LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Class THE ELECTRON THEORY DR. G. JOHNSTONS STONEY From a photograph by Elliott <& Fry. Frontispiece. THE ELECTRON THEORY A POPULAR INTRODUCTION TO THE NEW THEORY OF ELECTRICITY AND MAGNETISM BY E. E. FOURNIER n'ALBE \\ B.Sc. (LOND.), A.R.C.Sc. COMPILER OF "CONTEMPORARY ELECTRICAL SCIENCE" WITH A PREFACE BY G. JOHNSTONE STONEY 'ith Frontispiece, and Diagrams in Text LONGMANS, GREEN, A*ND CO. 39 PATERNOSTER ROW, LONDON NEW YORK AND BOMBAY 1906 All rights reserved SP PREFACE IN 1811 nearly a hundred years ago Avogadro promulgated the important law which bears his name, and which gives expression to the fact that all the more perfect gases, when reduced to the same pressure and temperature, will contain within a given volume the same number of gaseous mole- cules. The fact was established: but the reason why it is so was not then understood, nor till long afterwards, when in the forties and fifties of the last century some of the activities that go on within gases became gradually known. Until these later dates it was erroneously supposed, even by careful students of nature, that natural objects which to our senses appear at rest such as stones, coins, books, air which has been left for a long time undisturbed within a room are in reality devoid of any internal motion. As to gases, one of the illustrations made use of in those . days to help students to picture what they were supposed to be like, was that the molecules of a gas may perhaps resemble the stationary bubbles of a froth, which by expanding when warmed, contracting when 102823 vi PREFACE cooled, and by pressing against one another and against the walls of a containing vessel, behave in these respects very much like a gas. Under this view, Avogadro's Law was expressed by saying that the bubbles, or quasi-bubbles, are all of the same size whatever the gas may be, provided that they are compared with one another when at the same temperature and pressure. It was about sixty years ago when there appeared the first glimmerings of the knowledge which has since ripened into that which we now possess, that neither the molecules of any natural object nor the parts of which those molecules consist are ever at rest; that, on the contrary, swift and orderly movements are ever in progress among them and within them; and that where bodies appear to us to be stationary, it is only be- cause this great internal activity is on too small a scale, the parts moving too tiny, and the motions subject to too rapid changes of direction for senses like ours even when assisted by the micro- scope to obtain any suggestion that all this activity is going forwards. Accordingly, until other means than direct observation of arriving at the truth were discovered, every one remained under the delusion that the objects about us on the earth could be " brought to rest" i.e. absolutely freed from every motion except the celestial motion, which is consequent upon their being on a planet PREFACE Vll which rotates upon an axis, revolves in an orbit round the sun, and accompanies the solar system in its peregrinations through space. There was one man an Englishman who above sixty years ago perceived that this view of nature was a mistake, at least with reference to matter in the gaseous state. J. J. Waterston, in 1845 submitted a memoir to the Royal Society, in which he showed that the recognised properties of the more perfect gases indicate with emphasis that instead of consisting of stationary molecules pressing against one another, they are in reality swarms of much smaller bodies, so small that they leave much of the space unoccupied, in which they dart about amongst one another with extra- ordinary activity, and produce gaseous pressure by encountering one another or where turned back by the walls of a containing vessel. Waterston's contention led to results at variance with the views entertained by scientific men at the time, and his great discovery with the arguments in favour of it, were withheld from publication until long after- wards; so that this great advance in knowledge did not become generally known until, shortly after- wards, Professor Clausius of Geneva rediscovered the kinetic constitution of gases. His announce- ment of it was received with much scepticism. However, Clausius persisted, and in a masterly series of papers published in the later forties and viil PREFACE in the fifties of the nineteenth century he met objections, and piled proof upon proof, until the evidence could no longer be resisted. In the later developments of the theory he was assisted by other scientific men, among whom J. Clerk Maxwell was pre-eminent. Until some information can be acquired respect- ing the magnitudes with which we are dealing when investigating any branch of nature's opera- tions, we continue to be unable to form a satis- factorily clear notion of those operations. In the domain of Molecular Physics the first magnitude that was ascertained was when Clausius succeeded in estimating the speeds with which molecules in a gas are travelling about. At any one instant the individual molecules are darting about with very different speeds, but at each temperature there is a certain mean speed towards which the encounters which prevail within a gas tend to bring any speeds which too much differ from it, and round which the innumerable speeds tend to group themselves. The mean speed so defined is not the arithmetic mean of the values of v, but the square-root of the arithmetic mean of the values of v 2 . This mean speed Clausius succeeded in finding to be about 485 /^ metres per second . . . 1 (a) PREFACE ix Where T is the absolute temperature of the gas estimated in centigrade degrees, and p the relative specific gravity of the gas compared with air. Ex- pressed in miles per hour this mean speed is / =^ miles per hour \/ 273*p 1085 The arithmetic mean of the various speeds that prevail among the molecules is a different mean from that given above. It is somewhat less, and to obtain it we multiply the above value by 0*92132. Thus the arithmetic mean is 447 A / 97^7- metres P er second. Again, the temperature of our laboratories when experiments are being made in them may be taken to be about 16 C., which is the same as r=289. Introducing this value for r, we find that the arith- metic mean of the speeds at this temperature is 460 /- metres per second . . . 2 (a) V P which is the same as 1022 /- miles per hour . . . . 2 (b) so that, in the air about us, and at the tempera- tures to which we are most accustomed, the mole- cules of its principal gases are travelling with X PREFACE speeds of which the arithmetic mean is more than 1000 miles per hour. In order to get the arith- metic mean for each gaseous constituent of our atmosphere we must insert in the last expression the value of p for each gas. We thus find what it is in nitrogen, oxygen, argon, aqueous vapour, and the rest. The next important molecular magnitude to be discovered was when Professor Maxwell In 1859 and 1860 deduced from observations on the viscosity of gases, and also from the rate of diffusion of olefiant gas into air, the mean length of the little straight path along which a molecule of air darts between consecutive encounters. It is, at the temperature of 15 C. and at the pressure of an atmosphere, about 7'6 eighthet-metres ... 3 which is the mean of three determinations made by Maxwell. By an eighthet is to be understood the fraction represented by a unit in the eighth place of decimals, or by the symbol 10~ 8 ; and eighthet- metre is a convenient abbreviation for eighthet of a metre in like manner as a quarter-inch means the quarter of an inch. It is worth taking notice, here, that the mean length of the free paths of the molecules be- tween their encounters, although a giant among molecular magnitudes, falls short of the smallest PREFACE XI interval which the microscope can detect. Two minute specks on the stage of a microscope, even if separated by twice this interval, would never- theless be blurred together into the appearance of a single object, when viewed under the most favourable conditions, through the best of micro- scopes handled with the utmost skill. By comparing this small measure with the aver- age total distance which the molecule travels in a second, which we have found to be 460 metres (see equ. 2 (a)), we learn that the path pursued by the molecule within one second is a zigzag course, divided on the average into 6,000,000,000 little straight free paths between the encounters that it meets with. When Maxwell had determined the average length of the free path, it was easy to form a preliminary estimate of the number of molecules that are present; and, accordingly, this was at- tempted by the present writer in 1860, immediately after the publication of Maxwell's papers. What was sought in this preliminary effort was to deter- mine which power of 1000 is nearest in the geo- metric series to the number of molecules in a cubic millimetre of gas. This v a s found to be the sixth power, which is 10 18 ; from which it followed that the actual number of molecules is to be looked for within the group of numbers that intervenes between 10 18 -f x/1000 and 10 18 x A/1000, xii PREFACE i.e. it is a number greater than 3*16 x 10 16 and less than 3*16 x 10 19 . Other determinations of this im- portant physical constant have since been made, and some from data admitting of much closer approximation. From these we learn that we may now accept 4 x 10 16 as a trustworthy and reasonably close approximation to the number of gaseous mole- cules within a volume which is not far from being one cubic millimetre the gas, or mixture of gases, being at or near standard temperature and pressure. To this number of molecules within each cubic millimetre of dry air the principal constituents of the earth's atmosphere contribute nearly in the following proportions : Nitrogen .... Oxygen .... Argon 4 x 7810 000000 000000 molecules 4x2090000000000000 4 x 100 000000 000000 4 x 4 000000 000000 4 x 100000 000000 / 10000 000000) \ or 5000 000000 j " of N 2 2 A C0 2 Ne He Carbon dioxide Neon (about) .. * Helium (perhaps) . Minor constituents are also present, but in smaller numbers. These are krypton, xenon, and hydrogen, with probably a few molecules of ammonia and some of the oxides of nitrogen ; and of course there will be a variable amount of aqueous vapour present, if the air has not been completely dried. These various determinations enable us to con- struct our first picture of what each cubic milli- PREFACE xiii metre of the air about us really is. We are to imagine these enormous swarms of little missiles dashing about in every conceivable direction, each of the missiles successively encountering and occasionally grappling with about six thousand millions of its neighbours every second, and dart- ing along the free paths between these encounters with various speeds, but speeds that are so high that they average more than a speed of 1000 miles per hour. Wonderful as this picture is, we shall presently find that it falls almost infinitely short of the far more astonishing reality. We are enabled to see that this is so, by being already in a position to advance one step nearer to the reality, and by the prospect that then opens before us of further extensions into the still more deeply seated operations which are being carried on by nature. In fact While the investigations which revealed to us the kinetic constitution of gases, were in progress in the last century, another line of inquiry was being simultaneously pushed forward which touched upon deeper mysteries of nature. As an introduc- tion into this new region of exploration it will be convenient to recall one of the facts already referred to, that while the free paths of the molecules have very various periods, their average duration is about the six thousand millionth of a second. Let us then compare this brief duration with the vastly XIV PREFACE smaller periodic times of the alternating event which we call light. When this is done it is found that while a molecule of air has been travelling between one encounter and the next, 60,000 double vibrations of red light have on the average taken place, and twice that number of the extreme violet ray; and as the periods of all the motions within a molecule which give rise to visible spectral rays must lie between these limits, we are forced to admit that either that im- mense number of orbital motions have been on the average executed within the molecule during each of its flights, or else that periodic motion of some kind has been going on of so complex a kind that when resolved it furnishes that im- mense number of constituents. It is now no longer surprising that the temporary perturbation caused while two molecules have been grappling with one another has in most instances abun- dant time to pass away early in the interval between two encounters, so as to leave the greater part of the motions within the molecule to be executed in the undisturbed manner which the definiteness of the lines of a gaseous spectrum attests to us. The chemical elements are some of them gases in the state in which they usually present them- selves to us. A few of the others can be vapourised in a Bunsen's burner; and the rest can be vapourised PREFACE XV* and rendered incandescent in the arc-light, or, at all events, brought into a condition, when an electric spark passes between electrodes of the element, such that molecules will detach them- selves and travel along free paths as in a gas. In all these cases each element furnishes its charac- teristic spectrum of defined lines, each of which is a ray of light with its own definite period of undulation. These spectra make manifest the marvellous regularity of the motions that go on within the molecules of each element, when its molecules are freed from being interfered with by neighbouring molecules; and at the same time the complexity of that motion; with other information of the most instructive kind as regards the rela- tions in which the elements stand to one another. But the greatest achievement of all, and one to which we may reasonably look forward, has not yet been effected. No one has yet succeeded in tracing back from the periodicities, the intensities, and the other properties of the lines of the spectrum of an element, what that motion of the electrons within the molecules must have been to have been able to produce these precise effects. The information is given to us by nature in the spectrum exhibited to us. It is written there ; but in a language which has not yet been deciphered. Let us hope that this great discovery, which has thrown its shadow so plainly before us, XVI PREFACE will have been made before long. The ground has been prepared by many notable investigations Rydberg's, and Kayser and Runge's, on the series of lines which exist in the spectra of the elements, and the relationships which these investigations have brought to light ; the study of the Zeeman's effect, which we may hope will be within a moderate time made much more complete than it now is; and the many facts with reference to corpuscles, each of which either is or contains one electron, that have been elicited with great skill by Professor J. J. Thomson all these are, as it were, so many letters of the writing which has to be deciphered. Along with these we have the dynamical data that the spectrum as we see it, is caused by motions given to the electrons, or more probably to some one or two amongst them, by the general shaking up of a molecule when it has left off grappling with another molecule, and when its motions have settled