity of something like a kilometre per 
 second, would only suffice to impart a 
 velocity of ^ cm. per second to the hydro- 
 gen ions in an aqueous solution. Since 
 the value of the charge is the same in both 
 cases, the currents will differ enormously 
 in strength, the copper evincing by far the 
 greater conductivity. 
 
 We may now proceed to consider in de- 
 tail the behaviour of a cube of a dilute 
 solution of hydrochloric acid with a side 
 1 cm. long, introduced between two infinite 
 conducting plates kept at a difference 
 of potential of 1 volt ( = ^tnr electrostatic 
 unit). , 
 
 Its weight may be put down as one gramme, being 
 nearly the same as water. As regards its molecular 
 structure, it consists of water molecules, H 2 0, dis- 
 sociated water molecules, H + HO, dissociated mole- 
 
 HCI 
 
 FIG. 17. 
 
IO2 THE ELECTRON THEORY 
 
 cules of hydrochloric acid, H + Cl, and undissociated 
 molecules of the same, HC1. If the concentration 
 of HC1 is one-thousandth "gramme-molecule" per 
 litre, 1 or one-thousandth of the " normal" concen- 
 tration, the percentage of HC1 in solution will be 
 0*00365. We may then put down the following 
 census of molecules and ions contained in the cubic 
 centimetre of solution : 
 
 Neutral molecules of water H 2 . . . . 5 x 10 22 
 
 Total molecules of acid 1*81 x 10 18 
 
 Of these dissociated H + 01 l-8xl0 18 
 
 Of these undissociated HC1 2 x 10 18 
 
 Dissociated molecules of water H -f HO . . 10 14 
 
 Of these constituents, only the dissociated ions 
 play any part in the conduction of electricity, and 
 of these there are 18,000 derived from the acid for 
 one derived from water. Hence we are practically 
 reduced to the hydrogen and chlorine ions if we 
 wish to conduct electricity through the solution. 
 
 These must be present in equal numbers, as 
 otherwise the solution would have a charge. Thus, 
 if there were 1,000,001 hydrogen ions for every 
 1,000,000 chlorine ions, the solution could have a 
 positive charge equivalent to 310 companies, which 
 would charge it to a potential of over 100,000 volts. 
 
 1 A solution is said to contain one gramme-molecule per litre if 
 it contains M grammes per litre, M being the molecular weight of 
 the substance. That of HC1 being 35'5 + 1 = 36 '5, the weight in one 
 litre of water must be 36'5 grammes to give a "normal" solution 
 of one gramme-molecule. The water weighing 1000 grammes, the 
 percentage is 3'65. 
 
THE ELECTRIC DISCHARGE 1 03 
 
 Of the 1*8 x 10 18 ions of hydrogen and chlorine, we 
 must have, therefore, 0-9 x ICf 8 hydrogen ions, and 
 the same number of chlorine ions. Each of the 
 former has a positive charge equal to that of one 
 positive atom, and each of the chlorine ions has a 
 negative charge equal to that of one electron. The 
 simple hydrogen ion is a positive atom i.e. an atom 
 deprived of one electron. The simple chlorine ion 
 is a "negative atom" i.e. an atom provided with 
 an extra electron. But these charged atoms do not 
 travel singly through the water. Their motions 
 under the influence of electric force are so slow 
 that the only plausible explanation seems to be that 
 they are bound up with a number of neutral water 
 molecules which act as a drag, and hinder their 
 progress through the water. They are, so to speak, 
 "hydrated," and the chlorine atoms are hydrated 
 four or five times more heavily than the hydrogen 
 atoms, and are therefore four or five times slower. 
 If this were not so, it would be impossible to account 
 for the slowness of the ions, for the water molecules 
 are twice as loosely packed as the atoms in the 
 copper. There is plenty of room between them, 
 and hydrogen atoms, though so much larger than 
 electrons, would have a reasonably long free path 
 if they travelled singly. As it is, the hydrogen ions 
 are the fastest of all ions known, the next being 
 the ions of the combination HO, which, however, 
 are only half as fast. The mobility of these main 
 
104 THE ELECTRON THEORY 
 
 constituents of water accounts for many of those 
 characteristic qualities which make it the main 
 vehicle of the processes of life. 
 
 Whatever the amount of hydration may be and 
 its absolute amount is difficult to calculate it is a 
 constant quantity for the same ion at the same 
 temperature, whatever the chemical body from 
 which it may be derived. The "mobility" of the 
 ion is always the same at a given temperature. It 
 is measured by the steady velocity it acquires under 
 the influence of a "field" of one volt per centi- 
 metre i.e. an electric field of force in which the 
 potential varies by one volt for every centimetre 
 travelled in the direction of the force. 
 
 Arrhenius, in his " Textbook of Electrochemistry," 
 gives the following table of absolute velocities of the 
 most commonly occurring ions at a temperature of 
 18, under the influence of a fall of potential of 
 1 volt per centimetre: 
 
 Cations. Anions. 
 
 fi . , 
 
 . 3250X10- 6 
 
 OH ... 
 
 1780x10-6 
 
 K . . 
 
 . 670 , 
 
 Cl . . . 
 
 678 , 
 
 Na. . 
 
 . 451 
 
 f 
 
 I .... 
 
 685 
 
 i 
 
 Li . . 
 
 . 347 
 
 i . 
 
 NO, . . . 
 
 640 
 
 f 
 
 NH 4 . 
 
 . 660 
 
 i 
 
 CH 3 C0 2 . 
 
 350 
 
 f 
 
 Ag. . 
 
 . 570 
 
 ? 
 
 C 2 H 6 C0 2 . 
 
 320 
 
 i 
 
 The " cations " are those ions which take a positive 
 charge (i.e. lose one electron) and wander to the 
 cathode or negative plate. The " anions " are those 
 
THE ELECTRIC DISCHARGE 10$ 
 
 which take a negative charge i.e. an extra electron 
 and wander to the anode or positive plate. 
 
 " From these data," proceeds Arrhenius, " we can 
 calculate the mechanical force necessary to drive 
 a gramme-ion 1 through the water with a certain 
 velocity. The volt is so defined that the work 10 7 
 ergs is required to transport 1 coulomb against this 
 potential difference. Inversely, if the fall of poten- 
 tial is 1 volt per centimetre, then 10 7 dyne-cms, 
 (ergs) are required to transport 1 coulomb through 
 1 cm. against this fall i.e. the force necessary for 
 1 coulomb is 10 7 dynes = 10*18 kilogrammes. The 
 force required for a gramme-ion charged with 96,500 
 coulombs against the same fall of potential is there- 
 fore 
 
 96,500 x 10*18 = 983,000 kilogrammes. 
 
 This force drives a gramme-ion of hydrogen with 
 a velocity 325 x 10~ 5 cm. per second. The force 
 required in order that the velocity may be 1 cm. 
 
 10' 
 
 per second must be ^5 times greater i.e. it must 
 be 
 
 983,000 xlO^gQg x 1Q8 kilogrammes< 
 325 
 
 The following table gives the force in million 
 
 1 A gramme-ion contains as many grammes of the substance as 
 its simple ion is heavier than an atom of hydrogen. In other 
 words, it consists always of 0'9 quadrillion ions. 
 
106 THE ELECTRON THEORY 
 
 kilogrammes required to drive 1 gramme-ion through 
 water at 18 with a velocity of 1 cm. per second : 
 
 K . . . . 1467 
 
 Na ... 2180 
 
 Li .... 2833 
 
 NH 4 . . . 1490 
 
 H . . . . 302 
 
 Ag ... 1725 
 
 Cl . . . . 1450 
 
 I .... 1435 
 
 N0 3 . . . 1536 
 
 OH ... 552 
 
 CH 3 C0 2 . . 2810 
 
 C 2 H 6 C0 2 . 3110 
 
 "From these numbers it can be seen what enor- 
 mous mechanical forces are required to move the 
 ions through the solvent with an appreciable velocity. 
 As the temperature rises, these values, which are a 
 measure of the friction, decrease in about the same 
 ratio as that in which the mobilities of the ions 
 increase i.e. for most ions about 2*5 per cent, per 
 degree. 
 
 " The electrolytic friction of the ions is greater in 
 other solvents than in water. The addition of a 
 very small quantity of another non-conductor to 
 the water appreciably increases the friction of the 
 ions, and consequently diminishes the conductivity 
 of the solution, just as the internal friction of the 
 liquid is altered by a similar addition. The action 
 of foreign substances on the internal friction runs 
 almost parallel with that on the electrolytic friction. 
 Thus I have found that the addition of 1 per cent, 
 by volume of alcohol, ether, acetone, or cane sugar 
 raises the internal friction, and the electrolytic fric- 
 tion of the commonly occurring ions at 25 by the 
 amounts quoted. If greater quantities be added 
 
THE ELECTRIC DISCHARGE 1 07 
 
 there is a proportional increase in the electrolytic 
 friction; but also a diminution of the degree of 
 dissociation of the electrolyte, particularly if a con- 
 centrated solution of this is used." 
 
 These remarks of the great Swede show that the 
 two factors which determine conductivity viz. den- 
 sity of ions and mobility may both be affected by 
 substances which increase the viscosity of the solu- 
 tion. But as long as these are absent, we may 
 rely upon the constancy of that most important 
 factor, the mobility of the individual ion. 
 
 That being so, we may proceed to calculate the 
 electric current which will traverse the cubic centi- 
 metre of dilute solution we are contemplating. This 
 current consists of two streams of electrified matter. 
 One of these is the procession of positive H ions 
 towards the cathode, and the other is the procession 
 of negative Cl .ions towards the anode. If we make 
 any section across the lines of flow, a certain num- 
 ber of H ions will pass that section in one direction 
 every second, and a certain number a smaller 
 number of Cl ions will pass it in the other direc- 
 tion. The sum of these two numbers is the electric 
 current. 
 
 The two processions result in an accumulation of 
 H atoms at the cathode, and of Cl atoms at the 
 anode. But for the first second of time, at all 
 events, this accumulation will be small, and may 
 be neglected, as also may be the emptying of the 
 
IOS THE ELECTRON THEORY 
 
 neighbourhood of the anode as regards H atoms. 
 For the first stages we may suppose the whole of the 
 ions to be in motion. 
 
 The total number of H ions being 0'9xl0 18 , and 
 their mobility 0*00325, the proportion of them which 
 traverses any section will be 0*9 x 10 18 x 0*00325 per 
 second, or 2*77 x 10 15 ions per second. Since 1 
 ampere is a current of 8'79xl0 18 electrons per 
 second, the above current is equivalent to 3*15 x 10~ 4 
 ampere. This then is the positive current. The 
 negative current consists of chlorine ions, 0*9 x 10 18 
 in number, and having a mobility of 0-00068 cm. per 
 sec. The current due to them is, therefore, 0*9 x 10 18 
 X 0-00068 electrons, or 0'61 x 10 15 electrons per second, 
 which amounts to 0'69 x 10 ~ 4 ampere. 
 
 Hence we have as a net result : 
 
 Positive current . . 3*15 x 10 -^ ampere 
 Negative current . . 0*69 x 10 ~ 4 ampere 
 
 Total current . . 3*84 x 10" * ampere 
 
 or about one-third of a milliampere. 
 
 This calculation is fully confirmed by experiment, 
 and affords a very striking example of how the atomic 
 theory of electricity may be applied to obtain a clear 
 insight into what actually happens in an electrolytic 
 cell. The clearness of the theory in this connection 
 is due to the very definite data which are available 
 concerning the number of dissociated ions in solution. 
 This knowledge is by no means so precise in the case 
 
THE ELECTRIC DISCHARGE 109 
 
 of either metals or gases, and we cannot, therefore, 
 make similarly precise calculations for these. From 
 the electrical point of view, the dilute solution is the 
 best known of all substances. 
 
 The above calculation also gives us the resistance, 
 the resistivity, the conductivity ("conductance") and 
 specific conductivity of the solution. 
 
 A body is said to have a resistance of one ohm if 
 an E.M.F. of one volt applied to its terminals pro- 
 duces in it a current of one ampere. The current in 
 our case being only 3-84 x 10 " 4 ampere, the resist- 
 
 1 1 * 
 
 ance is correspondingly greater, and amounts to ^^ 
 
 = 2600 ohms. This is also the resistivity or specific 
 resistance of the electrolyte, since that is defined as 
 the resistance of 1 cm. cube. The conductivity is 
 the reciprocal of this, or 3*84 x 10~ 4 . 
 
 If, now, we increase the concentration of the solution, 
 we also increase its conductivity, since more ions will 
 be added to it. But the increase will not be in propor- 
 tion to the concentration, as less and less ions will be 
 dissociated. With one gramme-molecule of HC1 per 
 litre, the degree of dissociation will only be 59 per 
 cent, instead of 99 as before. There will be 1000 times 
 as many molecules, but the conductivity will only be 
 increased in the proportion of 59,000 : 99 or 596 : 1. 
 It will thus be 596 x 3-84 x 10~ 4 or 0-22, so that the 
 current passing will be about one-fifth of an ampere. 
 
 Our attention is next claimed by what happens at 
 
HO THE ELECTRON THEORY 
 
 the electrodes. The H atoms arrive at the negative 
 plate, which contains a vast number of electrons 
 ready to pass out of the metal into the solution 
 on the slightest provocation. Such provocation is 
 supplied by the H ions, which, having lost an electron 
 each, are positively charged, and attract electrons out 
 of the metal. When this takes place the positive 
 atom of hydrogen becomes a neutral atom. It im- 
 mediately disengages itself from the embrace of the 
 water molecules which have clung to it during its 
 charged state, attracted by some as yet mysterious 
 force, and becomes an ordinary gas. As it accumu- 
 lates, its pressure becomes such that the water can 
 no longer hold it in solution, and it escapes from the 
 water in the shape of bubbles. 
 
 At the anode the converse process happens mean- 
 while. The chlorine ion, having an electron to spare, 
 lets it pass into the positively charged plate, which is 
 poor in electrons, and the chlorine atom becomes an 
 ordinarily neutral atom of chlorine gas. But since 
 water can dissolve a great deal more chlorine than 
 hydrogen, the chlorine remains in solution, and 
 gradually diffuses from the anode towards the 
 cathode. In any case, we get an evolution of 
 hydrogen at the cathode, and chlorine at the anode. 
 The original hydrochloric acid is decomposed into its 
 constituents by this process of " electrolysis." 
 
 Faraday's "First Law of Electrolysis," maintains 
 that the quantity of substance decomposed is pro- 
 
THE ELECTRIC DISCHARGE 1 1 1 
 
 portional to the quantity of electricity passing 
 through. That this must be so is immediately 
 evident from the nature of the process as above ex- 
 plained. We must bear in mind that dissociation 
 and decomposition are not the same thing. The 
 former gives us charged ions, the latter gives us 
 neutral atoms and molecules. Every ion, having a 
 definite charge of one electron, or the lack of it, 
 must either receive an electron from the cathode 
 or give it up to the anode before it can become a 
 neutral atom. Both processes involve a passing of 
 an electron in the same direction, and therefore a 
 definite " quantity of electricity passing through." 
 Thus Faraday's First Law is self-evident in the 
 electron theory. 
 
 We have hitherto only dealt with hydrochloric 
 acid, which presents a very simple case of electro- 
 lysis. Other cases are not so simple. Take the case 
 of zinc chloride, ZnCl 2 . Here we have a molecule 
 consisting of three atoms instead of two. When 
 that becomes dissociated, each of the two chlorine 
 atoms will take away an electron from the common 
 stock, and leave the Zn with two vacancies. Each 
 zinc atom will therefore require two electrons to 
 neutralise it, and the number of zinc atoms produced 
 will be one-half the number of hydrogen atoms which 
 would be produced by the same current. The power 
 possessed by an atom of combining with one, two, 
 three, or more simple atoms like those of hydrogen 
 
112 THE ELECTRON THEORY 
 
 or chlorine is called the " valency " of the atom. In 
 the case of a metal, it is measured by the number of 
 electrons it is capable of giving up, or, in other words, 
 the number of elementary positive charges it is 
 capable of acquiring. We see then that the number 
 of atoms of any substance liberated by the current is 
 inversely proportional to the valency of the atom. 
 
 If the atoms had all the same valency, the weight 
 of the substance liberated would be simply pro- 
 portional to the weight of their atoms. But as they 
 have different valencies, we must divide the atomic 
 weight by the valency. Chemists call this quotient 
 the " chemical equivalent" of the substance. Thus 
 we obtain Faraday's Second Law of Electrolysis : The 
 amount of any substance liberated by a given electric 
 current in unit time is proportional to the chemical 
 equivalent of the substance. 
 
 The liberation of any gramme-equivalent (i.e. as 
 many grammes as the chemical equivalent weighs in 
 comparison with the hydrogen atom) requires the 
 passage of 96,537 "armies" or coulombs of electrons. 
 This is therefore the amount of electricity required 
 to liberate 1 gramme of hydrogen, 35*5 grammes of 
 chlorine, 8 grammes of oxygen, or 31-5 grammes of 
 copper. 
 
 When the two ions have the same mobilities, the 
 substances liberated at the two ions will have the 
 same concentration. This happens, for instance, in 
 the case of potassium sulphate, where the K and S0 4 
 
THE ELECTRIC DISCHARGE 113 
 
 ions have the same mobility. But in other cases, as 
 in that of HC1 above considered, the migration of 
 H away from the anode and towards the cathode 
 will be much more rapid than that of the Cl towards 
 the anode. The net result will be that, on the 
 whole, the acid will gravitate towards the cathode, 
 and leave the solution about the anode impoverished. 
 
 In the case of copper sulphate, on the other hand, 
 the salt is used up more rapidly at the cathode than 
 at the anode. For the mobility of Cu is 0-00048, 
 whereas that of S0 4 is 0-00069. The S0 4 ions clear 
 off towards the anode more rapidly than the Cu ions 
 do in the contrary direction, and the solution gets 
 diluted at the cathode. 
 
 I must add a few words on the manner in which 
 the ionisation is determined. It is found that a 
 body dissolved in a liquid has a certain pressure, 
 just as a gas has. The pressure is, in fact, the same as 
 the substance would have if the liquid were removed 
 and the molecules left suspended where they were. 
 This pressure is called the " osmotic pressure," and 
 can be exhibited by means of two communicating 
 tubes separated by a membrane which lets water 
 percolate through, but stops the dissolved substance. 
 Such a membrane is called " semiperrneable." Cer- 
 tain kinds of parchment paper act as such membranes 
 with regard to sugar. Now, if a solution of sugar is 
 put into one of the communicating tubes and pure 
 water into the other, the level of the sugar solution 
 
 H 
 
114 THE ELECTRON THEORY 
 
 is gradually seen to rise. It sucks water through the 
 membrane, and the sugar molecules are thus enabled 
 to occupy a larger volume than before. 
 
 The dissolved substances obey most of the laws of 
 gases, like those of Boyle, Gay-Lussac, and Avogadro. 
 The law of these maintains that the same volume of 
 any solution at the same temperature, and having 
 the same osmotic pressure, always contains the same 
 number of molecules or ions. 
 
 This law gives us a means of determining the 
 number of ions in a solution. For all ions act 
 osmotically as separate molecules. We need only, 
 therefore, determine the apparent increase in the 
 number of molecules in order to be able to follow 
 the gradual dissociation of the molecules as dilution 
 proceeds. An important corroboration of the results 
 thus arrived at is by determining the lowering of the 
 freezing-point of solutions or the raising of their 
 boiling-point with increasing concentration. The 
 dissociations calculated from these experiments lead 
 to the same results as those derived from obser- 
 vations of osmotic pressure and of conductivity. 
 
 6. Discharge through a Vacuum. An electrified 
 body can only be discharged through a vacuum if 
 charges can be projected out of the body into the 
 vacuum. For a vacuum by itself is a perfect in- 
 sulator. It does not convey electricity, for the same 
 reason that an empty can does not convey water 
 it does not contain any. If the electrified body is 
 
THE ELECTRIC DISCHARGE 11$ 
 
 brought into touch with a conductor, the swarms 
 of loose electrons in the conductor and the charged 
 body traverse the junction in one direction or the 
 other until the body is discharged, or the charge 
 divided between the two conductors according to 
 their capacities. If a solution of an electrolyte is 
 interposed between them, equilibrium is established 
 by a migration of ions in both directions through 
 the liquid. If a gas intervenes, the exchange is 
 carried on by means of any electrons or heavier ions 
 that may happen to be in the gas, or that may be 
 produced by collision or other ionising agency. But 
 these facilities are not available when a perfect 
 vacuum intervenes between two conductors at 
 different potentials. The only bodies capable of 
 furnishing carriers of electricity are the conductors 
 themselves. Now it is found that, although a con- 
 ductor may be charged to a potential of thousands 
 of volts, it is not easily discharged into a vacuum. 
 The extra electrons, or positive atoms, never number 
 more than one in a million ; but they are all on 
 the surface of the conductor on account of their 
 mutual repulsion. 
 
 Why, then, do they not leave it and fly out into 
 the vacuum? The force that holds them back is 
 not yet fully explained; but it is the same force 
 as that which prevents ions in a solution from 
 separating out before they are discharged. These 
 ions condense the liquid round themselves as long 
 
Il6 THE ELECTRON THEORY 
 
 as they are charged. They attract the neutral 
 liquid, and the neutral liquid attracts them, hold- 
 ing them fast until they lose their charges at the 
 opposite electrode. When ions happen to be con- 
 tained in a moist gas, they act as centres of 
 condensation, and it has been suggested that our 
 whole rainfall is due to ions in the atmosphere, 
 chiefly negative ions as well as electrons. This 
 condensing action is, no doubt, also active in metals, 
 and offers a certain hindrance to the free expulsion 
 of the charge from a conductor into a vacuum. 
 When a charged liquid is boiled, the vapour carries 
 off none of the charge. 
 
 Ultra-violet light has a powerful effect in facili- 
 tating the discharge of electrons from negatively 
 charged conductors, and entirely overcoming the hin- 
 drance ordinarily experienced. The light- waves may 
 be conceived as shaking up the neutral atoms con- 
 densed round the electron, and setting the latter free. 
 
 Now, suppose we have two conductors in a 
 vacuum at a difference of potential of one electro- 
 static unit (300 volts), and that by the action of 
 ultra-violet light or other agency the electrons in 
 the negative conductor are set free to enter the 
 vacuum. They will, of course, be repelled by the 
 negative conductor, and attracted by the positive 
 conductor, and, since nothing is stopping them, they 
 will fall freely from one to the other, and we can 
 calculate their velocity by the well-known laws of 
 
THE ELECTRIC DISCHARGE II 7 
 
 falling bodies. But a simpler way is to calculate 
 their energy, and deduce the velocity from that. 
 The energy required to drive one "company" (or 
 " electrostatic unit ") of electrons against one unit 
 difference of potential, or 300 volts, is 1 erg. When 
 the same company falls freely through the same 
 difference of potential its kinetic energy is therefore 
 also 1 erg. A single electron, possessing as it does 
 a charge of 3'4xlO- 10 units, will have a kinetic 
 energy of 3'4xlO- 10 ergs, and this, as we know, is 
 equal to half its mass multiplied by the square of 
 its velocity 
 
 Now m is 0*61 x 10~ 27 of a gramme, hence we 
 know v 
 
 2x3'4xlO- 10 
 
 " 0-61x10-27 
 and 
 
 v = 1 *06 x 10 9 cm. per sec. 
 
 This is truly an astonishing velocity, 6600 miles 
 per second ! It is about one-thirtieth of the 
 velocity of light. But strange as it may seem, 
 such a velocity has been actually observed in 
 vacuum tubes. Had the Newtonian opponents of 
 the wave-theory of light been acquainted with this 
 remarkable fact, the corpuscular theory of light 
 would have died harder than it did. 
 
 Since the velocity varies as the square root of the 
 difference of potential traversed, it would theoreti- 
 
Il8 THE ELECTRON THEORY 
 
 cally require 30 2 or 900 times 300 volts to impart a 
 speed equal to that of light to the electrons. The 
 voltage could be obtained, perhaps; but it would 
 not have the desired effect, since the resistance of 
 the ether to the motion of a very fast electron is 
 very considerable, and becomes infinite near the 
 speed of light. 
 
 Electrons projected with such velocities as these 
 are known as cathode rays. They were discovered 
 by Pliicker in 1858, and described by Crookes in 
 1879 under the name of " radiant matter," a name 
 which was much more appropriate than the scientific 
 world was inclined to believe at the time, or, indeed, 
 for many years after. Crookes, however, thought 
 the rays consisted of atoms, which were then con- 
 sidered the smallest possible bodies in the universe. 
 Nowadays the cathode rays would be more appro- 
 priately styled " radiant electricity." They are pro- 
 duced in a glass tube exhausted to one-millionth of 
 an atmosphere, thus leaving only 40 billion molecules 
 of gas per cubic cm. Crookes showed that they pro- 
 ceed in straight lines at right angles to the surface 
 whence they spring, that an obstacle placed in 
 their way casts a sharp shadow ; that they produce 
 a vivid phosphorescence when impinging upon glass, 
 or especially jewels; that they exert a mechanical 
 pressure where they fall, and that they can be 
 deflected by a magnet. To these important pro- 
 perties we must now add the still more remarkable 
 
THE ELECTRIC DISCHARGE 1 1 9 
 
 property of producing Rontgen rays when they 
 impinge upon a solid body. 
 
 Positively charged bodies can also be discharged 
 through a vacuum; but as there are no positive 
 electrons,, the smallest positive carriers are of atomic 
 dimensions, and are at least 1000 times heavier than 
 electrons. Since the charge of a positive atom is 
 the same as that of an electron, the electric force 
 upon it is also the same. But this force, having to 
 set in motion a body at least 1000 times heavier 
 than an electron, will produce in it a velocity at 
 least 1000 times less. Wien has actually found a 
 group of positive ions having one-thousandth of the 
 velocity of electrons, another having one twenty- 
 thousandth, and another having one-millionth of 
 their velocity. The last of these must consist of 
 groups of neutral atoms combined with one positive 
 atom each. Positive ions moving with these com- 
 paratively high velocities are called " canal rays," 
 since they are best observed by perforating the 
 cathode, and letting them emerge on the other 
 side. It is interesting to note that material par- 
 ticles of atomic dimensions can be endowed with a 
 velocity of six miles per second by a human agency. 
 This speed is about twice the velocity of a point at 
 the Equator due to the earth's rotation. 
 
 The prodigious velocities acquired by charged 
 particles in a vacuum probably play a very im- 
 portant part in the electric equilibrium of the 
 
120 THE ELECTRON THEORY 
 
 universe. Consider one or two points. The differ- 
 ence of potential between the earth and the sun is 
 about a billion volts, the sun being positive and the 
 earth negative. Any electrons expelled from the 
 earth will therefore travel towards the sun with a 
 constantly increasing speed, and will travel with a 
 velocity nearly equal to that of light over the last 
 stages. Its kinetic energy will go to keep up the 
 sun's heat. When it gets into the neighbourhood 
 of the sun it will exert its condensing action upon 
 the neutral gases there, and will form a small drop. 
 This drop will be exposed to the radiation of the 
 sun, which, according to Maxwell and Bartoli, exerts 
 a pressure sufficient to balance the weight of a very 
 small drop. The maximum pressure in comparison 
 with weight is exerted on a drop 8xlO~ 6 cm. in 
 radius, and having the density and capacity of water. 
 The radiation pressure is then 2*5 times the gravi- 
 tational attraction. Such drops are constantly being 
 repelled from the sun in enormous numbers. Their 
 expulsion keeps up the sun's positive charge ; but 
 that positive charge does not increase indefinitely, 
 since the sun drains vast tracts of space of the 
 electrons which abound in them. Arrhenius has 
 estimated that the sun drains the space as far out 
 as one-sixtieth of the distance of the nearest fixed 
 star of its free electrons, and thus maintains a 
 constant circulation of electricity throughout the 
 solar system. 
 
CHAPTER V 
 
 THERMO-ELECTRICITY 
 
 WE will now return to metallic conductors in order 
 to study the effect which heat exerts upon the dis- 
 tribution and motion of electrons in them. 
 
 The modern view of heat is that it is a rapid 
 motion of the smallest particles of matter. Before 
 the days of the electron theory, these smallest 
 particles were supposed to be atoms. We now know 
 that atoms are not the smallest existing particles; 
 but the electrons, which are at least as numerous 
 as the atoms in a metal, are at least one thousand 
 times lighter, and about a hundred thousand times 
 smaller. The equality of temperature throughout 
 the metallic mass means that the average kinetic 
 energy of the particles of all kinds is the same in 
 any small volume chosen at random. Now, since 
 the kinetic energy of a body is J mv*, where m is 
 its mass and v its velocity, two bodies at the same 
 temperature must have the same velocity if their 
 masses are equal; or, if they are unequal, their 
 velocities must compensate such inequality. If the 
 mass of one body is one-fourth of that of another 
 body, the square of its velocity must be four times 
 
122 THE ELECTRON THEORY 
 
 as large, and its velocity must be twice as large. 
 Now, since the mass of the electron is about 56 ooo- 
 of that of an iron atom, its velocity at the same 
 temperature must be 240 times as great. 
 
 The absolute temperature varies as the square 
 of the velocity of the particles. The "absolute" 
 temperature in degrees centigrade is reckoned from 
 the absolute zero of temperature, which is 273 
 below freezing-point. Thus the absolute tempera- 
 ture of melting ice is 273, and of boiling water 
 373. Hence, the velocities of the particles at 
 freezing-point and boiling-point will be as 
 
 V273 : v /373~, or 16-5 : 19'3. 
 
 In heating a wire from the freezing-point to the 
 boiling-point of water, the velocity of all its atoms 
 and electrons is increased 17 per cent. 
 
 Now we have seen that the electrons behave 
 practically like a gas capable of penetrating the 
 metal. When they are heated it is just as if the 
 pressure of a gas were increased by heating it. 
 Their pressure is also increased, and they make 
 their way into cooler parts, where the pressure is 
 less. 
 
 Here, then, we have a displacement of electrons, 
 and we know that a displacement of electrons con- 
 stitutes an electric current. It is therefore possible 
 to generate an electric current by heating a metal 
 unequally in different parts. 
 
THERMO-ELECTRICITY I 2 3 
 
 If the wire is bent into a ring, and it is heated 
 at one point, electron currents in opposite directions 
 will start from the hot point. There will, of course, 
 be no current round the circuit, since the two 
 opposed currents neutralise each other. But if the 
 wire on one side of the hot point is kept cool in 
 a water-jacket, the slope of pressure will be more 
 abrupt on that side, and the electrons will pass by 
 preference in that direction. There will, therefore, 
 be a resultant electron current in the direction of 
 the water-jacket, or a positive current in the reverse 
 direction. Any other means of making the slope 
 of temperature and kinetic pressure more abrupt 
 will have the same effect. Thus, if the wire is 
 passed slowly through a flame, leaving a steeper 
 gradient of temperature in front than behind, the 
 electron current will flow in the direction in which 
 the flame moves along the wire. 
 
 Conversely, if an electron current is sent along 
 a wire containing a hot point, it will carry the heat 
 along with it, producing a more gradual slope of 
 heat on the other side of the hot point. This may 
 be well observed in an iron wire. 
 
 The simplest way of altering the slope of the 
 heat-curve is by joining two metajs of different 
 conductivities for heat. Thus, if (Fig. 18) a bar of 
 lead and a bar of zinc are joined at A and heated 
 at the junction, the slope of temperature will be 
 more abrupt on the lead side than on the zinc side, 
 
124 THE ELECTRON THEORY 
 
 and an electron current will pass steadily from the 
 zinc to the lead and back through the wire outside. 
 Or, to use the older language, a (positive) current 
 will pass across the hot junction from lead to zinc. 
 
 If we leave the zinc-lead junction cool, and send 
 an electron current through it from the zinc to the 
 lead, it is evident that the same number of electrons 
 
 COLD HOT COLD 
 
 FIG. 18. 
 
 must pass every cross-section both of the lead and 
 the zinc. Since there is more resistance to be over- 
 come in the lead than in the zinc, the electrons 
 entering the lead must acquire an extra supply of 
 energy, and this can only be derived from the 
 motion of the atoms and electrons themselves. 
 Hence the junction A will be cooled. An electron 
 current in the reverse direction would heat the same 
 junction. This heating and cooling of junctions of 
 dissimilar metals by a current passing through is 
 known as the Peltier effect. 
 
 All the above reasonings have supposed that the 
 heating and cooling have no effect upon the electric 
 conductivity of the metal, nor upon its two factors 
 
THERMO-ELECTRICITY I 2 5 
 
 viz. the density and mobility of the electrons. But 
 in reality both these factors are profoundly affected 
 by heat, and the actual phenomena are therefore 
 more complicated than the above reasoning might 
 lead us to suppose. Before we are in a position to 
 deal fully with thermo-electric phenomena, we must 
 have some more information concerning these two 
 factors, and must also consider the difference of 
 potential between two metals or other conductors 
 produced by contact at ordinary temperatures. 
 
