V'^'-t wi ^^I's^'Sfi', yrU, d9 /901 CORNELL UNIVERSITY LIBRARY GIFT OF Prof. Guy E. Grantham Cornell University Librarv QC 721.F77 1907 Cornell University Library The original of tliis bool< is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31 92401 233751 9 THE ELECTRON THEORY BY TBB SAME AUTHOR TWO NEW WORLDS I. THE INFRA-WORLD 11. THE SUPRA-WORLD Crown 8to, 3s, 6d. net LONGMANS, GREEN, AND CO. LONDON, NEW YOKE, BOMBAY, AND CALCUTTA Dk. g. john.siois-e ^toxey From u fhotn,/raj3h hy Elliott d- Fry. A ?0'f;'LAR IMlii>DrCT!ON TO I'HE NiaV THEORY OF ELKCTKraTY AND MAGfiirii^vI BV E. E. i'HjRMER i/ALBE E.Sc. (L'Ni>,), A.B V.^t OOMriLKB OF " rOSII!M>'0aABY KtB ' .i..',ir/ SOJENCU" WITH A PRE PACE G. JOHNSTONE STONEY M,A.., .'C.!.: ?.K.S. SECOND EDDiO:) ^^:"^f<' ?-.wSl^' -tONE .VCONEY / . '-y L'lliott d- fry. THE ELECTRON THEORY A POPULAR INTRODUCTION TO THE NEW THEORY OF ELECTRICITY AND MAGNETISM BY E. E. FOURNIER d'ALBE B.Sc. (LoND.), A.R.C.Sc. COMPILER OF " CONTBMPORART ELECTRICAL SCIENCE" WITH A PREFACE BY G. JOHNSTONE STONEY M.A., SO.D., F.K.S. With Frontispiece, and Diagrams in Text SECOND EDITION LONGMANS, GREEN, AND CO. 39 PATERNOSTER ROW, LONDON NEW YORK, BOMBAY, AND CALCUTTA 1907 All rights reserved <^- t'n"^-- ■■^ PREFACE In 1811 — nearly a hundred years ago — Avogadro promulgated ttie 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 cooled, and by pressing against one another and against the walls of a containing vessel, behave VI PREFACE in these respects very mucli 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 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 PREFACE VU 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 Koyal 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 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. Till PREFACE 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'^- This mean speed Clausius succeeded in finding to be about 485 / ^ metres per second . . . 1 (a) 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 ^^^^ / aJn miles per hour . . . 1 (6) \/ zlo'p The arithmetic mean of the various speeds that PREFACE IX 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 / J_ metres per 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 t=289. Introducing this value for t, we find that the arithmetic mean of the speeds at this tempera- ture is 460 / - metres per second . . . 2 (a) V P which is the same as 1022 /i miles per hour .... 2 (6) 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 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 X PKBFACE 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 defiant 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"** ; 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 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 PREFACE XI (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 was found to be the sixth power, which is 10^* ; from which it followed that the actual number of molecules is to be looked for within the group of numbers that intervenes between 10'^-=- ^1000 and lO^^x VlOOO, i.e. it is a number greater than 3-16 x 10^^ and less than 3"16 x 10^^. 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^'' 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 XU PEEFACE the earth's atmosphere contribute nearly in the following proportions : > — Nitrogen . . . 4 x 7810 000000 000000 molecules of Nj Oxygen .... 4 x 2090 000000 000000 „ O2 Argon 4x 100 000000 000000 „ A Carbon dioxide . 4 x 4 000000 000000 „ CO2 Neon (about) . . 4 x 100000 000000 „ Ne IT V /I N . r 10000 000000) „^ Helium (perhaps). 4x| ^^ goog qoOOOoI " ^' 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- 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 1 A vacuum formed by pumping air out of a receiver till the residual pressure is reduced to the 10,000,000th of an atmosphere, would usually be spoken of as an exceedingly high vacuum. Nevertheless, it follows from what has been mentioned in the text, that, throughout this so-called vacuum, there remain about 4,000,000,000 molecules in every cubic millimetre of the space within the receiver. To get the numbers of molecules of the various gases, within each cubic millimetre, strike off the last seven ciphers from each of the numbers of the table in the text. PEEFACE xm 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 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. XIV PREFACE we are forced to admit that either that im- mense number of orbital motions have been on the average executed by electrons within the mole- cule during each of its flights, or else that periodic motion of some one or more of the electrons has been going on of so complex a kind that when fully resolved it furnishes that immense number of individual revolutions. It is now no longer surprising that the temporary perturbation caused while two molecules have been grappling with one another has in most instances abundant 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. In what way the lines of the spectrum of a gas are brought into existence, may be more definitely understood by remembering that — as can be proved ^ — the motion of each individual electron within a gaseous molecule, however complex that motion may be, is in all cases susceptible of being resolved into "elliptic partials," each of which produces the same physical effects as would an electron revolving pendulously, and therefore with unvarying periodic time, in the corresponding ellipse. Now, an electron ' See the paper on "The Cause of Double Lines, &c. &c.," in