down into that natural permanent state which is consequent upon whatever is the natural periodic swing within the molecule as modified by the fact that energy is escaping from the electrons into the surrounding aether. If the gas is condensed into a liquid or becomes a solid, the free space about its molecules disappears, or at least so much shrinks, that the perturbations caused by an encounter have not time to have passed away during any part of the transit of a molecule PREFACE XVll between one encounter and the next. Accordingly the spectrum of this object is no longer due to the natural swing of the motions within molecules freed from outside interference. When a gas is being condensed the motions within a molecule which have been perturbed during an encounter continue to be confused motions during an in- creasing proportion of the shortened flight of the molecule. Accordingly the lines of its spectrum become less sharply defined : as the condensation of the gas progresses its spectral lines widen, and ultimately they run together and present the appearance which is called a continuous spectrum, which sometimes occupies part, in other cases occupies the whole extent of the spectrum. Of this kind are the spectra of most solid and liquid elements when rendered incandescent by heat, or when the electrons that lie near the surface of the body have been set in motion by incident light falling upon them; which latter is the state of things most familiar to us. In all cases we may take it that objects become visible when the negative electrons and the mass of positive electricity within each chemical atom have been displaced in regard to one another, and set swinging in the way that can excite luminous undulations in the surrounding aether. In olden times the best conception that men could form of a gas was that it was somewhat xviii PREFACE like a froth of bubbles in which the molecules of the gas are represented by the bubbles of the froth. In those days even scientific men were not aware that any activities whatever were going on within calm air. Afterwards, when the kinetic constitution of gas became understood, the earlier crude conception was exchanged for a better one in which the molecules were represented as missiles travelling about with marvellous energy, whose numbers it was possible to estimate, as well as the average speed with which they dash about, and the average length of their little journeys. Another conception of nature, both truer and more recondite, was attained when it became under- stood that the molecules are far more than merely missiles, that while they are travelling about subtile events are all the time going on within each of them, involving rapidly alternating displacements of the electricity with which they are charged, and as a consequence the transmission of alternating electro-magnetic stresses in the form of waves through the surrounding aether. We thus are introduced to smaller entities than the missiles, to the negative electrons of which the number in each chemical atom seems, from a remarkable investigation by Professor J. J. Thomson, to be about the same as the number of times by which its atomic weight exceeds that of hydrogen ; with corresponding positive charges in each atom, PREFACE XIX equal in amount to the sum of its negative electrons, but not like the negative electricity split up into separate electrons. Here, then, the electron is introduced to us as a new entity. Is not it, too, a complex system within which in- ternal events are ever taking place ? And when this question can be answered shall we not be in the presence of the inter-active parts of an electron? And do not the same questions arise with respect to these? for there is no appearance of there being any limit to the minuteness of the scale upon which nature works. Nothing in nature seems to be too small to have parts in- cessantly active among themselves. Our present position is one which has been reached by slow steps, and we may reasonably hope that our successors will be able to continue to advance, as there is no visible limit. The inquirer who is now entering upon this depart- ment of the study of nature will find it much to his advantage to take as his starting-point the picture of nature, which has taken form in the mind of a thoughtful student of the present state of our knowledge, such as is presented in the fol- lowing pages. This, however, he shbuld entertain, not like a stereotype plate which must remain as it is, but rather like well and firmly set movable type, susceptible with ease of any im- provements the future may bring with it, while XX PKEFACE before and after each correction it is so firmly fixed in its frame that the most effectual use can be made of it. Before concluding this preface, I should wish to invite the attention of mathematical physicists to the remarkable table of dimensions which Mr. Fournier has given in his last chapter, in which the obscure uncertainties of ' the usual tables are avoided by the natural expedient of adopt- ing four fundamental units viz. units of mass, electricity, length, and time. Compare this simple system with those unsatisfactory systems into which specific inductive capacity and magnetic permeability have to be admitted without dimen- sions that can be assigned. G. JOHJSTSTONE STONEY. September 1906. CONTENTS CHAPTER PAGE I. INTRODUCTION 1 II. THE ORIGIN AND DEVELOPMENT OF THE ELECTRON THEORY 7 III. THE ELECTRON AT REST 1. Properties of the Electron . . 23 2. Electrons and Matter ... 25 3. Distribution of Free Charges . . 35 4. Energy of Position : Potential . . 39 5. Condensers ..... 52 6. Specific Inductive Capacity : . 62 7. Electrostatic Machines . . .65 IV. THE ELECTRIC DISCHARGE 1. Discharge in General ... 69 2. Discharge through Insulators . . 72 3. Discharge through Gases . . 75 4. Discharge through Solid Conductors . 83 5. Discharge through Liquids . . 98 6. Discharge through a Vacuum . .114 ^ V. THERMO-ELECTRICITY . . . . .121 VI. VOLTAIC ELECTRICITY . . . .134 VII. ELECTRO- DYNAMICS . . . . .146 xxl XXll CONTENTS CHAPTER PAGE VIII. MAGNETISM . . . . . . .159 IX. INDUCED CURRENTS . . . . . 176 X. RADIATION . , . . . . . 190 XI. MEASUREMENTS CONCERNING ELECTRONS . 206 XII. ELECTRICITY AND LIGHT / . . . 222 Refraction Dispersion and Colour Absorption and Reflection Polarisation Double Refraction Optical Rotation. XIII. MAGNETO-OPTIC PHENOMENA . . . 237 Zeeman Effect Faraday Effect Kerr Effect Macaluso-Cor- bino Effect. XIV. ELECTRICITY, HEAT, AND MAGNETISM . 252 Hall, Leduc, Nernst and v. Ettings- hausen Effects Longitudinal Effects. XV. RADIO-ACTIVITY . ;Y. ; * . . , 264 XVI. CONSTITUTION OF THE ELECTRON . . .280 XVII. DIMENSIONS OF ELECTRICAL QUANTITIES . 291 REFERENCES 305 INDEX . 309 LIST OF DIAGRAMS Dr. G. JOHNSTONE STONEY Frontispiece PIG. PAGE 1. Matter and Electricity Compared 2. Measurement of Electric Force 27 3. Equipotential Surfaces . 42 4. Proof of Law of Potential 43 5. Electric Images 50 6. Force Exerted by Charged Plane . . . * . 53 7. 54 8. Elementary Condenser 56 9. Leyden Jar . 57 10. Specific Inductive Capacity ...... 62 11. Point Discharge 78 12. Glow Discharge 80 13. Discharge through Copper 87 14. Successive Conductors 93 15. Length of Conductor 93 16. Elementary Circuit 96 17. Liquid Conductor 101 18. Thermo-electric Junction 124 19. Thomson Effect 132 20. Electrons passing along a Wire ..... 149 21. Magnetic Force of Electrons 152 22. Attraction of Two Circuits 154 23. Attraction of Current Elements 157 24. Constitution of a Magnet 162 25. Coaxial Solenoids 170 26. Explanation of Polarity 171 27. Magnetism of the Earth 188 28. Electric Waves in Wires . . .' * V- -< 197 29. Perrin's Experiment . . . . , . . . 208 30. Thomson's Deflection Experiment ..... 209 31. Zeeman Effect . . . .... . 245 32. Thermo-magnetic Phenomena 253 33. Transverse Effects 255 34. Longitudinal Effects 259 35. A Combination Diagram 261 xxiii 'Do Cutn T)e THE ELECTRON THEORY CHAPTER I INTRODUCTION THE object of this work is to place before the reader a concise and connected account of the new theory of electricity and magnetism, which, though, gene- rally accepted, has as yet hardly found its way into the elementary textbooks. The new theory gives us a grip of electrical and magnetic phenomena which was quite unattainable so long as we knew nothing about the real nature of electricity. We now know that electricity is a kind of subtle fluid consisting of electrons, or very small corpuscles, some thirty thousand times smaller than the atoms of ordinary matter. The electron theory is that theory which " reduces all electric and magnetic phenomena to the distribution and motion of these electrons. To gain a clear grasp of the nature and properties of the electron is, therefore, henceforth the first step in the knowledge of electricity. In presenting it to the reader, my first objects will be simplicity and A 2 THE ELECTRON THEORY lucidity, and I hope to enable those readers whose mathematical attainments have not transcended the elementary rules of algebra to master the essential principles of the science, so as to be able to apply them to practical problems. A theory has two functions one is to register a large number of isolated facts in due order, and the other is to give us an insight into their connection with each other, so as to be able to deduce one from the other and to predict new facts and produce effects hitherto unknown. The electron theory fulfils both these functions in a manner which no previous theory of electrical phenomena has been able, even remotely, to approach. In no branch of human knowledge have greater difficulties been encountered in framing an adequate theory than in the science of electricity. The be- wildering variety of the phenomena, the constant stream of new facts and discoveries, the revolutionary character of many of them, and the intangible nature of the agent itself, combined to render the formula- tion of an all-embracing theory difficult. But the reward of arduous work has been correspondingly great. To-day we know more about the atom of electricity than we do about the atom of ponderable matter. We can contemplate it as a centre of force producing the old phenomena of the pith ball and the gold leaf and the rubbed glass rod. We see it in swift motion in the vacuum tube, and in slow INTKODUCTION 3 motion along the current-bearing wire, now no longer the inscrutable mystery it was ten years ago. We observe its surgings to and fro in the alternating current, and follow the waves it emits across space into the wireless receiver. We imagine its orbital motion round the^-atqm it clings to, and the vista of magnetic phenomena flashes into view. We watch it dragging along that same atom through the electrolytic cell, and gain an insight into the secrets of chemistry such as seems likely to remodel that whole vast science. Not content with having an- nexed practically the whole of physics and chemistry, our new conception launches out into unexplored fields. It hints at the transmutation of the elements, the constitution and destruction of matter, the explanation of inertia, and an electrical theory of mechanics as an answer to the all-pervading influ- ence hitherto exercised by mechanical conceptions. The electron theory, this latest and widest of scientific generalisations, is the fitting reward of 150 years of laborious research. A somewhat unusual circumstance attending its victory lies in the fact that it supplements rather than displaces the older theories. It has something of Franklin's one-fluid theory about it, inasmuch as it links all electric phenomena with the distribution and motion of a kind of gas possessing a pressure and an atomic structure. It supplements the analytical specu- lations of Ampere and Weber by providing the 4 THE ELECTRON THEORY necessary material substratum, and fits itself, lastly, into the ether theories of Maxwell and Hertz by telling us what is at the ends of the lines and tubes of force whose distribution and motion have played such a useful and almost exclusive role in the electromagnetic theory of yesterday. This may partly account for the almost ominous silence with which the new theory has made its appearance in the electrical world. It has not been heralded by a flourish of trumpets, nor has it been received with violent opposition from the older schools. No one man can claim the authorship of it. The electron dropped, so to speak, into the supersaturated solution of electrical facts and specu- lations, and furnished the condensation nucleus required for crystallisation. One after another the molecules the facts of electricity fell into line, and one department of electrical science after another, crystal on crystal, clicked into its place, dispersion first, then electrolysis, then gas discharges, then radium rays, then metallic conduction, and," lastly, magnetism. Nor is the crystal fully shaped yet. The electron theory has to absorb every detail, to assimilate the vast store of accumulated facts, to find a place in the edifice for every loose brick, to strengthen every weak place, and there are still many, though they diminish daily in number and importance. Our textbooks, always shy of innovations, must INTRODUCTION 5 gradually be brought round to the newer views. They must be given courage to speak about " elec- tricity " a word they have lately been chary of using, as it conveyed no meaning! The scientific electrician had become accustomed to deal with " electrification " or "electric quantity" as the only thing he knew, and to leave the use (and misuse) of the word "electricity" to the layman. The electrical theorist found a refuge in differential equations involving pure quantities, and dealt with them by mathematical rules, alias generalisations from the results of experiments in counting. The practician, having no such vast experience in processes of count- ing, but having instead a close familiarity with the behaviour of bodies and substances, also derived from vast experience, found that the habits of thought thus acquired did not assist him towards an intimate knowledge of the nature of electricity. He did his best by annexing Faraday's semi-material "lines of force," and applying them to problems of induction with truly astonishing industrial results. What he will do when he gets a grip of the electron we can only faintly guess. Will the electron theory be final, or will it in turn be superseded by another theory? This is a very pertinent question, but more pertinent for the text- books and professors than for the research worker or the practician. In one sense, no theory is final. A final theory is the death of science. When a man 6 THE ELECTRON THEORY frames a theory he is delighted to find it confirmed everywhere. When he comes across a case where it fails, he should be equally delighted, for he has found a really new truth, a truth not contained implicitly in his theory. But a theory may be final in the sense that Newton's gravitational theory is final. That theory applies to all ponderable matter at distances beyond molecular range. The electron theory applies to all electrified and magnetised matter, and has even been made to include gravita- tion as a special case. If it can bring the whole of electrical and magnetic phenomena into one well- ordered system, not to speak of chemistry and mechanics, it will be of permanent and incalculable value. If it succeeds in analysing the chemical atom, it will abolish one of those puzzling complexi- ties of which the human intellect is so persistently impatient the variety of the chemical elements. Progress in this direction will tend to unify physical science, and