 I have indicated the general principles upon which 
 a full theory of thermo-electric effects must be based. 
 But this full theory is by no means worked out as 
 yet. The older theories stood quite helpless before 
 the puzzling variety of thermo-electric phenomena. 
 The electron theory gives us valuable help; but a 
 great deal remains to be done, and the research 
 student cannot choose a more promising field for 
 his labours, or one more likely to give him a rich 
 reward, than the connection between electricity 
 and heat. The direct conversion of thermal into 
 electrical energy in other words, the generation 
 of electricity direct from coal is a problem fraught 
 with great economic consequences. Thermo-electric 
 batteries have been employed for .some time in 
 galvanoplastic and other small installations ; but 
 their efficiency and durability still leave much to 
 be desired. Haphazard experiments are not likely 
 to lead to any radical improvement without the 
 
126 THE ELECTRON THEORY 
 
 probability of a long series of costly failures. 
 But a good working theory of thermo-electricity 
 may indicate the lines along which success 
 may be looked for with a reasonable degree of 
 probability. 
 
 The fact discovered by Seebeck is that when a 
 rod of antimony and a rod of bismuth are joined at 
 one end and heated at that end, and the bismuth 
 rod is bent round so as to join the antimony at the 
 other end, and that junction is kept cool, a (positive) 
 current flows across the hot junction from the 
 bismuth to the antimony. 
 
 This means, according to the electron theory, that 
 electrons travel across the hot junction from the 
 antimony to the bismuth, and across the cold 
 junction from the bismuth back to the antimony. 
 There is no real " positive current," since that would 
 need atoms for its transportation, and these could 
 only be bismuth atoms travelling across the hot 
 junction into the antimony. The end of the anti- 
 mony would thus be converted into an alloy of 
 bismuth and antimony. This has never been ob- 
 served; but it has been found that under extreme 
 pressure one metal may be forced to diffuse into 
 another, and when that takes place a real positive or 
 atomic current may pass. Under ordinary circum- 
 stances the electron current is the only electric 
 current large enough to be measured. But we may 
 suppose that a certain amount of atomic diffusion 
 
THERMO-ELECTRICITY 127 
 
 does take place even at ordinary pressures, and to 
 this atomic diffusion current we may attribute the 
 gradual degeneration of thermo-electric batteries. 
 
 Antimony and bismuth show one of the largest 
 thermo-electric effects known, and this fact no doubt 
 facilitated its discovery by Seebeck. But all com- 
 binations of metals may be used for generating 
 thermo-electric currents. The current-strength 
 obtained varies from one metal to another. We 
 know that the current is proportional to the conduc- 
 tivity and to the energy spent in driving an electron 
 round the circuit, and we have seen that this energy- 
 per-electron is called the electromotive "force'* 
 (E.M.F.). Now the E.M.F. generated by a bis- 
 muth-antimony couple whose junctions are kept at 
 boiling-point and freezing-point respectively is ^foj-th 
 of that of a Daniell cell, so that 200 couples would 
 have to be ranged in series in order to give the 
 E.M.F. of a single Daniell cell. Bismuth, being 
 costly, and its resistivity high, such a battery 
 would cost much more than the cell. But then 
 a current could be obtained from it at any time 
 by heating alternate junctions with boiling water 
 or steam. 
 
 E. Becquerel in 1864 compared a la^ge number of 
 metals with copper, and measured the E.M.F.'s they 
 yielded when combined with copper, with their 
 junctions kept at freezing-point and boiling-point 
 respectively. I quote his results : 
 
128 THE ELECTRON THEORY 
 
 Bismuth . 
 
 . -3-91 
 
 Platinum . 
 
 -0-09 to 0-38 
 
 Cobalt 
 
 . -2-24 
 
 Zinc . 
 
 -0-02 to 0-04 
 
 Nickel 
 German silver 
 
 . -1-63 
 . -1-26 
 
 Copper 
 Silver 
 
 
 + 0-026 
 
 Palladium . 
 
 . -0'82 
 
 Cadmium . 
 
 + 0-033 
 
 Mercury 
 Lead . 
 Tin . 
 
 . -0-48 
 . -0-187 
 . -0-147 
 
 Iron . 
 Antimony 
 Tellurium 
 
 + 0-95 to 0-67 
 + 1-41 
 + 39-95 
 
 Gas carbon 
 
 . -0-142 
 
 
 
 The figures mean thousandths of a Daniell 
 (1 Daniell = 1*1 volt), and the negative sign indi- 
 cates that the positive current flows across the hot 
 junction from the metal in question to the copper 
 i.e. that copper yields electrons to the metals across 
 the hot junction. 
 
 The E.M.F. of any two metals may be obtained by 
 adding up the figures for each, if of opposite signs, or 
 subtracting them, if of the same sign. 
 
 It will be seen at once that the commoner metals 
 have very poor thermo-electric effects. A zinc- 
 copper thermo-couple has only ^^th of the E.M.F. 
 possessed by a bismuth-antimony couple, so that it 
 would require 40,000 zinc-cooper couples to make up 
 an E.M.F. equal to that of a Daniell cell. 
 
 The thermo-electric force is, generally speaking, 
 proportional to the difference of temperature between 
 the junctions. The rise of the thermo-electric force 
 with the temperature is so constant and reliable that 
 a system of thermometry by thermo-couples has 
 been based upon it. But some couples, notably the 
 combinations with iron, show a gradual decrease of 
 
THERMO-ELECTRICITY I 2 9 
 
 the rise at higher temperatures, and at certain 
 differences of temperature there is a zero thermo- 
 electric force, or even a new force in the opposite 
 direction. 
 
 Liebenow has found an important relation between 
 the thermal and electric conductivities which enables 
 us to predict the thermo-electric force of a combina- 
 tion of two metals with some certainty. He finds 
 that the greater the conductivity for heat is in 
 comparison with the conductivity for electricity, the 
 more freely do electrons pass out from a metal 
 across a hot junction. He also finds that there is 
 an E.M.F. generated within the metal itself which 
 urges the electrons to proceed in the direction in 
 which heat is being propagated. This is just as we 
 should expect. The E.M.F. of the thermo-couple is 
 a differential effect, due to more electrons being 
 dragged along by the heat in one metal than in 
 another. If L is the conductivity for heat and S the 
 electric conductivity, the E.M.F. between two por- 
 tions of the same metal kept at two different 
 temperatures, say at boiling-point and freezing- 
 point, is proportional to /v/-g. This means that 
 
 whatever affects the two conductivities also affects 
 the E.M.F. of the metal concerned. Now we know 
 that the resistance of a metal increases with the 
 temperature; that is to say, the conductivity 
 diminishes as the temperature rises. Hence the 
 
 I 
 
130 THE ELECTRON THEORY 
 
 above ratio will increase with heating, if the thermal 
 conductivity remains constant. This is very gene- 
 rally the case, and whatever may be the difference 
 between two metals in their internal thermo-electric 
 forces, that difference is, as a rule, exaggerated on 
 further heating. But in some metals the difference 
 tends to disappear on heating, or to be reversed, and 
 then the E.M.F. of the couple passes through a 
 maximum, and then diminishes. 
 
 To help us in our search for the ideal thermo- 
 couple an ideal which, once realised, would be of 
 the utmost practical importance we may say that 
 
 what we want is two metals in which the ratio yr 
 
 is as different as possible. For instance, one of them 
 might have a very high, and the other a very low, 
 conductivity for heat in comparison with its electric 
 conductivity. Antimony has a high, and bismuth a 
 low ratio. 
 
 Another desideratum is that the ratios of the two 
 metals shall not tend to become equal as the tempera- 
 ture rises. For then a point (called the "neutral 
 point ") would be reached at which the wandering of 
 the electrons would be the same in both directions 
 away from the hot junction, and none would traverse 
 the junction. There would be no electron current, 
 and hence also no " positive current." 
 
 The ratio depends essentially upon the energy 
 of the carriers of thermal and electric energy in 
 
THERMO-ELECTRICITY I 3 I 
 
 proportion to their absolute temperature. The 
 carrier of the electrical energy is the electron, having 
 a mass of 10~ 27 gramme, which we will call m. The 
 carriers of thermal energy are both atoms and 
 electrons. If they are mainly atoms, we may put 
 their mass M at about 60,000 times that of the 
 electrons. Finally, if T is the absolute temperature 
 (i.e. 273 + the degrees centigrade), then we have the 
 internal thermo-electric force in a metal proportional 
 
 to ---. The best thermo-electric effect would 
 
 therefore be obtained by combining two metals 
 differing in such a manner that this ratio would be 
 great in one and small in another. Now that ratio 
 is, as we have seen, small in bismuth. The mass of 
 the carriers of heat is small. This means either that 
 there are few atomic clusters, or that the electrons 
 themselves diffuse the major part of the thermal 
 energy. In antimony, on the other hand, the carriers 
 of heat are mainly larger masses. There is more 
 energy in a gramme of antimony that in a gramme 
 of bismuth at the same temperature. Hence the 
 electrons, always tending to expend their energy 
 as rapidly as possible, pass by preference into the 
 bismuth. At the cold junction, where^the difference 
 of energy is not so marked, the electrons must, 
 perforce, return into the antimony under pressure 
 from the hot junction, and so the circuit is 
 completed. 
 
132 THE ELECTRON THEORY 
 
 When, on the other hand, an independent current 
 is sent across a junction from bismuth to antimony, 
 the increased energy in the antimony is generated 
 by absorption of heat at the junction. This is the 
 Peltier effect. The cooling of the junction in its turn 
 
 HOT 
 
 COLD 
 COLD 
 
 HOT 
 
 FIG. 19. 
 
 generates a current in the direction opposed to the 
 original current. This is an instance of the well- 
 known rule that whatever action an electric current 
 may exert, that action acts contrary to the current. 
 To put it briefly, all acts of an electric current are 
 suicidal. 
 
 To sum up, we have three thermo-electric effects. 
 The first, that discovered by Seebeck, shows an 
 electric current generated by the unequal heating 
 of the two junctions of two different metals. The 
 second, that discovered by Peltier, shows the cool- 
 ing of a junction of two different metals, which, if 
 heated, would produce a current in the same direc- 
 tion. When the current is reversed, the junction is 
 heated instead of being cooled. 
 
 The third effect is known as the Thomson or 
 
THERMO-ELECTRICITY I 3 3 
 
 Kelvin effect. It is really the most important effect 
 of all, the others being merely differential effects. It 
 consists in the transportation of electricity with a 
 current of heat, and vice versd. An ingenious 
 experiment for exhibiting this effect has been 
 devised by Le Roux. A current is sent through 
 three bars of copper, placed as shown in the figure. 
 The junctions on the right-hand side are heated, 
 while the other ends are cooled. There can be no 
 Seebeck effect, as the metal is everywhere the same. 
 But in one bar the electric current goes from cold to 
 hot, in the other from hot to cold. In one bar it 
 opposes the heat current, in the other it aids it. As 
 a consequence, the heat travels faster in one bar 
 than in the other, and disturbs the even flow of 
 the electric current. A galvanometer connected as 
 shown, and made to show no deflection when the 
 junctions are all at the same temperature, shows a 
 permanent deflection when heat is applied, thus 
 indicating that a current has been diverted into it. 
 
CHAPTER VI 
 
 VOLTAIC ELECTRICITY 
 
 UNDER the name Voltaic Electricity are comprised 
 a number of phenomena which depend upon differ- 
 ences in the behaviour of bodies towards electricity 
 apart from effects of temperature, magnetism, and 
 other factors. 
 
 These phenomena are connected with the most 
 intimate internal structure of the elements, and are 
 therefore of great variety, and of some uncertainty, 
 being often profoundly affected by surface conditions 
 and by slight impurities. But in the hundred years 
 since Volta discovered contact electricity, much has 
 been done in the way of establishing the general 
 principles which underlie the phenomena, and which 
 indicate their connection with chemical reactions. 
 
 Electrification by Contact. The fundamental fact 
 discovered by Volta in 1797 is that when a piece of 
 zinc touches a piece of copper, a spontaneous charge 
 of both metals takes place, the zinc being charged 
 positively and the copper negatively. 
 
 Since the combination of the two metals exerts 
 no electrical force at a distance, the positive electri- 
 fication of the zinc must be exactly equal to the 
 
 134 
 
VOLTAIC ELECTRICITY 135 
 
 negative electrification of the copper. This, when 
 stated in the language of the electron theory, 
 amounts to saying that a certain number of electrons 
 have passed across the point of contact from the 
 zinc to the copper. When the metals are separated, 
 their charges become more evident, being no longer 
 neutralised by each other. The charges can be re- 
 moved by connecting the metals to earth. In other 
 words, when the metals are connected with, say, a 
 water-pipe, electrons pass from the earth into the 
 zinc, and from the copper into the earth, until 
 copper, zinc, and earth are again at the same 
 potential. The process can then be repeated in- 
 definitely, always with the same result. 
 
 We may state the result by saying that copper 
 exerts a greater attraction upon electrons than zinc. 
 Hence, when electrons pass from zinc to copper, 
 work is done upon them, just as it is done upon 
 them when they pass from a negatively to a posi- 
 tively charged body i.e. from a body having an 
 excess of electrons to a body having a deficiency of 
 electrons. There is thus a natural or inherent differ- 
 ence of potential between them, which only comes 
 into operation when they are brought into contact, 
 and which then leads to the passage of electrons 
 from the zinc to the copper. This passage con- 
 tinues until the positive charge of the zinc and the 
 negative charge of the copper become so large that 
 the potentials due to them just balance the natural 
 
136 THE ELECTRON THEORY 
 
 difference of potential. The potential due to the 
 newly acquired charges thus forms a measure of 
 the natural difference of potential, and is called the 
 " contact potential " between the two metals. This 
 contact potential is found to be constant for the 
 same two specimens, subject to slight fluctuations 
 with temperature and surface condition. It amounts 
 to about three-quarters of a volt in the case of ordi- 
 nary commercial copper and zinc. This means that 
 when one " company " of electrons (i.e. one electro- 
 static unit of negative electricity) passes from 
 originally uncharged zinc to uncharged copper 
 across the junction, the amount of work done 
 upon it, and frittered away into heat, is ^^th of 
 a d^ne. 
 
 The larger the surfaces of the metals, and the 
 smaller their distance apart, the larger is their 
 " capacity" (p. 58) regarded as a condenser. Hence 
 also the larger is the amount of electricity which 
 must pass in order to bring up the difference of 
 potential to the amount required to balance the 
 natural difference of potential. Therefore, although 
 the contact potential is a constant quantity, the 
 actual charge of the metals depends upon their 
 dimensions and upon the intimacy of their contact. 
 This fact sheds considerable light upon electrifica- 
 tion by friction, where the rubbing of one body over 
 another increases the charge of each. 
 
 We must next endeavour to account for the fact 
 
VOLTAIC ELECTRICITY 137 
 
 that zinc has a greater tendency than copper to get 
 rid of its electrons. 
 
 We have seen above (p. 110) that metallic atoms 
 have a tendency to get rid of one or two electrons 
 each whenever they can find a non-metallic atom 
 ready to take up the electrons they themselves can 
 spare. 
 
 When zinc is immersed in a dilute solution of 
 one of its own salts say, zinc chloride the atoms 
 of the zinc have a powerful tendency to pass into 
 the liquid as positive ions. In endeavouring to do 
 so, they must somehow dispose of their superfluous 
 electrons. The zinc atoms already in solution are 
 unable to take up electrons without neutralising 
 and precipitating themselves, while the chlorine 
 atoms are already in charge of the electrons given 
 up by the dissolved zinc. The only alternative re- 
 maining is, therefore, to leave the electrons behind 
 in the mass of the metal, which is thereupon charged 
 negatively. Even when this negative charge is re- 
 moved by connection with earth, the solution of the 
 zinc cannot proceed much further, since the accumu- 
 lation of positive zinc ions in the liquid charges 
 the liquid positively, and thus prevents any further 
 positive atoms from entering it. The positive charge 
 of the liquid can be measured, and when that is 
 done, it represents a measure of the strength of the 
 tendency of zinc to give up its electrons and go into 
 solution. This tendency is called the " solution- 
 
138 THE ELECTRON THEORY 
 
 pressure" of the zinc. It is very similar to the 
 " vapour pressure" of a liquid, and like it, it can 
 be measured in atmospheres. The solution-pressure 
 of zinc is enormous: it is about a trillion atmos- 
 pheres. That of copper, in copper sulphate, is very 
 small, being about a trillionth of an atmosphere. 
 No wonder, then, that when copper and zinc are 
 brought into contact, the eagerness of the zinc to 
 dispose of its electrons should exhibit itself in the 
 extrusion of electrons from the zinc into the copper, 
 thus producing the phenomenon observed by Volta. 
 
 The facility with which zinc loses its electrons is 
 shown in a striking manner by some recent experi- 
 ments of Fuechtbauer. He produced a stream of 
 " canal rays," or positive gaseous ions, in a vacuum 
 tube, and let that stream impinge upon various 
 metals. He found that the metals, which were 
 platinum, silver, copper, zinc, and aluminium, all 
 gave off electrons under the impact of the canal 
 rays ; but that the electron current from the copper 
 was to that from the zinc in the ratio of 128 to 
 192. A still greater current (305) was obtained 
 from aluminium; but the behaviour of this metal 
 depends very largely upon its surface condition. 
 When polished with oil and pumice, it is more 
 positive than zinc, and therefore gives off electrons 
 still more easily; when cleaned with water and 
 dried in air, it is less positive than zinc. 
 
 Another set of phenomena which go to explain 
 
VOLTAIC ELECTRICITY 139 
 
 contact electricity is that of discharge by ultra- 
 violet light. This remarkable phenomenon, dis- 
 covered by Hertz, and studied in detail by Elster 
 and Geitel, Stark, and others, consists in the spon- 
 taneous discharge of a negatively charged body 
 when illuminated by ultra-violet light. It may be 
 exhibited as follows: A well-cleaned zinc plate is 
 mounted vertically, and exposed at short range to 
 the light of an arc lamp or an intense electric spark, 
 both of which contain abundant ultra-violet rays. 
 The zinc plate is connected with a sensitive electro- 
 meter. This then indicates a positive charge after 
 a short time. This gradually increases, and may 
 reach 30 volts if air is blown against it, in order 
 to remove the expelled electrons to a distance. This 
 shows that the zinc plate has given off negative 
 electricity i.e. electrons. The conclusion is con- 
 firmed by sucking the gas near the plate through 
 a metallic tube containing a plug of glass wool 
 at the other end. The tube becomes negatively 
 charged, owing to the absorption of the electrons 
 by its wall. 
 
 If the zinc plate is negatively charged to begin 
 with, it loses its charge very gradually in the dark. 
 But, if an earthed piece of copper* or brass wire 
 netting is placed over it, and it is illuminated with 
 ultra-violet light through the network, the charge is 
 rapidly dissipated. A positive charge is not affected 
 in this manner. If the copper netting is connected 
 
140 THE ELECTRON THEORY 
 
 through, a galvanometer and a battery with the zinc 
 in such a manner that the zinc is negatively charged, 
 the galvanometer indicates an electron current 
 passing steadily from the zinc to the copper and 
 back through the battery as long as the illumination 
 is kept up. 
 
 Such a current is called a " photo-electric current." 
 Similar currents are exhibited by other metals 
 besides zinc ; but in copper and platinum, for 
 instance, they are extremely feeble, owing to the 
 tenacity with which they retain their electrons. 
 
 Volta arranged a number of metals in a series 
 in such a manner that any metal combined with 
 any other metal further on in the series would be 
 positively charged. The Volta series is : Zinc, lead, 
 tin, iron, copper, silver, gold. He found, further, 
 that the contact force between any two of them was 
 equal to the sum of the contact forces of the inter- 
 mediate pairs. This is fairly obvious, since the drop 
 of potential in passing from one metal to a second, 
 and from the second to a third, must be equal to the 
 rise of potential in passing from the third back to 
 the first if there is to be conservation of energy. 
 Otherwise an electron, by passing round in this 
 manner, might be made to generate energy con- 
 tinuously out of nothing. 
 
 A more complete voltaic series is that given by 
 Hankel as follows : Aluminium, zinc, cadmium, 
 lead, tin, antimony, bismuth, German silver, brass, 
 
VOLTAIC ELECTRICITY 141 
 
 mercury, iron, copper, gold, palladium, silver, coke, 
 platinum. 
 
 That the voltaic series is determined by the ease 
 with which the metals lose electrons is proved by the 
 fact that the same series governs 
 
 (a) The solution pressure of a metal immersed in 
 a solution of one of its own salts ; 
 
 (6) The photo-electric current from a metal ; and 
 
 (c) The electron current from a metal when ex- 
 posed to canal rays. 
 
 It may therefore be taken that the contact force 
 between two metals, about which physicists have 
 been contending for a hundred years, is now reduced 
 to a simple principle, and that any further ex- 
 planation must tell us why some metallic atoms 
 hold electrons more firmly than others. A highly 
 ingenious explanation of this has recently been 
 furnished by J. J. Thomson, and will be dealt with 
 in the chapter on the constitution of the atom 
 and the nature of electrons. For the present, 
 we will take the different attractions exerted by 
 different metals upon the electron for granted. 
 
 Contact electrification is not confined to metals, 
 but is practically universal, not only between dis- 
 similar bodies, but between the same* bodies having 
 a slight difference of structure or surface condition. 
 We have already seen that a kind of contact E.M.F. 
 exists between two portions of the same body which 
 are at different temperatures, the only difference 
 
I4 2 THE ELECTRON THEORY 
 
 being that the difference of temperature has to 
 be artificially maintained. 
 
 Non-conductors also exhibit decided contact 
 forces. They may be determined by mounting them 
 between different metals. Thus, when paraffin-wax 
 is poured between plates of copper and zinc, the plates 
 acquire a certain difference of potential, which repre- 
 sents the sum of the contact forces between copper 
 and paraffin, and paraffin and zinc respectively. 
 
 Frictional Electricity. That frictional electri- 
 fication is simply a form of voltaic electricity is 
 evident from the fact that the electrification by 
 friction is of the same sign as the electrification 
 by contact. But frictional electrification is even 
 more sensitive to surface conditions than contact 
 electrification, no doubt because the intimacy of 
 contact is much greater. The greater intimacy of 
 contact, by increasing the capacity of the two bodies, 
 also increases the charges they acquire through the 
 same difference of potential. These charges may 
 be very high, and are confined to smaller areas 
 in non-conductors than in conductors, owing to the 
 fact that the latter distribute the charges uniformly 
 over their surfaces. Hence it may happen that 
 when two non-conductors are separated after being 
 rubbed together, the charges are very strong, and 
 lead to sparking and spluttering. This circumstance 
 explains why electrification by friction was the first 
 form of electrification discovered. 
 
VOLTAIC ELECTRICITY 143 
 
 Attempts have been made to arrange substances 
 in a series corresponding to Volta's series, in such, 
 a manner that any one of them, rubbed against 
 any subsequent one, is positively electrified. The 
 series given by Faraday is the following : Catskin, 
 flannel, ivory, quill pens, rock crystal, flint glass, 
 cotton, canvas, white silk, the hand, wood, lacquer, 
 metals (iron, copper, brass, tin, silver, platinum), 
 sulphur. 
 
 It appears from this series that all metals lose 
 their electrons less easily than most of the sub- 
 stances above enumerated. But caoutchouc, sealing- 
 wax, sulphur, collodium, and guncotton are still 
 more retentive of electrons, and therefore become 
 negatively charged even by friction against silk. 
 Gaugain has arranged the metals in a frictional 
 series which corresponds closely to Volta's contact 
 series. 
 
 The Galvanic Cell. In all these contact electri- 
 fications there is no passage of one material into 
 another. It is the electrons alone which pass, and 
 the substance which loses electrons most easily 
 becomes positively charged. But an entirely dif- 
 ferent state of things arises when a metal is 
 immersed in a liquid capable of dissolving it. In 
 this case it is the dissolved metal, and not the 
 solid lump, which loses electrons in order to form 
 hydrated ions, and as a general rule the electrons 
 are gathered up by the lump of metal, which 
 
144 THE ELECTRON THEORY 
 
 thereby becomes negatively charged. The greater 
 the solution pressure of the metal, and the greater 
 its tendency to lose electrons, the greater will 
 therefore be the number of electrons accumu- 
 lated by the metal itself. This result appears 
 strange until we realise that the zinc ions are the 
 result of a clustering of the solvent round the 
 zinc atoms a clustering which means a loss of 
 energy. Since the clustering, as we have seen, 
 can only take place if the zinc atom is charged, 
 and the zinc atom is incapable of taking up an 
 extra electron, it must lose one or two electrons 
 in order to get charged. Work must be done in 
 order to draw the positive zinc atom out of the 
 negatively charged metal, and the energy necessary 
 for this work is furnished by the clustering of 
 the molecules of the solvent. When, besides the 
 zinc, another metal, say copper, is immersed in 
 the same solvent, it may happen that the solution 
 pressures of the two metals differ very widely. 
 In that case the zinc will be much more highly 
 charged with electrons than the copper, and if 
 metallic connection is established between them, 
 an electron current will pass from the zinc to 
 the copper. In the older language this means 
 that a current or " positive current " passes from 
 the copper to the zinc. The passage of the current 
 will continue until the excess of electrons is drained 
 out of the zinc; but, as long as the zinc atoms 
 
VOLTAIC ELECTRICITY 145 
 
 go on dissolving and giving up electrons to the zinc, 
 a steady current will be maintained. 
 
 Take the case of an elementary galvanic cell, con- 
 sisting of a plate of copper and a plate of zinc 
 immersed in dilute sulphuric acid, and joined by a 
 wire outside the liquid. The liquid consists of water 
 molecules, acid molecules, H 2 S0 4 ; positive ions, H ; 
 and negative ions, S0 4 . Zinc atoms are constantly 
 going into solution, and giving up their electrons to 
 the zinc from which they issue. These electrons, 
 flowing round the outside circuit into the copper, 
 neutralise the H atoms ;in the neighbourhood of the 
 copper, and liberate the hydrogen from the liquid 
 in the form of bubbles. Thus, zinc disappears into 
 the liquid on one side, and hydrogen leaves the 
 liquid on the other side. Both zinc and hydrogen 
 are positively electrified atoms, and we, therefore, 
 have here a material " positive current," which, 
 however, is only really in existence in the layers 
 nearest to the electrode. The really continuous 
 current in the outside circuit is the electron current. 
 It is the only thing that moves in the wire. 
 
 All electric batteries work on the same principles 
 as those above set forth. They only differ in the con- 
 trivances made to increase the difference of solution 
 pressure, to facilitate the exchange of electrons, to 
 reduce the resistance of the liquid, to insure the 
 long continuance of the current, and to increase the 
 convenience and economy of practical working. 
 
 K 
 
CHAPTER VII 
 
 ELECTRO-DYNAMICS 
 
 UP to the present we have only considered such 
 mutual forces of electrons as are playing between 
 them when at rest. We have seen that one elec- 
 tron repels another placed near it at a distance of 
 one centimetre with a force of 1-16 x 10~ 19 dynes, 
 whatever material may intervene between them. 
 The same force is exerted between two neutral 
 atoms when they are deprived of one electron each, 
 and thereby converted into " positive atoms." % On 
 the other hand, an electron attracts a positive atom 
 with the same force. 
 
 These three forces are called electrostatic forces, 
 because the electric bodies are at rest. We now 
 proceed to consider the forces brought into play 
 when the electric bodies are in motion. 
 
 When two electrons travel side by side through 
 the ether, some of the repulsive force between them 
 apparently disappears. The amount of repulsive 
 force disappearing depends upon the velocity; it 
 increases in direct proportion with the velocity, and 
 when the electrons move with the velocity of light 
 
ELECTRO-DYNAMICS 1 47 
 
 the repulsive force disappears entirely, and the two 
 electrons cease to exert any action upon each other. 
 
 The same change of force takes place when two 
 positive atoms travel side by side through the ether. 
 
 Both these facts may be stated more clearly by 
 saying that two electrons or two positive atoms (or 
 similar charges of any kind) travelling side by side 
 through the ether exhibit a mutual attraction which 
 increases with the velocity, and which balances their 
 electrostatic repulsion as soon as they travel with 
 the velocity of light. 
 
 When an electron and a positive atom travel side 
 by side through the ether, their original attraction is 
 balanced by a mutual repulsion, so that again, when 
 they travel with the velocity of light, they exert no 
 mutual force. This implies that when a neutral 
 atom travels so fast as to nearly approach the 
 velocity of light, it becomes incapable of retaining 
 its electrons, and becomes " ionised/' 
 
 The facts form the basis of all the phenomena of 
 electro-dynamics, of magnetism, and of induction. 
 
 The forces due to the steady motion of electrons, 
 positive atoms, or charged bodies through the ether 
 are called magnetic forces. 
 
 Take a long copper wire, 1 mm. in Radius, stretch 
 it across the room, and send a current of 1 ampere 
 through it. What is the magnetic force due to the 
 steady motion pf its electrons ? 
 
 In the first place, we must know something of the 
 
148 THE ELECTRON THEORY 
 
 velocity with which the electrons are travelling 
 through the wire. They travel in a direction 
 opposite to what was hitherto called "the electric 
 current." They travel from the zinc to the copper 
 of a cell, or generally from the negative to the 
 positive-pole. There is no perceptible displacement 
 of the positive or neutral copper atoms. They are 
 firmly packed together, and cannot migrate, whereas 
 the electrons thread their way between them and 
 progress with a steady average speed, which is 
 directly proportional to the electromotive force 
 which drives them. Their motion constitutes the 
 real electric current, and produces all the heating 
 and magnetic effects which we associate with an 
 electric current. 
 
 The passage of one ampere across any section of 
 a wire means the passage of an "army" of 8*79 
 trillion electrons across that section every second 
 (p. 90). This number of electrons, which, in order 
 to emphasise the atomic conception, I have called 
 an "army," is usually called a "coulomb" of 
 negative electricity. It contains 3000 million " com- 
 panies" or electrostatic units of electric quantity. 
 One " company " contains 2930 million electrons. 
 We may therefore say that an electric " army " 
 contains about as many companies as the company 
 contains men. 
 
 Let an army of electrons traverse the point A in 
 the conductor AB. It takes one second to pass in 
 
ELECTRO-DYNAMICS 1 49 
 
 review at A. We want to know where its scouts 
 will be by the time the rearguard has arrived at A. 
 
 In order to determine this, we simply have to 
 find what length of the wire contains an 
 army of electrons available for convey- 
 ing electricity. We have estimated the 
 number of available electrons in 1 cubic 
 centimetre of copper at 380 trillion (p. 90). 
 An army of 8*79 trillion is therefore con- 
 
 8*79 
 tained in every -^r- cc. or 0'023 cc. of 
 
 copper. 
 
 Since the radius of the copper wire is 
 1 mm. its area is 0'01?r sq. cm., and its F 
 volume per cm. length is O'Ol-Tr cubic 
 centimetres, or 0*0314 cc. ; therefore the length of 
 copper required to contain an army of movable 
 
 electrons is ^^-. . = 0*723 cm. 
 
 Hence, by the time the rearguard passes A, the 
 vanguard is 0*723 cm. ahead, and the rearguard will 
 reach the same spot one second afterwards. In 
 other words, the speed with which the army marches 
 is 0*723 cm. per second. 
 
 This is the velocity of the electrons in a copper 
 wire 2 mm. in diameter, carrying a current of 1 amp. 
 Doubling the current means doubling the speed 
 of the electrons, and, therefore, quadrupling their 
 energy, which varies as the square of the speed, 
 
ISO THE ELECTRON THEORY 
 
 and quadrupling the heating. Doubling the re- 
 sistance while the current remains the same also 
 means doubling the speed ; but since the number 
 of electrons per unit length is halved, it only means 
 simply doubling the heat evolved per unit length 
 instead of quadrupling it. (Joule's Law.) 
 
 The magnetic force does not depend in any way 
 upon the resistance of the wire, but simply upon the 
 number and speed of the electrons i.e. upon their 
 momentum, m v. 
 
 The magnetic force may be tested by means of 
 a small magnetic needle which sets itself at right 
 angles to the current. That is the old familiar way 
 of measuring a current. But in these articles we 
 must proceed differently. Magnets, magnetism, and 
 magnetisation are all to be reduced to the distribu- 
 tion and motion of electrons. A magnet is a highly 
 complex system of spinning electrons. There is 
 nothing fundamental about it. The fact that the 
 electromagnetic system of units is based upon the 
 definition of a unit magnetic pole simply exhibits 
 the dire straits to which the older theories were 
 reduced when brought face to face with magnetic 
 force. The magnetic pole, being a thing whose true 
 nature was unknown, had to be regarded as an 
 elementary thing, not reducible to any other known 
 principle, just as water was considered an element 
 before Cavendish analysed it. Electric currents were 
 measured by magnets, instead of vice versa. In 
 
ELECTRO-DYNAMICS I 5 I 
 
 the future science of electricity the magnetic pole 
 will play a very subordinate part. 
 
 How, then, can we measure the magnetic force 
 due to the electrons moving in the wire ? 
 