the Scientific Transactions of the Royal Dublin Society, vol. iv., series ii. p. 563 (1891). In the analysis of motion which is not restricted to one plane, elliptic partials are what correspond to the harmonics that present themselves when motion in one plane is resolved by- Fourier's Theorem. PREFACE XV when undergoing periodic motion of any kind, pro- pagates electro-magnetic, that is to say luminous, waves through the surrounding aether ; and when the motion is of the simplest kind, viz. pendulous elliptic motion, what it will transmit through the sether is a single undulation which will have the same periodic time as the elliptic motion. A luminous undulation of this kind produces a single line in the spectrum of the gas. Accordingly, each partial whose periodic time is such that the re- volutions in its ellipse are repeated some number of times between 60,000 and 120,000, in the 6,000,000,000th of one second of time, will furnish a line in the visible part of the spectrum, and its existence is made known to us when we see the line in the spectrum. Partials which have other periodic times produce lines either in the infra-red or in the ultra-violet parts of the spectrum, and though lines so situated are not seen by the eye, their presence can be detected by photography, by observations with the bolometer, and in other ways. If any of the electricity within a gaseous molecule remains in bulk and is not divided into separated electrons, and if it be capable of moving within a confined space, it will be set surging by the more definite movements of the separate electrons in its neighbourhood. This would give rise to subsidiary effects in the spectrum of the gas, in the neighbour- hood of the definite lines produced by the separate electrons. Such subsidiary events have in many instances been observed. b XVI PREFACE 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 either be vapourised and rendered incandescent in the arc- light, or can be 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 due to 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. PKEFACfi xvil Let us hope that this great discovery, which has thrown its shadow so plainly before us, 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 effect, which we may hope will within a moderate time be 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 Pro- fessor J. J. Thomson — all these and some others are, as it were, so many letters of the writing which has to be deciphered. Preliminary approaches to the actual deciphering have been attempted by the wi'iter. Along with the above we have the dyna- mical data that the spectrum as we see it, is caused by motions given to the electrons, or more probably to some few among 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 molecule through its 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 XVUl PREFACE caused by an encounter have not time to have passed away during any part of the transit of a molecule 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. While 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 caUed 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 sohd and liquid elements when rendered incandescent by heat, as well as in that still more familiar case when the electrons that lie near the surface of a body have been set in motion by incident light falling upon them. 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 lumi- nous undulations in the surrounding aether. (1) In olden times the best conception that men could form of a gas was that it was somewhat like a froth of bubbles in which the molecules PREFACE XIX 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. (2) 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. (3) 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, equal in amount to the sum of its negative electrons, but not like the negative electricity split up into separate electrons. Here, then, the XX PREFACE electron is introduced to us as a new entity. (4) Is not it, too, a complex system within which La- 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? (5) And do not the same questions arise with respect to these? for there is no appearance of there being any limit to the miauteness of the scale upon which nature works. (6, &c.) Nothing in nature seems to be too small to have parts incessantly 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 should 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 before and after each correction it is so firmly fixed in its frame that the most effectual use can be made of it. G. JOHNSTONE STONEY. September 1907. AUTHOR'S PREFACE TO THE SECOND EDITION The very flattering reception accorded to the first edition of this work has encouraged me to spare no pains to bring it up to date. Recent researches have, fortunately, shown it to be unnecessary to make any very sweeping alterations in the text, as their results are in satisfactory agreement with the theory originally set forth in it. Nothing has oc- curred since last year to shake the faith of physicists in the electron theory, and the work of its detailed application is proceeding steadily. A significant sign of its acceptance is the almost complete ab- sence of attempts to formulate electrical theories not based upon electrons. The translation of this work into German and Italian goes to show that its distinctive features are also recognised abroad. I have embodied some of the latest contributions to the theory in an Appendix. I wish to thank the numerous reviewers for their XXll AUTHORS PREFACE uniformly friendly judgments and suggestions, and especially Mr. Joseph A. Gillott, Dr. T. M. Lowry, and the expert of the Chemists' Club of New York, for pointing out certain errors and omissions. E. E. FODRNIER d'ALBE. Chapelizod, December 1907. CONTENTS CHAPTER I. Introduction II. The Origin and Development of the Electron Theory ..... III. The Electron at Rest — 1. Properties of the Electron 2. Electrons and Matter 3. Distribution of Free Charges 4. Energy of Position : Potential 5. Condensers 6. Specific Inductive Capacity 7. Electrostatic Machines IV. The Electric Discharge — 1. Discharge in General 2. Discharge through Insulators . 