leave the road free for advance into those realms of infinitely greater complexity which harbour the phenomena of life. CHAPTER II THE ORIGIN AND DEVELOPMENT OF THE ELECTRON THEORY THE first serious attempt to formulate a theory of electricity as distinct from a vague guess or a pro- visional hypothesis was made by Benjamin Franklin, who announced his one-fluid theory in 1750 in his letters to Collinson. He supposed that a subtle fluid or "electric fire" was distributed throughout the world, that it was attracted by ordinary matter, but that its' particles repelled each other. The fluid can penetrate metals, but not insulators. Being, however, attracted by insulators, like glass, it ac- cumulates at the surface only. To explain why a glass rod should be electrified by friction, Franklin made the fantastic assumption that the glass, being expanded by the heat, takes up more than its ordinary share of the fluid, and seeks to give it up again on cooling. This explanation seems forced; but it should be remembered that frictional electri- fication is, up to the present day, the least explained of all electric phenomena. Franklin's theory, in order to be consistent, had 7 8 THE ELECTRON THEORY to assume that atoms of ordinary matter repel each other, and this was at once perceived to be at variance with the facts of gravitation and cohesion. But how close the agreement is between Franklin's one-fluid theory and the electron theory may be seen by putting the latter into Franklin's language as follows : " Through all corporeal nature one subtle matter is distributed, which contains the reason and cause of all electric phenomena. The particles of this fluid repel each other. All matter in its normal state contains a fixed quantity of this fluid. If any portion of matter is deprived of some of this fixed quantity, it attracts the fluid with a force proportional to the amount it has lost, and repels another portion of matter that has suffered a similar loss. All electric phenomena are due to the dis- tribution and motion of the particles of the fluid." Franklin's theory failed on the question of con- ductors v. insulators. He supposed that conductors could take up any amount of the fluid and store it throughout their substance, while insulators could only store it on their surfaces. The modern version is that conductors take up an additional amount of the fluid, within limits depending upon circum- stances, and store it on their surfaces only. On the other hand, they cannot be deprived of more than the " fixed quantity" mentioned above. But the fundamental difference between the old and ORIGIN AND DEVELOPMENT 9 the new views lies in the use of the words " posi- tive" and " negative." In an evil hour the elec- tricity derived from rubbed glass was called positive electricity, and the electricity derived from amber was called negative. The fact that the two elec- tricities neutralised each other made the terms justifiable : but there was nothing to indicate which kind was the real and only fluid. It was assumed, at haphazard, that the glassy electricity was the fluid, and for 150 years all algebraic signs continued to be placed in accordance with that idea, and they continue so to the present day. Thus we speak of the " positive pole " of a battery as the pole from which the glassy electricity appears to flow, whereas we know now that if there is a flow at all it is towards that same pole, the flow in the reverse direction being insignificant in comparison. This fundamental difference is not apparent in our Frank- linian version of the electron theory above ; but it makes a very radical difference, and places a serious obstacle in the way of popularising a logical ter- minology. We have to learn that the " negative" electricity is the electricity, and the negative current the current. In the present period of transition, great care must be exercised to prevent confusion, and a way of doing so will be indicated later on. The one-fluid theory, as we have seen, did not succeed very well in explaining frictional electri- fication. Hence, when, in 1759, Symmer brought 10 THE ELECTRON THEORY out his two-fluid theory, it met with a wide accept- ance, and continued in active possession until the phenomena in vacuum tubes began to exhibit an essential difference between positive and negative electrification. The fluid theories were marvellously ingenious, considering the poverty of the materials upon which they were based. In the whirl of subsequent dis- coveries, they were like guiding stars faintly visible through a mist. Sometimes they were almost lost sight of in the crowd of new facts and speculations ; but other forces were at work to bring order into the chaos. The greatest force was the advance in measurement. Lane's unit jar in 1781 was the true beginning of electrical science, if we accept the dictum that " Science is measurement." Coulomb's torsion-balance (1784-1788) gave us two new inverse- square laws in addition to the Newtonian one of gravitation. The mathematicians had begun to handle these new laws with fruitful results when the scientific world was startled with Galvani's frog in 1791, and kept in a state of agitation by the long controversy between Volta and Galvani concerning a third fluid, which the latter persisted in calling " animal electricity." Volta's pile in 1799, followed by Cruikshank's and Davy's electro- chemical work, closed the eighteenth century, which left the theory of electricity in wild confusion, and its devotees torn by endless dissension. ORIGIN AND DEVELOPMENT II This state of things, coinciding with the Napoleonic wars, accounts for the temporary collapse of electrical research in the new century. There is hardly any- thing to chronicle between 1800 and 1820, except perhaps young Grotthus's hypothesis (1805) and Poisson's mathematical treatment of electric and magnetic potential (1811), based upon Coulomb's laws. In revenge, the next twenty years brought forth a flood of discovery such as has rarely been crowded into so short a time, and remained un- equalled until the revolution of 1896. Ampere, Oerstedt, Biot, Savart, Seebeck, Ohm, Peltier, Fara- day, Weber, and Joule, all fall within this period. Truly a galaxy of genius and phalanx of philosophy. Oerstedt, in 1820, threw the first bridge between electricity and magnetism. Seebeck connected elec- tricity with heat, and Faraday linked the phenomena of electricity and motion, and laid the foundation of the two great modern theories of electricity and magnetism : Maxwell's ether theory and the electron theory. The latter foundation he laid, however, unwittingly, being personally disposed to consider rather what happened in the medium between bodies than what happened in the bodies them- selves. * It is interesting, in the light of the modern electron theory, to read some passages from Weber's Werke, where he foreshadows the atomic theory of electricity. Thus in vol. iv. p. 279, we read : 12 THE ELECTRON THEORY " Considering the general distribution of electricity, we may assume that an electric atom is attached to every ponderable atom." And again, p. 281 : " Let e be the positive electric particle ; let the negative one be equal and opposite, and let it be denoted by e. Let only the latter have a pon- derable atom attached to it, and let its mass be thereby increased to such an extent that the mass of the positive particle vanishes in comparison. We may then regard the particle e as stationary, and only the +e as revolving round e." [I have italicised the words which show that Weber's con- ception is exactly the reverse of the modern one.] He proceeds : " The two dissimilar particles, being in the molecular state of aggregation described, then represent an Amperian molecular current, for it can be shown that they fulfil the assumptions made by Ampere concerning his molecular cur- rents." Finally, on p. 292 : " The vis viva (leben- dige kraft) of all the molecular currents contained in the conductor increases, while the current passes through in proportion to the resistance and to the square of the current intensity." Substitute " electrons " for " molecular currents," and you have nearly the modern view of metallic conduction. The most important dates in Faraday's career were 1831 and 1833. In the former year he dis- covered electromagnetic induction, and did for a ORIGIN AND DEVELOPMENT 13 varying current what Oerstedt had done for a steady one viz. established the link between electricity and magnetism. This discovery naturally predis- posed him to devote his attention to the happenings in the dielectric medium rather than the conducting substance. And yet he made, two years after, a discovery of transcendent importance which was bound sooner or later to lead up to an atomic theory of electricity. It was that whenever two metals or other elements of the same valency are deposited or evolved in the electrolytic cell, the amounts of electricity consumed, as measured by Lane's unit jar or other instrument, are inversely proportional to the atomic weights of the elements. Or, in other words, that the electricity attached to every atom of a given valency is the same, and that if a metal is divalent its atom is associated with twice the usual atomic quantity of electricity. Commenting upon this discovery in his Faraday lecture, Helmholtz said : " If we accept the hypo- thesis that elementary substances are composed of atoms, we cannot avoid the conclusion that elec- tricity, positive as well as negative, is divided into definite elementary portions which behave like atoms of electricity." James Clerk Maxwell, who, following in Faraday's footsteps, worked out a beautiful and successful theory based upon the properties of the medium, also saw the force of this conclusion, without, how- 14 THE ELECTRON THEORY ever, being able to follow it up owing to tlie lack of experimental data. In the first edition of his "Electricity and Magnetism," published in 1873, he says (p. 312): "Suppose, however, that we leap over this difficulty by simply asserting the fact of the constant value of the molecular charge, and that we call this constant molecular charge, for convenience of description, one atom of electricity." Later on, however, he adds : " It is extremely improbable that when we come to understand the true nature of electrolysis we shall retain in any form the theory of molecular charges, for then we shall have ob- tained a clear basis on which to form a true theory of electric currents, and so become inde- pendent " of these provisional theories." Maxwell's vision here was clouded, for the theory "of molecular charges" now holds the field in undisputed possession, after decisive victories in four different quarters where its attacks were little dreamt of in 1873. The very next year an Irish physicist, G. John- stone Stoney, at the Belfast meeting of the British Association, drew attention to this "atom of elec- tricity" as one of the three fundamental physical units of nature (the others being the velocity of light and the constant of gravitation), and gave an approximate calculation of its value. He said : 1 1 See Scientific Proceedings of the Royal Dublin Society, Feb. 1881, p. 54. Philos. Mag., May 1881, pp. 385, 386. ORIGIN AND DEVELOPMENT 1$ " Finally, Nature presents us in the phenomena of electrolysis with a single definite quantity of elec- tricity, which is independent of the particular bodies acted on. To make this clear I shall ex- press ' Faraday's Law ' in the following terms which, as I shall show, will give it precision viz. for each chemical bond which is ruptured within an electro- lyte, a certain quantity of electricity traverses the electrolyte which is the same in all cases. This definite quantity of electricity I shall call Ej." He calculates the actual charge by dividing the quantity of electricity required for the electrolysis of 1 c. cm. of hydrogen by the number of hydrogen atoms in 1 c. cm. as given by Loschmidt, and finds 1Q- 20 " amperes " (now called absolute electromagnetic units of quantity). This figure compares well with the latest value for the electron viz. 1-1 x 10~ 20 E.M. units. In 1879 followed Crookes's epoch-making experi- ments on the mechanical properties of those mys- terious vacuum discharges called cathode rays by Goldstein, and studied by Plticker and Hittorf since 1859. Crookes, pushing the vacuum to the furthest attainable point, and leaving in the tube only one-millionth of the air originally contained in it, obtained what he called " radiant matter " in a fourth state, superior in dilution to the gaseous state, and marked by a still further disappearance of differentiating qualities such as is observed in 1 6 THE ELECTKON THEORY passing from solid to liquid and from liquid to gas. He actually constructed a little windmill driven by a torrent of electrons, of the real "electric fluid" as we now know it, without, however, quite realising the tremendous feat he had accomplished. His opinions and theories were smiled at as being too " grossly material," and the discoverer had to wait twenty years before they were brilliantly confirmed. The same year that witnessed Crookes's demon- strations before the Koyal Society saw the realisa- tion of the long-cherished dream of deflecting a current in a conductor by means of a magnetic field. Crookes had deflected his "radiant matter" by a magnet, and so what more natural than to expect that a magnet should deflect the same matter when picking its way through the substance of a metal! This was accomplished at last by Hall of Baltimore, by bringing a very thin film of gold into a strong magnetic field, and finding that the elec- tricity tended to make its way out by the sides when the current was turned on. If this discovery had been followed up with any spirit, the true import of the negative current as the real current would have been realised seventeen years earlier than it was. Hall himself observes: 1 "If we regard the electric current as a stream flowing from the negative to the positive pole, the phenomena observed indicate that two currents 1 American Journal of Mathematics, vol. ii. p. 287, 1879. ORIGIN AND DEVELOPMENT 17 parallel and in the same direction tend to attract each other. . . . Whether this fact, taken in con- nection with what has been said above, has any bearing upon the question of the absolute direction of the electric current, it is perhaps too early to decide." In the following year Von Ettinghausen actually claimed to prove that the current proceeded from the negative pole with a velocity of a few millimetres per second. This result was, as we shall see, not far from the truth. Taken in conjunction with the effect produced on light by reflecting it from a magnetised surface, discovered by Kerr in 1875, the Hall effect might have led very close to the modern electron theory, but for the difficulty of distinguishing between forces on electricity and forces - on conductors. Without any idea of the density or inertia of the particles of electricity, all quantitative deductions necessarily re- mained as vague as Franklin's original " electric fire." That avenue being barred, electric research took other directions. One of the most fruitful of these was electrochemical research, which, since Faraday's fundamental discovery, had occupied a school by itself, cultivating but little intercourse with the rest of the electrical world. Hittorf, Clausius, and Kohl- rausch had, with infinite patience, traced the migra- tion of the ions through the liquid in the electrolytic cell, discovered their mutual independence, and B 1 8 THE ELECTRON THEORY formulated the theory of ionisation, culminating in the memorable