 It is evident that the electrons alone produce 
 the magnetic force ; for the positive atoms are at 
 rest. They are equal in number to the electrons, 
 and therefore the wire has no electric charge as 
 a whole. The magnetic force cannot be discovered 
 by means of a charged electric body at rest, since 
 the magnetic force acts only between bodies when 
 they both move relatively to the ether in the same 
 direction. They must have an absolute motion 
 through the ether. Relative motion is not sufficient. 
 When one charged body moves through the ether 
 while the other is at rest, no magnetic force is 
 exerted between them. The ether, in the electron 
 theory, is supposed to be absolutely at rest. It 
 forms the standing ground from which all motion 
 may be measured in absolute terms. There is, 
 therefore, in the electron theory such a thing as 
 absolute motion, and it is this that determines 
 magnetic force. The greatest absolute motion 
 with which we are brought into practical dealings 
 is that of the earth round the sun, which is 
 3,000,000 cm. per second, or 19 miles per second. 
 This is only TWIR^ f the speed of light, so that 
 two charged bodies placed at noon in a line at 
 right angles to the sun's rays in the meridian plane 
 
IS 2 THE ELECTRON THEORY 
 
 would only lose O01 per cent, of their attraction 
 for each other, whereas they would not do so if 
 placed east and west. The experiment may be 
 tried some day, but the difficulties are very great, 
 since the charge on a conductor is easily dissipated 
 by the ions of the air, and the sources of error are 
 considerable. 
 
 The fact that we can discover magnetic force, even 
 if the electrons are moving with the small velocity 
 of about 1 cm. per second, is due to the enormous 
 quantities of electricity set in motion in a wire 
 quantities which we can never hope to obtain 
 separately. Whatever magnetic force the electrons 
 may exert owing to the earth's 
 dsl motion is compensated by the 
 
 B|e\ magnetic force exerted by the 
 
 positive atoms, owing to the 
 earth's motion. The one force 
 exactly balances the other, and 
 the only force remaining is that 
 of the electrons relatively to the 
 positive atoms i.e. relatively to 
 the wire itself. 
 FIG. 21. This is how it comes about 
 
 that we may, for magnetic pur- 
 poses, regard the ether as fixed to the earth, so 
 long as we are not dealing with bodies possess- 
 ing a free charge. The magnetic force between 
 two moving electrons varies inversely as the 
 
 t 
 
ELECTRO-DYNAMICS I 5 3 
 
 square of the distance. The magnetic force exerted 
 by an infinitely long wire containing moving elec- 
 trons upon an electron moving parallel to the wire 
 is simply inversely as the distance. For let there 
 be an electron at e (Fig. 21), moving parallel to 
 the wire A B, and let ds be a small portion of 
 the wire. The magnetic force exerted upon 6 is 
 
 proportional to ^~ , since the electron is not moving 
 
 along ds. The total force exerted by the portion of 
 the wire above A in the direction of r is proportional 
 
 to -, where i is the current and r the distance. A 
 similar force is exerted by the wire below A, so that 
 the total force is proportional to . The magnetic 
 
 force round a wire, therefore, decreases simply as the 
 distance increases. It may be measured by bringing 
 another current i' within r centimetres of the wire. 
 Then the force of attraction exerted upon 1 cm. 
 of the wire carrying the current i' by the infinite 
 wire carrying the current i is 
 
 2 ii' 
 
 dynes. 
 
 T * 
 
 If both i and i' are 10 amperes, and r is 1 centi- 
 metre, the force is 2 dynes. Hence a # current equal 
 to 10 amperes is called the " electromagnetic unit of 
 current strength/' It is ten times the practical 
 unit, the ampere. 
 
 In practice it is impossible to realise either an 
 
154 
 
 THE ELECTRON THEORY 
 
 infinite wire or a current element. We must there- 
 fore find a more practical method of determining 
 the ampere. 
 
 Take two wires, each 100 cm. long, and bend them 
 into circles. Mount them facing each other in 
 planes 1 cm. apart, and let them be 
 traversed by a current of 1 ampere 
 each. This can be secured either 
 by inserting a small battery some- 
 where in each circle, or connecting 
 them with a battery by means of a 
 short break in the circle. If the 
 two currents then go in the same 
 direction, they will attract each other 
 with a force of 2 dynes. If they go 
 in opposite directions, they will repel each other 
 with the same force. 
 
 Hence we arrive at the following definition of the 
 ampere, which is quite independent of magnets : 
 
 An ampere is that current which, when traversing 
 two circular conductors 1 m. in circumference in the 
 same direction, makes them attract each other with 
 a force of 2 dynes when separated by a distance of 
 1 cm. 
 
 More generally, the attraction between two cir- 
 cuits is 
 
 FIG. 22. 
 
 where c is the circumference in metres, i the current 
 
ELECTRO- DYNAMICS I $ 5 
 
 in amperes, and d the distance between the circles in 
 centimetres. 
 
 We thus have two definitions of the ampere, one 
 as the passage of 8*79 trillion electrons per second, 
 which may be called the chemical definition, and 
 the other as the current which exerts a certain 
 magnetic force, this being the electromagnetic 
 definition of the same quantity. Both definitions 
 are consistent and identical; but of the two the 
 chemical definition is the more fundamental. It 
 should be remembered that currents can be mea- 
 sured with the greatest accuracy, not by their 
 magnetic force, but by the passage of their elec- 
 trons through a liquid, as in the electrolysis of silver 
 nitrate or copper sulphate. 
 
 If the current were increased to such a pitch that 
 the electrons travelled through the wire with the 
 velocity of light, the attraction would be such that 
 it would counterbalance the enormous repulsion 
 exerted between the 138 armies of electrons in 
 each circuit, which is masked by the presence of 
 the positive atoms. 
 
 The fact that the force varies inversely as the 
 distance shows that the two circuits will tend to 
 approach each other with increasing* force, and will 
 ultimately coincide. When one circle is a little 
 smaller than the other, the maximum attraction is 
 at a distance equal to the difference of their radii. 
 
 In every case the magnetic force is at right angles 
 
156 THE ELECTRON THEORY 
 
 to the current. At any point in space the magnetic 
 force may be measured in dynes by the maximum 
 force experienced by 1 cm. length of a wire carrying 
 unit current. 
 
 Thus the magnetic force at the centre of a 
 circle due to a current passing through the circum- 
 ference is 
 
 This formula is the foundation of the measure of a 
 current by means of a small magnet. 
 
 When a long cylinder is wound with wire carrying 
 a current i, the magnetic force inside it is every- 
 where the same, and is equal to 4 irni, where n is the 
 number of turns per centimetre. Such a cylinder is 
 called a solenoid. It forms an artificial magnet 
 without iron. 
 
 The magnetic force due to a long wire carrying a 
 current of one ampere is ^ dyne at a distance of 
 1 cm. from it. The force is about the same as the 
 earth's horizontal magnetic force. It is the force 
 experienced by 1 cm. length of a wire carrying a 
 current of 10 amperes when placed at a distance 
 of 1 cm. from the first wire. 
 
 When two currents cross each other at an angle, 
 they tend to coincide with each other and flow side 
 by side in the same direction. Currents flowing 
 from or towards the same point attract each other. 
 If (Fig. 23, a) the current i were fixed and i' movable, 
 
ELECTRO-DYNAMICS I 5 7 
 
 the latter would be pulled round in the direction 
 of the arrows. If at the instant of crossing i the 
 current i' could be reversed, it would be repelled and 
 twisted round into the opposite direction. By revers- 
 ing it at every crossing a continuous rotation could be 
 produced, and a machine has been made to do this. If 
 (Fig. 23, b) i' were only free to move at right angles 
 
 FIG. 23. 
 
 to itself, it would be urged in the direction of 
 the arrow. If i is bent into a horizontal circle, and 
 i' is movable along it, it will rotate continuously, as 
 it does in a machine devised by Ampere. 
 
 We have dealt with the electrons moving in 
 wires as the most practical cases of electro-dynamic 
 attraction. But the attraction can also be observed 
 v/ith free electric charges. If a number of metallic 
 knobs are mounted on an ebonite wheel and charged, 
 and the wheel is set rotating, the charges form a 
 current of strength n e v, where e is the charge of 
 each knob, expressed in " armies " or coulombs, n is 
 the number of knobs, and v is their velocity. Thus, 
 
158 THE ELECTRON THEORY 
 
 if there are 1000 knobs charged with 300 companies 
 of electrons each (10"" 7 army), and the rim velocity 
 is 100 cm. per second, the current is 100 x 1000 
 X 10"*, or T ^ ampere. Currents of this order have 
 been obtained by Rowland by rotating a disc with 
 charged sectors. Two such wheels or discs attract 
 each other just as currents in wires would; but 
 the attraction being of the order of a millionth 
 of a gramme, is almost immeasurably small. 
 
 Electrons also influence each other when flying 
 free, the magnetic force between them being pro- 
 portional to their instantaneous velocities, and in- 
 versely proportional to the square of the distance 
 between them. If they are moving in parallel lines 
 but not abreast, the force must be multiplied by the 
 sine of the angle between their direction of motion 
 and the line joining them. If they are flying in 
 different directions, the force must be multiplied by 
 the cosine of the angle between their directions of 
 motion. 
 
 The forces between moving electrons are thus 
 perfectly determined. They consist of the electro- 
 static force, which may be regarded as invariable, 
 and the electro-magnetic force, which depends 
 upon their speed and direction. A clear grasp of 
 the play of these two forces is the first essential 
 step towards an understanding of electro-magnetic 
 phenomena. 
 
CHAPTEE VIII 
 
 MAGNETISM 
 
 WE saw in the last chapter that magnetic force is 
 due to the steady motion of electrons or charged 
 bodies generally ; but that the magnetic force exerted 
 by a metallic conductor carrying a current is due 
 solely to the motion of the electrons which constitute 
 that current. We saw, also, that magnetic force is 
 only exerted on other moving electrons or moving 
 charged bodies, but not on electrified bodies at rest. 
 
 I now intend to show that all magnetism consists 
 in the steady motion of electrons in small orbits, and 
 that all magnetic properties of bodies can be ex- 
 plained on this principle. By " magnetism " l^mean 
 thatjproperty whereby bodies exert magnetic force 
 without any discoverable electric current traversing 
 or surrounding them. ' 
 
 In broad outlines, the electron theory of magnetism 
 is as follows : The atoms of all bodies are surrounded 
 by several electrons describing orbits^ round them, 
 like the planets round the^ sun. When these orbits 
 are nearly in the same plane, as in the Solar System, 
 the bodies are " magnetic," or rather " paramagnetic," 
 like oxygen and aluminium. When, in addition, the 
 
l6o THE ELECTRON THEORY 
 
 orbits are large enough to influence each other across 
 the average distance separating the atoms, the bodies 
 are "ferromagnetic," like iron, cobalt, and nickel. 
 When, on the other hand, the orbits of the electrons 
 revolving round the same atom lie in various planes, 
 the bodies are not paramagnetic. They are usually 
 described as " diamagnetic." But in reality all bodies 
 are diamagnetic, and paramagnetism is a special 
 property which masks the inherent diamagnetism 
 of the bodies. A permanent magnet is a para- 
 magnetic body in which the orbits of the majority 
 of the electrons lie in parallel planes, with the re- 
 volutions in the same sense, and this parallelism is 
 maintained by the mutual attraction of the orbits. 
 
 Such, in short, are the main principles of mag- 
 netism according to the new theory, which owes its 
 successful application to magnetism chiefly to Prof. 
 Langevin, of Paris. 
 
 There is no " magnetic fluid," no " free magnetism," 
 no " magnetic pole." In the electron theory, mag- 
 netism as a distinct entity disappears, being resolved 
 into the steady motion of electrons. Thus passes a 
 conception which has given rise to more misunder- 
 standings and false speculations than perhaps any 
 other in the history of science. 
 
 I explained (p. 156) that an artificial magnet with- 
 out iron may be constructed by coiling a wire on a 
 cylinder, and sending a current through it. If the 
 current in the wire is one electro-magnetic unit ( = 10 
 
MAGNETISM l6l 
 
 amperes), and these are n turns for every centimetre 
 length of the cylinder, the magnetic force at the 
 centre of the coil is 4 TT n dynes. In other words, if i 
 is the current and n the number of turns, the total 
 current circulating round each centimetre length of 
 the solenoid is ni. This total current per unit 
 length we will denote by I electro-magnet units or 
 101 amperes. It is identical with what is known 
 as the intensity of magnetisation I. 
 
 A body has unit intensity of magnetisation if a 
 total current of 10 amperes circulates round unit 
 length of it, the length being reckoned in the 
 direction of the magnetic axis. 
 
 We will now proceed to explain how a permanent 
 magnet may be regarded as a body round which an 
 electron current is steadily circulating. 
 
 The idea that a magnet is made up of innumerable 
 smaller magnets of molecular dimensions is some 
 eighty years old. It was put forward by Ampere to 
 explain the fact that however much a magnet is 
 broken up, each fragment is a complete magnet. 
 Knowing that an electric current attracts or repels 
 another, according to its direction, he assumed that 
 each molecule of a magnetic substance was sur- 
 rounded by an electric current. Still, regarding 
 electricity as an imponderable fluid, he was unable 
 to say what constituted that mysterious molecular 
 current. No further light was shed on this matter 
 until the advent of the electron theory, although the 
 
 L 
 
l62 
 
 THE ELECTRON THEORY 
 
 conception of molecular currents was applied with 
 much success to magnetic phenomena by Weber, and 
 later by Ewing. 
 
 Ampere furnished an ingenious and successful ex- 
 planation of how a large number of small molecular 
 currents could make up a large magnet. 
 
 If the molecules were square in section and packed 
 close together, and each molecule had a current 
 
 circulating round it in 
 the direction of the 
 hands of a watch, then 
 a small section across a 
 magnetic needle, greatly 
 magnified, might be re- 
 presented by the diagram 
 
 t 1 
 
 t. I 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 1 
 
 t i 
 
 I 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t i 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 1 
 
 t 4 
 
 t 4 
 
 t 4 
 
 t 4 
 
 T 4 
 
 FIG. 24. 
 
 (Fig. 24). Wherever two 
 molecules join, there are 
 two currents in opposite directions, which, of course, 
 neutralise each other. It is only the currents on 
 the free sides of the molecules that exert any 
 magnetic effect outside the magnet. The net 
 effect is, therefore, as if a current equal to the 
 molecular current circulated round the outline of 
 the section. It is obvious that, whatever section is 
 taken, whether including a large or small number of 
 molecules, the current round the outline is always 
 the same, being equal to the molecular current, 
 which is invariable. 
 
 For Ampere's mysterious molecular currents, let 
 
MAGNETISM 163 
 
 us now substitute revolving electrons, or, rather, let 
 us define the molecular current as a convection of 
 electricity in the shape of electrons revolving round 
 each positive atom. 
 
 The above reasoning remains^ substantially the 
 same. True, the electrons do not describe square 
 paths; but the error introduced by regarding their 
 paths as square is not great, and the convenience of 
 calculation is considerably enhanced. As before, it is 
 only the electrons circulating in the outline that 
 count for external magnetic effect, and the current 
 round the section is equal to the molecular current, 
 which, in amperes, is equal to the number of armies 
 of electrons passing any point of the outline in one 
 second. 
 
 This theory can be tested quantitatively as follows. 
 The calculation is only roughly approximate; but 
 although several of the data are uncertain, it shows 
 that the electron theory of magnetism leads to no 
 absurdities when reduced to figures. 
 
 A cubic centimetre of iron is supposed, with good 
 reason, to contain about 10 24 (one quadrillion) atoms. 
 If there are 10 8 atoms ranged along one edge of the 
 cube, the total number in the cube will be 10 24 . Let 
 each atom have one electron revolving* round it, and 
 let all the circuits face one of the sides of the cube. 
 Then an electron current will circulate round the 
 four adjacent sides. The molecular current, reckoned 
 in electrons per second, is measured by the number 
 
1 64 THE ELECTRON THEORY 
 
 of revolutions per second of the electron round its 
 atom. This, as estimated on p. 32, is 2'2 x 10 15 . 
 Multiplying this number by 10 8 , the number of atoms 
 along one edge, we get for the total electron current 
 circulating round the cube (in other words, for its 
 " intensity of magnetisation ") the figure 
 
 2-2xl0 15 xl0 8 = 
 
 electrons per second. Since one ampere is a current 
 of 8-79 x 10 18 electrons per second, the above current 
 in amperes is 
 
 9-9 v 1O23 
 
 amperes. 
 
 It seems incredible that an enormous current 
 like that should circulate round a bit of iron the 
 thickness of one's finger without making it burst 
 into flame. But, then, we must remember that 
 the current does not heat a wire because electrons 
 move in it, but because their motion, acquired 
 under electric force, is stopped by collision every 
 now and then. In magnetic metals the electrons 
 are free to revolve, and in doing so they spend very 
 little energy. 
 
 The greatest intensity of magnetisation hitherto 
 actually observed is 1700 units, meaning that a current 
 of 17,000 amperes circulates round each centimetre 
 length of a bar of iron magnetised to saturation. 
 The agreement between these two figures viz. 
 
MAGNETISM 165 
 
 25,100 amperes for absolute theoretical saturation, 
 and 17,000 for the highest saturation practically 
 attained is remarkably good. But too much im- 
 portance should not be attached to it. The calcu- 
 lation is only intended to show that the electron 
 theory accounts for magnetism quantitatively as well 
 as qualitatively. To calculate the magnetisation 
 of different substances we shall have to know more 
 about the number of revolving electrons per atom, 
 the speed of revolution, and the size of their 
 orbit. 
 
 I have supposed in the above calculation that 
 only one electron revolves round each atom. This 
 is on a par with the observation that every atom 
 is only capable of losing one or two, or at most not 
 more than three, electrons. But it does not follow 
 that the atom only contains from one to three 
 electrons. The modern view is that the mass of 
 the atom contains a large number of electrons, 
 bound together by some hitherto mysterious body 
 of positive electricity. Thomson supposes that these 
 electrons revolve within the positive body, and 
 are influenced by magnetic forces. They probably 
 circulate in all sorts of planes, thus making up 
 a diamagnetic atom in the ordinary sense. The 
 detachable electron probably revolves at a greater 
 distance, somewhat like Neptune or the comets in 
 the Solar System, and it owes its predominant 
 magnetic effect to its large orbit. As we shall see, 
 
1 66 THE ELECTRON THEORY 
 
 two orbits influence each other in proportion to 
 their areas. In ferromagnetic bodies like iron, a 
 few electrons must possess exceptionally large orbits. 
 In soft, unmagnetised iron these orbits face every 
 way, or are bound up together in small groups. 
 When the soft iron is brought into a field of 
 magnetic force, the orbits, or what we may call 
 the molecular currents, are drawn round till their 
 own magnetic fields coincide with the external field. 
 The iron is then " magnetised." Needless to say, 
 the addition of all the molecular fields to the ex- 
 ternal field greatly strengthens the original field. 
 It would require very exceptional contrivances to 
 make a current of 25,000 amperes circulate round 
 a narrow tube. It is quite impossible with purely 
 electrical means to get such a current to circulate 
 within a space of a cubic centimetre. But by calling 
 in the aid of the molecular currents ready-made 
 currents, which only require "turning on" we 
 obtain the powerful magnetic fields with which the 
 electro-magnet is associated. 
 
 When the external magnetic field is removed, it 
 may happen that most of the molecular currents 
 remain in their new positions, being held there by 
 their mutual attractions. In that case we have 
 what is called "residual magnetism." In soft iron 
 this residual magnetism amounts to about 80 per 
 cent, of the magnetism induced in fairly strong 
 fields. But the slightest tap or other mechanical 
 
MAGNETISM 167 
 
 disturbance makes the molecular currents swing 
 back into their higgledy-piggledy state. In steel, 
 on the other hand, the residual magnetism is held 
 even when the field is reversed until the field 
 acquires a considerable strength. This indicates 
 that in steel the orbits are so large, or so close 
 together, that when they are once in line a con- 
 siderable force is required to turn them into other 
 positions. 
 
 This brings us to the consideration of magnetic 
 "moments." The turning couple experienced by a 
 molecular current, or any other electric current in 
 a magnetic field, is proportional to its magnetic 
 moment. This moment is made up of two factors, 
 one of them being the strength of the current, and 
 the other the area round which it circulates. If the 
 strength of a molecular current is 10 amperes, and 
 its area is 1 sq. centimetre, it experiences in a unit 
 magnetic field a maximum couple of 1 dyne-cm. 
 Generally, a circuit of area A, and current strength i, 
 has a moment = A.i. 
 
 If the current in a solenoid is I electro-magnetic 
 units per cm, length, its sectional area A sq. cm., 
 and its length I, then its magnetic moment is IA.L 
 The product IA or (current per unit length) (sectional 
 area) is called the "pole strength" of the solenoid 
 or other magnet. The name is justified by the 
 fact that, as far as the external force of the magnet is 
 concerned, it may be ascribed to two centres, situated 
 
 
1 68 THE ELECTRON THEOBY 
 
 at or near the two free ends of the magnet, and of 
 a " strength " equal to the product of the magnetic 
 intensity into the area. But these poles are mere 
 mathematical fictions of a high degree of artificiality. 
 When the bar is twisted into a complete circle, the 
 poles disappear, although the molecular currents 
 remain nearly the same as before. 
 
 The magnetic moment of a bar magnet of length 
 I and pole-strength IA is IA.L Or if m is put for 
 the pole-strength IA, the moment is ml. Hence 
 the moment of a bar magnet may be measured by 
 multiplying its pole-strength by its length. A unit 
 magnetic pole is possessed by a bar whose sectional 
 area multiplied by the total current circulating 
 round it per unit length is unity. Thus, if the 
 molecular currents circulating round a bar of 1 
 sq. cm. section amount to 10 amperes per cm. length, 
 that bar has unit magnetic poles. If it is 1 cm. long 
 it has unit magnetic moment. 
 
 The magnetic moment determines the magnetic 
 force exerted by a magnetic circuit or a solenoid at 
 any point far away from it in comparison with its 
 length. If any such point is chosen at random, 
 the force increases in direct proportion to the 
 moment. Thus, the force exerted by a small bar 
 magnet or magnetic needle may be doubled by 
 doubling either its length or its pole-strength. The 
 force^exerted by a molecular current or other small 
 plane circuit may be doubled by doubling either 
 
MAGNETISM 169 
 
 the current or the area. In both cases the process 
 is essentially the same. In the bar magnet the 
 current can only be doubled by doubling the length, 
 since the molecular currents cannot be altered. The 
 pole-strength can be doubled by doubling either I or 
 A. If steel bars are used, I is limited by a certain 
 maximum (17,000 amperes per cm. length), and the 
 pole-strength can only be doubled by doubling the 
 area, as in the case of the circuit. The analogy 
 between circuits and magnets is, therefore, very 
 far-reaching. The differences between them are 
 due to the great strength of the molecular currents. 
 This great strength, while offering many advantages, 
 suffers under the drawback that the molecular cur- 
 rents easily fall out of alignment, thus leading to 
 demagnetisation. The solenoid or other artificial 
 magnet is much feebler than the magnet containing 
 iron, but more reliable than the permanent magnet. 
 The best and strongest magnets are made up by 
 combining both forms, thus offering the certainty 
 of the solenoid and the strength of the iron 
 magnet. Such combinations, constructed by wind- 
 ing a current-bearing wire in many turns round a 
 soft iron core, are well known under the name of 
 electro-magnets. # 
 
 To make the analogy between magnets and sole- 
 noids more clear, it is necessary to go a little further 
 into the nature of a magnet pole. The conception 
 of poles, though misleading in many ways, has also 
 
170 THE ELECTKON THEORY 
 
 had its uses. It has furnished a convenient abbre- 
 viation for many physical terms, and has served to 
 give us some idea of the action of a magnetic field 
 upon a magnetic needle. But when that conception 
 was strained in order to account for the nature of 
 magnetism, it not only failed, but retarded actual 
 progress in that direction for generations. 
 
 The magnetic action of a long and thin solenoid, 
 like that of a long and thin magnet, may be sup- 
 
 FIG. 25. 
 
 posed to be concentrated at two points very near 
 the ends, which are called its poles. But every 
 turn of the solenoid, like every section of the mag- 
 net, exerts its magnetic force quite independently of 
 any other turn or section. Its action is not abolished 
 or " neutralised " by that of any other part. It per- 
 sists intact, and if a turn in the centre of a solenoid 
 appears neutral, it is only because we are not using 
 the proper means of demonstrating its magnetic 
 action. 
 
 That the action appears to be concentrated at 
 the poles is, so to speak, an illusion, due to the 
 peculiar way in which the actions of the individual 
 turns sum themselves up. 
 
MAGNETISM 171 
 
 Consider two solenoids of equal length, but dif- 
 ferent thicknesses (Fig. 25), placed one inside the 
 other. The electron currents, when looked at from 
 the left-hand end, all appear to revolve in the direc- 
 tion of the hands of a watch. They therefore all 
 attract each other, and since they are already as 
 close together as they can be, they will not alter 
 their relative position if they are free to move. In 
 other words, there is no resultant force upon them ; 
 
 \ B 
 
 FIG. 26. 
 
 they are in a position of equilibrium. Now let the 
 smaller solenoid be pulled part of the way out of 
 the larger one (Fig. 26). Then the two portions 
 between B and C are in equilibrium with respect 
 to each other as before; but the portions A B 
 and C D are not. The portion A B attracts every 
 turn in the smaller solenoid. The attraction is pro- 
 portional to the moment of each turn of the larger 
 solenoid, and inversely proportional t6 the cube of 
 its distance. On the other hand, the attraction is 
 directly proportional to the number of turns between 
 A and B. If A B = I, we therefore have the attrac- 
 tion proportional to , and also to I itself. The 
 
172 THE ELECTRON THEORY 
 
 result is that it is proportional to ^ or l/ 2 . It is 
 
 inversely as the square of the distance. 
 
 The above reasoning supposes that the length 
 of the solenoids is great in comparison with their 
 diameters. This provision need not disturb us, 
 since without it we cannot speak of poles at all, 
 even in bar magnets. 
 
 If one of the solenoids is reversed, the attraction 
 will be converted into a repulsion, and the smaller 
 one will be expelled from the larger one. If, how- 
 ever, the two solenoids are laid alongside each other 
 in the same direction, currents proceeding in the 
 same direction will be adjacent to each other, and 
 will attract each other. If the solenoids are placed 
 side by side, but not end to end, they will tend to 
 move so as to bring their ends together, in order to 
 have the attracting currents as close together and 
 as numerous as possible. Here, again, we have the 
 illusion of polar action. But since the currents 
 have only one point in contact, the attraction is 
 much feebler than when one solenoid is inside the 
 other. 
 
 The inverse square law may be deduced from a 
 general principle of the integral calculus. This 
 principle, which is capable of many useful applica- 
 tions, is as follows : When a force exerted by an 
 infinite line upon a point outside it varies as the 
 Tith power of the distance between the point and 
 an element of the line, the total force exerted by 
 
MAGNETISM 173 
 
 the infinite line varies as the (n + l)th power of 
 the distance between the point and the line. Thus, 
 if the point is an electron and the line is a line of 
 electrons, the repulsion between the electron and 
 each element of the line varies inversely as the 
 square of the distance i.e. as the ( 2)th power of 
 the distance. Hence the total repulsion varies as 
 the (-l)th power of the distance i.e. inversely as 
 the distance. 
 
 The magnetic force exerted by a small circuit 
 varies inversely as the cube of the distance. Hence 
 the magnetic force exerted by an infinite line threaded 
 with such circuits varies inversely as the square of 
 the distance. Since, in the case of a circuit placed 
 outside an infinite solenoid, the force is parallel to 
 the solenoid itself, and equal in both directions, the 
 two halves of an infinite solenoid will compensate 
 each other, and the resultant force will be zero. 
 But if the solenoid is infinite in one direction only, 
 a resultant force will appear, which is inversely pro- 
 portional to the square of the distance from the end. 
 This force will be apparently due to the existence of 
 the end. It will be greatest at the end, and will 
 appear to be concentrated there. In short, the 
 illusion of the magnetic " pole " is complete. 
 
 Let this end be dipped into iron filings. It will 
 magnetise some of them, and enable them to adhere 
 to each other. The adhesion will be strongest where 
 the molecular circuits can place themselves in paral- 
 
174 THE ELECTRON THEORY 
 
 lelism with the solenoid circuits, so as to form whirls 
 of molecular currents proceeding from the end of 
 the solenoid. The solenoid has " poles " just as a 
 bar magnet has, neither more nor less. 
 
 The pole-strength is unity, as shown above, when 
 the product of the sectional area of the solenoid into 
 the total current carried per cm. -length is unity. 
 If the sectional area is one square millimetre, the 
 current per cm.-length must be 100 electro-magnetic 
 units, or 1000 amperes, since 1 sq. cm. = 100 sq. mm. 
 The pole of the solenoid is then a unit pole. The 
 pole of a magnet of the same section, with a mole- 
 cular current of 1000 amperes circulating round it 
 per cm.-length, is also a unit pole. Both unit poles 
 have an important property. A unit magnetic pole, 
 placed at a distance of 1 cm. in air from another 
 unit pole of the same sign, repels it with the force of 
 one dyne. 
 
 This is the law upon which the " electro-magnetic " 
 system of units has been based. The " electrostatic " 
 system, on the other hand, is based upon the inverse- 
 square law governing the forces between quantities 
 of electricity. The establishment of two different 
 systems of units was unavoidable before magnetism 
 had been reduced to electrical principles. But it 
 was unfortunate, and it considerably increased the 
 difficulties of the learner. The whole of the mag- 
 netic and electric units can now be reduced to terms 
 of electric quantity. The volt, ampere, ohm, cou- 
 
MAGNETISM I ^ 5 
 
 lomb, and other practical units are retained intact ; 
 but instead of basing them upon a mathematical 
 abstraction like a magnetic pole, they will be inter- 
 preted in terms of Nature's own unit of electricity, 
 the electron. 
 
CHAPTER IX 
 
 INDUCED CURRENTS 
 
 WE have hitherto only considered steady currents, 
 which, in metals, are constituted by the motion of 
 electrons only, with a constant average velocity. 
 This motion takes place in a direction opposite to 
 what was hitherto described as the direction of " the 
 current/' and gives rise to a magnetic force in the 
 surrounding space, which is proportional to the 
 momentum of the electrons. 
 
 We have next to consider the case where electrons 
 are started or stopped in other words, where the 
 current varies. 
 
 Now, we know that all electrons in a wire are con- 
 stantly being stopped by collision with neutral atoms, 
 and started again along the electric field of force as 
 soon as they are liberated. But these startings and 
 stoppages make no difference to the external magnetic 
 action, since they are so exceedingly numerous, and 
 all stages in the process are represented at any given 
 instant. On the whole, the external effect is just as 
 if the electrons were moving with a steady speed 
 through the wire. The only indication we have of 
 
 the actual collisions is the heat developed in the 
 
 176 
 
INDUCED CURRENTS 177 
 
 wire, which represents the energy of motion trans- 
 formed into heat when the electron is stopped. But 
 what happens when all the electrons are stopped at 
 the same instant ? 
 
 What does happen is very much like what happens 
 when any larger body is stopped. The energy of 
 motion is transformed into some other form of 
 energy, and is eventually radiated out into space 
 in the form of heat or other ether waves. 
 
 The kinetic energy or energy of motion of a 
 ponderable body is equal to half the product of 
 its mass into the square of its velocity = \ m v 2 
 Thus, the kinetic energy of one gramme moving with 
 a velocity of 1 cm. per second is erg. In other 
 words, by stopping it we may make it perform 
 half an erg of work. It also takes half an erg of 
 work to impart to the gramme a velocity of 1 cm. 
 per second. This amount of work is done when- 
 ever we exert a force of 1 dyne over a distance 
 of J cm. 
 
 On this principle, let us calculate the energy of 
 motion of an electron. Its mass is taken to be 
 0*6 x 10~ 27 gramme (see p. 23). Its velocity can 
 never exceed that of light, which is 3 x 10 10 cm. per 
 second. Hence, the kinetic energy of the electron 
 can never be greater than J x 0-6 x 10~ 27 x 3 2 x 
 10 20 or 2*7 X 10~ 7 erg. Similarly, the kinetic energy 
 of a " company " (one electrostatic unit) of electrons 
 is always less than 800 ergs, and the kinetic energy 
 
 M 
 
178 THE ELECTRON THEORY 
 
 of one coulomb, or " army," of electrons is always 
 less than 2*38 billion ergs. 
 
 The amount of energy required for imparting a 
 given velocity to an electron is, however, affected by 
 a magnetic field. That this must be so is evident 
 from the principle of the conservation of energy. 
 When an electron moves parallel to a current-bearing 
 wire in the same direction as the electrons in the 
 wire, it is attracted towards the wire. In other words, 
 it possesses an energy of position (or potential energy) 
 in addition to its own energy of motion. This energy 
 of position is directly proportional to the velocity of 
 the electron, since the attraction between it and the 
 wire is directly proportional to that velocity. It is 
 also proportional to the momentum of the electrons 
 in the wire in other words, to the magnetic field 
 generated by them. 
 
 It is, therefore, more difficult to start an electron 
 in the same direction as other moving electrons than 
 to start it in empty space. It requires more energy, 
 more expenditure of work. The excess is directly 
 proportional to the magnetic field created by the 
 electrons in the wire, or simply to the magnetic field, 
 howsoever created. 
 
 Matters can be set right by imparting an extra 
 amount of momentum to the electron in proportion 
 to the magnetic field. This momentum may be im- 
 parted to it by bringing a force to bear upon it for a 
 definite time. Now, a force acting for a certain time 
 
INDUCED CURRENTS 
 
 produces what is called an "impulse." A force of 
 one dyne acting for one second produces an impulse 
 of one dyne-second. If it acts upon one gramme, it 
 produces in it a velocity of one centimetre per second. 
 Acting on a kilogramme, it produces a velocity of 
 Y^J- cm. per second. Acting upon a milligramme, 
 it imparts to it a velocity of 10 metres per second. 
 In every case, the same impulse produces the same 
 momentum. 
 