3. Discharge through Gases 4. Discharge through Solid Conductors 5. Discharge through Liquids 6. Discharge through a Vacuum . V. Thermo-Electricity .... VI. Voltaic Electricity VII. Electro-Dynamics .... PAGE 1 23 25 35 39 52 62 65 69 72 75 83 98 114 121 134 146 XXIV CONTENTS CHAPTEB PAGE VIII. Magnetism . .... 159 IX. Induced Currents 176 X. Radiation 190 XI. Measurements concerning Electrons . 206 XII. ELEcraiciTT and Light .... 222 Refraction — Dispersion and Colour — Absorption and Reflection — Polarisation — Double Refraction — Optical Rotation. XIII. Magneto-Optic Phenomena . . 237 Zeeman EfEect — Faraday Effect — Kerr Effect — Macaluso-Cor- bino Effect. XIV. Electricity, Heat, and Magnetism . 252 Hall, Leduc, Nemst and v. Ettings- hausen Effects — Longitudinal Effects. XV. Radio-Activity 264 XVI. Constitution of the Electron . . . 280 XVII. Dimensions or Electrical Quantities . 291 Appendix 305 References . .... 319 Index . 323 LIST OF DIAGRAMS Dr. G. Johnstone Stonet • • Frontispiece FIG. PAGE 1. Matter and Electricity Compared 24 2. Measurement of Electric Force 27 3. Equipoteutial Surfaces . 42 4. Proof of Law of Potential 43 6. 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 . 197 29. Perrin's Experiment 208 30. Thomson's Deflection Experiment . 209 31. Zeeman Effect .... 245 32. Thermo-magnetic Phenomena . 253 33. Transverse Effects .... 265 34. Longitudinal Effects 259 36. A Combination Diagram . 261 "Oo 6um gWme "Oe Agus ononA ha ti-6ineAnn THE ELECTRON THEORY CHAPTER I INTEODUCTION 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, theirefore, henceforth the first step in the knowledge of electricity. In presenting it to the reader, my first objects will be simplicity and 2 THE ELECTEON 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 fxilfils 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 INTRODUCTION 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 atom 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 hkely 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 s upplemen ts 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 TKE ELECTKON THEOKY 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. I 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 — feU into line, and one department of electrical science after another, crystal on crystal, chcked 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 m,eaning ! 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 O THE ELECTRON THEORY frames a theory he is delighted to find it confirmed everywhere. "\Mien 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 puzzhng 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. Frankhn's theory, in order to be consistent, had 8 THE ELECTBON 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 (p. 86). The one-fluid theory, as we have seen, did not succeed very well in explaining frictional electri- fication. Hence, when, in 1759, Symmer brought lO 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 I I 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 I 3 varying current what Oerstedt had done for a steady one — viz. established the hnk 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 the 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 : ^ ' See Scientific Proceedings of the Royal Dublin Society, Feb, 1881, p. 54. Phaoi. Mag., May 1881, pp. 385, 386. ORIGIN AND DEVELOPMENT I S "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 ]^Q-2o c< amperes " (now called absolute electromagnetic units of quantity). This figure compares well with the latest value for the electron — viz. I'l x lO-^" 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 Pliicker 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 ELECTRON THEOBY 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 Royal 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 HaU 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:^ — "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 I 7 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 difEculty 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- rausoh had, with infinite patience, traced the migra- tion of the ions through the liquid in the electrolytic cell, discovered their mutual independence, and I 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 Hoff's 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 20 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 Eontgen 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 confirmed 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 2 1 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, Drude, 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, Larmor, 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 [_ 1. Properties of the Electron. — The electron is the smallest electrified, body capable of separate existence. Its mass is approximately O'SlxlO"^^ grammes. Its radius