announcement by Arrhenius in 1884 that at infinite dilution all molecules of the electro- lyte would be dissociated and free to obey electric forces. This discovery, together with van't HofFs work on osmotic pressure, formed the foundation on which Ostwald and Nernst have since been able to raise the imposing edifice of the chemistry of ionisation. Meanwhile, Maxwell's electromagnetic theory was radiating out from Cambridge, and gradually attract- ing to itself the leading thinkers of the Continent, who felt the inadequacy of the mathematical theories of Weber, Clausius, and Riemann, based upon action at a distance between charged points. Maxwell's successor at Cambridge, J. J. Thomson, took his first step towards the modern corpuscular theory of electricity in the light of Maxwell's views of electromagnetic energy by calculating, in 1881, the " quasi-inertia " possessed by a charged body in virtue of its charge alone. But the doubts engendered by the two main lines of thought were removed with dramatic suddenness by a few simple experiments made by Hertz, at Bonn, in 1888. He proved that electric force has a finite rate of propagation, and that, if a body is charged, the field of force around it does not per- vade all space instantly, but takes a certain time very short, but still measurable to reach a distant ORIGIN AND DEVELOPMENT 1 9 point. The speed was found to be the same as that of light viz. 186,000 miles per second. This momentous discovery turned the tables com- pletely on the theories of instantaneous action at a distance, and enthroned Maxwell's theory in every Chair in Europe and America. For half a genera- tion after those experiments men were feverishly engaged in testing dielectrics, and making them convey waves of electromagnetic force, the wave of research itself culminating in the triumphs of wire- less telegraphy. In the struggle for the mastery of the dielectric, the harmless necessary conductor was in sore danger of being lost sight of altogether. But already there were indications of the dawn of a new light pro- ceeding from the vacuum tube a piece of apparatus which, owing to its many vagaries, had acquired an evil reputation as a kind of theory-trap, and had for some time been shunned by all but the most reckless or courageous pioneers. Arthur Schuster was the first to break distinctly new ground, by calculating, with the aid of the magnetic deflection, the ratio of the charge to the inertia possessed by what he, rather unfashionably, called the cathode- ray particles. This ratio came out. very high, in- dicating that either the charge must be high or the mass very small. Every one thought there was something wrong about this measurement, especially when, in 1893, Lenard succeeded in persuading the 2O THE ELECTRON THEORY rays to pass out through an aluminium " window'' into the open air, and proclaimed them, on the strength of their absorption, to be composed of ether waves. We now know that Schuster was right and Lenard wrong; but it took five years of controversy before Lenard gave way before an avalanche of new facts, and finally surrendered. Towards the end of 1895 the world was startled by the announcement that a professor in Wiirzburg had discovered rays which could penetrate the human body and show up the bones . as shadows. This discovery, made by Rontgen by means of a vacuum tube, converted the latter from being the most despised into being the' most universally popular of scientific instruments. In the nineteenth century four epochs stand out as of transcendent importance in the life-history of the science of electricity. They are 1820, 1833, 1888, and 1896. In 1820, with Oerstedt, Ampere, Biot, and Savart, the twin sciences of magneto- electricity and electro-dynamics started into being. In 1833 Faraday linked them with chemistry. In 1888 Hertz annexed the ether and enthroned Max- well's theory; and finally, in 1896, the electron theory was enthroned above all others as their culmination and fulfilment, with almost equal suddenness and with much less opposition than that which Maxwell's theory had encountered. In that year, Zeeman, of Leyden, discovered that ORIGIN AND DEVELOPMENT 21 the spectrum of the light from a sodium flame could be modified by a powerful electromagnet, the lines being doubled when seen in one direction and trebled when seen in another. This phenomenon, mysterious at first sight, was found to be fully explained by a theory formulated by H. A. Lorentz sixteen years before a theory which reduced the action of matter on light to the presence of minute charged corpuscles revolving round the atoms. The same year also saw the discovery of uranium radiation by H. Becquerel. The vast significance of these discoveries was perceived in the following year, when J. J. Thomson succeeded in determining the ratio of the charge to the mass of the cathode- ray particles, and, to his great surprise, found this ratio to be identical with that of the Lorentz corpuscles. Discoveries now followed in rapid succession. Rutherford extended the corpuscular theory to atmospheric electricity. The Curies discovered radium and its radiation of electrons, and then proved that radium emits heat and charged particles without cessation. Everywhere, and sometimes in the most unexpected quarters, the same electron the same fundamental quantity of " ; negative" elec- tricity was rediscovered. Schuster-, Simon, Kauf- mann, Townsend, Wilson, Riecke, t)rude, and a host of others busied themselves with investigating its properties; and one realm of electrical science 22 THE ELECTRON THEORY after another was annexed to the all-embracing electron theory. Abraham, Sommerfeld, Bucherer, Wien, Larnior, Langevin, and Lodge extended the theory, both mathematically and experimentally, and reconciled it with the fundamental equations of Maxwell and Hertz. Nor is the work yet com- pleted. Every day brings new material and new conquests. A fresh zest has been given to research in all branches of electricity, and hosts of workers are engaged in pushing the new conceptions to their logical conclusion. When they have reached the engineers and practical men, new discoveries and inventions of far-reaching import may be confidently anticipated. CHAPTER III THE ELECTRON AT REST &J 1. Properties of the Electron. The electron is the--smallest--^leatrified body c arable.. j>__ .separate existence. Its inass is approximately 0*61 xlO~ 27 grammes. Its radius is roughly estimated at 10~ 13 cm. Its charge consists of what has hitherto been called " negative " electricity i.e. the electricity possessed by a stick of sealing-wax when rubbed with wool. The fundamental property of the electron which distinguishes it from ordinary matter is that it repels another electron, instead of attracting it, as two pieces of matter would do. When one electron is placed at a distance of 1 cm. in a vacuum from another electron, it repels it with a force of 1*16 x 10-19 dynes, a force which is something like a quad- rillionth of a pound. This force may appear excessively small, but, as a matter of fact, it is enormous. It is more than a trilKon trillion times (more precisely, 10 43 times) greater than gravita- tional attraction, which accounts for the weight of bodies on the earth's surface and the motion of 23 24 THE ELECTRON THEORY the heavenly bodies. How enormous it is may be realised by the following imaginary experiment. Let two masses, M M x (Fig. 1), say of lead, weighing 1 gramme each, be placed 1 cm. apart. They will attract each other with a force of 6*6 x 10~ 8 ^ ^ dynes, a force quite too small to be measured by any known instrument. But now let 2 grammes of pure negative electricity, E E x , made up of electrons, be placed side by side ^ /9\ at ^6 same distance. They will ^ repel each other with a force of E| 314 x 10 34 dynes, or 320 quadrillion WO - L tons! Even if they were placed, one at the North Pole of the earth, and the other at the South Pole, they would still repel each other with a force of 192 million tons, and that in spite of the fact that the force decreases with the square of the distance. That force would be capable of imparting to each of these grammes of pure electricity a velocity equal to that of light in less than a millionth of a second, and would only fail to do so owing to the fact that the inertia of each electron becomes infinite, or nearly so, as it approaches the velocity of light. In any case, it is obvious that the experiment must remain purely imaginary. We obtain somewhat less appalling figures if we suppose there to be only 1 gramme of pure THE ELECTRON AT REST 25 electricity, and a single electron placed at 1 cm. from it. The force is still 194 million dynes; but >if we separate the two bodies, as before, by the distance of the earth's axis, the force reduces itself to the inappreciable amount of l'2xlO~ 10 dynes. Small as this force is, it must be remembered that the mass at one end of its line of action has been reduced in the same proportion, so that the single electron will be projected just as before with the same explosive velocity. We should have to remove it as far as the sun to reduce the acceleration to something like manageable proportions, and even at that enormous distance ( = l*53x!0 13 cm.), the force exerted by 1 gramme of pure electricity on earth upon all the free electrons in the sun would suffice to impart to them a velocity equal to that of light in 20 seconds. It is quite evident from the above considerations that in all ordinary electrical phenomena, we are dealing with a very minute quantity of free elec- tricity. Let us attempt to arrive at some idea of its amount. 2. Electrons and Matter. We deduce from the laws of electrolysis that every atom of matter is capable of temporarily uniting with a definite quantity of electricity, which is exactly proportional to its chemical valency, but is otherwise indepen- dent of the nature of the element. Thus in the electrolysis of hydrochloric acid every atom of 26 THE ELECTRON THEORY chlorine brings to the anode a definite quantity of negative electricity, a quantity which we can measure with a galvanometer. Knowing the weight of the chlorine evolved and the weight of the atom of chlorine (as we do), we can find by a simple calculation that the quantity transported by each atom is, as nearly as we can make it out, just one electron. We therefore conclude that every atom of chlorine in the electrolytic cell has one electron somehow associated with it, but associated in such a manner that it is ready to be detached when a finite force is brought to bear upon it. In the normal state the chlorine atom does not carry this electron with it, and it is therefore uncharged. Other elements such as hydrogen and the metals are also uncharged in the normal state. Each atom contains a number of electrons, but their electrical action is compensated by some force within the atom which, for lack of a better term, we may call "positive electricity"; but each of their atoms, when placed in an electrolytic cell and subjected to electric force, is liable to temporarily lose an electron or two electrons if the element is divalent and thereby become " positively " charged. We have, therefore, reason to suppose that in any uncharged lump of a divalent metal say a ball of copper there are at least twice as many electrons as there are atoms. Since the connection THE ELECTRON AT BEST 27 between the atoms and these electrons is not rigid, we may suppose that this proportion is liable to variations. When the electrons are in excess of the usual number, we find that the ball is negatively charged; when there is a deficiency, the ball is positively charged. Having seen above what enor- mous forces the electrons are capable of exerting upon each other, we have no difficulty in conceiving adequate causes for such variations. Now, when the balls are thus charged, it is found that the electrons, or the positively charged atoms, in spite of their mutual repulsion, do not shoot out of the metal into the sur- rounding air. They traverse the metal with very little friction, but experience a great resistance at the boundary between metal and air. They therefore take up a position of equilibrium on the surface itself, and stay there, leaving the interior of the metal uncharged. Next, suppose that two small copper balls, A and B, are suspended side by side by in- sulating fibres 1 m. long (Fig. 2). Let them be negatively charged, so as to repel each A B other, and remain 1 cm. apart. Then the force between them is easily proved to be -zfafh part of their weight. If their radii are 1 mm. each, what number of free electrons will suffice to produce the necessary repulsion ? 28 THE ELECTRON THEORY The following data are easily calculated : Volume of each ball . . . 4*2 x 10~ 3 cm. Weight (density 8'93) . . 3'75 x 10~ 2 gr. Force of repulsion . . . 1*87 x 10~ 4 gr. = 0*184 dynes. This is the force that would be exerted by 1260 million electrons upon an equal number placed at a distance of 1 cm. in air. This is, then, the number of free electrons in each ball. The number seems exceedingly high, but we shall soon see that it is but an insignificant fraction of the total available electrons present. According to the most trustworthy estimates, the total number of atoms contained in a cubic centi- metre of solid copper is about one quadrillion, or 1*23 x 10 24 . Now each of our balls having a volume of 4-2 x 10- 3 c. cm., would contain (1-23 x 10 24 ) (4-2 x 10~ 3 ) atoms, and double that quantity of detachable elec- trons, or 10,300 trillion. The ratio of detachable electrons to extra electrons is therefore 10,300 trillion ^ g 1,260 million Hence if, for every eight billion combined electrons in the copper, we add one extra electron, we obtain the necessary force of repulsion. Since a neutral atom deprived of an electron repels another such atom with the same force as that which exists be- tween two electrons, we may also produce the same THE ELECTRON AT REST 29 repulsion by removing from each ball one electron out of every eight billion that are in it ; they then repel each other by virtue of their positive charges. On account of the intensity of the forces called into play, it is found practically impossible to remove more than about one-billionth of the detachable elec- trons, or add more than that proportion to those already there. This explains why the charging or discharging of a body produces no perceptible differ- ence in its weight. If, however, by some special contrivance, electrons or positive atoms are continu- ally discharged from a body, the body is gradually disintegrated. This happens to the cathode in a vacuum tube and to the positive carbon in the arc lamp. We may now formulate the forces between electrons and positively charged atoms a little more precisely as follows: (a) Every electron placed at a distance of 1 cm. from another electron repels it with a force of 1/16 x 10~ 19 dynes. (6) Every neutral atom from which one electron is removed repels any similar atom placed at a distance of 1 cm. with the same force viz. 1*16 x 10~ 19 dynes. And, on the other hand, (c) every electron attracts every neutral atom from which one electron is removed, when placed at a distance of 1 cm. from it, with the same force viz. 1-16 X 10~ 19 dynes, or if two, three, &c., electrons have been removed, with a force two, three, &c., times that amount, (d) All these forces vary in- 30 THE ELECTRON THEORY versely as the square of the distance, unless that distance is so small as to become comparable with the dimensions of the atom (i.e. 10~ 8 cm.). 