 In order, therefore, to start an electron through a 
 magnetic field, an extra impulse has to be given to it 
 in proportion to the strength of the magnetic field. 
 Now, if the electron is already in motion, and a 
 current is suddenly sent through a neighbouring 
 wire, a magnetic field will be created round the 
 electron. If it fails to receive the necessary extra 
 impulse, the impulse will be deducted from its own 
 velocity. The debt has to be paid somehow. 
 
 If, instead of a single electron, there is a crowd of 
 them moving in another wire, the state of things will 
 be the same. When the magnetic field is started, 
 they all receive a set-back. Their velocity is reduced 
 by a certain amount proportional to the magnetic field. 
 
 If the magnetic field is reversed, the impulse 
 is also reversed, and instead of a retardation the 
 electrons receive an acceleration of the same amount. 
 In both cases the impulse is in the direction opposite 
 to that of the current in the wire, and proportional to 
 that current. 
 
180 THE ELECTRON THEORY 
 
 This is the principle of electro-magnetic induction, 
 or the production of currents by changes in other 
 currents. 
 
 The fundamental phenomena of induced currents 
 were discovered by Faraday, and formulated by him 
 in the language of " lines of force." I have so far 
 avoided this expression in order to concentrate atten- 
 tion upon the events happening within the conducting 
 wire. I shall now introduce it, but with the restric- 
 tions and limitations imposed by the new atomic 
 theory of electricity. 
 
 When a sheet of paper is laid over a bar magnet 
 and dusted with iron filings, the filings arrange them- 
 selves in curved lines, which approximately represent 
 the direction in which a free magnetic pole would 
 travel if placed in the magnetic field. These lines 
 are called " lines of force," because the tangent at any 
 point of one of the curves represents the direction in 
 which the resultant magnetic force would urge the 
 free magnetic pole. 
 
 Now, Faraday imagined that all space round a 
 magnet is filled with some invisible lines correspond- 
 ing in direction to these lines of iron filings. To 
 these ethereal lines he ascribed a physical reality and 
 physical properties, such as a tension along them and 
 a pressure at right angles to them. He was thus en- 
 abled to "explain" a variety of magnetic phenomena, 
 or, rather, to summarise them in the light of his 
 fundamental assumption of physical lines of force. 
 
INDUCED CURRENTS l8l 
 
 It cannot be denied that the conception of lines 
 of force has been of great practical utility. It has 
 enabled engineers to visualise the happenings in a 
 magnetic field. In the hands of Maxwell and his 
 brilliant successor at Cambridge, the method of lines 
 and tubes of force has been used to describe and 
 measure magnetic phenomena with marked success ; 
 but, so far, all attempts to demonstrate their real 
 existence in the ether have utterly failed. The very 
 fact that a unit magnetic field can be arbitrarily 
 defined as containing a certain number of lines per 
 square centimetre implies that these lines have no 
 real existence. 
 
 Within a permanent magnet there is very little 
 doubt that the molecular currents are mostly ar- 
 ranged in rows with their axes in the same line, thus 
 forming magnetic filaments, or elementary solenoids. 
 These, at all events, really exist. They number 
 about 10 16 per square cm. of cross-section, and that 
 number measures the intensity of magnetisation. 
 The lines of force that are supposed to continue 
 them outside the magnet may be used to measure 
 the magnetic force at any point outside. It is 
 simply equal to the number of lines vertically cut- 
 ting unit area at that point. A unit-magnet pole 
 is defined as a pole emitting 4?r lines of force, so 
 that there is one line passing through every sq. cm. 
 of a sphere of 1 cm. radius described about it. This 
 definition at once shows the purely arbitrary char- 
 
1 82 THE ELECTRON THEORY 
 
 acter of the assumptions made ; but it enables us to 
 state the law of electro-magnetic induction in a terse 
 manner, as follows : 
 
 The impulse of electro-magnetic induction pro- 
 duced by the creation or destruction of a magnetic 
 field is at right angles to the lines of force, and 
 proportional to their density. When their density 
 is changed it is proportional to the difference of 
 density. 
 
 It does not matter how the field is made to vary, 
 whether by moving the current-bearing wire, vary- 
 ing the current, or moving a permanent magnet. 
 The impulse of induction is proportional to the 
 change in the field i.e. the change of density 
 and direction of the lines of force. 
 
 The simplest cases to investigate are those in 
 which the magnetic field is uniform. We have 
 seen above (p. 156) that the field inside a long 
 solenoid is 4 Trni units, where i is the current through 
 the wire, and n the number of turns per cm. This 
 field is nearly the same at any point within the 
 solenoid, and is independent of its diameter. We 
 will, therefore, operate with a large solenoid 10 cm. 
 in diameter, having ten turns to the centimetre 
 length, bearing a current of 1 ampere, and having 
 a total length of 1 metre. The magnetic force 
 inside it will then be 4 ?r x 10 x 1, since 10 amperes 
 are just one Electro-magnetic unit of current. The 
 magnetic force inside will be 126 units, or about 
 
INDUCED CURRENTS 183 
 
 600 times the earth's horizontal magnetic force in 
 our latitudes. In the language of the " lines of force," 
 there will be 126 lines of force penetrating every 
 square cm. placed across the axis of the solenoid. 
 The total number of lines of force through the sole- 
 noids will be 126 x its area. The radius being 5 cm., 
 its area is 25 ?r, or 784 sq. cm. Hence the total 
 " lines " passing through its interior amount to 9880. 
 
 Let a small circle of wire of radius 1 cm. be placed 
 within the solenoid, with its plane at right angles 
 to the axis of the solenoid. Its area will then be 
 3*1416 sq. crn., and the number of lines of force 
 passing through it will be 3-1416 x 126 = 396. 
 
 When the current in the solenoid is broken, its 
 magnetic field is suppressed. The electrons in the 
 circle of wire thereupon experience a force tending 
 to make them circulate in the same direction as 
 the former current in the solenoid. It is just as 
 if part of the momentum of the electrons in the 
 solenoid had been transferred to those in the circle. 
 Now, the rate of transfer of this momentum will 
 vary, of course, with the rate of stoppage of the 
 original current i.e. with the rate of change in 
 the magnetic field. The amount of momentum 
 transferred varies with the extent to which the 
 magnetic field created by the solenoid is covered. 
 If matters were reversed, and the circle bore the 
 original current, the solenoid would receive the 
 whole of its electric momentum on stoppage of the 
 
1 84 THE ELECTRON THEORY 
 
 current. But, as it is, the circle will only receive 
 a portion which is proportional to its area, and the 
 rate at which it receives it measures the electro- 
 motive force " induced " in the circle. 
 
 We have thus arrived at these two important 
 principles : 
 
 1. The induced E.M.F. is proportional to the rate 
 of change of the magnetic field. 
 
 2. In a uniform field, the induced E.M.F. is pro- 
 portional to the area of the circuit into which it is 
 induced. 
 
 Faraday's conception of lines of force enables us 
 to combine these two principles into a single rule, 
 worded as follows : 
 
 The E.M.F. induced in a circuit by a change 
 of magnetic field intensity is proportional to the 
 number of lines of force added to, or withdrawn 
 from, its area in the unit of time. 
 
 Thus the starting or suppression of the 369 lines 
 of force passing through the area of the circle within 
 one second will induce in the circle an E.M.F. of 
 one 396 units. These units, it should be stated, 
 are not the volt or practical unit, but the 
 electro-magnetic unit of 10~ 8 volts. The E.M.F. 
 will, therefore, be very feeble, and, indeed, all 
 but undiscoverable. But it can be increased by 
 shortening the time during which the change in 
 the field takes place. If the current were broken 
 in a millionth of a second, the E.M.F. would be 3*96 
 
INDUCED CURRENTS 185 
 
 volts. If, instead of one circle of wire, there was a 
 short coil of 10 turns, the E.M.F. would be 39-6 volts. 
 
 The current through the circle of iron depends 
 not only upon the induced E.M.F., but also upon 
 the resistance of the wire. If the induced E.M.F. is 
 3-96 volts, and the resistance O'OOl ohm, the current 
 strength will be 3960 amperes. But this current 
 will only last as long as the E.M.F. lasts i.e. for 
 one-millionth of a second. Hence the quantity of 
 electricity passing any section of the wire circle is 
 not 3960 coulombs, but 0-00396 coulombs. But 
 this quantity is quite independent of the rate of 
 change in the magnetic field. A slow rate of change 
 means a small E.M.F., but a current more lasting in 
 proportion. Hence we get the simple rule: The 
 quantity of electricity passing any section of a con- 
 ductor is proportional to the change in the number 
 of magnetic lines of force passing through the area 
 of the circuit. 
 
 The " number of lines of force passing through an 
 area " is called the " magnetic flux " through that 
 area. Hence the quantity of electricity passing is 
 measured by the change in the magnetic flux 
 through the circuit. As long as the magnetic flux 
 goes on changing the electricity passes through the 
 circuit, and its speed depends upon the rate at 
 which the magnetic force changes. Its direction 
 is determined by the direction of the magnetic field. 
 
 The direction of a magnetic field is determined by 
 
I 86 THE ELECTRON THEORY 
 
 reference to the earth. The body of the earth is 
 itself a magnet, and it has a north and a south 
 magnetic pole. Every permanent magnet has also 
 two poles, and much confusion has been occasioned 
 by the various methods of naming them. When it 
 was known that unlike poles attract each other it 
 was thought to be most logical to call that end of the 
 magnetic needle which points towards the north its 
 south pole, and the south-seeking end its north pole. 
 But popular usage adhered to the practice of calling 
 the northernmost pole the north pole, and vice versa. 
 This practice is even now adhered to on the Conti- 
 nent. The best way out of the difficulty is that 
 suggested, I believe, by Silvanus Thompson, who 
 calls the north end of the needle the north-seeking 
 pole and the south end the south-seeking pole. This 
 is clear and precise. But all these ambiguities are 
 avoided if we refer all definitions to the motion of 
 electrons. If a zinc and copper couple are floated in 
 dilute sulphuric acid, and the wire joining them is 
 turned into a coil, that coil turns its plane in a 
 direction at right angles to the magnetic meridian, 
 and in such a manner that the zinc is towards the 
 east and the copper towards the west. This means 
 that the electrons in the upper wire flow in the 
 direction of the sun's motion in the heavens, and in 
 the lower half of the coil they flow from west to east. 
 Hence the electron current in the earth's surface also 
 flows from west to east, or contrary to the sun's 
 
INDUCED CURRENTS l8/ 
 
 apparent motion. It flows, in fact, in the direction 
 of the earth's revolution. Now, it has been proved 
 that the mere rotation of a negatively charged sphere 
 about its axis generates a magnetic field at its surface, 
 and it might be supposed that that is the origin of 
 the earth's magnetism ; but a simple calculation, on 
 the basis of the earth's high electrical potential, 
 shows that the earth's motion is only capable of 
 accounting for about one ten-thousandth part of the 
 actual magnetic field. The actual field appears to 
 be due partly to discharges from and into interstellar 
 space, and partly to thermo-electric effects. It is 
 known that, when a point in an iron wire is heated, 
 and the slope of temperature is steeper on one side 
 than on the other, there is an electron current from 
 the steeper to the less steep side. Now, such a 
 difference of steepness is actually observed in the 
 case of the earth. The rise of temperature in the 
 morning is more rapid than its fall in the afternoon. 
 The point of maximum temperature is under a 
 meridian about 30 east of the sun's position, and 
 there is a steep temperature gradient towards the 
 west, and a flatter gradient towards the east. If the 
 earth behaves like iron in this respect and iron is 
 one of the commonest constituents, not only of the 
 earth, but of other heavenly bodies we should expect 
 an electron current to pass from west to east. This 
 would explain the larger part of the earth's mag- 
 netism ; but, of course, nobody can claim that it gives 
 
188 
 
 THE ELECTRON THEORY 
 
 a complete explanation until we can test it with some 
 quantitative rigidity. In any case, it is useful to 
 remember that the electron current round the earth 
 proceeds from west to east, counter-sunwise (Fig. 27). 
 In a magnetic needle, M, the electron current runs 
 so that on its side nearest the ground the electrons 
 run in the same direction as they do in the ground. 
 
 Whenever, therefore, a 
 north - seeking pole of 
 a needle points towards 
 us, we know that the 
 electron current revolves 
 round it in the direction 
 of the hands of a watch. 
 And when the end of a 
 solenoid points towards 
 us, and the electron cur- 
 rent, on its way from 
 the zinc to the copper, 
 passes round it clock- 
 wise, we know that that 
 solenoid, suspended or 
 
 floated freely, will point the same end towards the 
 north. A smaller solenoid within it will have a 
 current in the same direction induced in it when 
 the main current is broken, and a current in the 
 opposite direction when the main current is started 
 again. 
 
 Since the electron current in the wire consists of a 
 
 FIG. 27. 
 
INDUCED CURRENTS 189 
 
 vast number of moving electrons, it may be regarded 
 as a bundle of innumerable conductors of very small 
 diameter, and it is evident that these will influence 
 each other. It will be more difficult to start a 
 current in a thick wire than to start the same 
 aggregate current in a number of thin wires taken 
 separately. The phenomenon whereby a current in 
 a wire hinders its own increase or decrease is called 
 self-induction. It is measured by the " coefficient of 
 self-induction," or, shortly, the " inductance," and is 
 numerically equal to the magnetic flux through the 
 circuit when unit current flows through it. In a 
 long straight solenoid traversed by unit current (10 
 amperes), the magnetic force is 4 TTO, where n is the 
 number of turns per unit length. If A is the area of 
 the section, the number of lines of force passing 
 through each turn is 4 TrnA. ; and since there are n 
 turns per unit length, the number of lines is 4 7m 2 A f 
 so that the inductance of a solenoid of length I is 
 4 TrnHA.. This is equal to twice the energy in the 
 magnetic field due to unit current. 
 
 The inductance may be enormously increased by 
 putting an iron core into the solenoid, as in that case 
 the lines of force due to the molecular currents are 
 added to those of the solenoid. 
 
CHAPTER X 
 
 RADIATION 
 
 HITHERTO we have considered electric actions with- 
 out reference to the time taken in transmitting them 
 from one place to another. We have dealt with 
 them as we would with the phenomena of gravi- 
 tation. It is known from astronomical observa- 
 tions that gravitational force is transmitted through 
 space with a practically infinite velocity, a velocity 
 so great that we cannot discover any time interval 
 elapsing between the establishment of a given con- 
 figuration of gravitating masses and the action of 
 the gravitational force predicted by Newton's law. 
 If, for instance, gravitation were transmitted through 
 space with the velocity of light, there would be a 
 certain retardation or lag of the force between two 
 celestial bodies behind their geometrical positions. 
 If a body were falling towards the sun and were 
 crossing the earth's orbit, the force exerted by the 
 sun upon it at every instant would not be the force 
 due to its position at that instant, but would be the 
 force due to the position it occupied eight minutes 
 before that instant, since the gravitational force 
 would take eight minutes to traverse the distance 
 
 190 
 
RADIATION 191 
 
 between the sun and the earth's orbit. Such a lag 
 would upset all calculations based upon Newton's 
 simple law of attraction, and could not fail to be 
 discovered. 
 
 It was thought for a long time that electric and 
 magnetic forces were propagated instantaneously 
 throughout observable space, or, at least, with the 
 speed of gravitational force. In that case a mag- 
 netic field produced by exciting an electromagnet 
 would no sooner be established in our laboratories 
 than its influence would extend to the sun and the 
 fixed stars. Likewise, if we could suddenly create 
 or destroy a lump of matter, an increase or dimi- 
 nution of gravitational force would be instantly felt 
 throughout the universe. 
 
 If a magnetic-field were to oscillate between a 
 maximum and a minimum value, its influence at 
 any point outside oscillates at the same rate; but 
 the distance between two successive maxima of 
 influence depends upon the rate of its propagation. 
 With an infinite speed, the "wave-length" or distance 
 between successive maxima would be infinite. If 
 we had any means of creating or destroying matter, 
 we could produce gravitational waves of infyaite 
 wave-length. But the science of optics has made 
 us familiar with a velocity of propagation which, 
 though very large, is still quite measurable. It is 
 the velocity of light, which is 3 x 10 10 cm. per second, 
 or 186,000 miles per second, and the experiments of 
 
THE ELECTRON THEORY 
 
 Hertz have proved that a magnetic field is pro- 
 pagated outwards with that velocity. This means 
 that when a magnet is made and unmade, waves of 
 magnetic force travel out into space with a wave- 
 length proportional to the time elapsing between 
 two successive makes or breaks. If a break occurs 
 every eight minutes, the wave-length is equal to the 
 distance of the earth from the sun. If it occurs a 
 million times per second, the wave-length is about 
 one-sixth of a mile. 
 
 There is thus a close analogy between the pro- 
 pagation of light and the propagation of magnetic 
 force. Both processes may be classed under the 
 word " radiation," which may be defined as a pro- 
 cess in which a disturbance is propagated through 
 space without the intervention of ponderable matter. 
 Light-rays, heat-rays, and rays of magnetic force 
 come under this heading. Cathode rays do not, 
 since they are simply projected electrons, nor canal 
 rays, since they are projected positive atoms. 
 
 We have in the previous chapters become familiar 
 with three electric actions at a distance : (1) Electro- 
 static force, or the force between charged bodies 
 at rest. (2) Magnetic force, or the force between 
 charged bodies in steady motion. (3) Inductive 
 force, or the force between charged bodies under 
 acceleration. 
 
 The second and third of these forces do not come 
 into play until electric charges i.e. electrons or 
 
RADIATION 193 
 
 positive atoms are moved. Since we can produce 
 such motion at will, we can determine the velocity of 
 propagation of these forces by the methods employed 
 in determining the velocity of light without the aid 
 of heavenly bodies, or by somewhat similar methods. 
 But we cannot either create or destroy an electric 
 charge. Electricity is not a mode of motion. It is 
 as indestructible as matter itself. Hence we cannot 
 determine the velocity of propagation of electrostatic 
 force by purely terrestrial experiments. If we knew 
 the exact value of the electric charges of the planets, 
 there would be a faint chance of discovering a finite 
 rate of propagation of the electrostatic force between 
 them ; but we have already seen (p. 70) that that 
 force is insignificant in comparison with the gravi- 
 tational force between them. 
 
 We cannot, therefore, say anything about the rate 
 at which electrostatic force is propagated. Like that 
 of the other static force, gravitation, it may be 
 infinite ; and we have as much right to speak about 
 electrostatic rays or waves as we have to speak of 
 rays or waves of gravitational force. 
 
 But the rate at which the dynamic forces (2) and 
 (3) are propagated is well known. They are pro- 
 pagated through space with the velocity of light, and 
 if any matter containing free electrons or positive 
 atoms intervenes, their rate of propagation is lessened, 
 just as the velocity of light is diminished under the 
 same circumstances. 
 
 N 
 
194 THE ELECTEON THEORY 
 
 Consider two parallel wires of infinite length, along 
 which electron currents move in the same direction. 
 There is a magnetic attraction between them which 
 remains constant as long as the currents remain the 
 same. There is no electrostatic force, and no in- 
 ductive force between them. The magnetic force 
 being steady, there are no magnetic waves, no mag- 
 netic radiation. But let the current in one wire, 
 which we will call A, diminish steadily to zero, then 
 the magnetic field will also decrease steadily to zero, 
 and the magnetic force between the wires will vanish. 
 It is interesting to note the precise manner in which 
 the magnetic force vanishes. The magnetic force is 
 conditional upon the existence of two magnetic 
 fields, each due to an electron current. 
 
 When the current in A falls to zero, the magnetic 
 field of A vanishes at the same instant. But only at 
 the wire itself. It takes some time to vanish in 
 regions some distance away from the wire. At B 
 it only vanishes after an interval of time, which 
 depends upon the distance between A and B. If 
 that distance is 186,000 miles, then the magnetic 
 force on B persists for one second after the current 
 in A has ceased to flow. The decrease of magnetic 
 force in A thus produces a pulse of demagnetisation 
 extending into infinite space with the velocity of 
 light. This pulse is accompanied by a pulse of 
 inductive force. As we have seen in the last chapter, 
 an acceleration or retardation of electrons in a wire 
 
RADIATION I9S 
 
 produces a displacement of electrons in the opposite 
 direction in a neighbouring wire, the displacement of 
 electrons across any section of the wire being pro- 
 portional to the change in the strength of the mag- 
 netic field. We have, therefore, two different effects 
 produced in B when the current in A diminishes to 
 zero. 
 
 (a) The magnetic force between A and B diminishes 
 as the current in A diminishes. 
 
 (6) The electrons in B undergo an inductive 
 acceleration in the direction of the main current 
 while the decrease in A continues. 
 
 In (a) we have, therefore, a steady diminution of a 
 force acting in the line joining A and B. In (6) we 
 have a steady force acting at right angles to 'the line 
 joining A and B, and lasting only as long as the 
 current in A is undergoing a change. The forces (a) 
 and (b) are in the plane of the two wires, but are at 
 right angles to each other. 
 
 Now, the force (a) is a " magnetic " force, and is, 
 by the older methods, measured as the force upon 
 a magnetic " pole." But the magnetic lines of force 
 are supposed to mark out the lines along which a 
 "free magnetic pole" would travel. There is no 
 such thing as a free magnetic pole; but if there 
 were, it would revolve round and round a current- 
 bearing wire. The magnetic lines of force will there- 
 fore cut the plane containing the wires A and B at 
 right angles. Hence it is usual to say that the 
 
196 THE ELECTRON THEORY 
 
 magnetic force is always at right angles to the 
 "electric" (inductive) force, and both are in the 
 plane of the wave front i.e. in the plane normal to 
 the direction of propagation. Since in the modern 
 theory all magnetic forces are resolved into forces 
 on moving electrons, the magnetic force acts in the 
 direction of propagation of the wave. It is a " longi- 
 tudinal " force, while the inductive force is a " trans- 
 verse " force, and only the latter is in the plane of 
 the wave-front. 
 
 These considerations lead up to the important 
 conception of an electro-magnetic wave. Since no 
 magnetic wave can be created without changing the 
 magnetic force and thus producing an inductive 
 pulse, and since no induction is possible without 
 moving electrons and (therefore) magnetic fields, it 
 follows that in all electro-magnetic waves we have 
 the two forces, the magnetic and the inductive, 
 which go hand in hand, and are always at right 
 angles to each other. 
 
 It is these electro-magnetic waves that are used in 
 wireless telegraphy, and the same waves, when much 
 smaller in wave-length, produce all the phenomena 
 of light. 
 
 Consider a single electron swinging up and down 
 in a vertical path one centimetre long. Let its 
 motion be a simple harmonic motion, like that of 
 a piston-rod; then its velocity will be greatest in 
 the middle of its run, and least at the ends. The 
 
RADIATION 
 
 I 9 7 
 
 
 
 5 
 
 O </ + * + + 
 
 magnetic field due to its motion will therefore be 
 greatest when the electron is passing the centre of 
 its path, and least when its motion is being reversed. 
 On the other hand, the acceleration (and retardation) 
 will be greatest at the ends of the path, and the 
 inductive force due to the electron will be greatest 
 when its motion is being 
 reversed. The electron, 
 therefore, sends out two 
 systems of waves into the 
 surrounding space, which 
 are both propagated with 
 the velocity of light, but 
 retarded with respect to 
 each other in such a 
 manner that the maxi- 
 mum of one coincides 
 with the minimum of the 
 other. 
 
 A single electron would, 
 of course, not give rise 
 to an appreciable electro- 
 magnetic effect ; but very perceptible waves may be 
 generated by means of an induction coil discharged 
 through a conductor of some capacity. 
 
 Let an induction coil be discharged through a 
 spark-gap, consisting of two metallic knobs, Fig. 28, 
 connected with metallic plates to increase the 
 capacity. The discharge is, of course, oscillatory, 
 
 FIG. 28. 
 
198 THE ELECTRON THEORY 
 
 since the primary current in the coil is made 
 and broken in rapid succession. An oscillatory dis- 
 charge means the surging to and fro of electrons. 
 The number of oscillations per second has been de- 
 termined by observing the sparks in a revolving 
 mirror. Trowbridge and Duane found a rate of 
 oscillation amounting to five million per second for 
 a small capacity. With a larger capacity the oscilla- 
 tions would be slower. 1 
 
 The oscillations are perceived most easily by 
 mounting two plates facing those attached to the 
 knobs, and stretching out two parallel wires with free 
 ends, as shown. This arrangement is due to Lecher, 
 and is an improvement on the apparatus by which 
 Hertz was first enabled to demonstrate the existence 
 of electric waves. 
 
 The surgings of the electrons in the gap produce 
 inductive pulses in the secondary plates, which urge 
 the electrons in them up and down in unison, but 
 always in the opposite direction from the acceleration 
 of the electrons in the gap. These pules are trans- 
 mitted along the wire, and under their influence the 
 electrons in them are urged to and fro along it, just 
 as particles of water describe circles when a wave 
 passes. 
 
 When the pulse or surge of electrons arrives at 
 
 1 The period of oscillation is given by the equation T = 2 
 where L is the self-induction and C the capacity of the 
 circuit. 
 
RADIATION 199 
 
 the end of the wire, it accumulates there and re- 
 bounds, just as a water-wave does against a sea-wall. 
 The analogy with the water-wave goes even further. 
 For when a water-wave makes straight for a sea- 
 wall, and is thrown back, it combines with the 
 advancing wave to form stationary waves, and the 
 water moves up and down in the same place, like a 
 violin string. Similarly, the direct and reflected 
 pulses of an electron current combine to form 
 stationary waves in a wire, marked off from each 
 other by " nodes" at which there is no accumula- 
 tion of electrons, but a very rapid motion to and 
 fro. These nodes, and the "ventral segments" be- 
 tween them, are a well-known phenomenon in the 
 vibration of strings and rods. The distance between 
 two successive nodes is half the wave-length of the 
 electric pulse. When the wires are bridged by a 
 spark-gap, the nodes are marked by the absence of 
 sparks, and the centres of the ventral segments by 
 a maximum of sparking. But a more sensitive 
 detector of waves is a highly exhausted glass tube, 
 which shines out when laid across from one ventral 
 segment to the other, but remains dark at the nodes. 
 When another bridge, consisting of a plain wire, is 
 added, the tube generally ceases to respond, since 
 all oscillations are disturbed. But if the wire is 
 laid across between two nodes, the tube flashes 
 out at a corresponding ventral segment, and is not 
 extinguished even when all the other nodes are 
 
200 THE ELECTRON THEORY 
 
 bridged. In this manner the wave-system along 
 the wire may be mapped out, and the wave-length 
 determined experimentally. In one experiment, 
 where the frequency was five million per second, 
 the wave-length was found to be 57 metres. Hence 
 the velocity of propagation was 5 x 10 6 x 5700 cm. 
 per sec., or approximately 3 x 10 10 cm. per sec. 
 This is the velocity of light, and thus we have 
 the experimental proof that electric pulses are 
 propagated along a wire with the velocity of 
 light. 
 
 By reflecting waves in air from a metallic plate, 
 Hertz proved in the same manner that electro-mag- 
 netic waves are propagated through air with the 
 same velocity. He thus furnished a brilliant prac- 
 tical confirmation of Maxwell's guess, that light 
 itself is an electro-magnetic phenomenon, and con- 
 sists of electro-magnetic waves of very short wave- 
 length. 
 
 The frequency of the discharge of a condenser 
 is very great, the oscillations being counted by 
 millions per second. Yet it is not great enough 
 to give waves as short as those of light. By 
 diminishing the capacity and inductance of the 
 wave-producing system, Lebedew succeeded in re- 
 ducing the wave-length to half a centimetre. But 
 since the wave-length of yellow light is so small 
 that 20,000 of its waves go to the centimetre, it is 
 clear that our oscillating systems must be made 
 
RADIATION 201 
 
 more rapid before we can produce light directly by 
 motion of electric charges. 
 
 When, however, we recollect that the oscillation 
 of electrons about positive atoms takes place with 
 a frequency of about 10 15 vibrations per second, the 
 phenomena of light receive a simple explanation. 
 For every electron describing a straight or elliptical 
 path sends out waves of both magnetic and induc- 
 tive force, and every electron revolving in a circle 
 gives rise to a steady magnetic field, and a revolving 
 field of inductive force. 
 
 We have already considered the oscillation of an 
 electron to and fro, and seen that it necessarily sends 
 out waves of magnetic and inductive force which, 
 when of the proper size, must become perceptible 
 to our eyes as light. If too long, they constitute 
 infra-red or heat waves ; if too short, they consti- 
 tute ultra-violet rays, which are powerfully actinic. 
 When, instead of oscillating in a straight line, the 
 electron describes an elliptical orbit, it has both a 
 change of velocity and of acceleration towards its 
 centre of force in the positive atom; but when it 
 describes a circle, its velocity is constant. It ex- 
 periences a constant acceleration towards the centre 
 of the circle, and this acceleration is , effective in 
 producing a pulse of inductive force, though power- 
 less to change the velocity with which the electron 
 revolves. The direction of the acceleration is con- 
 stantly changing revolving, in fact and hence the 
 
202 THE ELECTRON THEORY 
 
 inductive force revolves also. The wave sent out 
 into space is a twirl something like what one may 
 produce by laying a string over a table and 
 quickly twisting one end of it. If the wave is 
 visible as light, it is described in optics as " cir- 
 cularly polarised," in a direction depending upon 
 the direction of revolution of the electron. When 
 the electron simply oscillates to and fro, or appears 
 to do so from the point of vision (as a revolving 
 electron appears to do when viewed from one side) 
 the light is said to be "plane-polarised." But the 
 plane of polarisation is not that in which the 
 electron oscillates, but is at right angles to it. 
 For when an electro-magnetic wave is intercepted 
 by glass at a certain angle called the polarising 
 angle, the wave is reflected only when the 
 electric oscillation takes place in a plane normal 
 to the plane of incidence. This experiment dis- 
 poses of the old controversy with regard to the 
 true motion with respect to the plane of polarisa- 
 tion. 
 
 When another revolving electron is met with by 
 a circularly polarised wave a " twirl," as described 
 above it retards or accelerates the revolution of 
 the electron. If both revolve in the same direction 
 the revolution of the second electron is retarded 
 by the inductive pulse, which, as we have seen, is 
 always in the direction opposite to the motion of 
 the charge from which the inductive force proceeds. 
 
RADIATION 203 
 
 For the same reason the motion of an electron re- 
 volving in a direction contrary to the direction of 
 the radiating electron is accelerated. If the elec- 
 trons thus impinged upon do not revolve in planes 
 normal to the direction of propagation of the pulse, 
 their acceleration or retardation will be reduced in 
 proportion with the projection of their orbit upon 
 the normal plane. But we see in any case that, 
 whether they are accelerated or retarded, the net 
 effect of the pulse is to counteract the magnetic 
 field which emits the pulse. This also happens 
 when one circuit induces a current in another 
 circuit. But note the important difference. In a 
 wire the inductive impulse fritters itself away in 
 overcoming the resistance of the wire, and convert- 
 ing itself into heat. In freely revolving electrons 
 there is no such waste of energy. A magnetic field 
 suddenly established induces a permanent change 
 of velocity in the orbital motion of the electrons, 
 which lasts until the magnetic field is annulled. 
 That permanent change of velocity always acts in 
 opposition to the field whose creation produced it. 
 Now, when a body is magnetised in a direction 
 opposed to the direction of the field, we call it 
 " diamagnetic." We are, therefore, driven to the 
 conclusion that all bodies containing electrons in 
 orbital motion round atoms are diamagnetic. The 
 Zeeman effect shows that all bodies contain such 
 electrons, therefore all known substances are funda- 
 
204 THE ELECTRON THEORY 
 
 mentally diamagnetic. But since the change 
 of velocity actually produced does not exceed 1 
 part in 100,000, it is almost inappreciable as a 
 rule; and when the orbital circuits influence each 
 other sufficiently to swing round into line, the 
 paramagnetic effect is sufficient to completely 
 mask the fundamental diamagnetism of the sub- 
 stance. 
 
 The above considerations make it clear why some 
 substances absorb light while others do not. Those 
 substances which contain free electrons not per- 
 manently bound to separate atoms allow their 
 electrons to follow freely the magnetic and induc- 
 tive forces at play within the light-wave, and the 
 motion thus produced is absorbed and frittered 
 away into heat. These substances are the good 
 conductors, more especially the metals. Solutions, 
 whose ions have a mobility far below that of elec- 
 trons in metals, are much more transparent than 
 the latter, and the insulators, especially those of a 
 low dielectric constant, absorb light least. It is 
 also readily understood that when electrons in an 
 illuminated body happen to be revolving with the 
 same period as the incident light, the change of 
 velocity is much greater than if they are not. Their 
 orbital equilibrium is more easily upset, and the 
 electrons fly away from their atoms and roam at 
 large. This is what is called "optical resonance." 
 It accounts for the fact that some wave-lengths of 
 
KADIATION 205 
 
 light are more easily absorbed than others. It 
 accounts, in fact, for the phenomena of colour. It 
 also makes clear to us why a body absorbs most 
 easily light of the same colour and wave-length 
 as that which it emits itself a fundamental and 
 important law of radiation. 
 