is roughly estimated at 10~i^ 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 10^13 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 trillion trillion times (more precisely, 10*^ times) greater than gravita- tional attraction, which accounts for the weight of bodies on the earth's surface and the motion of S3 24 THE ELECTRON THEOEY the heavenly bodies. How enormous it is may be realised by the following imaginary experiment. Let two masses, M M^ (Fig. 1), say of lead, weighing 1 gramme each, be placed 1 cm. apart. They wUl attract each other with a force of 6*6 x 10"* ^k ^ dynes, a force quite[too small to be ^ measured by any known instrument. ) But now let 2 grammes of pure negative electricity, E Ej, made up of electrons, be placed side by side ^j^ ^f^ at the same distance. They will repel each other with a force of ^ ^' 31-4x103* dynes, or 320 quadrillion Fig. 1. ^^„„ , 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 2$ 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 1'2 x 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-53xl0i^ 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 unitirig 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 2 6 THE ELECTRON THEOBY 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 REST 2 7 between the atoms and these electrons is not rigid, wc 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 1 be negatively charged, so as to repel each A B other, and remain 1 cm. apart. Then the ^^'^" ^' force between thom is easily proved to be Tr^th part of their weight. If their radii are 1 mm. each, what number of free electrons will suffice to produce the necessary repulsion ? 2 8 THE ELECTRON THEORY The following data are easily calculated : — Volume of each ball . . . 4-2 x 10-^ cm. Weight (density 8-93) . . 375 x 10"^ gr. Force of repulsion . . . 1-87 x 10"' 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 102*. Now each of our balls having a volume of 4-2 X 10-3 c^ cQj^ ^oui^ contain (1-23 x lO^*) (4-2 x 10-^) atoms, and double that quantity of detachable elec- trons, or 10,300 trilUon. The ratio of detachable electrons to extra electrons is therefore 10,300 trillion „ , .„. — i-— - — rpp — = 8 billion. 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 ELECTEON AT REST 29 repulsion by remoTing 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-millionth 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~^^ dynes, (b) 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~i^ 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~^^ 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~^ cm.).^ 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~^ 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 lO"^*^ The force then becomes ^^^^-16^ " o^ 1"16 X 10"^ dynes. 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"^) : 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 v?hich the inter- vening space is fiUed up. Matter free from electrons would have no electrical effect whatever, and can be theoretically r^laoed 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 3 1 would give it a speed measured by the ratio of the force to the mass, or — y«^;o-; = 19x10- <=- 0'61 X 10 ''^ 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 h«ve seen, 1*16 x lO"^ dynes. The centrifugal force of a body of mass m describing an orbit of radius R with a velocity t; is '^ • Substituting for 32 THE ELECTEON THEORY m the mass of the electron (0-61x10-" gramme), and for K its distance from the centre of the atom (10-^ cm.), we get — 0-61 X 10-27 ^ ^ 1-16x10-3 = 10- which gives v = ±1-38x10^ cm. per second. This orbital velocity of the electron, though large, is quite conceivable, inasmuch as it is still less than rr^th. 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 2-2x101^ or 2200-Jiillion. As we shall see below, the revolving electron sends out ether-waves into space with the velocity of light (3 x lO^" cm. per second). Hence the length of these waves is ^^10^ or 136 X 10-^ mm. 2-2 X 1015' 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-' cm. instead of 10-*, 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, 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-^ mm. This light is also invisible, being about six times longer in wave than the most extreme red light of the spectrum. It is " infrar-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""^ 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 sufiSciently free to pass from one atom to another. If they surround a metal, they 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 off'er 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 ELECTRON 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 ELECTKON 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 milhon 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 unnjth 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 ELECTRON 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 ^pinus 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"^" " 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 ( = ^^ gramme). Now since one electron or positive atom repels another at 1 cm. with a force of 1-16 x lO'i^ dynes,i and the force varies with both masses, the repulsive force of 1 djme would be produced by 2-93 x 10' electrons, or 2930 milhon. 