1 It follows from the law of attraction that an elec- tron cannot be removed from a neutral atom without a very great force as compared with its mass. The attraction between them is the strongest cohesive force we know, and if it accounts for cohesion to any perceptible extent, the force required will at least be that necessary to rupture the metal or other sub- stance. If the law of attraction holds good down to molecular dimensions, which are of the order of 10~ 8 cm., we can calculate the force between an elec- tron and the atom it is being induced to leave. We need only divide the attraction at 1 cm. by the square of the distance, or 10~ 16 . The force then becomes 116 1 Q-L Q ~ 19 > orl>16xlQ " 3 d y nes - This force, acting upon an electron for one second, 1 According to the electron theory of gravitation (W. Sutherland, Phil. Mag., Dec. 1904), the attraction between opposite charges is greater than the repulsion of similar charges in the ratio of (1 + 10" 43 ) : 1, thus accounting for a very small resultant attraction. In the electron theory the attractions and repulsions are, like gravitational force, independent of the manner in which the inter- vening space is filled up. Matter free from electrons would have no electrical effect whatever, and can be theoretically replaced by pure ether in all electrical problems. The effects hitherto ascribed to the " specific inductive capacity " or dielectric constant of the medium are accounted for by the charges which that medium contains. THE ELECTRON AT REST 31 would give it a speed measured by the ratio of the force to the mass, or 1-16 x lO- 3 , A24 cm. 0-61x10- ==19xl 4 sec: This result shows that any electron coming within the radius of molecular action would be instantly captured and absorbed by a positively charged atom. Since the number of free electrons in the universe is by all accounts strictly equal to the number of positively charged atoms, or, rather, valencies of such atoms, it is difficult to conceive how it is pos- sible for any electrons to have remained free at all. Were they all to become absorbed, as they some day will be most likely, there would be no electric action of any kind, and, we suspect, no chemical action either, and two sciences would become superfluous. To understand why we have escaped that fate, we may take an analogy on a very large scale. The force exerted by the sun on the earth is some four trillion tons. Yet the earth does not fall into the sun, on account of the centrifugal force generated by its own velocity. Let us see what velocity would be required to keep the electron from being absorbed by the atom. The force to be counterbalanced is, as we have seen, 1*16 x 10~ 3 dynes. The centrifugal force of a body of mass m describing an orbit of radius R with a velocity v is ~ . Substituting for 32 THE ELECTRON THEORY m the mass of the electron (0-61 x 10~ 27 gramme), and for R its distance from the centre of the atom (10~ 8 cm.), we get which gives v = 1*38 xlO 8 cm. per second. This orbital velocity of the electron, though large, is quite conceivable, inasmuch as it is still less than -^ih the velocity of light (the utmost attainable speed). Knowing the size of the orbit, we can calculate the number of revolutions it makes per second. This is 2-2 x 10 15 or 2200 billion. As we shall see below, the revolving electron sends out ether-waves into space with the velocity of light (3 x 10 10 cm. per second). Hence the length of these waves is 3 X 1Q1< L r 136 x 10- 6 mm. 2-2 x 10 16 ' This wave-length is about one-third of that of the shortest visible light-waves. The waves emitted by the electron are thus waves of ultra-violet light. Now, by Kepler's law we can easily find what dis- tance between electron and atom would give us any required wave-length. By that law the squares of the periods of revolution are in the same ratio as the cubes of the distances. If, therefore, we make the distance 10~ 7 cm. instead of 10~ 8 , we increase the distance ten times, and the cube of it 1000 times. The wave-length will, therefore, be increased in the THE ELECTRON AT REST 33 ratio of VlOOO : *Jl 9 or 31-6 times. This gives for the wave-length of the light emitted by the electron in its new orbit the value 4300 x 10" 6 mm. This light is also invisible, being about six times longer in wave than the most extreme red light of the spectrum. It is " infra-red." An intermediate value of the distance will give visible light. The yellow light of sodium would require a distance of 2-66 x 10~ 8 cm. between the electron and the atom. Of course, the electrons in a solid metal have widely varying velocities, and hence they give a continuous spectrum when the average velocity is high enough i.e. when the body is hot enough ; otherwise they radiate heat-waves of great length and small energy, in accordance with the law of exchanges. The above considerations show that we must con- ceive a metal to be composed of a mass of metallic atoms pretty closely packed, so that the electrons, in their constant vibration due to a finite temperature, are often and easily exchanged between them. They therefore pass from one atom to another with com- paratively little frictional loss of energy. The metals are called " good conductors of electricity " on account of this property. In other bodies, such as glass, ebonite, shellac, quartz, oil, indiarubber, and porcelain, there are only very few electrons sufficiently free to pass from one atom to another. If they surround a metal, they c 34 THE ELECTRON THEORY prevent the electrons escaping from it even under the influence of a considerable force. Hence they are called " insulators." That they do contain their due ratio of electrons to atoms is shown by the strain to which an electric force subjects them, and by the influence they exert upon light which passes through them. A vacuum, offering, as it does, no resistance to the motion of an electron, is, in that sense, a perfect conductor ; but not in the accepted electrical sense. To conduct electricity, a body must be able to pro- vide carriers for its connection. These carriers are the electrons and positive atoms, with or without extra matter attached to them. The vacuum, con- taining no such carriers, is a perfect insulator. This conflict of characteristics warns us that our definition of a good conductor is not complete. To conduct electricity well, a body must contain free electric charges, and offer but a slight resistance to their motion in the direction of the electric force. These free electric charges are either single electrons or portions of neutral matter associated with positive or negative charges. A good conductor is one which con- tains a large number of free electric charges (called "ions"), and offers but slight resistance to their motion. The " conductivity " of any material is de- fined, in accordance with the electron theory, as the number of ions in unit of volume multiplied by the steady speed acquired by them under the influence THE ELECTEON AT REST 35 of unit electro-motive force. In accordance with this definition, we must declare the ether to be a perfect insulator. 3. Distribution of Free Charges. We have seen that a metal consists of a vast number of atoms (about one quadrillion per cubic centimetre), and about double that number of electrons. These are in rapid motion, and the ether waves they emit in consequence of that motion constitute their radiant heat. Every body radiates heat, unless it is at the absolute zero of temperature ( 273 C.), and it is enabled to do so by the heat it receives in exchange from its surroundings. In an insulator, the electrons are incapable of moving outside the range of the atoms to which they are attached. An electric force displaces them slightly; but when the force is withdrawn, they return more or less rapidly to their former position of equilibrium. In a conductor matters are different. The motion of both atoms and electrons is much more violent, and electrons are constantly running free, colliding with atoms and with each other, whirling round atoms, locked up with them, liberated by collision with other electrons or atoms, and starting on the same round over again. * This difference between dielectrics and conductors is not as yet fully explained, but several circumstances shed light upon it. In the first place, conductors are usually heavier 36 THE ELECTRON THEORY than dielectrics. Therefore the atoms are heavier or more closely packed, and the electron is claimed by a greater number of neighbouring atoms. Secondly, conductors, mostly metals, have a low specific heat, which means that a comparatively small amount of heat suffices to give them the molecular velocity corresponding to a given temperature. Hence they radiate and absorb heat-waves readily, and the " exchange " above referred to is more lively in conductors than in dielectrics. We shall for the present confine our attention to conductors, and more particularly to metals, or to copper as a particularly good conductor. In this metal it has been roughly estimated that every electron combines with an atom, and is liberated again about a hundred million times per second. For every 5000 seconds which it spends locked in the embrace of an atom it roams free for one second. It is these roaming electrons which produce all the phenomena of conductivity. We may suppose that they constitute TO Voth of the total number of electrons in the copper; but this number is very uncertain, and must vary with the temperature and the quality of the metal. The roam- ing electrons do not constitute an electric charge, since they are balanced by an equal number of positively charged atoms contained in the conductor. What will happen if a mass of free electricity, such as we have contemplated above, but containing THE ELECTION AT REST 37 a smaller and more manageable number of electrons, is brought near a lump of metal containing neither an excess nor a deficiency of electrons ? Obviously, the free electrons in the lump of metal will be repelled, and will make their way as far as they can in the opposite direction. The charged atoms left behind will be attracted, and will crowd towards the mass of electricity. When equili- brium has been attained, the point of the conductor nearest the store of electrons will be found to be positively charged, and the point farthest away will be found negatively charged, with a more or less gradual transition at intermediate points, according to the shape of the conductor. This is the well- known phenomenon of "charge by influence," dis- covered 150 years ago by Jipinus in St. Petersburg. To keep in touch with reality, it will be well to obtain some quantitative idea of this charge, and to do so we must deal with a larger quantity of elec- tricity than that of a single electron. The most natural procedure would be to make our unit consist of a certain large number of electrons, say a multiple of ten. But this is barred by the uncertainty which still surrounds the precise charge of the electron. J. J. Thomson's latest estimate is 34 x 10~ 10 " electro- static units," and this is the value we have assumed throughout our calculations. But in practical measurements the unit is defined as that quantity which, when placed in a vacuum at a distance of 38 THE ELECTRON THEORY 1 cm. from an equal quantity of the same sign, repels it with a force of 1 dyne ( = | T gramme). Now since one electron or positive atom repels another at 1 cm. with a force of 1-16 X 10" 19 dynes, 1 and the force varies with both masses, the repulsive force of 1 dyne would be produced by 2*93 xlO 9 electrons, or 2930 million. This quantity of 2930 million electrons (more or less) is what is called the ''electrostatic unity of quantity," being derived from measurements of electrostatic force. For the purposes of this work, in which the reader is to be constantly reminded that electricity has an atomic structure, we shall prefer to call the 2930 million electrons (the equivalent of one "electrostatic unit" of negative electricity) a " company " of electrons, and the same number of charged atoms (or any other objects) a "company" of such atoms or objects. The number 2930 million is for the present assumed to be correct, but it may have to be slightly modified in course of time. We may now re-state our laws of repulsion as follows : (a) One company of electrons repels another company placed at 1 cm. from it with a force of 1 dyne. (6) One company of neutral atoms deprived of one 1 The dyne is the force which, acting for one second on a mass of one gramme, produces in it a speed of 1 cm. per second. It is the 981st part of a gramme. THE ELECTRON AT REST 39 electron each repels another such company at 1 cm. with a force of 1 dyne. (c) One company of electrons attracts a company of neutral atoms deprived of one electron each with the force of 1 dyne. (d) These forces vary inversely as the square of the distance (the distance being large as compared with that between the individual electrons or atoms). 4. Energy of Position : Potential. When motion takes place in spite of a resistance, work is being done. When the motion is steady the force produc- ing it is equal to the force resisting it, and the work is measured by the distance covered. If the resist- ance encountered between two points is due to con- tact with intervening matter, the amount of work done in passing from one point to another depends upon the path. Thus, in driving from one town to another, the work is less over a good road than a bad one. If, however, one road is twice as good as another and also twice as long, the total work is the same. The badness of a road is measured by the resistance it offers to the vehicle, and the work is measured by the product of the distance and resist- ance, so that if the work along two routes is the same, the length of each route must be inversely as its " badness " (resistance). When the resistance is due, not to intervening matter, but to the repulsion of a distant body, the 4O THE ELECTRON THEORY work done simply depends upon the distance from that body, and is quite independent of the path traversed. Ignorance of this fact has inspired most of the unsuccessful seekers after perpetual motion. If the repelling distant body is a point or very small sphere, and a series of concentric spheres are constructed round it, work has to be done on the repelled body to make it pass from one sphere to the next ; but no work is required to move it along the surface of any given sphere, since all points on that surface are at the same distance from the repellent body. In passing from one sphere to the next inner one, a certain amount of work must be done. When the repelled body returns to its first sphere, that work is given up again, and can be used to overcome some other resistance. A body thus capable of per- forming work owing to its position, is said to possess " potential energy," in other words, a potentiality of work. Clearly, the potential energy will be the greater the nearer the body is to the repellent body. But how can the actual amount of the total potential energy be measured? The problem presents one obvious difficulty the repulsive force extends into infinite space, so that the potential energy would appear to be infinite; that is to say, the repelled body can be made to do work to an infinite extent, for however great the distance to which it may have been repelled, there is still some remainder of repulsion ready to act upon it and make it work. THE ELECTRON AT REST 41 This argument, though plausible, is vitiated by the fact that the sum of an infinite number of infinitesimal quantities is not infinite, but limited. That this must be so may be illustrated by a few familiar examples. One of them is the old Greek dilemma about Achilles