CHAPTER XI 
 
 MEASUREMENTS CONCERNING ELECTRONS 
 
 IN this chapter I intend to specify the experiments 
 which have led to the general acceptance of the 
 electron theory, and brought the scientific world face 
 to face with the electron itself. Hitherto I have 
 taken the electron for granted, and the reader may 
 have been inclined to wish for some evidence of 
 the existence of a body over 1000 times lighter 
 than the atom of hydrogen, which latter has 
 been until recently regarded as the smallest pos- 
 sible material particle. That evidence shall now 
 be furnished. 
 
 When a vacuum tube is exhausted to one-millionth 
 of an atmosphere, the luminous phenomena previously 
 observed give way to the phenomenon of cathode 
 rays, which proceed in straight lines from the 
 cathode or negative electrode, and produce a green 
 fluorescence on the walls of the tube. 
 
 These cathode rays are electrons, projected by the 
 cathode with an enormous velocity. 
 
 That this is so is proved by the following facts : 
 
 1. The "rays" convey a negative charge. 
 
 206 
 
MEASUREMENTS CONCERNING ELECTRONS 207 
 
 2. They consist of minute particles of matter. 
 
 3. These particles have a constant charge, amount- 
 ing to 3*4 x 10 ~ 10 electrostatic unit. 
 
 4. The particles have a mass about a thousand 
 times smaller than the hydrogen atom. 
 
 5. They move with a velocity little less than that 
 of light. 
 
 These facts were gradually recognised as the result 
 of a large number of difficult and often highly 
 ingenious experiments undertaken with a view to 
 elucidate the nature of cathode rays. When the ex- 
 periments were first undertaken nobody expected to 
 find the cathode particles to be identical with the 
 electrons postulated by Lorentz in order to explain 
 the Zeeman effect. Many experimenters actually 
 thought that the cathode rays were electro-magnetic 
 waves, and claimed to have proved that they were. 
 It was only when new and crucial experiments were 
 made, and successfully repeated everywhere, that the 
 truth was made manifest to a wondering world. 
 That was in the year 1897, and since that year the 
 electron has become the corner-stone of electrical 
 science. 
 
 That the cathode rays convey an electric charge 
 was already proved by Jean Perrin in 1895. His 
 apparatus is illustrated in the diagram (Fig. 29), 
 which shows a vacuum tube provided with two 
 electrodes. 
 
 The cathode C is a disc of aluminium, and the 
 
208 THE ELECTRON THEORY 
 
 anode A B D E is a box of aluminium with an 
 opening towards the cathode. Inside this box is 
 a hollow cylinder, F, connected with an electroscope 
 or an electrometer. When the tube is sufficiently 
 exhausted and a current sent through it, cathode 
 rays are projected from C into the box and the inner 
 cylinder, which at once acquires a negative charge. 
 That this charge is really due to the rays is proved 
 
 IE- Dl 
 
 5T- 1 E, 
 
 FIG. 29. 
 
 by deflecting the cathode beam with a magnet, 
 whereupon F remains uncharged. 
 
 If, then, the rays consist of charged particles, the 
 next question is as to the size and charge of each 
 individual particle, and the velocity with which it is 
 moving. 
 
 There are several different ways of determining 
 these. The most obvious way is to expose the 
 particles to a lateral pull. When water is projected 
 from a horizontal orifice the jet describes a parabola 
 under the influence of the earth's attraction. The 
 distance to which the jet carries depends upon the 
 force with which it is projected in other words, 
 upon its velocity. The greater that velocity, the less 
 
MEASUREMENTS CONCERNING ELECTRONS 2 09 
 
 will the jet fall towards the ground in traversing a 
 given portion of its path. Now the cathode beam is 
 a jet of electrified particles, travelling at such a pro- 
 digious rate that their weight exerts no perceptible 
 effect upon their path. But stronger deflecting forces 
 are readily available. Since it is the electric field 
 between the cathode and anode that generates their 
 velocity, another field acting at right angles to their 
 
 FIG. 30, 
 
 path will produce a strong deflection. The apparatus 
 used by J. J. Thomson to perform this experiment 
 is shown in Fig. 30. C is the cathode, A and B 
 are thick metallic diaphragms serving as the anode, 
 and provided with horizontal slits. The deflecting 
 electric field is established between the plates D and 
 E, which are large enough to give a fairly uniform 
 field. The cathode beam is made into a narrow 
 horizontal strip in passing through A and B, and 
 this strip is bent into a parabola while traversing 
 the field between D and E, and after leaving this 
 it continues in a straight line till it impinges on a 
 scale, F, which measures its deflection. 
 
 Now the effect produced by the deflecting field 
 
 o 
 
210 THE ELECTRON THEORY 
 
 depends upon three factors. One of these is the 
 speed of the particles, which we have already referred 
 to. \ Another is their electric charge, which controls 
 the force exerted by the field upon them. Evidently 
 the greater their charge the more will they be 
 deflected. The third factor is the mass of the 
 particles. The greater their mass i.e. their inertia 
 the more force will be required to deflect them 
 from their path. If e is the charge of a particle, 
 
 and m its mass, its deflection is proportional to ^. 
 
 This all-important ratio becomes known as soon 
 as the velocity of the particles is determined. Its 
 interest is enhanced by the fact that in electrolysis 
 the ratio of the electricity transported to the mass 
 transported is fixed for each element, being 95,000 
 coulombs per gramme in the case of hydrogen. The 
 discovery of a similarly constant ratio in gaseous 
 discharges was therefore eagerly sought after. 
 
 Since there are two unknown quantities, ~ and 
 
 m 
 
 v (the velocity), we require two independent equations 
 in order to determine them. The electric deflection 
 furnishes one equation. The other may be derived 
 either from the magnetic deflection, from the differ- 
 ence of potential, or from the heat developed. 
 
 A method devised by Wiechert, and employed by 
 d'Arsonval, is particularly effective in determining 
 directly the velocity v. It is based upon the deflec- 
 tion of cathode rays by a magnetic field. We have 
 
MEASUKEMENTS CONCERNING ELECTRONS 211 
 
 seen above (p. 147) that an electron in motion is 
 attracted by another moving parallel to it. If the 
 electrons were free to move in any direction, and not 
 forced to move along a wire, they would approach 
 each other. A wire bearing a current exerts a 
 similar " magnetic " force upon moving electrons by 
 virtue of the electrons moving along it. The force 
 is directed towards the wire; but since the "lines 
 of magnetic force" (i.e. the lines along which a 
 magnetic pole would move) are circles round the 
 wire, the attraction exerted upon a moving electron 
 is at right angles to the lines of magnetic force. If, 
 therefore, a vacuum tube is placed between two 
 magnet poles so that the magnetic lines of force cross 
 the path of the cathode rays horizontally, the rays 
 are deflected up or down according to the polarity of 
 the lines of force. When the magnetic field is due to 
 the poles of an electro-magnet fed by an alternating 
 current, the cathode beam is deflected up and down 
 with the frequency of the alternate current itself, and 
 the fluorescent spot which it produces on the glass 
 wall, or better, on a special fluorescent screen, moves 
 up and down as the direction of the current changes. 
 Now it is found that whatever may be the frequency 
 of an alternating current, the luminous^ spot follows 
 the alternations instantly. No undulation can be 
 observed along the cathode beam as it is observed in 
 the case of a rope swung up and down at one end. 
 This shows already, without further confirmation, 
 
212 THE ELECTRON THEORY 
 
 that an almost incredibly short time must elapse 
 between the cathode particle leaving the cathode 
 and arriving at the wall. But the time taken can be 
 actually measured by means of two successive electro- 
 magnets placed some distance apart and traversed 
 by the same high-frequency current. M. d'Arsonval 
 succeeded in bringing a current of the enormous 
 frequency of 10,000,000 oscillations per second to 
 bear upon the rays. He then placed a slit just 
 beyond the first electro-magnet, so as to shut off 
 all the cathode rays except those which produced 
 the luminous spot highest on the screen. These are 
 the rays that passed the first magnet, just at the 
 maximum of magnetisation in one direction. On 
 passing the second electro-magnet, the cathode rays 
 are again deflected in the same direction; but on 
 placing the electro-magnets further apart and taking 
 care that they are always in the same magnetic state 
 at a given instant, a position is found in which the 
 second electro-magnet produces no further deflection. 
 This happens when the time taken by the cathode 
 rays to traverse the distance between the two electro- 
 magnets is one-quarter of the period of the alternat- 
 ing current ; for then the magnetising current, being 
 midway between two opposite maxima, is zero. Now 
 the period being a 10,000,000th of a second, this 
 quarter-period is a 40,000,000th of a second. M. 
 d'Arsonval found the proper distance between the 
 electro-magnets to be 75 centimetres. Hence the 
 
MEASUREMENTS CONCERNING ELECTRONS 213 
 
 speed of propagation of the cathode rays or projected 
 electrons was 75x40 millions = 3000 million cm. per 
 sec., or one-tenth of the velocity of light 
 
 This startling result leads to some surprising con- 
 clusions. The velocity is a million times greater 
 than that of the fastest express train, and a milli- 
 gramme of matter moving with that speed has ten 
 times the destructive energy of a railway train at top 
 speed. 
 
 This velocity being known, the ratio can be 
 
 m 
 
 determined from the electrostatic deflection. But it 
 is simpler to determine it from the magnetic deflec- 
 tion itself. The magnetic force upon the electron is 
 always at right angles to its path. That path must 
 therefore be an arc of a circle as long as it lies in the 
 magnetic field and the field has a constant strength. 
 The curvature of the path may be calculated from 
 ordinary mechanical principles. The centripetal 
 force equals the product H e v, where H is the 
 magnetic field and e the charge. The centrifugal 
 
 force is ^^, where m is the mass of the electron, v 
 
 T 
 
 its velocity, and r the radius of curvature. Hence 
 
 or 
 
 e v 
 
 r m = Hr 
 
214 THE ELECTRON THEORY 
 
 The value obtained by Wiechert in 1899 was 
 465 x 10 15 , meaning that a gramme of cathode rays 
 represents a charge of 465,000 billion electrostatic 
 units or "companies" of electrons. 
 
 Instead of measuring the velocity, it may be 
 eliminated between two equations by calculating it 
 from the observed difference of potential, which must 
 impart to the particles a velocity simply depending 
 
 upon -. In this manner, Kaufmann found, in 1898, 
 
 the value 558 x 10 15 , and Simon in 1899 : 559-5 x 10 15 . 
 Other methods, capable of greater or less accuracy, 
 have been devised and employed by J. J. Thomson, 
 Lenard, Becquerel, and others ; but they all confirm 
 the order of magnitude found above. 
 
 A very important and significant observation made 
 
 by all was that the ratio - depends neither upon the 
 
 gas contained in the vacuum tube nor upon the 
 metal of the electrodes. This result is surprising if 
 the cathode rays are atoms of ordinary matter. It 
 would mean not only that ordinary matter is capable 
 of travelling with a speed approaching that of light ; 
 but that every atom has an electric charge propor- 
 tional to its weight. For such a state of things there 
 is no precedent. In electrolysis every atom conveys 
 a charge proportional to its valency and quite in- 
 dependent of its weight. The atoms of magnesium, 
 zinc, and cadmium, whose weights are in the pro- 
 
MEASUREMENTS CONCERNING ELECTRONS 21$ 
 
 portion of 24 : 65 : 112, each convey exactly the 
 same quantity of electricity through the electro- 
 lytic cell. It would be strange if the amounts of 
 electricity they conveyed through the vacuum tube 
 were as 24 : 65 : 112. 
 
 But there is an even more remarkable difference 
 between cathode rays and electrolysis. In electrolysis 
 
 the ratio , or the charge conveyed by unit mass of 
 fn 
 
 the electrolyte (or required for decomposing it), varies 
 from one metal to another, m changing from one 
 atom to another, while e remains constant except for 
 changes of valency. For hydrogen, the lightest of 
 
 the known elements, the ratio is 0'286 x 10 15 , or 
 
 m 
 
 about 2000 times smaller than the same ratio for 
 cathode rays. This means that the mass conveying 
 the atomic charge is either 2000 times larger than 
 the mass of the cathode particle, or that the charge 
 of the hydrogen atom is 2000 times smaller than 
 that of the cathode particle. 
 
 The former alternative seemed barred by the im- 
 possibility of assuming the existence of anything 
 smaller than the atom of hydrogen. The whole 
 tradition of the atomic theory rebelled against such 
 an idea. Nevertheless the next great step in dis- 
 covery was the momentous one of determining the 
 actual charge and the actual mass of the cathode 
 particles, and thus to establish not only the existence 
 of material particles much smaller than atoms, but 
 
2l6 THE ELECTRON THEORY 
 
 the existence of a primordial form of electric matter 
 hitherto unknown. 
 
 The Cavendish Laboratory at Cambridge will 
 be for ever memorable as the place where" this 
 momentous measurement was first carried out. 
 The measurement was in the first instance not 
 made with cathode rays, but with the slowly moving 
 particles which are the chief agents in gaseous 
 conduction. 
 
 When a gas is put into a conducting state, say, by 
 exposure to Rontgen rays, it remains for a little 
 time in that state, even after the rays have ceased. 
 If, however, the gas is bubbled through water, or 
 filtered through a plug of cotton wool, its con- 
 ductivity disappears. Again, when the gas is passed 
 between two plates, one of which has a high negative 
 charge, while the other is insulated, the negative 
 particles will all be driven against the insulated 
 plate, and their total charge can be measured by 
 an electrometer connected with the plate. This 
 charge is evidently equal to n e, where n is the 
 number of particles, and e their charge. The total 
 charge n e being measured, it remains to determine 
 n in order to find e, the charge on each particle. 
 This is J. J. Thomson's famous " counting experi- 
 ment," which is best described in his own words : * 
 
 "The method by which I determined n was 
 founded on the discovery by C. T. R. Wilson, that 
 
 1 J. J. Thomson, " Electricity and Matter," 1904, p. 75. 
 
MEASUREMENTS CONCERNING ELECTRONS 217 
 
 the charged particles act as nuclei round which small 
 drops of water condense when the particles are 
 surrounded by damp air cooled below the satura- 
 tion point. 
 
 "In dust-free air, as Aitken showed, it is very 
 difficult to get a fog when damp air is cooled, since 
 there are no nuclei for the drops to condense around. 
 If there are charged particles in the dust-free air, 
 however, a fog will be deposited round these by a 
 supersaturation far less than that required to pro- 
 duce any appreciable effect when no charged particles 
 are present. Thus, in sufficiently supersaturated 
 damp air, a cloud is deposited on these charged 
 particles, and they are thus rendered visible. This 
 is the first step towards counting them. The drops 
 are, however, far too small and too numerous to 
 be counted directly. We can, however, get their 
 number indirectly as follows: Suppose we have a 
 number of these particles in dust-free air in a closed 
 vessel, the air being saturated with water vapour. 
 Suppose, now, that we produce a sudden expansion of 
 the air in the vessel. This will cool the air ; it will 
 be supersaturated with vapour, and drops will be de- 
 posited around the charged particles. Now, if we know 
 the amount of expansion produced, we Qan calculate 
 the cooling of the gas, and therefore the amount of 
 water deposited. Thus we know the volume of water 
 in the form of drops, so that if we know the volume 
 of one drop we can deduce the number of drops. 
 
2l8 THE ELECTRON THEORY 
 
 To find the size of a drop we make use of an investi- 
 gation by Sir George Stokes on the rate at which 
 small spheres fall through the air. In consequence 
 of the viscosity of the air small bodies fall exceed- 
 ingly slowly, and the smaller they are the slower 
 they fall. Stokes showed that if a is the radius of a 
 drop of water, the velocity v with which it falls 
 through the air is given by the equation 
 
 where g is the acceleration due to gravity = 981, 
 and fju the coefficient of viscosity of air = 0*00018. 
 Thus 
 
 v = l-21 x 
 
 hence, if we can determine v we can determine the 
 radius, and hence the volume of the drop. But v 
 is evidently the velocity with which the cloud round 
 the charged particle settles down, and can easily be 
 measured by observing the movement of the top of 
 the cloud. In this way I found the volume of 
 the drops, and thence n the number of particles. 
 As ne had been determined by electrical measure- 
 ments, the value of e could be deduced when n was 
 known. In this way I found that its value is 
 
 3*4 x 10 " 10 electrostatic c.g.s. units. 
 
 Experiments were made with air, hydrogen, and car- 
 bonic acid, and it was found that the ions had the 
 
MEASUREMENTS CONCERNING ELECTRONS 219 
 
 same charge in all these gases a strong argument in 
 favour of the atomic character of electricity." 
 
 The ratio - is the same for cathode rays, for 
 
 negative carriers of gaseous discharges, and for the 
 negatively electrified particles emitted by metals 
 when exposed to ultra-violet light, or raised to the 
 temperature of incandescence. In each case the 
 charge of each particle is the same, while its mass is 
 less than a thousandth of the mass of the hydrogen 
 atom. J. J. Thomson proposed the name "corpuscle" 
 for these natural units of negative electricity. 
 " These corpuscles are the same, however the electri- 
 fication may have arisen, or wherever they may have 
 been found. Negative electricity in a gas at a low 
 pressure has thus a structure analogous to a gas, the 
 corpuscles taking the place of the molecules. The 
 'negative electric fluid/ to use the old notation, 
 resembles a gaseous fluid with a corpuscular, instead 
 of a molecular, structure." 
 
 Instead of the word "corpuscle," the new word 
 " electron," proposed by Dr. G. Johnstone Stoney, 
 has now been almost universally adopted as being 
 more specialised and unmistakable. Prof. Thomson 
 sums up his conclusions in the following passage, 
 in which I have substituted " electrons " for " cor- 
 puscles " : l 
 
 "These results lead us to a view of electrifica- 
 
 i J. J. Thomson, " Electricity and Matter," 1904, p. 88. 
 
220 THE ELECTRON THEORY 
 
 tion which has a striking resemblance to that 
 of Franklin's ' One-Fluid Theory of Electricity.' 
 Instead of taking, as Franklin did, the electric fluid 
 to be positive electricity, we take it to be negative. 
 The c electric fluid ' of Franklin corresponds to an 
 assemblage of electrons, negative electrification being 
 a collection of these electrons. The transference of 
 electrification from one place to another is effected 
 by the motions of electrons from the place where 
 there is a gain of positive electrification to the place 
 where there is a gain of negative. A positively 
 electrified body is one that has lost some of its 
 electrons. We have seen that the mass and charge 
 of the electrons have been determined directly by 
 experiments. We in fact know more about the 
 ' electric fluid ' than we know about such fluids as 
 air or water." 
 
 Since these remarkable experiments were per- 
 formed, they have been repeated again and again 
 with constantly increasing precision. The electrons 
 have been rediscovered in several other fields of 
 research, notably the phenomena presented by 
 radium, one of whose radiations is constituted by 
 
 cathode rays or projected electrons. The ratio ~ 
 and the values of e and m are now known with 
 considerable accuracy, though the ratio is still 
 much better determined than its two constituents. 
 Side by side with the advances on the experimental 
 side have been the theoretical advances. The 
 
MEASUREMENTS CONCERNING ELECTRONS 221 
 
 electron theory has been developed in its mathe- 
 matical aspects, and has given occasion for many 
 notable results and speculations. But the measure- 
 ments made between 1896 and 1898 and outlined 
 above form the foundation on which the imposing 
 structure of the electron theory has since been 
 raised. 
 
CHAPTER XII 
 
 ELECTRICITY AND LIGHT 
 
 THE discovery that light consists of waves of electric 
 and magnetic force (p. 200) has vastly extended the 
 spheres both of electrical and of optical science. 
 But that discovery was made before the days of 
 the electron theory, and was embodied mathe- 
 matically in a set of differential equations, having 
 but a slender connection with the structure of actual 
 matter. The electro-magnetic theory of light re- 
 placed the older theory, which regarded the ether 
 as behaving like an elastic solid wherever very 
 rapid vibrations were concerned. But the experi- 
 mental basis of the electro-magnetic theory was 
 meagre, and it left a vast array of facts entirely 
 unexplained, notably those of the absorption and 
 dispersion of light. Indeed, its chief exponents 
 were always careful to point out that they knew 
 nothing concerning the intimate structure of those 
 materials whose specific inductive capacities or 
 magnetic permeabilities figured in their formulae. 
 In his " Theory of Optics," Prof. Schuster refers 
 to this tendency as follows: 
 
 "There is at present no theory of optics in the 
 
ELECTRICITY AND LIGHT 223 
 
 sense that the elastic solid theory was accepted fifty 
 years ago. We have abandoned that theory, and 
 learnt that the undulations of light are electro- 
 magnetic waves differing only in linear dimensions 
 from the disturbances which are generated by oscil- 
 lating electric currents or moving magnets. But so 
 long as the character of the displacements which 
 constitute the waves remains undefined, we cannot 
 pretend to have established a theory of light. This 
 limitation of our knowledge, which in one sense is 
 a retrogression from the philosophic standpoint of 
 the founders of the undulatory theory, is not always 
 sufficiently recognised, and sometimes deliberately 
 ignored. Those who believe in the possibility of a 
 mechanical conception of the universe, and are not 
 willing to abandon the methods which from the 
 time of Galileo and Newton have uniformly and 
 exclusively led to success, must look with the 
 gravest concern on a growing school of scientific 
 thought which rests content with equations correctly 
 representing numerical relationships between diffe- 
 rent phenomena, even though no precise meaning 
 can be attached to the symbols used. The fact that 
 this evasive school of philosophy has received some 
 countenance from the writings of Heinrich Hertz, 
 renders it all the more necessary that it should be 
 treated seriously and resisted strenuously." 
 
 The electron theory, by dealing with the elemen- 
 tary carriers of electricity, has brought a powerful 
 
224 THE ELECTRON THEORY 
 
 new weapon to bear upon optical problems, and has 
 already accomplished a great deal in the way of 
 their elucidation. But it will be some time before 
 the facts of optics are completely marshalled in 
 order, and linked with those of chemistry, elec- 
 tricity, and magnetism. Their variety is almost 
 infinite, and their full explanation involves revolu- 
 tionary changes in the theory, not alone of optics, 
 but of chemistry as well. I shall, therefore, have 
 to content myself with a brief outline of the main 
 facts. 
 
 (a) Refraction. All electro-magnetic waves are 
 transmitted with the velocity of light (3 x 10 10 cm. 
 per sec.) in media free from electric charges. This 
 is one way of stating the electron theory of refrac- 
 tion. It means that when the progress of a wave 
 is retarded, that retardation is due to the presence 
 of electrons or positive atoms. It is this presence 
 of electrons which accounts for the specific inductive 
 capacity or dielectric constant of a medium (see p. 
 62), and Maxwell's theory indicates a simple rela- 
 tion between the velocity of propagation v of an 
 electro-magnetic wave through a medium, and its 
 dielectric constant K. It is as follows : 
 
 that is to say, the square of the velocity of the wave 
 varies inversely as the dielectric constant. Let us 
 
ELECTRICITY AND LIGHT 22$ 
 
 see what information our theory can give us in this 
 matter. 
 
 The force between two charged bodies possessing 
 charges E and E 1 , and placed d cm. apart, is 
 
 EE* 
 
 Kd* 
 
 That is to say, the force decreases as the dielectric 
 constant increases. Now, according to our theory, 
 a "dielectric" is a body consisting of molecules or 
 atoms, to which electrons are closely attached in 
 such a manner that very few of them roam at large 
 among the atoms. When a dielectric is introduced 
 between two condenser plates charged positively and 
 negatively respectively, the electrons are pulled to- 
 wards the positive plate, and the positive atoms 
 towards the negative plate. Each electron is, there- 
 fore, separated from its atom ; but not so far as to 
 be pulled away by the next atom. The electrons on 
 the surface facing the positive plate will constitute 
 a negative surface charge, and the positive atoms 
 facing the negative plate constitute a positive sur- 
 face charge ; and these surface charges, by freeing the 
 interior of the dielectric from some of the electric 
 force, reduce the internal field, and thus .also reduce 
 the difference of potential between the condenser 
 plates, thereby increasing the capacity of the con- 
 denser. So much for the dielectric constant. 
 
 Now, as regards the propagation of waves. Let an 
 
 P 
 
226 THE ELECTRON THEORY 
 
 oscillatory current surge up and down one of the 
 plates ; in other words, let the free electrons in the 
 plate be made to oscillate up and down in rapid 
 succession. This, as explained on p. 179, leads to a 
 downward and upward thrust of all electrons in the 
 neighbouring space. In the upper half of its path 
 the oscillating electron is exposed to a downward 
 force, and therefore sends out an upward impulse 
 into surrounding space. Any electron which follows 
 this impulse will therefore oscillate in a reverse 
 direction, and will neutralise to some extent the 
 effect of the original oscillation in the space beyond, 
 just as in transmitting oscillations along a stretched 
 string the weight of an element of length shields the 
 further elements for a short time. The more elec- 
 trons capable of oscillation there are in the dielectric, 
 and the feebler the forces which tend to keep them 
 in position, the slower will be the rate at which an 
 electric wave is propagated. These are the same 
 conditions as those which account for a high 
 dielectric constant. It is, therefore, clear that a 
 high dielectric constant means a slow rate of wave- 
 propagation, and vice versa. The exact numerical 
 relation between the two quantities is not apparent 
 from these simple considerations ; but a glance at 
 the ordinary laws of wave-propagation will explain 
 Maxwell's law in an elementary manner. Whenever 
 a wave is propagated through a medium, we find 
 that the velocity of propagation is proportional to 
 
ELECTRICITY AND LIGHT 227 
 
 the square root of the force which tends to bring 
 back the body into its place when pulled out of it. 
 Now, in the case of an electron subject to periodic 
 impulses in opposite directions, the velocity with 
 which it follows the impulses of the original oscilla- 
 tion and those of other intervening electrons depends 
 upon the strength of the impulses so transmitted. 
 Now, the force across a dielectric varies, as we have 
 seen above, inversely as the dielectric constant K. 
 Hence the velocity of propagation, which varies as 
 the square root of the force, will vary as 1 
 Hence 
 
 K' 
 
 This relation holds good as long as the oscillations 
 in the condenser plate are slow, and far below the 
 natural period of oscillation of electrons about their 
 positive atoms. 
 
 When an electro-magnetic wave reaches a dielec- 
 tric, its velocity is reduced. When it hits its surface 
 at right angles, it is propagated in the same direc- 
 tion, only more slowly than before, and the wave 
 front is always parallel to the surface. When, how- 
 ever, the wave arrives at an angle to the surface, 
 the portion which arrives first begins to be retarded 
 sooner than the rest, and the wave front is bent 
 round or "refracted." The laws of refraction are 
 adequately dealt with in the older textbooks of 
 optics. 
 
228 THE ELECTRON THEORY 
 
 (b) Dispersion and Colour. Prismatic effects and 
 dispersion generally are due to some waves being 
 propagated more slowly than others. They are 
 therefore refracted to different degrees, and separated 
 into the well-known optical spectrum. This pheno- 
 menon is called dispersion. It is memorable that 
 the theory of dispersion was the breeding-ground of 
 the electron theory. A theory involving the dis- 
 placements and vibrations of elementary charges 
 had been applied to dispersion by Prof. Lorentz, of 
 Amsterdam, for several years before it was confirmed 
 by the discovery of the Zeeman effect. In fact, the 
 phenomena of dispersion had always been the great 
 stumbling-block in the way of the Maxwell-Hertz 
 theory, which told us nothing about them. The 
 electron theory of dispersion has been worked out 
 mainly by Schuster in Manchester and Drude in 
 Giessen. It is embodied by the latter in an equation l 
 which might as well be quoted here, as it states the 
 matter very concisely. It is 
 
 In this equation n is the refractive index, N the 
 number of electrons per cubic centimetre, X the 
 wave-length of the incident light, L the wave-length 
 of the natural wave emitted by the electrons in their 
 ordinary oscillation, and 6 is inversely proportional 
 to the force tending to keep the electrons in their 
 
 1 P. Drude, Annalen der PJiysik, No. 9, 1904, p. 681. 
 
ELECTRICITY AND LIGHT 229 
 
 central positions. For short, we might call 6 the 
 "laxity." 
 
 Many interesting results may be read in this 
 equation. In the first place, if N = 0, ri 2 = 1, and 
 n = 1. That is to say, the velocity in the dielectric 
 is the same as in pure ether. It is only the electrons 
 which retard the wave. Further, the greater the 
 " laxity " 6, the greater is the refractive index, and 
 the slower the wave in the dielectric. This has 
 already been mentioned under refraction. 
 
 The first and second terms on the right-hand side 
 are independent of the wave-length X, and if only 
 those terms had to be considered, there would be no 
 dispersion. The third term, however, involves X, and 
 we see at once that its amount depends both upon 
 the wave-length of the incident light and the natural 
 waves emitted by the vibrating electrons. If X is 
 very large in comparison with L, we may neglect L 2 
 in comparison with X 2 , and put X 2 L 2 = X 2 , and the 
 third term becomes approximately 
 
 _:N0L 2 
 
 X 2 ' 
 
 As X becomes gradually smaller, this term becomes 
 gradually larger, and hence also n becomes gradually 
 larger. This means that the shorter the waves are 
 the more they are refracted. Any one observing a 
 spectrum formed by a prism will see that the blue 
 rays, which have a shorter wave-length, are more 
 deviated than the red rays, which have a greater 
 
230 THE ELECTRON THEORY 
 
 wave-length. This is what is called normal dis- 
 persion. 
 
 When X is extremely large i.e. the incident 
 oscillation extremely slow the third term becomes 
 zero, and the equation reduces to 
 
 n* = 1 + N 6. 
 
 This is independent of the wave-length, so that 
 very long waves are not dispersed. They are all pro- 
 pagated with the same velocity, which simply depends 
 upon the density and " laxity " of the electrons in the 
 medium. This dependence may be arrived at by 
 remembering that the "refractive index" n of a 
 medium is the ratio of the velocity of propagation of 
 light in the ether to the velocity in the medium 
 
 where V x is 3 x 10 10 cm. per sec. Thus we have 
 
 Or 
 
 This last equation teaches us several valuable 
 things. For long waves, the velocity of propagation 
 in a dielectric depends upon the velocity in the ether, 
 and upon a term involving the density and laxity of 
 the electrons in the medium. The more electrons 
 there are, and the more easily they are displaced from 
 
ELECTRICITY AND LIGHT 231 
 
 their positions, the more slowly will the long waves 
 travel through them. But we have also seen that 
 
 Therefore we have 
 
 1 + tt ~K' 
 or K = 
 
 This is an important formula defining the specific 
 inductive capacity (or "dielectric constant") K in 
 terms of the electron theory. It may be calculated 
 if we know the density and laxity of the electrons in 
 the substance. And, conversely, we may calculate 
 the product of the density and laxity if we know 
 the dielectric constant. 
 
 To return to Drude's equation 
 
 When \ becomes smaller and smaller the third 
 term becomes larger and larger, and the refraction 
 becomes more and more pronounced. When X = L 
 i.e. when the incident light has the natural periods of 
 the electrons an extraordinary situation is created. 
 The denominator becomes zero, and 'therefore the 
 whole fraction becomes infinite. Hence n 2 also 
 becomes infinite, and the velocity of propagation 
 becomes zero. The wave is stopped. If X decreases 
 
232 THE ELECTRON THEORY 
 
 still further, the denominator increases again, but 
 becomes a negative quantity. This means that the 
 refractive index is diminished instead of being in- 
 creased. When the difference X 2 L 2 is still ex- 
 cessively small, the third term is an excessively large 
 negative quantity, and may well be much larger than 
 the second term. In this case we shall have the still 
 more extraordinary situation that n 2 is smaller than 
 unity ; in other words, that a vibration very slightly 
 shorter than the natural vibration of the electrons 
 is propagated with a velocity greater than that of 
 light. 
 
 When X diminishes still further the denominator 
 increases and the third term as a whole becomes 
 smaller. The limit is reached when X=0, and then 
 we have 
 
 tf = i + N e + N e = i + 2 N o, 
 
 JL 2 
 
 so that here again we have a limiting value for 
 infinitely short waves, which is somewhat higher 
 than the value for infinitely long waves, and again 
 independent of the wave-length. Infinitely short 
 waves are therefore not dispersed either. 
 
 In general, we have the important conclusion that 
 electrons or other charged bodies only influence the 
 velocity of propagation of the incident wave when 
 ike period of oscillation of that wave happens to be 
 not very different from their own. 
 
ELECTRICITY AND LIGHT 233 
 
 The extraordinary occurrences which take place 
 when the two periods of oscillation nearly coincide 
 are known as anomalous dispersion. 
 
 (c) Absorption and Reflection. When the wave- 
 length of the incident light-wave happens to be the 
 same as the natural wave-length emitted by the 
 electron, the wave is stopped. As we have seen in 
 the elementary case investigated above, the elec- 
 trons are always in the phase opposite to that of the 
 original oscillation. They, therefore, compensate the 
 incident wave, and prevent it from exerting any 
 effect inside the body. But in doing so they must, 
 of course, absorb more energy than they do in their 
 natural state. The usual consequence is that they 
 are shaken and swung out of their normal orbit in 
 the neighbourhood of their positive atoms, and shot 
 off into the interior of the substance, there to roam 
 at large and collide with other atoms in rapid suc- 
 cession. Each of these collisions means a stoppage 
 of an electron, and hence an electro-magnetic wave 
 impulse. These irregular impulses constitute radiant 
 heat, which travels away into space and is lost. The 
 whole process is termed absorption. It means that 
 the incident light is not transmitted, but converted 
 
 into heat in the manner stated. 
 