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. (b) 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 40 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 wiR 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 4 1 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 yfo mile ahead. When Achilles runs that distance, the tortoise is tis^-^ 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 "'' 100 + 10,000 '*' 1,000,000' ^■ 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 -Vir. The tortoise will therefore have gone exactly ^V of a mile when Achilles overtakes it. Another example is this. If you stand on a bridge over two parallel Hues 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. 42 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 iato 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 KEST 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 ELECTRON THEORY P and Q. In the next compartment, the work ■will be ^ instead of y, and the next again it will Extending this to infinity, the total work done ( = the total potential energy) is W W W W W+T+4+^ + i6 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 At R it is At S it is 2W-W=W. In other words, the potential energies at P, Q, R, S are as 2:l:i:i or 1 : i : i : i. THE ELECTEON 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 frovi 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 cm., 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 | erg. Hence the total potential energy equal 2 x J erg = 1 erg. Since E P = l 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 repelHng 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. (b) 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 very surface of the sphere. It is -5, 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 2 E — 1 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-l) + l E 2 ~2- The average potential during formation was, there- E fore, 2^, and since the total number of units to be brought to that potential was E, the total energy consumed in the process was ^^2R-^R- Or, if V is the final potential 5, the total energy consumed is ^ E V. 48 THE ELECTEON 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 (5-6x101'') 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 i ^ ergs = i^ J '- = 16 X 10'* 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 matter consisting exclusively of positively charged atoms ranges from 16 x 10^^ ergs to 4 X 10^* 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 Ej^, and on the second body Eg, and their distance R, the potential is E E ^5^^ ■ This potential is mutvxil, as it only depends upon their relative position, and it does not matter whether E^ has been brought up to Eg 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 signs, say E^ and —Eg, and the result ' „ — ^ 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^ and — E^ are equal, the total potential at any point equidistant from them is zero, being in one case -^ and in the other — ^. 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^ is a luminous point and AB a reflecting surface, Eg will be the " image " of Ej. We might have any other such points on the side of Ej, 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 it to earth), opposite charges I would have to be distributed over the surface, so as to make up for the charges taken away, and keep £^ the force at every point above the ~^ 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 ■ ■ 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^ and Eg is 2 R, the distance of the plane from E^ is R. Now the work required to bring a company of electrons from infinity to E within R cm. of the charge Ej was -^ while Ej was alone in space. This amount has become zero at one point, owing to the presence of Eg. 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 5 1 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 d3Tie 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 THEOBY 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 maxiTYium. 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 deahng 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. f THE ELECTRON AT REST 53 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 Fig. 6. 54 THE ELECTRON THEORY the repulsion of the electrons outside the cone is practically imperceptible.^ 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., ah, of the plane will be (p. 38) — 1x1000 . , -3qq^= J^ 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^ and PcZi, and let Pc^ be = 2 Pc. Then if the imaginary surface c^d'- 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 Pd^ to Pe\ 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 THE ELECTRON AT REST 5 5 out a new surface, c^e^ whose size is the greater the more Pc^ slants to the surface. This slant compen- sates the slant of the push of the repelling electrons on c^e\ 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 (radms)2, or, since the radius is 100 cm., the total force is 27r X 0-1 X 1002 dynes = 27rx 1000 dynes, or 277 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 imit = 27rtr 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. $6 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^Bi 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\ for instance, the force due to AB is 27rcr, and the force due to A^B^ is —27ra, •pi and the sum of the two forces is zero. In other words, the positive charge on A^B^ "neutralises" the negative charge on AB for all infinite space outside the two ° ° surfaces. Fig. 8. What is the difference of potential be- tween AB and A^B^ ? In other words, what work wiU have to be spent on a company of electrons to bring it from A^B^ 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 27r