and the tortoise. A tortoise is a mile ahead of Achilles, who starts in pursuit. Achilles runs 100 times as fast as the tortoise, so that when he has run the mile, the tortoise is T ^j- mile ahead. When Achilles runs that distance, the tortoise is I0 ooo mile ahead, and so on. So that Achilles will always get nearer the tortoise, but never quite up to it. The solution is that the sum of these quantities 1 + loo + 10,000 + 1,000,000' &c< is a finite number, as is evident when written as a decimal fraction 1-0101010101 a number which is certainly smaller than 1*0102, and is exactly equal to - 1 //-. The tortoise will therefore have gone exactly ^ of a mile when Achilles overtakes it. Another example is this. If you stand on a bridge over two parallel lines of railway, the rails seem to meet on the horizon. If you stand over one line, the rails, if running straight along an infinite plane, will meet in a point on a level with your eyes. THE ELECTRON THEORY If a train is travelling out along the other line of rails, it will approach the first line as the distance increases. It can never cross it, as the rails are all supposed to be parallel. If the train, therefore, moves on for infinite time it will always be approaching that point on the horizon, but never reaching it. We see, then, that infinities and infinitesimals may often be combined into finite quantities subject to ordinary arithmetic. This may encourage us to tackle the problem of the total potential energy of a repelled body. For this purpose we will surround the repelling body E with a series of concentric spheres (Fig. 3). The surfaces of these spheres are called " equipotential sur- faces," since the re- pelled body has the same potential energy while it remains in the same surface. We will not draw these spheres at random, but make their successive diameters so that the same amount of work is done in passing from any sphere to the next. Since the force of repulsion varies inversely as the square of the radius, the distance between two successive spheres must vary directly as the square of their FIG. 3. THE ELECTRON AT BEST 43 mean radius. At twice the distance, therefore, the equipotential surfaces will be four times as far apart. Now place a small negatively electrified body, say, a "company" (1 E.S. unit) of electrons, at E and another at a point P. The problem is to find its total potential energy at P i.e. the work that has been done on it to bring it up to P from an infinite distance, or the work that it is capable of doing in retiring to an infinite distance. To simplify matters, describe a special sphere passing through P, and others with radii twice, four times, eight times, &c., as large, passing through Q, R, S, &c. (Fig. 4). In passing from P to Q, the company cuts a cer- tain number of equi- potential surfaces, and this number measures the work done upon it. Let this work be de- noted by W. In pass- ing from Q to R, its experience will be pre- cisely similar, except that, the distance be- tween successive surfaces being four times what it was before, the rate of work will be one- fourth. Since, however, the distance traversed is twice as great, the actual work done between Q and R will be one-half that done between FIG. 4. 44 THE ELECTBON THEORY P and Q. In the next compartment, the work W 4 will be -j- instead of -5-, and the next again it will be J. Extending this to infinity, the total work done ( = the total potential energy) is W W W W Now, as every one can easily try for himself, the sum of to infinity, is just = 2. Hence the total work is 2W. This is the potential energy of the company when at P. The potential energy at Q will be 2W-W=W. At R it is At S it is In other words, the potential energies at P, Q, R, S are as or THE ELECTRON AT REST 45 Since the distances are as 1:2:4:8, we find that the potential energy at a point is inversely as the distance of the point from the centre of the repellent body. To obtain the actual value of the energy in foot- pounds or other units of work, we need only deter- mine the work done between P and Q and double the amount. If the force at P is 1 dyne, the force at Q must be \ dyne. If the distance between P and Q is 1 crn., the work must lie between 1 cm. x 1 dyne and 1 cm. x J dyne. The work of overcoming or exerting a force of 1 dyne through 1 cm. is called "1 erg": hence the work between P and Q is somewhere between 1 erg and erg. By constructing a large number of equi- potential surfaces between P and Q by the rule given above and counting them, we find that the actual work is just J erg. Hence the total potential energy equal 2 x \ erg = 1 erg. Since E P = 1 cm., and the force at P is 1 dyne, E must be, by definition, just one company of electrons. Hence we have obtained the following important and fundamental result : The total work required to bring up one electrostatic unit (one "company") from infinity to within 1 cm. of another similar and equal unit is 1 erg, and if the distance varies, the total work varies inversely as the distance. 46 THE ELECTRON THEORY If we increase the repellent body, the work varies as the quantity of electricity, since the effects of two " companies " would be simply added up. But if we double both the repelling and the repelled body, the work is quadrupled. If we keep the repelled body always equal to one unit or company of electrons, we obtain a convenient measure for the potential energy which the repelling body is capable of imparting. The work performed upon one com- pany or unit in bringing it up from infinity to a point P against the repulsive force exercised by E is called the potential function, or shortly the potential at P due to E. The following theorems are imme- diately evident : (a) All points in an equipotential surface are at the same potential. (6) A charge will always tend to move from a point of higher to a point of lower potential. (c) The force at any point is proportional to the rate of change of potential along the line of force i.e. to the crowding together of the equipotential surfaces. (d) All points on the surface of a conductor are at the same potential. For if they were not, electricity would travel from the higher to the lower potentials until they were levelled up. We have supposed the repellent body E to be a very small sphere. But it may be a sphere of con- siderable size without disturbing our calculations, so THE ELECTRON AT REST 47 long as the electrons or positive atoms are uniformly distributed over the surface. For then they act outwardly as if they were all concentrated at the centre. We can, therefore, find the potential at the n very surface of the sphere. It is -p, where E is the number of units or " companies," and R the radius in centimetres. That being so, we can calculate the total work required to form the repellent body. Let us build it up unit by unit. To bring the first two companies within R centimetres of each other re- quired g dynes. The next unit took double the o t -p _ -i work, or ^ dynes, the last unit required -^- dynes. We get at the sum of these terms by taking the average of the charges during formation. This average is E The average potential during formation was, there- TT fore, 5, and since the total number of units to be Z Lx brought to that potential was E, the total energy consumed in the process was E _E p Or, if V is the final potential ^, the total energy consumed is E V, 48 THE ELECTRON THEORY To return to our gramme of pure electricity (p. 24), which we found to produce such alarm- ing results even at the distance of the sun, we can now calculate the energy required to make it. The gramme, as we have seen, consists of half a trillion (5-6 xlO 17 ) companies. This is E. We will suppose these concentrated on a sphere 1 cm. in radius, so that R = l. Then the energy required to build it up is ,E 2 .(5'6xl0 17 ) 2 K ergs = y - j L = 16 x 10 34 ergs, or a billion horse-power working for 680,000 years. The same energy would, of course, be required to build up the same number of charged atoms ; but if only 1 gramme of charged atoms is to be built up, the number of companies will be less in proportion to the weight of the atom. Now the atoms are from 1000 to 200,000 times heavier than an electron, and the number of companies per gramme 1000 to 200,000 times less. Hence the energy required to build up a gramme of positively electrified matter ranges from 16 x 10 28 ergs to 4 x 10 24 ergs, still an enormous amount. Since the potential due to a small charged body at a point outside it is simply measured by its charge divided by the distance of the point from its centre, the potential energy, or simply potential of any other charged body placed at that point, will be the product THE ELECTRON AT REST 49 of its charge by the potential at that point. If the charge on the first body is E x , and on the second body E 2 , and their distance R, the potential is E E ^~ 2 This potential is mutual, as it only depends upon their relative position, and it does not matter whether E x has been brought up to E 2 or vice versd. If there are several bodies conferring a potential, the total potential is got by simply adding up the separate potentials, remembering, however, that if the force is attractive instead of repulsive, the potential is negative. The charges will have opposite pi ., -pi signs, say E x and E 2 , and the result * ^ 2 is a negative potential i.e. work is gained instead of spent in bringing the charges together. It follows that if the two charges E x and E 2 are equal, the total potential at any point equidistant pi from them is zero, being in one case -^ and in the THl other jj. Now all the points equidistant from two other points are contained in a plane surface normal to the line joining them, and bisecting that line (Fig. 5), it will be noticed that we have here a well-known case of optics. If E t is a luminous point and AB a reflecting surface, JE 2 will be the " image " of E r We might have any other such points on the side of E^ and if we had equal and opposite charges at the same distance on the other D SO THE ELECTRON THEORY side, the surface AB would still be an equipotential surface at zero potential. Conversely, if the charges on the other side were taken away, and the surface were kept at zero potential throughout (as a metal plate could be kept at zero potential by connecting A it to earth), opposite charges would have to be distributed over the surface, so as to make up for the charges taken away, and keep Ea the force at every point above the ~g surface the same as before. This consideration enables one to calculate the distribution of the electric charge by "influence." The method is a very fruitful IG * ' and valuable one. It is called the " method of electric images." Since the surface AB is an equipotential surface, no work is required to move a body along it. If the distance between E x and E 2 is 2 R, the distance of the plane from E x is R. Now the work required to bring a company of electrons from infinity to E within R cm. of the charge E x was ^- while E x was alone in space. This amount has become zero at one point, owing to the presence of E 2 . This shows that the potential due to one charge may be counter- balanced and annulled by the potential due to another. Hence, though the potential due to each THE ELECTRON AT REST 51 body by itself remains precisely the same always, the net potential at any given point depends upon every free charge in the whole of space, and can therefore acquire any value we please. If the point in question happens to be on the surface of a charged conducting sphere, it follows that the " potential of that sphere " is equally subject to the influence of surrounding charges, being lowered by any free charge of the opposite sign. In order to restore its potential to the former high figure we must increase the charge on it. If the potential has been halved, we must double the charge, in order to restore the potential. If the potential is very low, the conductor can carry a great charge ; it has, so to speak, a great carrying capacity. This conception of capacity is a very important one, so we must define it more precisely : " The capacity of a conductor is the charge required to raise it to unit potential." A sphere of radius 1 cm. has unit potential (1 dyne per unit charge repelled) when it contains unit charge (1 "company"). If its radius is 2 cm. its potential is J, and to bring it to the same potential its charge must be made 2 companies; if 3 cm., 3 companies, and so on. Hence we have the general rule : The capacity of a sphere is proportional to its radius. If the charged sphere has an elastic surface, the mutual repulsion of the charges will tend to bring about an extension of the surface. This may be 52 THE ELECTRON THEORY proved by blowing a soap-bubble, and then charg- ing it. The bubble expands, and its capacity increases. When two oppositely charged conductors approach each other, the potential of each is lowered and the capacity increased. Here again the spontaneous motion leads to an increase of capacity. When two similarly charged bodies repel each other and move apart, their potential is lowered, and, again, their capacity increased. This is a general rule; If charged conductors are free to move, they always move so as to make their potential a minimum, and their capacity a maximum. The motion thus engendered leads, of course, to a diminution of potential energy. By the law of the conservation of energy, there can be no loss of total energy, so what is lost in potential energy is gained in energy of motion or kinetic energy. We shall have to consider this kinetic energy later on when dealing with the electron in motion. 5. Condensers. We have learnt that when a positively charged conductor is brought near a negatively charged one, the capacity of each con- ductor is increased. To simplify matters, consider an infinite plane conducting surface, AB (Fig. 6), and a point, P, outside it. Let the electrons be uniformly dis- tributed over the surface out into infinite space, THE ELECTRON AT REST and let P contain one company of electrons; then we can prove that the repulsion between the plane and P is independent of the distance of P from the plane, as follows : Draw PD, PE, two lines equally inclined to the plane. Draw similar lines all round P, so as to make a cone with P for its apex. The base of the cone will be a circle in the plane surface AB, and all the electrons in that circle will repel P. Let their total repulsion be 1000 dynes. Now remove P to twice the distance, keeping the angles between the lines and the plane the same as before. The lines forming the sides of the cone will be double their previous length, and the base four times its previous area. There will there- fore be four times the number of electrons to exert their repulsive force; but since their distance is twice what it was, we must divide the force by 4 (the square of the distance), and the net force will be the same as before. The argument will hold good whatever the size of the angle at the apex, and hence we may make it so large, and the cone so flat, that B FIG. 6. 54 THE ELECTRON THEORY the repulsion of the electrons outside the cone is practically imperceptible. 