 
 
 But it may happen that the electrons are not 
 thus shaken off, but continue to vibrate in accord- 
 ance with the period of the incident vibration, or 
 rather, half a period behind it. Then they will 
 
234 THE ELECTRON THEORY 
 
 practically constitute a set of independent sources 
 of light, and will radiate the light out into the space 
 on the side of the incident light. In fact, we shall 
 have reflection. When the surface is quite smooth, 
 and dotted evenly with electrons of the same period, 
 the reflection will be " regular " or geometrical. The 
 angle of reflection will be equal to the angle of 
 incidence. The explanation is the same as that 
 given in the ordinary textbooks, and is based upon 
 Huyghen's principle. 
 
 In practice, it is found that most bodies can be 
 " polished," and that all bodies reflect some light. 
 This means that all known bodies contain some 
 electrons, however small in number, which vibrate 
 in the period of the incident light. 
 
 (d) Polarisation. Light may consist of various 
 species in accordance with the manner in which the 
 electro-magnetic vibration takes place. When the 
 electron vibrates in the same straight vertical line, 
 the light is said to be plane-polarised in a horizontal 
 plane. When it vibrates in a circular orbit, the light 
 emitted along the axis of the orbit is "circularly 
 polarised," and this circular polarisation may be 
 either right-handed or left-handed, according to the 
 direction of rotation. When the orbit is an ellipse, 
 the light is elliptically polarised. Finally, the elec- 
 trons, or a large aggregate of them, may send out 
 light in all kinds of polarisation in turn, and then 
 we have ordinary or natural light. 
 
ELECTRICITY AND LIGHT 235 
 
 Ordinary light may be converted into plane polar- 
 ised light by sending it through a body whose elec- 
 trons are capable of vibrating in one plane only, as 
 in tourmaline. The transmitted light will then be 
 found to be plane-polarised in a plane at right angles 
 to that direction of vibration. 
 
 (e) Double Refraction. Calcspar is a carbonate 
 of calcium of the formula CaC0 3 . Each molecule 
 contains five electrons capable of vibrating pretty 
 freely. But only two of these are capable of vibrat- 
 ing in the direction of the crystallographic axis. 
 The other three, if they vibrate along that axis at 
 all, do so with a very great rapidity, implying a very 
 small "laxity," 6. The consequence of this is that 
 when a beam of light is sent through calcspar at 
 right angles to the axis, only two electrons per 
 molecule take part in the vibration. The term N 6 
 in Drude's equation is small. Hence the refractive 
 index is small, and the velocity of propagation great. 
 When, on the other hand, a beam of light is sent 
 along the axis, all the five electrons are free to take 
 part. N is larger, n is larger, and the velocity is 
 smaller. Hence light is more slowly transmitted 
 along the axis than across it. This gives rise to the 
 phenomena of double refraction. * 
 
 (/) Optical Rotation. When a plane-polarised 
 beam of light is transmitted through turpentine, a 
 sugar solution, a plate of quartz, or other substances, 
 its plane of polarisation is found to have been turned 
 
236 THE ELECTRON THEORY 
 
 on emergence. This would be difficult to explain 
 but for the fact that a harmonic vibration in a 
 straight line may always be considered as made up 
 of two circular vibrations in opposite directions. 
 
 One of these circular vibrations is transmitted 
 with greater speed than the other, and when the 
 two circular beams recoinbine into a plane-polarised 
 beam on emergence, the plane has been turned round 
 in the direction of the circular vibration which has 
 been transmitted more rapidly. 
 
 In crystals this rotation may be considered as 
 due to a greater ease of acceleration of electrons in 
 one direction than in another, owing to the con- 
 figuration of the atoms in the molecule and the 
 piling of the molecules in regular rows. In solutions 
 and liquids, on the other hand, it must be due to 
 unsymmetrical structure of the molecule alone, which 
 is the same from whichever side it is viewed. For 
 the rotation takes place in the same sense whatever 
 may be the direction of transmission. As a matter 
 of fact, Becquerel has shown that the molecules of 
 all substances showing optical rotation (or " rotatory 
 polarisation ") in the liquid state, contain unsaturated 
 carbon atoms. 
 
CHAPTER XIII 
 
 MAGNETO-OPTIC PHENOMENA 
 
 THE connection between magnetism and light was 
 long sought after before the time of Faraday, who 
 was the first to discover a phenomenon linking those 
 two domains of physics. It is now known that 
 magnetism influences the plane of polarisation of 
 light, both when the magnetic field is applied to 
 the source of light and when it is applied to the 
 material which transmits the light. The first effect 
 is known as the Zeeman effect. The last is called 
 magneto-gyration or magneto-optic rotation, and 
 includes the effects discovered by Faraday, Kerr, 
 and Macaluso and Corbino. 
 
 (a) The Zeeman Effect. In dealing with the pheno- 
 mena of radiation and of diamagnetism, we have 
 become familiar with the effect of a magnetic field 
 upon the rate of revolution of an electron round a 
 positive atom. We have seen that whatever change 
 it produces, that change tends to oppgse the mag- 
 netic field which produces it. Diamagnetism is a 
 kind of permanent electro-magnetic induction. We 
 know that induced currents are always opposed to 
 the charge which induces them. It is as if the 
 
 237 
 
238 THE ELECTRON THEORY 
 
 electric momentum the momentum of electric 
 charges destroyed in one body reappeared in 
 another, just as in a collision there is a transfer 
 of momentum; but the sum of all momenta re- 
 mains the same, action and reaction being equal 
 and opposite. Ordinary induced currents are of 
 short duration, simply because the electrons set 
 in motion fritter away all their energy in collision 
 with neutral atoms. If the induced currents are 
 of molecular dimensions, and consist in the accele- 
 ration or retardation of the rate of revolution of 
 the electron round the positive atom, they are 
 permanent so long as the inducing field remains 
 at the same value. When the field is annihilated, 
 the acceleration it produced is converted into a 
 retardation, and vice versd. 
 
 All bodies are fundamentally diamagnetic, and 
 in all of them, therefore, the effects above indicated 
 take place whenever the magnetic field changes. 
 They are brought into evidence by the magneto- 
 optic effects now to be described. 
 
 That a magnetic field exerts an action upon the 
 light transmitted through a magnetised medium 
 was already known since Faraday's last researches. - 
 But an effect of a magnetic field upon the spectrum 
 of a flame, that is to say, upon a source of light, * 
 had been looked for repeatedly without success. 
 The credit of having discovered this effect and 
 furnished its mathematical explanation belongs ex- 
 
MAGNETO-OPTIC PHENOMENA 239 
 
 clusively to Holland. Dr. P. Zeeman, of Leyden, 
 announced his discovery in 1897, having failed 
 on a previous occasion to find any effect. With 
 the aid of a strong magnet and better spectro- 
 scopic apparatus than any of his predecessors had 
 used, Zeeman attacked the problem the second 
 time with success. He placed a Bunsen flame 
 containing common salt between the poles of the 
 electro- magnet and focussed the light on the slit 
 of his spectrometer, arranging the flame so that 
 the D-lines were sharply defined. As soon as the 
 magnet was excited both lines widened out very 
 much. By a careful series of subsidiary experi- 
 ments he showed that the widening was due directly 
 to the action of the field, and was not a secondary 
 effect such as might be caused by changes of density 
 in the flame. 
 
 These results were communicated before publica- 
 tion to Prof. Lorentz, who showed Dr. Zeeman that 
 the widening could be predicted from Lorentz's 
 theory that light is generated by the vibrations 
 of electrically charged particles or electrons ; and 
 that the same theory indicated that the edges of 
 the widened lines should be plane -polarised or 
 circularly polarised according as the light falling 
 upon the slit came from the source in a direction 
 perpendicular or parallel to the lines of magnetic 
 force, and that the amount of the widening would 
 give the ratio of the charge to the mass of the 
 
240 THE ELECTRON THEORY 
 
 luminous particles. Zeeman was able to verify 
 fully the predictions as to polarisation, and de- 
 duced from Lorentz's equations, as a rough value 
 
 for the ratio , the value 10 7 electro-magnetic units 
 
 per gramme. This is about one-half of the value of 
 the ratio for electrons as determined subsequently. 
 
 Further investigation soon showed that the ap- 
 parent broadening of the lines was in reality due 
 to their being split up into several components. 
 This spliting up was different in accordance with 
 the direction along which the beam of light from 
 the source traversed the magnetic field. When the 
 source was viewed along the lines of magnetic force 
 the D-lines appeared double, and when the line of 
 view was at right angles to the lines of force the 
 D-lines appeared treble. The polarisation of the 
 lines also differed according to the line of view, 
 the doublets consisting of two lines circularly 
 polarised in opposite directions, and the triplets 
 consisting of plane-polarised lines, the plane of 
 the central line being at right angles to that of 
 the side lines. These various effects were com- 
 pletely accounted for by the electron theory tenta- 
 tively formulated by Prof. Lorentz of Amsterdam. 
 This theory had been regarded as purely speculative 
 until it received this startling confirmation. The 
 discovery of the Zeeman effect, in conjunction with 
 Thomson's counting experiment, made the specula- 
 
MAGNETO-OPTIC PHENOMENA 241 
 
 tion into a theory of unprecedented generality and 
 fruitf ulness. 
 
 In view of the importance of the Zeeman effect, 
 I shall endeavour to make its theory as clear as 
 possible, and the student will do well to master it, 
 even at the cost of some effort. 
 
 Lorentz's theory supposed that luminous vibra- 
 tions are due to the rotation of " electric mole- 
 cules " about attracting masses. Lorentz knew 
 nothing about the charge or mass of these mole- 
 cules when he formulated his theory, and does 
 not seem to have suspected their identity with 
 the carriers of electricity in electrolysis. He sup- 
 posed them to rotate in all kinds of directions at 
 random, and in orbits varying from a circle to an 
 ellipse, and even a straight line. Knowing that 
 a charged body is deflected out of its path by a 
 magnet, he was quite prepared to find that the 
 orbits were influenced by a magnetic field, but 
 had no data to enable him to guess whether such 
 an effect could be discovered experimentally. But 
 when the effect was observed, his theory enabled 
 him at once to explain it, and even to give parti- 
 culars which had not yet been observed, but which 
 further experiments immediately verified., 
 
 Consider a beam of light from a sodium flame 
 mounted between the poles of a powerful electro- 
 magnet, giving a field of 5000 units, and viewed 
 along the lines of magnetic force, through per- 
 
242 THE ELECTRON THEORY 
 
 forations made for that purpose in the pole-pieces. 
 A delicate spectrometer shows the two yellow sodium 
 lines D x and D 2 , having wave-lengths of 589*6 and 
 589*0 x 10~ r cm. respectively, with a dark interval 
 between them. As soon as the electro-magnet is 
 excited, the lines broaden out to nearly twice their 
 ordinary width, and when a larger magnifying power 
 is used, each line is seen to be split into two, the 
 interval being about Ath of that between the origi- 
 nal lines. This means that the period of the original 
 vibration has been changed by about rwbiroth of its 
 value in each component. This effect is very small, 
 but still discoverable with the best modern apparatus. 
 The original vibration thus modified consists of 
 the rotation of electrons about positive atoms. 
 These take place in all sorts of planes, but we 
 need only consider the projections of their orbits 
 upon the cross-section of the beam of light, since 
 only transverse vibrations affect the eye. And 
 here again, we need only consider circular orbits, 
 since all others can be reduced to them. These 
 circular rotations can take place in a clockwise or 
 anti-clockwise direction. Likewise, the molecular 
 electron currents in the magnet can be in the two 
 directions. Let them be clockwise as seen by the 
 observer ; that is to say, let the pole furthest from 
 the observer be a north-seeking pole. Then all 
 the clockwise electrons in the flame will be re- 
 tarded, and all the anti-clockwise electrons will be 
 
MAGNETO-OPTIC PHENOMENA 243 
 
 accelerated, according to the laws of electro-magnetic 
 induction. The difference in the period thus pro- 
 duced is, according to Lorentz 
 
 where t is the difference of periodic time, - is 
 
 the ratio of charge to mass of the electrons, H the 
 magnetic field, and T the original period of all 
 electrons constituting the original vibration. In- 
 stead of all the electrons having the same period, 
 we shall have one set with a longer period, and 
 the other with a shorter period. The difference 
 of period means a difference of wave-length and a 
 difference of refraction, and hence also a separation 
 in the spectrum. This is the Zeeman effect as 
 seen in the direction of the lines of force. It will 
 be readily seen that it gave Prof. Lorentz a welcome 
 
 opportunity of calculating the important ratio -, 
 
 since all the other quantities in the above equation 
 are known. 1 
 
 The unexpectedly large value of the ratio gave 
 
 1 If we put - = l-9x 10 7 , H = 5000, and T = 2x 10- we get 
 
 *= 1-9 x 10 7 x 5000 x 4 x 10-30 x _ , 
 
 4?r 
 
 = 3xlO- 2 <> 
 
 and 1=_L_ 
 
 T 66000 
 
 which agrees with the observations within the limits of error. 
 
244 THE ELECTRON THEORY 
 
 rise to various speculations ; but the smallness of 
 the mass could not be accounted for, since no 
 mass smaller than the hydrogen atom was known 
 at that time. 
 
 A further spectroscopic examination of the split 
 lines showed that they consisted of circularly polar- 
 ised light, the direction of rotation being in opposite 
 directions in the two lines. A most important 
 result was deduced from observing the direction of 
 rotation in the two lines. Zeeman found that the 
 electrons producing the longer wave-length were 
 rotating clockwise, and the electrons producing the 
 shorter and more refrangible waves were rotating 
 anti-clockwise. This proved that the light-bearing 
 rotations were those of negatively charged particles only. 
 Indeed, we know from the laws of induction that 
 the clockwise rotations are retarded by clockwise 
 molecular electron currents, thus lengthening the 
 waves and increasing the refrangibility, whereas the 
 others are accelerated. 
 
 So much for the phenomenon as observed along 
 the lines of magnetic force. At right angles to the 
 lines of force a triplet is observed instead of a 
 doublet. The two circular vibrations we have been 
 considering are seen end-on, and, therefore, appear 
 plane - polarised, the plane of polarisation being 
 parallel to the lines of force, and, therefore, at right 
 angles to the vibrations of the electrons. There is 
 the same difference of period as before, and, there- 
 
MAGNETO-OPTIC PHENOMENA 
 
 245 
 
 fore, the same separation. But in this case there 
 are also the vibrations along the lines of force in- 
 fluencing the eye, but suffering no influence from 
 the magnetic field, since electrons are only affected 
 by such a field when they cross the lines of magnetic 
 force. There being no difference of period produced 
 in this case, the original vibration remains, and a 
 central line appears between the other two. Being 
 due to vibrations along the lines of force, the rays 
 are polarised in a plane at right angles to the lines 
 
 I 
 
 
 
 ; 
 
 
 
 1 
 
 I 
 
 \ 
 
 FIG. 31. 
 
 of force. In this case there can be no doubt as to 
 the direction of vibration of particles giving rise 
 to polarised light, and an old optical controversy, 
 already partly decided by Hertz's experiments, is 
 thus finally set at rest. 
 
 This is the famous Zeeman effect in jfts simplest 
 form. The main phenomena are shown in the 
 diagram (Fig. 31), where the solid line shows the 
 ordinary D a line, the punctuated lines show the 
 circularly polarised lines as seen along the lines of 
 
246 THE ELECTRON THEORY 
 
 force, and the shaded lines are the lines polarised in 
 two different planes, as seen across the lines of force. 
 
 But the effect is not in reality as simple as it 
 would appear from the above description. The 
 very fact that there are two different sodium lines 
 shows that the electrons revolving round the sodium 
 atom have two different natural periods, or that 
 each atom has two electrons revolving round it, 
 like two satellites with different periods. But 
 affairs are still more complicated in the spectra 
 of the heavier metals, some of which have hun- 
 dreds of spectrum lines distributed apparently at 
 random. This means a great number of electrons 
 attached to each atom, or perhaps to a complicated 
 group of atoms, and so much within each other's 
 sphere of influence that they disturb each other's 
 motion, and superpose extra vibrations of higher 
 frequencies upon their fundamental periods. Ac- 
 cordingly we find, notably in the magnetic metals, 
 some very complicated Zeeman effects, lines being 
 split up into four, five, seven, or even nine com- 
 ponents. But, far from being a discouragement, this 
 bewildering variety has been a valuable stimulus to 
 research into the intimate structure of the chemical 
 atom. The spectrum is, so to speak, the anatomical 
 atlas of the chemical atom, and the index to this 
 atlas is supplied by the Zeeman effect. 
 
 For it has been found that the lines of each 
 element can be grouped into several series which 
 
MAGNETO-OPTIC PHENOMENA 247 
 
 follow in harmonic succession, and where each series 
 shows the same Zeeman effect in all its lines, but * 
 where the effect alters from one series to another. 
 Apart from this, there is a mathematical analysis 
 of the atomic vibrations yet to come, and, perhaps, 
 before very long, we shall have definite information 
 concerning the number of electrons circulating 
 round the atom of some element, and concerning 
 the manner in which these revolving electrons give 
 rise to its complicated spectrum. We may thus 
 arrive at a knowledge of the atomic system as 
 precise as is, on a much larger scale, our know- 
 ledge of the motions and perturbations of the 
 planets in the Solar System. 
 
 (b) The Faraday Effect. The first magneto-optic 
 effect discovered was that named the Faraday 
 effect. When plane-polarised yellow light is sent 
 through bisulphide of carbon contained in a mag- 
 netic field of 5000 units, in the direction of the 
 lines of force, the plane of polarisation is found 
 to have been turned through an angle of three 
 and a half degrees for every centimetre of the 
 liquid traversed by the beam. The sense of the 
 rotation is contrary to the direction of the electron 
 currents constituting the magnet. In other words, 
 it is in the same direction as the (positive) " current " 
 which excites the magnet. 
 
 This phenomenon admits of a simple explanation 
 on the basis of the electron theory. 
 
248 THE ELECTRON THEORY 
 
 Every plane-polarised beam may be considered 
 as consisting of two beams circularly polarised in 
 opposite directions. The beam circularly vibrating 
 in the direction of the electron currents of the 
 magnet is retarded, owing to molecular induction 
 within the liquid, and the oppositely rotating beam 
 is accelerated. When, therefore, the two beams 
 combine again on emerging from the liquid, the 
 plane has been turned in the direction of the faster 
 rotation that is to say, in the direction opposed to 
 the electron currents of the magnet. 
 
 This is the explanation reduced to its simplest 
 terms. But this effect, like the Zeeman effect, 
 shows a variety of detail. The rotation per cm. 
 in unit magnetic field (a quantity known as Verdet's 
 constant) changes from one substance to another, and 
 in a few rare cases even becomes negative. Thus 
 in carbon bisulphide, it is 0*042 minutes of arc, in 
 water 0'012, in glass 0*02 to 0*09, while in com- 
 pressed air it is 0*0003, and increases with the 
 pressure. 
 
 To return to Drude's equation (p. 228). If the 
 velocity of propagation is v y the refractive index n, 
 the density of rotating electrons N, their " laxity " 0, 
 the length of wave naturally emitted by them L, 
 and the incident wave-length X, we have 
 
 This equation shows that, as the natural period 
 
MAGNETO-OPTIC PHENOMENA 249 
 
 L increases, the velocity v diminishes that is to 
 say, if the rotating electron is retarded by magnetic 
 force or otherwise, it transmits the incident light 
 with a smaller velocity. Now we know that the 
 electron is retarded when it rotates in the same 
 direction as the electrons producing the magnetic 
 field. Hence the circularly polarised beam trans- 
 mitted by the opposite rotation will be propagated 
 more quickly. 
 
 This supposes that X 2 is larger than L 2 . If it 
 is not, the denominator and, therefore, also the 
 whole fraction becomes negative, and the larger 
 the natural wave-length the greater will be the 
 velocity. This is then a case of anomalous dis- 
 persion. It occurs when L 2 is larger than X 2 
 i.e. when the proper period of the electrons is in 
 the infra-red. Normal dispersion occurs when the 
 proper period of the electron is in the ultra-violet. 
 
 These considerations explain why the Faraday 
 effect is sometimes reversed. 
 
 (c) The Kerr Effect. Kerr discovered that plane- 
 polarised light reflected from the polished poles of 
 an electro-magnet is elliptically polarised. Recent 
 experiments have shown that this is simply a 
 special case of the Faraday effect. All reflected 
 light penetrates for some very small depth into 
 the reflected surface. Light reflected from iron 
 passes through a few molecular layers, and repasses 
 them on being reflected. These two passages 
 
2 SO THE ELECTRON THEORY 
 
 amount to a transmission through the substance 
 of iron. Now, iron has been examined in very 
 thin transparent films produced by cathode dis- 
 integration, and found to exert a very powerful 
 Faraday effect. It is, therefore, not surprising 
 that the passage of light even through the very 
 thin films required for reflection should suffice to 
 produce a very perceptible rotation of its plane of 
 polarisation, more especially as the effect of both 
 passages is in the same direction. Therein lies a 
 fundamental difference from purely optical rotation. 
 When a beam of light is sent through an " opti- 
 cally active " substance, both going and returning, 
 its plane is not rotated at all. Transmission in 
 one direction is compensated by transmission in the 
 reverse direction. In magneto-optic rotation the 
 turning of the plane of polarisation is always in the 
 direction of the (positive) magnetising current, and 
 hence the rotation is proportional to the number of 
 times the beam is transmitted either way. 
 
 (d) Macaluso-CorUno Effect. Shortly after Zee- 
 man's discovery, two Italian physicists, Macaluso 
 and Corbino, announced that, on transmitting a 
 plane-polarised yellow beam through sodium vapour 
 placed in a magnetic field, there was a strong mag- 
 neto-optic rotation in the neighbourhood of the 
 absorption bands. This follows as a matter of 
 course from the above facts and considerations. 
 We have already seen that when X is very nearly 
 
MAGNETO-OPTIC PHENOMENA 2$ I 
 
 equal to L, the third term in Drude's equation 
 becomes enormous, and hence the velocity of trans- 
 mission is powerfully affected when the wave-length 
 of the incident sodium light is nearly the same as 
 the wave-length of the period proper to the electrons 
 rotating in the electric field. 
 
 The whole chapter of magneto-optics, like that of 
 the galvano-magnetic and thermo-magnetic effects 
 to be dealt with next, still bristles with problems 
 awaiting solution. But the electron theory has 
 for the first time indicated the general lines along 
 which a complete solution of outstanding questions 
 may be looked for. 
 
CHAPTER XIV 
 
 ELECTRICITY, HEAT, AND MAGNETISM 
 
 THE relations between electricity and heat have 
 already been dealt with in the chapter on Thermo- 
 electricity (p. 121). As already stated, they involve 
 the intimate structure of the chemical elements, 
 and are therefore less definite than most of the 
 other electrical properties of matter. When these 
 relations are complicated by the presence of a 
 magnetic field, their investigation becomes by no 
 means easier; but the more multitudinous and 
 complicated they are, the more information do 
 they give us concerning the hidden structure of 
 the chemical atom and the building up of solid 
 substances. 
 
 Let a thin metallic plate (Fig. 32) be traversed 
 by a current from the battery B. According to the 
 electron theory, this current consists mainly in the 
 motion of electrons from the negative terminal to 
 the positive terminal i.e. in the direction opposed 
 to what is conventionally called the current. The 
 positive atoms move in the opposite direction, but 
 
ELECTRICITY, HEAT, AND MAGNETISM 253 
 
 being hampered by their much greater size, the 
 part which they contribute towards the convection 
 of the current is insignificant. 
 
 Now let the north-seeking pole, N, of an electro- 
 magnet be brought under the plate. Then the 
 following four phenomena are observed. 
 
 FIG. 32. 
 
 1. A difference of potential between the sides. 
 
 2. A difference of temperature between the sides 
 of the plate. 
 
 3. A change in the electrical conductivity of the 
 plate. 
 
 4. A change in the conductivity for heat. 
 
 If, instead of an electric current, a 'current of 
 heat is directed through the plate in the same 
 direction, as, for instance, by heating C to boiling 
 point and keeping D cool, the same four pheno- 
 
254 THE ELECTRON THEORY 
 
 mena are observed. Thus we have eight galvano- 
 magnetic and thermo-magnetic phenomena, which 
 show an intimate connection between currents of 
 heat, currents of electricity, and magnetism. 
 
 Now it must be stated at once that these effects 
 vary very much, both in quantity and direction, 
 from one substance to another, and there is only 
 one substance bismuth in which all the eight 
 effects have as yet been measured. Such measure- 
 ments are very difficult to carry out, on account 
 of the many sources of error, and the decisive influ- 
 ence of even slight impurities. Nevertheless, some 
 valuable rules have been discovered, and the electron 
 theory has shown itself well able to cope with these 
 strange phenomena. 
 
 In every case the effect is proportioned to the 
 intensity of the electric current or heat current. 
 This is readily understood. It is also inversely pro- 
 portional to the thickness of the plate. This also 
 is capable of a simple explanation. 
 
 The transverse effects (1) and (2) and the cor- 
 responding ones in the case of the heat current are 
 proportional to the magnetic field. The changes of 
 conductivity are supposed to be proportional to the 
 square of the magnetic field, but are generally very 
 feeble. 
 
 Transverse Effects. The effects in bismuth may 
 be summarised as follows : A current of heat pro- 
 duces the same effects as a current of electrons. It is 
 
ELECTRICITY, HEAT, AND MAGNETISM 255 
 
 deflected by a magnetic field in the same direction 
 as cathode rays are deflected. In a plate traversed 
 by either a heat current or an electron current, 
 a magnetic field increases the resistance and the 
 
 COLD 
 
 WARM 
 
 'HALL 
 
 thermal conductivity. A deflection of the current 
 of heat to one side is accompanied by a negative 
 charge acquired by that side. 
 
 The four transverse effects are shown diagram- 
 matically in Fig. 33, where the circles with arrow- 
 heads indicate the direction of revolution of the 
 
256 THE ELECTRON THEORY 
 
 electron currents which produce the magnetic field, 
 and the long arrows represent the heat currents or 
 electric currents. 
 
 The Hall effect in bismuth is easily explained. 
 The electrons constituting the electron current 
 thread their laborious way through the crystalline 
 agglomerations of bismuth atoms, and whenever 
 they are free to follow the electric force they dart 
 forward in the direction of the electron current 
 i.e. from right to left. But while traversing their 
 free path they are subject to deflection by the 
 magnetic force. This will urge them towards the 
 lower edge of the plate, and that edge, there- 
 fore, acquires a negative charge. The upper edge, 
 being drained of electrons, acquires a positive 
 charge, and when the two edges are joined by a 
 wire, a small but steady current passes through 
 the wire. 
 
 To understand the analogous effect of a heat 
 current, it must be remembered that electrons are 
 particles capable of conveying energy of motion, 
 and that they therefore are just as capable of pro- 
 pagating heat as the heavier atoms are. But in 
 most substances heat has the effect of dissociating 
 neutral atoms. More electrons are split off and set 
 roaming at large. There is a greater number of 
 free electrons in unit volume of the hot metal than 
 in unit volume of the cold metal. To equalise this 
 difference of density, electrons diffuse from the hot 
 
ELECTRICITY, HEAT, AND MAGNETISM 257 
 
 metal to the cold metal, and thus constitute an 
 electron current which travels in the same direction 
 as the heat current. 
 
 The Nernst effect falls under this explanation. 
 The electrons constituting part of the heat current 
 are deflected in the same direction as those con- 
 veying the electric current, and accumulate in the 
 lower edge of the plate as before. 
 
 No sooner is the difference of potential estab- 
 lished between the opposite edges than a cross- 
 current sets in to equalise it. But the rapidity 
 with which this process of equalisation takes place 
 depends upon the resistance of the plate, and this 
 is the greater the thinner it is. It is, therefore, 
 readily understood that the Hall and Nernst effects 
 are inversely proportional to the thickness of the 
 plate, as stated above. 
 
 The Ettingshausen and Leduc effects are similarly 
 explained. Though tabulated separately from the 
 other two effects, they are really inseparable from 
 them. The Hall and Ettingshausen effects occur 
 together, the cold edge being positively charged 
 and the warm edge negatively, and the Nernst 
 and Leduc effects are similarly linked. The 
 former are called " galvano-magnetic," and the 
 latter " thermo-magnetic," effects. As before, the 
 equalisation of temperatures between the opposite 
 edges depends upon the intervening conductivity 
 for heat. 
 
 B 
 
258 THE ELECTRON THEORY 
 
 Effects similar in every respect, but much feebler, 
 are presented by carbon and nickel. Of the four 
 effects described, the Hall effect was the first dis- 
 covered, and it is always the easiest to observe, 
 since no measurements of temperature are involved. 
 Even with very thin plates and strong fields, the 
 E.M.F. between the edges does not exceed a few 
 thousandths of a volt. But that is well within 
 our powers of measurement. It is by far the 
 largest in bismuth, being 400 times greater than in 
 nickel, which comes next in order. It is smallest 
 in tin and lead. 
 
 The Hall effect depends upon a difference in 
 the mobilities of the positive and negative carriers 
 of electricity, and its existence in metals confirms 
 the supposition that metallic conduction is carried 
 on mainly by electrons. In liquids, the effect has 
 been looked for in vain, for two reasons. The 
 ions in liquids are much more thinly scattered 
 than in metals, and their mobilities are much 
 more nearly equal. It may be roughly esti- 
 mated that in most ordinary metals the mobility 
 of the electron exceeds that of the positive atoms 
 100 or 200 times. In electrolytes, no ion ever 
 has a mobility more than about 10 times that 
 of another ion. Hence it is clear that the Italian 
 physicists who started in search of the Hall effect 
 in liquids attempted practically an impossible 
 task. 
 
ELECTRICITY, HEAT, AND MAGNETISM 259 
 
 Owing to the fact that free electrons have a 
 great tendency to condense water about them, 
 and to form heavier negative ions, they do not 
 act as carriers in liquids. In gases, on the other 
 hand, they are present in large 
 numbers, and gaseous conduc- 
 tion is carried on mainly by 
 electrons and positive atoms. 
 Hence there is quite a per- 
 ceptible Hall effect in gases, 
 especially hot gases, where 
 the ionisation is great. The 
 Hall effect has been proved to 
 exist in flames without much 
 difficulty. 
 
 Longitudinal Effects. The 
 longitudinal effects are not re- 
 versed by reversing the magnetic 
 field. They simply depend 
 upon the state of things at the 
 ends of the plate, and are in- 
 dependent of the charge or 
 temperature of the sides. 
 
 The four effects are shown diagrammatically 
 in Fig. 34. The electron currents are deflected 
 in the direction in which the arrows are bent, and 
 the heat currents are deflected in the same direction 
 when electrons are diverted towards the lower edge 
 of the plate, instead of making straight for the left- 
 
 FIG. 34. 
 
260 THE ELECTRON THEORY 
 
 hand edge ; the left-hand edge will naturally be less 
 negatively charged than before. It will, in fact, rise 
 in positive potential, and will become comparatively 
 more positive than the right-hand edge that is to 
 say, the original difference of potential is increased. 
 The same thing would happen if the plate were 
 made either longer or thinner. It amounts to this, 
 then : that the magnetic field increases the resistance 
 of the bismuth. The increase in a field of 10,000 
 units amounts to as much as one-third of the 
 original resistance. This property is so constant 
 and reliable that it has been used for measuring 
 the strength of magnetic fields. All that is re- 
 quired is a small coil of bismuth and a resistance- 
 box. The resistance of the coil of bismuth indicates 
 the strength of the magnetic field at the place where 
 it happens to be. It can even be used for alternating 
 magnetic fields; but these must not be too rapid, 
 as otherwise the electrons have no time to get 
 deflected out of their paths, and then the resistance 
 remains constant. 
 
 The fourth longitudinal effect is a direct in- 
 crease of the " thermal resistance," or a diminution 
 of the conductivity for heat. The cool end 
 of the plate becomes cooler than before as soon 
 as the magnet is excited. It gives up less heat 
 to the cooling water than it did before. Again 
 the effect is as if the plate had been lengthened. 
 It is due, as before, to the deflection of the elec- 
 
ELECTRICITY, HEAT, AND MAGNETISM 26 1 
 
 trons which constitute the largest part of the heat 
 current. 
 
 The other two effects are reciprocal effects of 
 currents of heat and of electricity. The heat 
 current consisting mainly of electrons, any deflec- 
 tion of it implies a deflection of (negative) elec- 
 tricity, and wherever there is an accumulation of 
 heat there is also an accumulation of electrons in 
 other words, a negative electrification. 
 
 The eight effects may be combined into a 
 single diagram (Fig. 35), where the arrows show 
 the direction and de- 
 flection of a current, 
 which may be either 
 a heat current or an 
 electron current. 
 