1 Having thus seen that the repulsion is the same at any distance, let us calculate its amount. Let the point P be 100 cm. from the plane, and let the plane contain 1000 companies on every sq. cm. Then the repulsion between the nearest square cm., ab, of the plane will be (p. 38) 1x1000 1002 = T L dyne. Now describe round P a sphere which just touches the plane. Take another square cm. in the surface, say, cd. Then, if there were 1000 companies on cd they would repel P with the same force as before viz. 01 dyne. But this force would not be so effective as before, since it is inclined to the vertical. Now produce PC and fd to Pc 1 and Pd\ and let Pc 1 be = 2 PC. Then if the imaginary surface c l d l had the same surface density as cd its force on P would be the same, since its charge would be four times and its distance doubled. In producing T*d l to Pe 1 , and completing the intersections with the plane, we mark 1 We must add that for the above reasoning to hold good the density of the electrons on the surface must be very great ; other- wise the redistribution of the electrons, owing to the repulsion of FIG. 7. THE ELECTRON AT REST 55 out a new surface, c l e l t whose size is the greater the more Pc 1 slants to the surface. This slant compen- sates the slant of the push of the repelling electrons on c l e l , and we find that their force is O'l dyne also, as before. The same argument would hold good for any square cm. we choose to cut out of the hemi- sphere turned towards the plane. Hence the total push is as many times O'l dyne as there are square centimetres on the surface of the hemisphere, viz. 2ira (radius)*, or, since the radius is 100 cm., the total force is 27T x O'l x 1002 dynes = 27rxlOOO dynes, or 2?r times (6*2832 times) the number of companies on each square cm. of the plane. The companies or units per square cm. are called the " surface density of electricity," and are denoted by a. Hence we have Force on 1 unit = 27ro- at any distance from an infinite charged plane on either side. In passing through the plane only the direction of the force changes, and not its amount. P, would produce the same effect as a charge of a company of positive atoms placed at the " image " of P in the plane. This image would attract P, and so lessen the repulsion. If, however, the surface density is great, this attraction may be left out of account, as it has no perceptible influence. 56 THE ELECTRON THEORY Now let there be two infinite parallel conducting planes at a distance, D, from each other (Fig. 8), and let them have equal surface densities of opposite sign, so that if AB contains, say, 1000 companies of electrons per square centimetre, A 1 !? 1 contains 1000 companies of positively charged atoms per square centimetre. Then we can prove that there is no electric force in the field except in the space between the two planes. At a point P 1 , for instance, the force due to AB is 27ra-, and the force due to A^ 1 is 27r<7, p 1 and the sum of the two forces is zero. In other words, the positive charge on A. 1 W "neutralises" the negative charge on AB for all infinite space outside the two Q D | surfaces. FIG. 8. What is the difference of potential be- tween AB and A^ 1 ? In other words, what work will have to be spent on a company of electrons to bring it from A*Bi to AB ? It will obviously be the product of the force into D. Now the force on a company of electrons is a repulsion by AB amounting to 27rcr, and an attrac- tion by A. l E l to the same amount. These two forces being in the same direction, they add up, and the total force at any point between the planes is 4?rcr. Hence the work on one company is 47ro-D, and that is the difference of potential between AB and AB 1 . THE ELECTRON AT REST 57 A system like the above, consisting of two con- ductors separated by a non-conductor, is called a " condenser." The most familiar example of a condenser is the Leyden jar (Fig. 9), in which the conductors are made of tinfoil stuck on 1 the outside and inside of a glass jar, and the non-conductor is the glass. (H; The capacity of a condenser is measured by the charge which must be imparted to either conductor to make the difference of potential between them one unit, so that one erg of work must be spent to take a company of electrons from one conductor to another. Since the difference of potential between the two planes is and this is = 1, we have for the capacity per unit area of the condenser consisting of two infinite planes. This increases inversely as D, so that if we make D small enough, and the plates close together, we can get a condenser of any capacity we please. The advantage of condensers of large capacity is that we can store up great charges in them with little work, and with little tendency to wasteful discharge, as there is no force outside the coatings. Hence the name " condenser." 58 THE ELECTRON THEORY If, however, the plates are connected by a wire or other conductor, the mutual repulsion of the electrons towards each other and the positive atoms towards each other will force both into the wire, where they will meet, and electrons will be absorbed by the positive atoms to form neutral atoms. Their potential energy will be liberated and pass first into the form of motion, and then into heat. If the wire is interrupted by a short gap of air, this discharge will break through the air and produce a spark the well-known spark from the knob of a Leyden jar. The condenser consisting of two infinite planes is, of course, incapable of practical realisation, and is only introduced for theoretical purposes. It enables us, however, to pass to practical construc- tions without sacrificing our results of calculation. If the plates were, say, 1 metre square each, the capacity of the condenser would be 100 2 approximately; but the distribution of the charges over the plates would not be uniform, as they would be crowded towards the edges. On the other hand, the charges on the central portions would be practi- cally uniform, and if we could separate out a single square centimetre at the centre of each plate, we should approach very closely to the theoretical per- fection of our infinite planes, and could safely apply THE ELECTRON AT REST 59 our formulae. If we make a clean cut round the small area, but connect it by a fine wire with the larger area, so as to keep it at the same potential as the larger area, we may regard the two small areas as forming an ideal parallel-plate condenser amenable to calculation. Thus, if their areas are 1 sq. cm., and their charges 1000 companies, and they are 1 mm. apart, the capacity of the small condenser is _! ___ _ _ =0-795. 47rx 0-1 "12-6x0-1 The charge being 1000 companies, the difference of potential is 1000 without introducing the plate. We see, therefore, that a conductor introduced between two coatings of a condenser increases its capacity. If, instead of a plate, a multitude of small conductors were introduced, their effect would depend upon their density and size, but it would have the effect of increasing the capacity of the condenser. The quality whereby a substance introduced be- tween the coatings of a condenser increases its 64 THE ELECTRON THEORY capacity is called the inductive capacity of the substance, and its specific inductive capacity is measured by the ratio by which the capacity of the condenser is increased on substituting the substance for air between the coatings. The specific inductive capacity of a medium, discovered and named by Faraday, is now usually called its dielectric constant. Here are a few values : Glass, 3 to 7 ; ebonite, 2 to 3*5 ; mica, 7 to 10 ; petroleum, 2 ; alcohol, 25 ; ice, 78 ; metals, infinite. Condensers are now usually made of mica, on account of its high dielectric constant. The specific inductive capacity of a medium is due to the number of electrons it contains, and to the extent to which these electrons are displaced out of their normal positions under the influence of an external electric force. In many media, notably guttapercha, this displacement takes some time to disappear after discharge, while in mica there is very little of this remanent electrification. The electron theory is as yet unable to state what is the configuration or mobility of electrons which produce the various inductive capacities of media. It is known, however, from Maxwell's electromagnetic theory of light, that the dielectric constant is pro- portional to the square of the time required by long waves of electric force to traverse the medium. If two charges are separated, not by a vacuum, nor THE ELECTRON AT REST 65 by air (whose dielectric constant is very little higher than that of a vacuum), but by a medium of dielectric constant, K, the force between them will be, not but -j^ 2 . This should be remembered when the charged bodies are immersed in a medium other than air. In the same way, the potential of a TTjl charged sphere of radius, R, becomes , and its energy is reduced K times. 7. Electrostatic Machines. An electrostatic ma- chine is a machine used for the mechanical separa- tion of electrons from positive atoms. The earliest machine of the kind consisted of a piece of amber and a woollen cloth wherewith to rub it. This was improved upon by Otto von Guericke in 1663, who made a machine of a sphere of sulphur, which was rotated on its axis while the hand rubbed against it. The sulphur withdrew electrons from the hand, and thus became negatively electrified. This process is termed " electrification by friction/* and was, for centuries, the only known way of pro- ducing an electric charge. A glass rod rubbed with silk is the most usual frictional apparatus for ex- periments on a small scale. In this case, the silk withdraws electrons from the glass, leaving the latter " positively " charged. The process whereby bodies become electrified by friction is still very obscure. It is known that it 66 THE ELECTRON THEORY depends largely upon the condition of the surface, and the chemical nature and structure of the bodies. Of commonly known bodies, a catskin gives up electrons most easily, and sulphur absorbs them most easily, so that a machine made of those two sub- stances is very effective. We may suppose that there are at the surface of every uncharged body a number of electrons ready to part company with the positive atoms to which they are attached. A catskin would be particularly rich in those loose electrons, and sulphur particularly poor. The effect of rubbing the two together is to give the loose electrons an opportunity to pass from the skin to the sulphur, where they are more strongly held. Once we have a charged body, it is easy to obtain other charged bodies by influence. We have seen above (p. 37) that if a conductor is brought near a negatively charged body say, a block of rubbed sulphur the free electrons are pushed to the end farthest from the sulphur and the positive atoms are attracted towards it. If we break the conductor in two, and take away the sulphur, we obtain a negatively charged conductor and a positively charged conductor. Or, instead of breaking the conductor in two, we may make it up of two con- ductors in metallic contact, and separate them while still in the vicinity of the sulphur. Or we may let the repelled electrons pass into the earth, and then break the connection and obtain a positively charged THE ELECTRON AT REST 67 conductor only, and this process may be repeated indefinitely, so that we can manufacture any number of positive atoms from a single charge of electrons, though not without setting free an equal number of electrons. The earliest electrostatic machines separated electrons and positive atoms by friction, and then used their mutual attraction for storing them in condensers. This storage is closely akin to the storage of water in vessels, cisterns, and reservoirs, where it is held by the attraction of the earth. Only the substances used are adapted to very different requirements. For water, air is pervious and metal impervious. Hence the water is sur- rounded by metal or other solids on the side nearest the earth. For electricity, on the other hand, air is impervious and metal pervious. Hence the charged metal must be " insulated " by means of some non- conductor. The more modern machines work by influence, and are more efficient, but their efficiency is still far from perfect. The ideal electrostatic machine is one in which electrons can be separated from positive atoms with an expenditure of work which can be entirely recovered on allowing the two electricities to re- combine. A limit is set to the amount of electricity separated and stored in condensers by the " dielectric strength " of the medium. When the air or other dielectric 68 THE ELECTRON THEORY between the coatings of a condenser is subject to a certain limiting stress, an electron breaks out from the negative coating and rushes across towards the positive coating. In doing so it collides with a number of neutral atoms, and breaks them up into " ions " of opposite signs. These ions practically re- duce the distance between the coatings, and thereby increase the stress. This, again, leads to a rush of further electrons and positive atoms towards each other, and we have a whirl and turmoil of movements, collisions, separations, and recombinations. We have, in fact, an electric spark ; or if it takes place on a large scale in the atmosphere, we have lightning and thunder. CHAPTER IV THE ELECTRIC DISCHARGE 1. Discharge in General. Whenever an electron moves from one space into another, it may be said to produce a discharge from the first space into the second. But an " electric discharge " is usually under- stood to mean the process whereby a body loses the charge that marks it off, electrically speaking, from its surroundings. These " surroundings," such as tables, walls, &c., are usually connected with the earth by more or less good conductors, and bodies cease to exhibit an electric charge when they are at the same potential as the earth. Now what is the potential of the earth ? In other words, what is the work required to bring a company of electrons from infinity to the surface of the earth ? The question is not easily answered, but the work may perhaps be roughly estimated at a million dynes. For the charge of the earth is negative. It repels electrons, and attracts positive atoms. It behaves in that respect like an electron, and who knows but that if an electron were magnified to the size of the earth it might show a marked resemblance to our own 70 THE ELECTRON THEORY planet? The resemblance is increased by the fact that the sun has a large positive charge, estimated by Arrhenius at 25xl0 10 " coulombs" ( = 7'5xl0 20 companies), which gives it a potential of 10 10 units or 3 billion " volts." The sun thus resembles a positive atom with a number of negatively charged electrons in the shape of planets revolving round it. But the analogy fails when we measure the forces between the sun and planets. For the electric attraction is found to be quite imperceptibly small in comparison with the gravitational attraction, and astronomers may safely leave it out of their calculations. Even if the negative potential of the earth is a million units (300 million "volts") as supposed, its action upon an electrified body near its surface will be excessively small. If this potential were solely due to the earth's own charge, that charge would be 6 x 10 14 companies, and this may be supposed to be con- centrated at the centre i.e. at a distance below us of 6 x 10 8 cm. Consequently the repulsion exerted upon one company of electrons at the surface will be or about j^fo of the normal weight of a milligramme. This quantity is beyond the limit of sensibility of our most delicate balances. There is, however, a constant streaming of elec- tricity up and down through the air, which is greatly influenced by the weather, and gives rise to the THE ELECTRIC DISCHARGE 71 phenomena of thunderstorms and atmospheric elec- tricity in general. Outside the atmosphere the earth behaves as a highly charged body, and discharges of its negative electricity become occasionally visible about the poles in the shape of the Aurora. 