 Reversed E/ects. It 
 appears from the above 
 details that the elec- 
 tron theory of metallic conduction suffices for 
 explaining all the manifold relations between heat, 
 electricity, and magnetism as far as bismuth is 
 concerned. But in other metals the transverse 
 effects are different, while the longitudinal effects 
 are, as a rule, too small to be observed. In 
 antimony, cobalt, and tellurium the direct (Hall 
 and Leduc) effects are reversed, and in iron 
 they are all reversed. This means that the 
 laws of metallic conduction are modified by other 
 
 -f 
 
262 THE ELECTRON THEORY 
 
 influences. The effects in cobalt are too small 
 to draw any conclusions from them ; but in 
 antimony and tellurium the reversal of the two 
 effects indicates a structure which allies those metals 
 to the non-metallic elements. There is probably 
 very little direct dissociation into positive atoms and 
 electrons. The dissociation is probably more like 
 what we have in electrolytic dissociation, each elec- 
 tron gathering neutral atoms round it to form 
 heavier ions. The electron, thus weighted, has no 
 advantage of mobility over the positive ions, and 
 may even be inferior in mobility to the latter. That 
 the reciprocal effects hold good shows that heat 
 produces a splitting-off of electrons, as in bismuth. 
 
 This does not appear to be the case in iron, 
 where it is known that heat does not produce a 
 spontaneous evolution of free electrons. We know 
 from the strong magnetic properties of iron that 
 the molecules of iron are quite free to place them- 
 selves in any direction they choose, and that they 
 do place their magnetic axes into coincidence with 
 the axis of a magnetic field. This indicates a great 
 freedom of the ponderable material of iron. Its 
 treble valency also shows that one positive atom 
 can bind several electrons. It may therefore well 
 happen that most of the electrons are bound up 
 with atoms, while a large number of positive atoms 
 are roaming free, and although they have not the 
 great mobility of the electrons, they make up for 
 
ELECTRICITY, HEAT, AND MAGNETISM 263 
 
 that by their superior numbers. The same con- 
 siderations will explain the reversal of the Thomson 
 effect in iron, without having recourse to the as- 
 sumption of free positive electrons, which are not 
 indicated by any other phenomenon. 
 
CHAPTER XV 
 
 RADIO-ACTIVITY 
 
 A NEW branch has been added to physical science 
 within the last ten years. The phenomena of 
 radio-activity are impossible on the basis of the 
 older atomic theory of chemistry, though they add 
 new proofs of the atomic structure of matter. They 
 are largely electrical phenomena, and are quite 
 inconsistent with the view, sometimes tentatively 
 put forward, that electricity, like heat, is a mode 
 of motion. The phenomena of radio-activity have 
 confirmed the atomic structure of matter, but have 
 abolished the dogma of the indestructibility of the 
 atom. They have created a new department of 
 chemistry by giving us access to the hidden re- 
 cesses of the atom itself. They have also defi- 
 nitely established the atomic structure of electricity, 
 substituting the indivisible and indestructible elec- 
 tron for the chemical atom, now no longer considered 
 either indivisible or indestructible. 
 
 That, surely, is a tremendous revolution, a re- 
 volution for which the closing years of the nine- 
 teenth century will be for ever memorable. 
 
 This is not the place to give a detailed account 
 
 264 
 
RADIO-ACTIVITY 265 
 
 of the phenomena presented by the radio-active 
 substances. I shall restrict myself to those phe- 
 nomena which have an immediate bearing upon the 
 electron theory. 
 
 In the course of the present sketch of the chief 
 facts of electricity and magnetism in the light of 
 the electron theory, I have only incidentally referred 
 to radio-activity, preferring to establish the theory 
 first in regions more familiar to the student. I 
 think I can claim to have shown that in the more 
 ordinary electric phenomena, the electron theory not 
 only explains observed facts much better than any 
 other theory hitherto accepted, but unifies all facts in 
 a manner hitherto unapproached, and forms a firm 
 and fruitful basis for further research. In pro- 
 ceeding, however, to radio-activity, we find that the 
 electron theory becomes paramount and indispens- 
 able, and that it seems likely to annex the greater 
 part of physics and the whole of chemistry. 
 
 The radio-active bodies hitherto investigated are 
 uranium, thorium, radium, actinium, and polonium. 
 Of these uranium and thorium were well known 
 to chemists before the discovery of radio-activity. 
 The others were discovered by their radio-active 
 properties. 
 
 Radio-activity a term invented by Madame Curie, 
 now Professor of Chemistry at Paris University 
 consists in the spontaneous emission of cathode 
 rays, canal rays, or Rontgen rays that is to say, 
 
266 THE ELECTRON THEORY 
 
 of electrons, positive atoms, or ether-pulses, or of 
 several of these at the same time. 
 
 The " positive atoms " emitted are, however, not 
 atoms of the substance itself, but atoms of a very 
 much lighter substance, consisting of either hydro- 
 gen or helium, probably the latter. This is the 
 most astounding fact of the whole new range of 
 phenomena. A well-defined chemical atom, with 
 a characteristic spectrum of its own, splits into two, 
 one of them an atom of a gas found in the sun and 
 the earth, the other a substance which undergoes 
 further decomposition by giving off more atoms of 
 helium and electrons, and finally, perhaps, trans- 
 forms itself into some other known " element." 
 
 The substance showing the greatest number of 
 radio-active phenomena, and those in the fullest 
 detail, is radium, discovered by Prof, and Madame 
 Curie in 1898. It is supposed to be " descended" 
 from uranium, and it develops into lead after six 
 intermediate changes. Each change takes a defi- 
 nite time to complete itself in a given weight of 
 the substance. As Rutherford says, 1 " There can be 
 no doubt that in the radio-elements we are wit- 
 nessing the spontaneous transformation of matter, 
 and that the different products which arise mark 
 the stages as halting-places in the process of trans- 
 formation, where the atoms are able to exist for a 
 
 1 " Radio-activity." By E. Rutherford : Cambridge University 
 Press, 1905. 
 
RADIO-ACTIVITY 267 
 
 short time before again breaking up into new 
 systems." 
 
 Radium is a metal closely allied to barium in its 
 chemical properties. Its atomic weight is 225, and 
 is only exceeded by the two radio-active elements 
 uranium (240) and thorium (232*5). The atoms of 
 radium are in imperfect equilibrium ; but the break- 
 up of an atom occurs so rarely that only one atom 
 in ten thousand million breaks up every second in 
 one gramme of pure radium. Since a gramme of 
 pure radium contains about 4xl0 21 atoms, this 
 means that one gramme of pure radium spon- 
 taneously breaks up 4 x 1 11 of its atoms every 
 second. The break-up of the atoms results in the 
 projection of a positively charged helium atom with a 
 velocity in many cases approaching the velocity of 
 light. These charged particles are the so-called (st- 
 rays, whose nature was a mystery until their deflection 
 by a magnet was clearly established by using a very 
 strong field. The proportion between radium atoms 
 present and radium disintegrated is very constant, 
 and quite independent of heat or any other physical 
 or chemical agent. The more the radium is disin- 
 tegrated, the more slowly will the remainder disin- 
 tegrate. The rate of disintegration, as, well as the 
 intensity of the a-rays, decreases, as they say, accord- 
 ing to an exponential law. The most convenient way 
 of stating the stability of such a body as radium is 
 to state the time a gramme of the substance would 
 
268 THE ELECTRON THEORY 
 
 take to transform or disintegrate half its atoms. 
 This time, T, is 1300 years in the case of radium. 
 We therefore see that if pure radium has a certain 
 radio-activity to-day, that activity will have fallen 
 to half its present value in A.D. 3206. Meanwhile, 
 what becomes of the products of disintegration ? 
 
 The helium atoms fly off into the surrounding 
 gas and ionise its molecules by collision. They are 
 stopped in 3 cm. of air at atmospheric pressure ; but 
 not before they have produced about 86,000 ions 
 for each helium atom stopped. Now a billion 
 helium atoms do not give much helium, certainly 
 not a measurable quantity. But that quantity 
 becomes discoverable by spectroscopy when it is 
 multiplied about 100 million times, and this takes 
 about 100 million seconds, or about four years. 
 Helium has actually been observed by Ramsay 
 and Soddy in the spectrum of a tube containing 
 radium after a considerable lapse of time. More- 
 over, helium is found occluded in all radium 
 minerals in proportion to the amount of radium 
 present, having been accumulated there since the 
 radium was formed. 
 
 What remains of the radium atom after the 
 helium atom is split off forms an atom of an inert 
 gas resembling argon. This gas emanates from the 
 radium mineral, and can be drawn off in a current 
 of air and condensed at a temperature of 150 C. 
 It is called Radium Emanation. Its atomic weight 
 
RADIO-ACTIVITY 269 
 
 is 221, since that of the helium atom is 4, and of 
 the radium atom 225. 
 
 The atom of emanation gives off another a- 
 particle or helium atom, which goes to swell the 
 amount of helium evolved direct from radium, 
 and what then remains is no longer a gas, but a 
 solid, which deposits itself on the walls of the vessel, 
 and is called radium A, with an atomic weight of 
 217. 
 
 This change is much more rapid than that of the 
 radium into emanation. The emanation is much 
 more unstable than the radium itself. While 
 radium takes 1300 years to transmute itself by 
 half, the same process is accomplished in radium 
 emanation in 3*8 days. 
 
 If, therefore, the emanation is drawn off into a 
 separate tube, half of it is precipitated on the walls 
 within 3*8 days, with evolution of helium. If now 
 the helium and the remaining emanation is drawn 
 off by a current of gas, we have a deposit of radium 
 A on the walls of the tube far too minute to be seen 
 or weighed, but discoverable by its radio-activity. 
 For radium A also decomposes. It is soluble in 
 strong acids, which, however, do not affect its rate of 
 disintegration. It can be volatilised at 1000 C.,but 
 again without affecting its rate of inevitable decay. 
 Its disintegration is accompanied by another expul- 
 sion of a helium atom the third so far and the 
 remainder forms another solid deposit called radium 
 
2/O THE ELECTRON THEORY 
 
 B. This conversion completes itself half in three 
 minutes, and is the most rapid of all radium trans- 
 formations. Radium B volatilises at 700 C. It 
 disintegrates in turn, transforming itself by half in 
 2 1 minutes. But this transformation is not accom- 
 panied by any expulsion, and probably consists in 
 some rearrangement of material within the atom. 
 
 The next stage is radium C, another solid sub- 
 stance, which volatilises at 1000 C., and makes up 
 for the absence of rays in radium B by emitting no 
 less than three different kinds of rays. Each atom 
 of radium C which decomposes throws off a helium 
 atom and an electron, and gives rise to an electro- 
 magnetic wave-pulse or Rontgen ray. Its time of 
 half-decay, T, is 28 minutes. Radium B was dis- 
 covered solely through the initial irregularity of the 
 curves of decay of radium C. These three pro- 
 ducts, radium A, B, and C, together form the active 
 deposit due to radium emanation. But after their 
 disintegration, which, we have seen, does not take 
 many minutes, they give rise to three further pro- 
 ducts, called radium D, E, and F respectively, which 
 together form the " permanent " active deposit. T 
 is about 40 years in the case of radium D, and the 
 change is another rayless one. T for radium E is 
 six days. It is non-volatile, but gives off electrons 
 and Rontgen rays. The final product is radium F, 
 whose T is 143 days. It gives off helium atoms 
 (a-rays) only, and is deposited on bismuth from 
 
RADIO-ACTIVITY 271 
 
 solution. This radium F is an exceedingly in- 
 teresting body. All its properties are identical 
 with those of another radio-active body discovered 
 independently by Madame Curie, and called by her 
 " Polonium," in honour of her native country, and 
 also by Marckwald in Germany, who found it 
 associated with tellurium, and therefore styled it 
 " radio-tellurium." The credit of accomplishing the 
 long and laborious researches for tracing the parent- 
 age of polonium belongs to Rutherford, of Montreal. 
 Here is the full pedigree : 
 
 Radium gives off helium atoms. 
 
 Emanation 
 
 .1 
 
 Radium A 
 
 Radium B no rays. 
 
 Radium C helium atoms, electrons, and X-rays. 
 
 Radium D no rays. 
 
 Radium E electrons and X-rays. 
 
 Radium F helium atoms. 
 
 = Polonium = radio-tellurium. 
 
 It will be remembered that all these changes, 
 except the evolution of helium, are undiscoverable 
 by chemical or even spectroscopic means. The sub- 
 stances only identify themselves by their radiations, 
 and the manner in which that radiation decays. 
 The radiations may be observed in different ways ; 
 but the most convenient method is by the ionisa- 
 tion of air, whereby a delicate electroscope is dis- 
 
272 THE ELECTRON THEORY 
 
 charged. For aught we know, many more changes 
 may be continually going on, not only in radio- 
 active bodies, but in ordinary matter. The a-rays or 
 helium atoms cease to produce ionisation when their 
 velocity falls below the enormous figure of 10 9 cm. 
 per second, or one-thirtieth of that of light. Con- 
 sequently, it is quite possible that all matter may 
 be gradually disintegrating, but not with the ex- 
 plosive violence of the radio-active bodies, and there- 
 fore unperceived. Many indications go to show 
 that polonium itself eventually changes into either 
 lead or bismuth. 
 
 Uranium, thorium, and actinium show a some- 
 what similar life-history ; but in their case the first 
 product formed is not an emanation, but a solid. 
 Uranium gives rise to " Uranium X," and any 
 further change is at present unknown. Uranium 
 takes about 600 million years to transform itself by 
 half. Each atom which disintegrates gives off an 
 a-particle (helium atom), and leaves behind an atom 
 of a new substance, which disintegrates much more 
 easily. This new substance is called uranium X. It 
 was for some time considered to be the sole active 
 constituent of uranium. Its discovery is described 
 by Kutherford as follows : 
 
 "The experiments of Mme. Curie show that 
 the radio-activity of uranium and radium is an 
 atomic phenomenon. The activity of any uranium 
 compound depends only on the amount of that 
 
KADIO- ACTIVITY 273 
 
 element present, and is unaffected by its chemical 
 combination with other substances, and is not 
 appreciably affected by wide variations of tempe- 
 rature. It would thus seem probable, since the 
 activity of uranium is a specific property of the 
 element, that the activity could not be separated 
 from it by chemical agencies. In 1900, however, 
 Sir William Crookes showed that, by a single 
 chemical operation, uranium could be obtained 
 photographically inactive, while the whole of the 
 activity could be concentrated in a small residue 
 free from uranium. This residue, to which he gave 
 the name of ' Ur X,' was many hundred times more 
 active photographically, weight for weight, than the 
 uranium from which it had been separated. The 
 method employed for this separation was to pre- 
 cipitate a solution of the uranium with ammonium 
 carbonate. On dissolving the precipitate in an 
 excess of the reagent a light precipitate remained 
 behind. This was filtered, and constituted the 
 Ur X. The active substance Ur X was probably 
 present in a very small quantity, mixed with im- 
 purities derived from the uranium. No new lines 
 were observed in the spectrum. A partial separa- 
 tion of the activity of uranium was also effected by 
 another method. Crystallised uranium nitrate was 
 dissolved in ether, when it was found that the 
 uranium divided itself between the ether and water 
 present in two unequal fractions. The small part 
 
 S 
 
2/4 THE ELECTRON THEORY 
 
 dissolved in the water layer was found to contain 
 practically all the activity when examined by the 
 photographic method, while the other fraction was 
 almost inactive. These results, taken by them- 
 selves, pointed very strongly to the conclusion that 
 the activity of uranium was not due to the element 
 itself, but to some other substance associated with 
 it, which had distinct chemical properties. 
 
 " Results of a similar character were observed by 
 Becquerel. It was found that barium could be 
 made photographically very active by adding barium 
 chloride to the uranium solution and precipitating 
 the barium as sulphate. By a succession of preci- 
 pitations the uranium was rendered photographi- 
 cally almost inactive, while the barium was strongly 
 active. 
 
 "The inactive uranium and the active barium 
 were laid aside; but, on examining them a year 
 later, it was found that the uranium had completely 
 regained its activity, while that of the barium had 
 completely disappeared. The loss of activity of 
 uranium was thus only temporary in character/ 7 
 
 The obvious explanation of this peculiar be- 
 haviour was that uranium continually evolves some 
 substance much more active than itself, which can 
 be chemically separated from it. This new sub- 
 stance, Uranium X, decays to half- value in 22 days, 
 instead of hundreds of millions of years. The 
 original uranium can only be identified by a feeble 
 
RADIO-ACTIVITY 275 
 
 radio-activity consisting in the expulsion of helium 
 atoms. 
 
 Thorium and actinium give rise to similar pro- 
 ducts called thorium X and actinium X respec- 
 tively. From these a gas or emanation is developed, 
 which, however, is extremely unstable and takes only 
 a few seconds to decay by half. Thorium emana- 
 tion gives rise to two successive decomposition 
 products called thorium A and thorium B. They 
 form a deposit on bodies and are concentrated on 
 the cathode in an electric field. Thorium A is 
 more volatile than thorium B. 
 
 Lastly, actinium emanation gives rise to actinium 
 A and actinium B, which are deposited on bodies 
 concentrated on the cathode in an electric field, and 
 are soluble in ammonia and strong acids : they are 
 volatilised at the boiling-point of water. Actinium 
 A can be separated from actinium B by electrolysis. 
 Both thorium B and actinium B emit three sorts 
 of rays, while their " parents " emit none. Their 
 life period counts by minutes. 
 
 These are all the radio-active bodies and disin- 
 tegration products hitherto known. The list will, 
 no doubt, soon be extended possibly into the 
 region of well-known bodies like lead, mercury, 
 and gold. Research is busy with the momentous 
 question as to whether any artificial method can 
 accelerate or retard this process of disintegration. 
 This is a question not at all easy of solution. The 
 
276 THE ELECTRON THEORY 
 
 effect of heat may not be to accelerate or retard 
 decay, but to make the presence or absence of a 
 given substance either more or less evident to us, 
 as they differ in melting-point or volatility. The 
 fact that uranium shows the same activity in liquid 
 air and at ordinary temperatures goes to show that 
 the activity resides within the atom itself, P. Curie 
 also found that the luminosity of radium and its 
 power of exciting fluorescence in bodies were retained 
 at the temperature of liquid air. If a radium com- 
 pound is heated in an open vessel, it is found that 
 the activity, measured by the a-rays, falls to about 
 25 per cent, of its original value. This, however, 
 is explained by Rutherford as not being due to a 
 change in the radio-activity, but to the release 
 of the radium-emanation, which is stored in the 
 radium. No alteration is observed if the radium is 
 heated in a closed vessel, from which none of the 
 radio-active products are able to escape. 
 
 Of all the radio-active materials mentioned, 
 radium possesses the most striking properties. It 
 is two million times more active than uranium, 
 and a few milligrammes suffice to produce strong 
 photographic action, to discharge electroscopes, to 
 give a brilliant luminosity to a fluorescent screen, 
 and to produce dangerous and painful effects on 
 the skin. All radium compounds shine in the 
 dark, especially when dry. A small quantity has 
 been known to give light enough to read by in a 
 
RADIO-ACTIVITY 277 
 
 dark room, though that practice is by no means to 
 be recommended. But it is not the purest pre- 
 parations of radium salt that give most light. A 
 strong admixture of barium increases the lumi- 
 nosity, which is by no means so well-defined a 
 property as the radio-activity. 
 
 A radium preparation usually a few milli- 
 grammes of radium bromide mounted between 
 thin glass plates gives out a-rays, /3-rays (which 
 are identical with projected electrons and cathode 
 rays), and the so-called y-rays, or ether pulses, 
 which do not consist of any kind of projected 
 particles. The a-rays are, as mentioned above, 
 in all probability atoms of helium, and are, there- 
 fore, very much bulkier than electrons. The latter 
 have, indeed, a hundred times more power of pene- 
 tration than the former, and can pass through a 
 sheet of aluminium half a millimetre thick. But 
 this power of penetration is surpassed over a hun- 
 dred times by the y-rays, the most penetrating 
 radiation known, which can pierce through 3 in. of 
 aluminium and J in. of lead ! 
 
 That these three radiations are simultaneously 
 emitted by the radium preparation is readily 
 understood if we consider that the preparation 
 contains not only the original radium, wKich slowly 
 evolves helium atoms, but also the emanation and 
 the active deposits, including radium C, which 
 gives off all those classes of rays. 
 
278 THE ELECTRON THEORY 
 
 The three radiations are readily separated by a 
 strong magnetic field. If a thin line of radium is 
 placed along the lines of force in a narrow hori- 
 zontal trough, the y-rays shoot straight upwards, 
 while the /3-rays, being electrons, are bent over to 
 one side, and the a-rays deflected to a very much 
 slighter extent towards the other side. Those 
 electrons that are projected in a line at right 
 angles to the trough describe complete circles if 
 free to do so, and it is possible to make them 
 record their presence on a photographic film at any 
 point in the circumference. Such tracings of the 
 path of the electrons projected by radium are 
 capable of great delicacy. Kaufmann succeeded 
 in showing both their magnetic and electric de- 
 flection simultaneously, and was thus enabled to 
 
 determine the ratio of the charge to the mass. 
 
 It turned out to be exactly the same as the value 
 deduced from cathode rays and from the Zeeman 
 effect, and thus furnished a striking proof of the 
 fundamental importance and identity of electrons. 
 
 A remarkable phenomenon, first observed by 
 Curie, is that radium maintains itself steadily at a 
 temperature about 3 above its surroundings. This 
 heat is most due to the expulsion of helium atoms. 
 It has been calculated that 1 gramme of radium 
 gives off 100 gramme-calories of heat per hour. 
 This would mean that during its whole " life " it 
 
RADIO-ACTIVITY 279 
 
 would give off 1/6 X 10 9 gramme-calories, or about a 
 million times more energy, weight for weight, than 
 was hitherto known in any chemical reaction. This 
 fact enables us to realise the vast forces which may 
 become available once we can control the rate of 
 disintegration of the atom. It confirms what was 
 said in the initial chapters with regard to the vast 
 stores of energy perceptible in the most elementary 
 electrical phenomena as soon as we deal with them 
 on a molecular scale. 
 
CHAPTER XVI 
 
 CONSTITUTION OF THE ELECTRON 
 
 WE have seen that practically all the known pheno- 
 mena of electricity and magnetism can be explained 
 by assuming that 
 
 1. The electric current consists in the motion of 
 very small electric particles called electrons, having 
 a definite and constant charge, and a definite mass 
 which is constant, but becomes larger at very high 
 velocities. 
 
 2. These electrons are usually associated with 
 atoms of ordinary matter, round which they de- 
 scribe circular or elliptical orbits, with periods 
 approaching those of visible light-waves. 
 
 3. That there is a force of attraction between 
 the atoms and the electrons belonging to it which 
 continues to act when they are separated, but 
 rapidly decreases with increasing distance. 
 
 4. That atoms deprived of electrons repel each 
 other. 
 
 5. That electrons mutually repel each other. 
 
 6. That electrons moving side by side through 
 the ether attract each other with a force propor- 
 
 280 
 
CONSTITUTION OF THE ELECTRON 28 1 
 
 tional to their speed, and inversely proportional to 
 the square of their distance apart. 
 
 7. A change of momentum of an electron pro- 
 duces a change of momentum in every other electron 
 in the opposite direction. 
 
 These assumptions and their corollaries embrace 
 nearly all the facts hitherto accumulated. They 
 are few in number surprisingly few considering 
 the vast array of facts they cover and certainly 
 fewer than those which form the basis of any of 
 the older theories. But the human mind is never 
 satisfied to take things, even simple things, for 
 granted. These things must be " explained " in 
 their turn that is to say, they must be reduced 
 to other and fewer and more familiar ideas. Such 
 curiosity is legitimate so long as there are any 
 facts remaining unaccounted for. But if it should 
 be found that all facts are satisfactorily explained 
 by the assumptions of the electron theory, then 
 the science of electricity will be complete, and 
 further research into the cause and reasonableness 
 of the fundamental assumptions will add nothing 
 new to electrical science. They may add to our 
 knowledge, indeed ; but that new knowledge will 
 constitute a new science. This is made evident 
 by a glance at mathematical astronorfiy. All its 
 facts are accounted for by Newton's law of gravita- 
 tion, which states that two heavenly bodies attract 
 each other with a force proportional to the product 
 
282 THE ELECTRON THEORY 
 
 of their masses, and inversely proportional to the 
 square of their distance apart. Further research 
 into the nature of gravitational force will not 
 amplify mathematical astronomy, nor will it enable 
 us to predict astronomical events with greater 
 accuracy than before. If, however, the law of 
 gravitation should be found to be subject to ex- 
 ceptions, the theory will have to be recast, and 
 this will mean, not a retrogression, but an advance 
 towards new and more general truths. 
 
 As J. J. Thomson says, the electron is at present 
 better known than the atom. It is likely, there- 
 fore, that an electron theory of the chemical atom 
 will shortly come into being. Such a theory is 
 made necessary by the facts of radio-activity where 
 atoms are found throwing off electrons and positive 
 particles. These electrons and positive particles 
 must therefore have been constituents of the atom. 
 
 The atom, with its detachable electrons, is some- 
 times compared to the solar system. The analogy 
 is somewhat far-reaching, and deserves to be pointed 
 out, if only to assist the memory and the imagina- 
 tion. 
 
 If the solar system is an atom on a large scale, 
 the sun must be regarded as the positive nucleus, 
 and the planets as the electrons. It is actually 
 found that the sun has a positive charge, and the 
 earth a negative charge. But these charges are 
 comparatively infinitesimal, and do not perceptibly 
 
CONSTITUTION OF THE ELECTRON 283 
 
 influence the force between them. In this point, 
 therefore, the analogy fails. On the other hand, 
 the ratio of the masses is very instructive. That 
 of Jupiter is about one- thousandth of that of the 
 sun, and approaches the mass of an electron in 
 comparison with a hydrogen atom. The mass of 
 the earth is ^TO-THF f that f the sun an( ^ this 
 ratio is nearly the same as that of an electron to 
 the atoms of the heavy metals. We may say, 
 therefore, that in the solar system we have ex- 
 amples of the various actual ratios of mass as 
 between an electron and its positive nucleus, 
 though in the case of atoms it is the atoms 
 themselves, and not the electrons, which vary in 
 mass. 
 
 The solar system may be regarded as a magnetic 
 molecule. The charge of the earth is at the very 
 least 2 5 million coulombs or " armies " of electrons. 
 This charge passes round the sun once every year, 
 so that the current represented by the earth's 
 motion is 25 million coulombs per annum, or just 
 about 1 ampere (O'l " electro-magnetic " unit of 
 current). The magnetic moment (see p. 167) of the 
 system sun-earth may be obtained by multiplying 
 the current by the area round which it circulates. 
 The area of the earth's orbit is about 10 27 square 
 centimetres, so that the magnetic moment of the 
 system sun-earth is 1 26 c.g.s. units. This moment 
 is too small to exert any measurable effect outside 
 
284 THE ELECTRON THEORY 
 
 the solar system, not to speak of influencing the 
 orientation of the planetary orbits of other stars. 
 Hence we see, as before, that magnetic and electric 
 forces play no appreciable part in the motions of 
 the heavenly bodies. 
 
 It may well be, however, that the sun's positive 
 electric charge just balances the negative charges 
 of the planets, in which case the solar system 
 would represent a neutral atom of matter. If, 
 under such circumstances, another neutral solar 
 system were to approach ours sufficiently closely 
 to entice Neptune from its allegiance to our own 
 sun, we should have an illustration of two atoms 
 combining, and then separating with opposite 
 charges, our solar system being positively charged, 
 and the foreign system negatively, having captured 
 one " electron/' Neptune, from us. Thus we should 
 represent, say, a mercury atom, and the foreign solar 
 system, say, a chlorine atom. 
 
 As matters stand, the solar systems of the 
 visible universe do not seem to approach together 
 so closely as to interfere with each other's planets. 
 The visible universe thus represents a gas rather 
 than a liquid or solid, except that portion called 
 the Milky Way, which appears to have a con- 
 sistency capable of giving it a metallic appearance 
 if it could, by some magic means, be reduced to 
 tangible dimensions. 
 
 The visible stars number quite a thousand million. 
 
CONSTITUTION OF THE ELECTRON 285 
 
 Now, the smallest object visible in a microscope 
 contains at least a hundred million atoms. We 
 may take it for granted, then, that the visible uni- 
 verse, whose outer edge is the Milky Way, if reduced 
 in the same proportion that an electron bears to 
 the earth, would resemble something rather like a 
 human blood corpuscle, and would contain about 
 the same number of atoms. 
 
 A blood corpuscle is too small to observe indi- 
 vidually its electric and magnetic properties, not to 
 speak of examining the properties of its individual 
 atoms and electrons. A large number of universes 
 would have to be taken together, and the results 
 would be average values. If we can imagine a 
 giant of this new Brobdingnag endeavouring to 
 arrive at some measurements of the masses, veloci- 
 ties, and electric charges of the stars and planets 
 " atoms " and " electrons " he would call them he 
 might very well find the same average value for 
 each million of them which he might pick out at 
 random. He might find that the ratio of the 
 charge to the mass of each detachable planet was 
 the same, and that the charge of each planet ap- 
 proached a standard value within the limits of hi 
 powers of measurement. He would naturally arrive 
 at the same conclusion as we do with regard to the 
 electrons viz. that they are absolutely constant 
 and equal bodies, constituting the physical units 
 and vehicles of electricity. 
 
286 THE ELECTRON THEORY 
 
 Further, our giant might be able to sort the 
 various solar systems according to their masses, 
 and establish certain " chemical " affinities between 
 systems of different mass. He might find that the 
 masses, which he would call " atomic weights," 
 showed a certain constancy, and a determining influ- 
 ence upon the affinity and chemical characteristics, 
 and would thus be led to discover a large-scale 
 " periodic law/' He might, by compression or 
 chemical treatment, bring the solar systems closer 
 together, and enable a certain number of planets to 
 roam at large among the fixed stars. He would 
 thus have produced a " conductor." Finally, he 
 might succeed in turning the ecliptics of the 
 various solar systems into the same plane, and 
 thus would produce a " magnet " of stupendous 
 magnitude. 
 
 We thus see that much insight into molecular 
 physics may be gained by considerations of astro- 
 nomical phenomena happening on a much larger 
 scale. 
 
 The scale by which we must reduce the visible 
 universe to get it down to microscopic dimensions 
 is 10 22 to 1. The radius of the solar system is, 
 roughly, 10 U cm. This, on dividing by 10 22 , be- 
 comes 10~ 8 cm., the radius of an atom. Neptune, 
 one of the most " detachable " planets we have, 
 may be likened to a detachable electron. Its 
 radius is about 10 9 cm., and this, reduced in the 
 
CONSTITUTION OF THE ELECTRON 287 
 
 same proportion, becomes 10~ 13 cm., the radius of 
 an electron. The mass of Neptune bears about the 
 same ratio to that of the solar system as that of 
 an electron bears to that of a lithium or oxygen 
 atom, so that the analogy still holds good. The 
 distance between the sun and the nearest fixed 
 star is about 10 18 cm., and this, divided by 10 22 , 
 becomes 10~ 4 cm., or 0*001 mm., which is the mean 
 free path of a molecule of air on a high mountain. 
 
 If, besides reducing the linear dimensions from 
 10 22 to 1, we suppose the present velocities of the 
 heavenly bodies to be maintained, we obtain some 
 very interesting and suggestive results. Since Nep- 
 tune takes some 220 years to revolve once round the 
 sun, its " frequency " of revolution (i.e. revolutions per 
 second) is 1*5 x 10~ 10 . Since the path is reduced 
 10 22 times, the frequency of describing it will be 
 increased in the same proportion, and will become 
 1'5 x 10 12 . This is the frequency of some infra- 
 red waves of light. The frequency of the planet 
 Mercury will become 1*25 x 10 15 , which lies in the 
 ultra-violet. All the other planets will produce 
 spectrum lines intermediate between these i.e. 
 lying in the visible spectrum. The asteroids will 
 produce a broad band instead of a line, and there 
 will be certain extra lines due to perturbations of 
 the planets by each other. The solar system will, 
 therefore, present a spectrum much resembling the spec- 
 trum of a chemical element. This is a striking feature 
 
288 THE ELECTRON THEORY 
 
 of the analogy between an atom and a planetary 
 system. 
 
 We may also, of course, reverse the process by 
 taking the Lilliput world of the atom and the elec- 
 tron, and enlarging it by the factor 10 22 , leaving all 
 its velocities as they were. An atom of, say, oxygen 
 would thus become of the same size as the solar 
 system, and its two detachable electrons would 
 closely resemble Uranus and Neptune as regards 
 size, distance from the sun, and period of revolution. 
 One of the electrons more closely bound up with 
 the atom, and assisting in producing the phenomena 
 of magnetism and radiation, but not of conduction, 
 might resemble the earth in size, and distance from 
 the sun, and might revolve round the latter in one 
 sidereal year. We naturally expect an electron, 
 when enlarged to the size of the earth, to be a 
 perfectly smooth sphere. At least, so we are accus- 
 tomed to find it described. But such a sphere is, in 
 reality, absolutely inconceivable ; nor is it necessary 
 to imagine it to be so. An electron may have a 
 structure resembling that of the earth in every par- 
 ticular, and yet not only could that make no differ- 
 ence to its electrical or astronomical properties, but 
 the fact of its having such a structure would remain 
 for ever unknown to us, considering the scale of 
 phenomena which are accessible to our senses. We 
 may therefore, without in the least interfering with 
 the efficiency of the electron as a universal vehicle of 
 
CONSTITUTION OF THE ELECTRON 289 
 
 electrical manifestations, imagine it to be a veritable 
 microcosm, a world in which life might not very 
 materially differ from life on our earth. Indeed, 
 considering that time and space would be reduced 
 in the same constant and uniform proportion, it 
 is doubtful whether our present instruments, thus 
 suddenly transformed, would be able to indicate the 
 occurrence of any fundamental change. This is 
 but another illustration of the well-known principle 
 that size and length of time are purely relative, 
 and depend upon comparison with standards. If all 
 dimensions, including the standards, were reduced 
 in the same proportion, or if all things were accele- 
 rated or retarded in the same proportion, we should 
 be absolutely unaware that anything had happened. 
 
 On the other hand, if any intelligent being could 
 be transferred from the microcosm to our present 
 world, and could keep up some connection with the 
 microcosm, his busy life here would appear to the 
 inhabitants of the microcosm to be a changeless 
 eternity, since any change measurable by them 
 would take millions of their years to accomplish 
 itself. 
 
 We here enter upon the region of pure specula- 
 tion, and it is not the function of a scientific work 
 to deal with occult problems of that kind. But 
 since the electron theory promises to guide us 
 further into the mysteries of matter than anything 
 attempted hitherto, it is necessary to discuss the 
 
 T 
 
2QO THE ELECTRON THEORY 
 
 general prospect even cursorily. To sum up, we find 
 in the fruitful and suggestive astronomico-chemical 
 analogy a boundless vista of worlds within worlds, 
 which, while rightly preventing us from setting a 
 limit to the multiplicity of possible phenomena, 
 comforts us with the reflection that for our purposes, 
 and as far as our present senses are concerned, the 
 multiplicity of phenomena has an absolute limit, 
 which makes it possible to look forward to the 
 eventual formulation of a theory embracing all 
 phenomena accessible to our senses. 
 
CHAPTEE XVII 
 
 DIMENSIONS OF ELECTRICAL QUANTITIES 
 
 THE discovery that electricity has an atomic struc- 
 ture, that its carriers are discrete particles, brings 
 the desirability of recasting our dimensional formulae 
 into renewed prominence. We find that electricity 
 is as fundamental as mass, perhaps, indeed, more 
 fundamental, and all indications point to the ad- 
 vantage of recognising electricity as a fundamental 
 natural quantity. The other fundamental quanti- 
 ties so far recognised are length, mass, and time. 
 They are called fundamental quantities because, 
 while none of them can be measured in terms of 
 the rest of them, the three quantities are capable of 
 measuring other more complex quantities. Thus, 
 we require no fundamental unit for velocity. We 
 measure it in terms of our units of space and time, 
 as cm. per second, or miles per hour. Neither do 
 we require a separate fundamental unit for work, 
 which can be expressed in foot-pounds * or horse- 
 power-hours. There is nothing to prevent us adopt- 
 ing a special unit for it, such as the erg ; but this 
 unit is not fundamental, as it can be reduced to 
 
 mass, space, and time. 
 
 291 
 
2Q2 THE ELECTRON THEORY 
 
 A formula which expresses the manner in which 
 the three fundamental units enter into the com- 
 position of derived units is called a dimensional 
 formula. These formulae are very useful in giving 
 us an analysis of the structure of a physical quan- 
 tity, much as chemical formulae reveal to us the 
 structure of the chemical molecule. They are also 
 useful for converting quantities from one system of 
 measurement to another. 
 
 The fundamental quantities mass, length, and 
 time are denoted by the symbols M, L, and T re- 
 spectively. Of these, L is the most fundamental of 
 all, since M and T are often measured as lengths 
 on a scale referred to the dimensions of the earth. 
 T is referred to the time of rotation of the earth 
 about its axis. M is referred to L and T by the 
 stipulation that the unit of mass is the mass of 
 water contained in one cubic centimetre when at its 
 greatest density. Thus we see that size and rotation 
 of the earth as a whole give us our standards of 
 space and time, and that a peculiar chemical sub- 
 stance water gives us the standard of mass. This 
 again illustrates the less fundamental character of 
 mass. 
 
 The measurement of an area requires two inde- 
 pendent measurements of length, the results being 
 multiplied together. Denoting each measurement 
 by L, the measurement of an area may, therefore, be 
 denoted by L 2 , and the measurement of a volume 
 
DIMENSIONS OF ELECTRICAL QUANTITIES 293 
 
 by L 3 . The last formula also indicates that when 
 the linear scale is altered in any ratio, the numerical 
 result will be altered in the third power of that 
 ratio, since the three results of the separate measure- 
 ments of length are affected in the same manner. 
 
 The measurement of a velocity involves the simul- 
 taneous measurement of a length and a time. The 
 velocity increases with the length, and decreases 
 with the time taken to describe it. The dimensional 
 
 formula of velocity is, therefore, ^, or, as it is more 
 
 usually written, LT' 1 . In measuring acceleration, 
 we measure the velocity acquired in a certain time. 
 There are, therefore, two independent measures of 
 time involved in the same determination, and 
 the dimensional formula becomes LT~ 2 . Force is 
 measured by the mass moved and the velocity it 
 acquires in unit time. Its dimensional formula 
 is MLT" 2 . Work or energy, measured by the 
 product of force into distance, is represented by 
 ML 2 T- 2 , and so on. 
 
 It has sometimes been proposed to eliminate M 
 from the dimensional calculus and to reduce it to 
 L and T, as these are more fundamental. This can 
 be done as soon as we can obtain an equation from 
 which M may be evolved in terms of L apd T. For 
 this purpose we must find another permanent and 
 universal property of mass besides that of always 
 acquiring the same velocity under a given impulse. 
 If, for instance, all bodies were equally dense, mass 
 
294 THE ELECTRON THEORY 
 
 would become identical with volume, and its furmula 
 would be L 3 . This, of course, is not by any means 
 the case. But there is another universal property 
 of mass, discovered by Newton. It is that the force 
 of attraction between two masses is directly pro- 
 portional to the product of the masses and inversely 
 proportional to the square of the distance between 
 
 them. This force may therefore be put = -= or 
 
 M 2 L" 2 . A force, as we may have seen above, has 
 the dimensional formula M L T" 2 . Hence we have 
 
 MLT- 2 = M 2 L- 2 
 
 which cannot be true unless either (a) some other 
 quantity, such as the density of the ether, is left 
 out of account, or (&) mass is expressible in terms of 
 L and T. For it is obvious that the dimensional 
 formulae must be the, same on both sides of the 
 equation. We can never equate a length with a time, 
 since they are two essentially different quantities. 
 It would be like saying, for instance, that three 
 horses equal three dogs. Adopting the alternative 
 (6), and dividing both sides by M, we obtain 
 
 L T- 2 = M L- 2 or M = L 3 T- 2 
 
 which may be regarded as the product of a length 
 into the square of a velocity. Since, however, we 
 are as yet in entire ignorance of what that supposed 
 velocity and length may signify, the gain is trifling. 
 We might, indeed, measure the masses of different 
 
DIMENSIONS OF ELECTRICAL QUANTITIES 295 
 
 bullets of the same size by the depth to which 
 they penetrate into wood when fired with a given 
 velocity ; but the new method would be clumsy 
 in comparison with the usual weighing methods. 
 Besides, the discarding of M would make us lose 
 a definite and useful physical conception which 
 appeals directly to our muscular sense. 
 
 Now, all the arguments in favour of retaining 
 mass as a fundamental quantity also tell in favour 
 of recognising electric quantity as a fundamental 
 quantity. And it has a natural unit, the electron, 
 of a much more prevailing and universal kind. 
 
 Electric quantity may be measured by any one 
 of the many sets of phenomena in which the amount 
 of it present plays a decisive part. 
 
 We have already described the two chief systems 
 of measuring electricity, one derived from electro- 
 static repulsion (p. 38), and the other from electro- 
 dynamic or magnetic force (p. 148). To these may 
 be added the chemical system, which furnishes 
 the most accurate method, though usually based 
 upon the electro-magnetic system. The electrostatic 
 system derives its unit of electricity from the re- 
 pulsion of two quantities of the same sign placed at 
 unit distance apart. This is like deducing the unit 
 of mass from its gravitational attraction. The 
 
 equation is 
 
 MLT-2=E 2 L- 2 
 
 where E is the quantity of electricity. If we wish 
 
296 THE ELECTRON THEORY 
 
 to reduce E to M, L, and T, we must solve the 
 above equation for E. We obtain 
 
 This dimensional formula for E is very complicated, 
 and its interpretation is made difficult owing to the 
 fractional index of M, which seems irrational. And 
 even if we adopt it we do not know what pro- 
 perties of the medium we are leaving out of account. 
 Besides, we obtain a different dimensional formula 
 for E when we deduce it from some other property, 
 such as magnetic force. It is, therefore, more 
 advisable to consider quantity of electricity a funda- 
 mental quantity, and to refer it to the electron as 
 a standard, or to any of its measurable effects. By 
 doing this we obtain a uniform, simple, and rational 
 system of dimensional formulae, as will be seen in 
 what follows. 
 
 The fundamental units are M mass, L length, 
 T time, and E electricity. We obtain the following 
 dimensional formulae : 
 
 Electric quantity, E. 
 
 Surface density of electricity, or quantity of elec- 
 tricity per sq. cm., EL" 2 . 
 
 Electric current, quantity of electricity passing a 
 given surface in one second, E T" 1 . 
 
 Current density, current per sq. cm. of section 
 across conductor, E T" 1 L~ 2 . 
 
 Electric force, same formula as force, M L T" 2 . 
 
DIMENSIONS OF ELECTRICAL QUANTITIES 297 
 
 Electrostatic field, force exerted on unit quantity 
 of electricity, M L T' 2 E" 1 . 
 
 Electric potential, work done on unit quantity, 
 M L 2 T- 2 E- 1 . 
 
 Dielectric constant, (density of electrons) X (dis- 
 placement in unit field), E 2 M" 1 Ir 3 T 2 . 
 
 Resistance, by Ohm's law, E.M.F. / current, 
 
 ML 2 T -l E -2 
 
 Resistivity or specific resistance, resistance of 1 cm. 
 cube, M L 3 T- 1 E~ 2 . 
 
 Conductivity (specific), inverse of resistivity, 
 M- 1 L- 3 T E 2 . 
 
 This last admits of a simple interpretation in 
 accordance with the electron theory (see p. 108). 
 We may write it 
 
 E_ L E 
 
 L 3 " T ' MLT- 2 ' 
 Or 
 
 (electrons per c.c.) x (velocity of electrons) x ( g-r^ ) 
 
 That is to say, the specific conductivity is measured 
 by the number of free electrons per cubic cm., 
 multiplied by the steady speed which each free 
 electron acquires in a unit field. 
 
 We also get the following magnetic formulae : 
 
 Magnetic moment, current multiplied by area round 
 which it circulates, E T" 1 L 2 . 
 
 Magnetic pole-strength, magnetic moment per unit 
 length, ET- 1 !,. 
 
 Magnetic force, same as force. 
 
298 THE ELECTRON THEORY 
 
 Magnetic potential, work per unit magnet pole, 
 M -I LT -I E -I. 
 
 Magnetic field, force per unit magnet pole, 
 E -i MT -i 
 
 Intensity of magnetisation, magnetic moment per 
 unit volume, ET" 1 L~ 1 , which means the current 
 circulating round unit length of the magnet. 
 
 Strength of a magnetic shell, E T' 1 ( = current 
 circulating round it), 
 
 Magnetic flux, field multiplied by area, 
 
 E -1 MT -1 L 2 
 
 Magnetic susceptibility, intensity of magnetisation 
 acquired in unit field, E 2 M' 1 L' 1 . 
 
 Finally, for inductance, or the coefficient of self- 
 induction, being the E.M.F. induced in a circuit by 
 unit charge of current per second, we obtain 
 
 M L 2 T- 2 E" 1 , or M L* E~ 2 . 
 
 The above dimensional formulae exhibit at a 
 glance the structure and derivation of the various 
 electric and magnetic quantities, and their con- 
 nection with the unit of electricity. 
 
 Practical Units. The natural unit of electricity 
 is the electron. But it is so excessively small that 
 it would be necessary to adopt a large multiple of 
 it in practice say, a trillion electrons, or 0*112 
 coulomb sufficient to pass 0'126 milligrammes of 
 silver through an electrolytic cell. This, however, is 
 at present impossible, since the charge of an electron 
 
DIMENSIONS OF ELECTRICAL QUANTITIES 299 
 
 is not known with, sufficient accuracy. In any case, 
 it would be unwise to dislocate electrical engineer- 
 ing by displacing the present units unless some 
 very great advantage would accrue therefrom. The 
 practical unit of electricity is the coulomb, which 
 contains 8*79 trillion electrons. This unit I have 
 sometimes called an " army " of electrons, not in 
 order to displace the word coulomb, but to empha- 
 sise the atomic structure of electricity, and also to 
 distinguish it from the much smaller electrostatic 
 unit or "company" (see p. 38). The ratio of the 
 two units is 3 x 10 10 , or the figure representing the 
 velocity of light. The magnetic attraction between 
 two electrons moving side by side through the 
 ether just balances their electrostatic repulsion 
 when their velocity reaches that figure. 
 
 The practical unit of current strength is the 
 amp&re, consisting in the passage of one coulomb 
 per second through any cross-section of the con- 
 ductor. If a current of one amp&re is sent through 
 an electrolytic cell or voltameter consisting of silver 
 electrodes immersed in a solution of silver nitrate, 
 the current deposits 1-118 milligrammes of silver 
 per second. This is the legal definition of current 
 strength. It may also be arrived at through mag- 
 netic attraction (see p. 153), and that* is how the 
 unit of current was originally fixed. But the 
 " electro-magnetic " unit of current is ten times 
 the value of the ampere. 
 
3OO THE ELECTRON THEORY 
 
 The next most important unit is that of differ- 
 ence of potential. To bring a quantity of electricity 
 from a point at low potential to a point at high 
 potential requires an expenditure of work. This 
 work per unit quantity measures the difference of 
 potential between the two points. We might define 
 unit difference of potential as existing between two 
 points when it requires one " erg " of work to bring 
 one " company " or electrostatic unit of electrons 
 from one to the other. This is the electrostatic 
 unit of difference of potential. The practical unit 
 is the volt, which is ^^-th part of this. To take one 
 coulpmbjbhrough a difference o_f potential of one volt 
 requires an expenditure of 10 million ergs, a quan- 
 tity which has been called one "joule," after Joule, 
 the discoverer of the law of heating in current- 
 bearing wires. Conversely, when one coulomb falls 
 through one volt, one joule of work may be derived 
 _from it. As a rule, it is represented by the heat 
 in the wire, generated by the stoppages of the 
 electrons. 
 
 The most obvious way of defining conductivity 
 would be to ascribe unit conductivity to a substance 
 containing one free electron per cubic cm., capable of 
 acquiring a steady speed of one cm. per second, under 
 the influence of a field of one volt per cm., or to stipu- 
 late that in such a field one electron per second should 
 pass through every square cm. of the cross-section. 
 But in practice the conductivity is derived from 
 
DIMENSIONS OF ELECTRICAL QUANTITIES 30 1 
 
 the resistance, and this is derived from the current 
 and voltage. A conductor has a unit resistance 
 of one " ohm " if a current of one ampere flows 
 through it on applying a difference of potential of 
 one volt to its ends. 
 
 The work done by a current is measured in joules. 
 The rate of work or " power " is measured by the 
 product of current and voltage, the unit being the 
 watt, consisting of one joule per second. Many 
 practical electricians measure the work in watt- 
 seconds or kilowatt-hours rather than in joules. 
 One kilowatt-hour is 3,600,000 joules, or 3'6 X 
 10 13 ergs. 
 
 It has already been stated (p. 168) that unit 
 magnetic pole is possessed by a long thin magnet 
 of 1 sq. cm. sectional area if the current circulating 
 round it amounts to one .electro-magnetic unit 
 (=10 amperes) per cm. le'ngth. In this case the 
 practical unit (the ampere) is not adopted, and the 
 same may be said of the other magnetic quantities, 
 which were originally based upon the repulsion 
 between two similar magnet poles. The most im- 
 portant of these are the magnetic moment (length 
 multiplied by pole strength), the magnetic field 
 (force per unit pole), intensity of magnetisation (mag- 
 netic moment per unit volume), and the magnetic 
 susceptibility (magnetisation in unit field). The 
 magnetic " permeability " is the total field existing 
 in the interior of a substance when immersed in 
 
302 THE ELECTRON THEORY 
 
 unit field. It is measured by 1 + 4?rK, where K 
 is the magnetic susceptibility. The " induction " B 
 is the product of the permeability and the field 
 strength. It represents the actual internal mag- 
 netic field of the substance. 
 
 /This magnetic " induction " must be carefully 
 distinguished from the electro-magnetic induction 
 which gives rise to induced currents, and also from 
 the electrostatic induction or "influence," which 
 gives rise to charges in bodies when brought into 
 an electric field. It is unfortunate that this word 
 has acquired three different meanings. / 
 
 When a current through a conductor changes, 
 the inertia of the moving electrons, whether due to 
 their own motion or to the reaction of surrounding 
 electrons, represents a store of energy which is 
 expended in resisting the change, and this store of 
 energy per unit quantity in motion may be measured 
 in volts. When the current either decreases or 
 increases at the rate of one ampere per second, and 
 the E.M.F. thus induced in the circuit is one volt, 
 the conductor is said to have unit inductance. 
 This unit of inductance is called one henry. It is 
 10 9 times the unit derived from theoretical con- 
 siderations of the E.M.F. induced in a conductor 
 traversed by lines of force, where the inductance is 
 defined as the number of lines of force added to or 
 subtracted from those traversing the circuit owing 
 to the change of current (see p. 189). 
 
DIMENSIONS OF ELECTRICAL QUANTITIES 303 
 
 The development of electrical science has suffered 
 much by the existence of three different systems 
 of electrical units, called the electrostatic, electro- 
 magnetic, and the practical units respectively. This 
 multiplicity of systems was due to ignorance as to 
 the real nature of magnetism, and to the prevalence 
 of false analogies between electric and magnetic 
 phenomena. We now see that magnetism is re- 
 ducible to the revolution of electrons. It has 
 sometimes been urged as an objection to this view 
 that there would have to be some gyroscopic action 
 due to the innumerable minute molecular gyro- 
 scopes constituted by the revolving electrons. But 
 this objection leaves out of account the extreme 
 shortness of the period of revolution, a shortness 
 which enables the electron to follow a rotation 
 much as a high-frequency galvanometer needle gives 
 a dead-beat reading. 
 
 The electron theory, with its logical corollary 
 the recognition of electricity as a fundamental 
 quantity gives a consistent and comprehensive 
 view of all the facts of electricity and magnetism 
 hitherto accumulated. Within the next few years 
 we shall, no doubt, witness its application to every 
 detail of electrical science. 
 
EEFERENCES 
 
 To some of the Principal Papers dealing with Electrons, arranged 
 alphabetically according to Authors. 
 
 ABRAHAM, MAX : Dynamics of the Electron (Annalen der PhysiJc 10, 
 pp. 105-179, 1903). 
 
 ARRHENIUS, S. : lonisation (Textbook of Electro-chemistry). 
 
 BECQUEREL, HENRI : Uranium Radiation, &c. (Oomptes Rendus 122, 
 pp. 301, 359, 420, 501, 559, 689, 762, 1086, 1896 ; 129, p. 996, 
 1899). 
 
 CROOKES, Sir WILLIAM: Radiant Matter (British Association, 
 Sheffield, 1879). 
 
 CURIE, P. and S. : Radium (Comptes Rendus 127, p. 1215, 1898). 
 
 DRUDE, P. : Electron Theory of Metals (Annalen der Physik 1, p. 566, 
 1900 ; 3, p. 369, 1900). 
 
 Optics (Lehrbuch der Optik). 
 
 ELSTER and GEITEL : Atmospheric Electricity (Physikalische Zeit- 
 schrift 1, p. 11, 1899; p. 245, 1900; 2, p. 116, 1900; p. 590, 
 1901 ; 3, p. 305, 1902). 
 
 FLEMING, J. A. : Electronic Theory (Popular Science Monthly, 
 May 1902). 
 
 GIESE, W. : Corpuscular Theory of Conduction (Wiedemann's An- 
 nalen 37, p. 576, 1889). 
 
 HERTZ, H. : Influence of Ultra-violet Light on the Electric Dis- 
 charge (Wied. Ann. 31, p. 983, 1887). 
 
 KAUFMANN, W. : Electro-Magnetic Mass of the Electron (Gottinyer 
 Nachrichten, p. 90, 1903). 
 
 305 U 
 
306 REFERENCES 
 
 LANGEVIN, P. : Mobility of Ions in the Atmosphere (Oomptes Rendus 
 134, p. 646, 1902). 
 
 - Theory of Magnetism (Journal de Physique, October 1905). 
 LARMOR, JOSEPH : " Ether and Matter." 
 
 LENARD, P. : Cathode Rays in the Open Air ( Wied. Ann. 51, p. 225, 
 1894). 
 
 LODGE, Sir OLIVER : On Electrons (Electrician, 1903). 
 LORENTZ, H. A.: Propagation of Light (Wied. Ann. 9, 1880). 
 
 - Zeeman Effect (Paris Congress, 1900, Report, vol. iii. p. 1). 
 
 - Metallic Absorption and Emission (Proceedings Amsterdam 
 Academy , 1902-3, p. 666). 
 
 MCCLELLAND, J. A. : Conductivity of Flame Gases (Philosophical 
 Magazine 46, p. 29, July 1898). 
 
 MARX, ERICH : Hall Effect in Flame Gases (Physikalische Zeitschrift 
 2, p. 412, 1901). 
 
 , H. : Dynamics of the Electron (Comptes Rendus 140, 
 p. 1504, 1905). 
 
 RlECKE, E. : Electron Theory (Annalen der Physilc 4, p. 378, 1901 ; 
 7, p. 401, 1902 ; Physikalische Zeitschrift 2, p. 182, 1901). 
 
 RUTHERFORD, E. : Uranium Rays (Phil. Mag. 47, p. 109, 1899). 
 
 - Radium Rays (Phil. Mag. 5, p. 177, 1903). 
 
 - and SODDY: Disintegration Products of Radium (Phil. Mag., 
 p. 576, 1903). 
 
 SCHUSTER, ARTHUR : Discharge through Gases (Proceedings Royal 
 Society 47, p. 526, 1890). 
 
 - Metallic Conduction (Phil. Mag. 38, p. 151, 1904). 
 
 SIMON, S. : Ratio of Charge to Mass (Wied. Ann. 69, p. 589, 1899). 
 
 STARK, J. : lonisation by Shock (Annalen der Physilc 7, p. 417, 1902; 
 PhysiJcal. Zeitschr. 5, p. 51, 1903). 
 
 STONEY, G. JOHNSTONE: Elementary Quantity of Electricity 
 (British Association, Belfast Report, 1874 ; Transactions Royal 
 Dublin Society 4, p. 563, 1891). 
 
REFERENCES 307 
 
 THOMSON, J. J. : Electric and Magnetic Effect of Moving Electrified 
 Bodies (Phil. Mag. 11, p. 229, 1881). 
 
 THOMSON, J. J., and E. RUTHEKFOED: Passage of Electricity 
 through Ionised Gases (Phil. Mag. 42, p. 392, 1896). 
 
 Cathode Rays (Phil. Mag. 44, p. 293, 1897). 
 
 Electric Charge Transported by Ions (Phil. Mag. 4.6, p. 528, 
 
 1898 ; 5, p. 346, 1903). 
 
 Theory of Gaseous Conductivity (Phil. Mag. 47, p. 253, 1899). 
 
 lonisation by Discharge (Phil. Mag. 50, p. 278, 1900). 
 
 TOWNSBND, J. S. : Gaseous Conductivity produced by Shock (Phil. 
 Mag. 1, p. 198, 1901). 
 
 Diffusion of Ions in a Gas (Philosophical Transactions Royal 
 
 Society 193A, p. 129, 1900). 
 
 WIECHEBT, E. : Velocity and Magnetic Deflection of Cathode Rays 
 (Wied. Ann. 69, p. 739, 1899). 
 
 WIEN, W. : Electric Discharge in Gases ( Wied. Ann. 65, p. 440, 
 
 1898). 
 
 Electro- Magnetic Foundation of Mechanics (ArcMves Neer- 
 
 landaises, 5, p. 96). 
 
 WILSON, C. T. R. : Condensation Nuclei (Phil. Trans. Royal Society 
 192A, p. 403, 1899). 
 
 WILSON, H. A. : Charge of Gaseous Ions (Phil. Mag. 5, p. 429, 
 1903). 
 
 NOTE. Most of the above papers are reprinted in Les Quantites 
 JElemcntaires d' Jtllectricite : Ions, Electrons, Corpmcules, published by 
 the French Physical Society in 1905 (Gauthiers Villars, Paris). 
 
INDEX 
 
 ABEAHAM, 22 
 
 Absorption of light, 204, 233 
 Actinium, 272 
 Ampere unit, 91 
 
 definitions of, 155 
 
 "Army" of 8'79 trillion elec- 
 trons, 91 
 
 Arrhenius, 99, 104 
 Astronomical analogy, 282 
 Atoms in 1 cc. copper, 28 
 
 BECQUEEEL, 21, 127, 214 
 Bucherer, 22 
 
 CANAL rays, 119 
 
 Capacity, 51 
 
 Cathode rays, 
 
 Circuit, 98 
 
 Circular polarisation, 202 
 
 Clausius, vii 
 
 Colour, 205, 228 
 
 " Company" of 2930 million 
 
 electrons, 38 
 Condensers, 52 
 Conduction in liquids and solids, 
 
 difference, 101 
 
 metallic, nature of, 84 
 
 Conductivity, 297 
 
 elements of, 107 
 
 Conductors, nature of, 35 
 Constitution of the electron, 
 
 280 
 
 Contact electrification, 134 
 Corpuscle, 219 
 
 Coulomb's magnetic law, 174 
 Coulomb unit, 91 
 Crookes, 81, 273 
 Curie, 21 
 Madame, 265 
 
 DAEK space, 79 
 
 d'Arsonval, 211 
 
 Dependent discharge, 77 
 
 Detachable electrons, 28 
 
 Diamagnetism, 160, 204 
 
 Dielectrics, 225 
 
 Dielectric strength, 67 
 
 Dimensions of electric quanti- 
 ties, 291 
 
 Direction of flow of current, 9 
 
 Discharge in general, 69 
 
 through insulators, 72 
 
 through gases, 75 
 
 through solid conductors, 
 
 83 
 
 through liquids, 98 
 
 through a vacuum, 114 
 
 Dispersion, 228 
 
 Dissociation, 99 
 
 Distribution of free charges, 35 
 
 Double refraction, 235 
 
 Drude, 21,228 
 
 ELECTEICITY a fundamental 
 quantity, 295 
 
 Electro-dynamics, 146 
 
 Electrolysis, 98 
 
 Electro-magnetic waves, 196, 
 227 
 
 Electrometers, 60 
 
 Electro-motive force, 97 
 
 Electron at rest, 23 
 
 charge of, tf '4 x 10" 10 elec- 
 trostatic units, 37 
 
 mass of, 0-61 x 10' 37 gr., 23 
 
 name, 219 
 
 properties of, 23 
 
 radius of, 10- 13 cm., 23 
 
 theory of gravitation, 30 
 
 309 
 
INDEX 
 
 Electrons and matter, 25 
 Electrostatic machines, 65 
 Elster and Geitel, 139 
 Emanation, 268 
 Equipotential surface, 46 
 Erg, 86 
 
 Ettingshausen effect, 257 
 Ewing, 162 
 
 FAEADAY, 5, 180 
 
 effect, 247 
 
 Faraday's laws of electrolysis, 
 
 110, 112 
 
 Ferro-magnetism, 160 
 Fluid theory, 7 
 Franklin, 3, 7, 220 
 Frequency of revolution, 32 
 Frictional electrification, 65, 142 
 Fuechtbauer, 138 
 
 GALVANIC cell, 143 
 Galvano-magnetic effects, 252 
 Galvanometer, 156 
 Glow discharge. 79 
 Gramme-molecule, 102 
 
 HALL effect, 16, 256 
 Hankel series, 140 
 Heating effect of current, 92 
 Helium, 268 
 
 Helmholtz on "Atoms of Elec- 
 tricity," 13 
 Hertz, 139 
 Hydrated atoms, 103 
 
 IMAGES, electric, 50 
 Independent discharge, 77 
 Induced currents, 176 
 Inductance, 189, 298 
 Induction, 302 
 Infinite series, 41 
 Influence, 37 
 Insulators, 53 
 
 Intensity of magnetisation, 161 
 Internal resistance, 97 
 lonisation, 68, 71, 76, 86, 147 
 
 JOULE'S law, 92, 150 
 Joule unit, 300 
 
 KAUFMANN, 21, 214, 278 
 Kayser and Runge, xvi 
 Kerr effect, 249 
 Kilowatt hours, 301 
 Kinetic energy, 177 
 Kirchhoff's laws, 95 
 
 LANGEVIN, 22, 160 
 
 Larmor, 22 
 
 Lecher wire system, 198 
 
 Leduc effect, 257 
 
 Lenard, 19, 214 
 
 Leyden jar, 57 
 
 Liebenow, 129 
 
 Lines of force, 4, 5, 180 
 
 Lodge, 22 
 
 Longitudinal magneto - thermal 
 
 effects, 259 
 Lorentz, 21, 228, 239 
 
 MACALUSO and Corbino, 250 
 
 Magnetic flux, 185 
 
 force, 147 
 
 moment, 167 
 
 pole, 160 
 
 repulsion, 174 
 
 shell, strength of, 298 
 
 susceptibility, 298, 301 
 
 Magnetism, 159 
 
 Magneto-optics, 237 
 
 Maxwell, x 
 
 Maxwell-Bartol's pressure, 120 
 
 Maxwell's ' ' Atom of Electri 
 city," 14 
 
 Mean free path, xi 
 
 Measurements concerning elec- 
 trons, 206 
 
 Molecular magnets, 161 
 
 NEGATIVE atoms, 103 
 Nernst effect, 257 
 
 OHM'S law, 92 
 
 Ohm unit, 98 
 
 Optical rotation, 235 
 
 Orbital velocity of electrons, 32 
 
 Osmotic pressure, 113 
 
INDEX 
 
 PARAMAGNETISM, 159^, 
 Peltier effect, 124 
 Permeability, 301 
 Photo-electric current, 140 
 Plane -polarised vibrations, 202 
 Point discharge, 78 
 Polarisation of light, 234 
 Pole-strength, 167 
 Polonium, 271 
 Positive atoms, 27, 31, 36, 38 
 
 and negative, 9, 65 
 
 Potential, 39, 46 
 Power, 301 
 Practical units, 298 
 Propagation of electric force, 
 
 193, 200 
 of waves, 226 
 
 RADIANT matter, 15, 81 
 Radiation, 190 
 Radio-activity, 264 
 Radio- tellurium, 271 
 Radium, 267 
 
 products, 269 
 
 Rate of decay, 268 
 Reflection, 233 
 Refraction, 224 
 
 Repulsion, mutual, of two elec- 
 trons, 23 
 
 Residual magnetism, 166 
 Resistance, definition, 90 
 Resistivity of electrolytes, 109 
 Riecke, 21 
 
 Rontgen rays, 88, 11* 
 Rotation, optical, 235 
 Rutherford, 21, 266 
 Rydberg, xvi 
 
 SATURATION current, 82 
 Schuster, A., 19, 21, 84, 222, 228 
 Seebeck's discovery, 126 
 Self-induction, 189 
 Semi-permeable membranes, 113 
 
 Simon, 21, 214 
 
 Solar system a magnetic mole- 
 cule, 283 
 Solenoid, 156 
 Sommerfeld, 22 
 Spark, electric, 77 
 Specific inductive capacity, 62 
 Stark, 139 
 
 Stoney, G. Johnstone, 14, 219 
 Symmer, 9 
 
 THERMO-ELECTRICITY, 121 
 Thermo-magnetic effects, 252 
 Thompson, Silvanus, 186 
 Thomson, J. J., 21, 37, 84, 181, 
 
 209, 214, 217 
 Thomson effect, 132 
 Thorium, 272 
 Townsend, 21 
 
 ULTRA-VIOLET light, discharg- 
 ing effect of, 116 
 Unit of current, 91, 153 
 Units, fundamental, 292 
 Uranium, 272 
 
 VACUUM an insulator, 34 
 Velocity of cathode rays, 116 
 Volt, 300 
 
 Voltaic electricity, 134 
 Volta series, 140 
 
 WATERSTON, vii 
 
 Watt unit, 301 
 
 Wave-lengths, 32 
 
 Weber's molecular currents, 12 
 
 Wiechert, 211, 214 
 
 Wien, 22, 119 
 
 Wilson, 21, 217 
 
 ZEEMAN, 20, 228, 278 
 effect, 237 . 
 
 Printed by BALLANTYNE, HANSON & Co. 
 Edinburgh &> London 
 
UNIVERSITY OF CALIFORNIA LIBRARY 
 BERKELEY 
 
 Return to desk from which borrowed. 
 This book is DUE on the last date stamped below. 
 
 DEC 3 1947 
 
 FEB 7- 1955 
 JAN I 11955 
 
 r\ 
 
 OCT 3 1362 
 
 REC'D LC 
 
 OCT 2 '63-12 
 
 
 
 LD 21-100m-9,'47(A5702sl6)476 
 
VB 095^6 
 
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