1 The conductivity of the air, like that of any other body, depends solely upon the density and mobility of the ions or charged bodies contained in it. These ions may be single electrons or positive atoms, or they may be these associated with more or less neutral matter. The presence of these ions in the air con- stitutes the "ionisation" of the atmosphere. There can be no discharge without ionisation. This is a fact which has only recently come to light. It has been known for a long time that every charged body exposed to the air is gradually dis- charged. But that was attributed to moisture or particles of dust, or even to the charging of air molecules. We know now that the discharge takes place when both moisture and dust particles are rigidly excluded, but does not take place if ionisa- tion is prevented. If there is ionisation, the amount of such ionisation determines the rate at which the body is discharged. Now ions may be contained in solids, liquids, or gases, and discharge may therefore take place through any of these, or even through a vacuum. But in the case of a vacuum, the ions have to be provided by 1 See P. Villard, Comptes Rendu*, July 9, 1906. 72 THE ELECTRON THEORY the discharging body itself, since the vacuum is otherwise a perfect insulator. In other cases, too, the discharge has to furnish the ions as it goes along. This is notably the case in the electric arc lamp and the spark discharge, where the air is too poor in ions to convey the whole discharge. But before such a discharge can be inaugurated, it is necessary, as a rule, that a few ions should exist in the medium through which the discharge is to take place. If no such ions exist, the medium is a perfect insulator. A discharge can only be made to pass through by means of a great force sufficient to pro- ject ions from the charged bodies, and mechanically break down the insulator. All these various forms of discharge may be classi- fied under five heads, accordingly as they take place through insulators, gases, solid conductors, liquid conductors, or a vacuum. 2. Discharge through Insulators. Insulators are substances which contain no roaming electrons. Their electrons are firmly bound up with atoms, and the latter again are usually bound up together in complex molecules. The substances are therefore, as a rule, chemically inactive : they do not oxidise, and they do not dissolve in water. Paraffin, a typical and valuable insulator, is named from its lack of chemical action (parum affinitatis). And chemical affinity, as we shall see, is a matter of detachable electrons and nothing else. THE ELECTRIC DISCHARGE 73 When the electrons of a substance are not detach- able from their atoms or molecular groups, they can- not easily be made to enter a metal to neutralise the positive atoms which that metal may contain. And, on the other hand, the positive atoms being amply provided with electrons, are not prone to combine with electrons from outside. Many of the best insulators, like paraffin, beeswax, gut taper cha, mica, ebonite, and amber, are highly complicated carbon compounds. They have no great density ; their molecules are not closely packed, and their atoms are not heavy. The complex molecular aggregations are well separated from each other, and the electrons are effectively imprisoned in them. If an insulator like benzene, C 6 H 6 , is bounded on one side by a surface containing a large number of free electrons, and on the other side by a surface contain- ing a large number of free positive atoms, the electrons in the benzene molecules will be wrenched to a greater or less extent out of their position and pulled to- wards the positive atoms; whereas the carbon and hydrogen atoms, and more especially the latter, will be pulled towards the surface containing the excess of electrons. If there were any roaming electrons in the insulator they would find their way out, and would neutralise the positive atoms wherever they encountered them, thus producing a discharge. But a good insulator being a substance which contains no such roaming electrons, no discharge will take 74 THE ELECTRON THEORY place unless the force is strong enough to pull the electrons out of the benzene molecules and set them a-roaming. When that happens, events will begin to march rapidly: electrons will fly towards the positive terminal. They will be as quickly replaced by others from the negative terminal surface. These double combinations will give rise to a considerable commotion, which will break up further molecules and impart a conductivity to the insulator by pro- viding it with free electrons and free positive ions. In the direct line joining the terminals a rapid separation and recombination of ions will occur, and will go on at an increasing rate as the conduc- tivity of the insulator increases. The heat produced will volatilise the liquid insulator, and through the ionised gas the discharge will pass like an avalanche, the ions acquiring a velocity growing with the free path along which they travel under the impulse of the electric force. Even when that force is spent, the ions will continue to fly on, like a pendulum swinging up against gravity, and like it, they will return, producing a momentary current in the oppo- site direction. This may be followed by several minor oscillations, until at last the energy is all radiated away into space, and equilibrium is re- established. Such is the process which we witness in the elec- tric spark, or, on a larger scale, in the lightning- flash. If the insulator is a solid, the path of the THE ELECTRIC DISCHARGE 75 discharge is marked by a perforation. Glass, mica, ebonite, cardboard may be pierced in this manner. It takes some 30,000 volts (100 electrostatic units of potential) to pierce a thickness of 1 mm. of the best insulators. This means that the work done in passing from the negative to the positive termi- nal by one company of electrons is 100 ergs. This energy is sufficient to produce the necessary num- ber of ions to keep a further discharge going. If the thickness of the insulator is greater, the difference of potential required is also greater, but not in the same proportion. If D is the thickness of dielectric, the necessary difference of potential increases as UD 2 so long as the distance does not exceed a few centimetres. It requires 58,000 volts to pierce a plate of mica (a complex silicate of aluminium and other metals). This great insulat- ing power is due not only to the complexity of the molecules, but to their segregation in numerous successive strata. 3. Discharge through Oases. When a positively charged conductor is placed near a negatively charged conductor in air, the opposite charges crowd towards the surface facing the other conductor. The air produces no effect beyond slightly reducing the effective distance between the conductors, which it does by the displacement of the charges constituting its neutral atoms,- the electrons straining towards the positive conductor, and the positive atoms straining 76 THE ELECTRON THEORY towards the negative conductor. The superfluous electrons in the metal are so much entangled with the molecular aggregates of the metal that even their mutual repulsion and the attraction of the opposite charges in the positive terminal fail to send them out into the open air. And the same state of things obtains among the superfluous posi- tive atoms in the positive terminal, except that they are held even more firmly than the electrons. For actual expulsion, some strong agency is neces- sary. Radioactive substances like radium and uran- ium are in such a state of unstable equilibrium that an atomic catastrophe every now and then sends an electron or positive atom flying out into space. But ordinary substances require either a high tem- perature or ultrar-violet light, or the impact of ions, to enable their own ions to escape. It is only under exceptional conditions that the mere pressure of similar charges suffices to project some of them outside the conductor. When, however, the air is ionised, i.e. filled with particles each linked with an electron or positive atom, these ions beat against the terminal opposed to them in sign, and shake or pull the opposite charge out of the metal. There are a number of ways of ionising air. It can be done by simply heating it or illuminating it with ultra-violet light, or transmitting Rontgen rays or Becquerel rays through it. The energy thus THE ELECTRIC DISCHARGE 77 supplied is converted into the potential energy of ionisation. But since the ions are constantly re- coinbining, the ionisation must be kept up artificially. When this is done an electric discharge can take place through air, just as through a metallic con- ductor a silent and steady and invisible discharge. The only difference is that the fall of potential is not uniformly distributed, being more rapid near the terminals, where ions of the opposite sign con- gregate. Such a discharge is called a " dependent discharge," depending as it does upon a constant supply of external energy for ionisation. When, on the other hand, the discharge furnishes its own ions as it goes along, we have an " indepen- dent discharge." This is done in a variety of ways. The most familiar example is the electric arc lamp, where the carbon terminals give off vapour of car- bon, and furnish the ultra-violet light necessary for its ionisation. Another familiar example, and the oldest known, is the electric spark, and its great natural counter- part, the lightning-flash. Both these are almost invariably intermittent, lightning being a quick suc- cession of flashes in the same direction, often pre- ceded by a feeble pilot discharge wjiich passes from one stray ion to another, just as it finds them, and thus marks out a forked path for the main discharge to traverse. The forms of discharge which allow the greatest 78 THE ELECTRON THEORY insight into the actual processes going on are the point, brush, and glow discharges, chiefly in rarefied gases. A point discharge between a metallic point and a plate is the simplest form of gas-discharge known. Let a sharp point, P, be placed opposite a circular plate, AB, in air (Fig. 11). Let the point be kept at a negative potential, and AB at a positive potential. x Then when the difference of poten- ^ <= tial is sufficient, say a few hundred volts, a glowing steady spark is seen at the point. This spark really consists of two luminous strata separated by a narrow dark space. A few stray positive atoms are re- quired to start the discharge. They are attracted to the point, near which they find an intense and concentrated electric force. Their motion towards the point is constantly accelerated, and when they get close up to it, it is sufficiently rapid to split up the gaseous molecules into ions. This splitting up is facilitated by the presence of the metal, which appears to exert what chemists call a " catalytic " action. The region where this splitting up takes place is the luminous layer immediately adjoining the point. The electrons liberated by the ionisation are repelled by the point, and fly out into the gas. They also are accelerated until they re- B THE ELECTRIC DISCHARGE 79 quire sufficient energy to ionise the gas, and their field of action is marked by the second luminous stratum. The dark space between, called the " dark cathode space," is the region where both kinds of ions are acquiring energy of motion, but not spend- ing it, and therefore not producing any luminous effects. This double ionisation also goes on when the point is positively charged, and the plate negatively. Only then the dark space is still smaller. When the difference of potential is very great, the electrons from the negative point fly beyond the region of ionisation and attack the gas further towards the plate, ionising it freely. This beautiful phenomenon is known as the brush discharge. Tesla's flame discharges and the discharges obtained by means of the Wehnelt interrupter, are varieties of it. The form of discharge showing the greatest variety of phenomena is the glow discharge, as seen in vacuum tubes. It is this form of discharge, indeed, which, after being a great source of per- plexity, ultimately was instrumental in elucidating the whole realm of electric discharges. The reduc- tion of the pressure of the gas allows freer play to the ions. It gives them a greater " free path " along which they can follow the acceleration of the electric field, and thereby acquire kinetic energy. Ionisation is thus facilitated, and conductivity more rapidly acquired, 80 THE ELECTRON THEORY The slow discharge in a vacuum tube consists normally of five distinct parts viz. the cathode layer A, the dark cathode space B, the negative glow C, the intermediate space D, and the positive column E (Fig. 12). The three luminous layers (shown dark in the diagram) are those in which ionisation is going on. They are the scenes of conflict and collision, whereas the other spaces are the scenes of free fall along the lines of electric force. At the cathode layer A, positive atoms are T FIG. 12. ionising the gas next the cathode with the help of the metal. As in the case of the point discharge, the ions thus formed follow the electric force, the positive atoms neutralising the free electrons of the cathode, and the electrons traversing the dark cathode space to ionise the neutral atoms in the body of the gas at C. There again, both positive atoms and electrons are liberated, and the latter move still farther towards the anode, producing further ionisation when they have acquired sufficient velocity, and then we get the positive column E. Sometimes it happens that all the electrons pro- ceeding from C have nearly the same velocity. THE ELECTRIC DISCHARGE 8 1 They then reach ionising speed within nearly the same distance, and are stopped at the beginning of the positive column. Before they can acquire further ionising power, they must traverse another dark space, and so on alternately, the final result being the " stratified " positive column, which forms such a striking display when the tube is long enough. If the tube is shortened, the positive column is gradually " swallowed " by the anode until the discharge resembles the ordinary point discharge. The above is a general outline of the main phenomena in gaseous discharges. But they ex- hibit an almost infinite variety, and still offer a fruitful field of investigation. When the exhaustion of the vacuum tube is carried to a very high point, the phenomena become of profound interest to the electron theory. For the electrons projected from the cathode play a very prominent, and eventually an almost exclusive, part. They proceed in straight lines from the cathode, like rays of light, and are therefore commonly called "cathode rays." It was Crookes who first pronounced them to be a kind of matter (" radiant matter"), and we now know that they consist of particles about 200,000 times smaller than the ordinary atoms viz. the electrons themselves. But the positive atoms also take the appearance of rays. When the cathode is per- forated, such rays are seen to emerge from the F 82 THE ELECTRON THEORY back of it. They have been called "canal rays," but they simply consist of positively charged atoms, or atoms or molecular aggregates deprived of electrons. A noteworthy fact with regard to gas discharges is that the amount of electricity passing (the " current ") is not necessarily proportional to the difference of potential between the electrodes. It depends upon the ionisation, and that is influenced and enhanced by the passage of the discharge itself, owing to collision between the ions. In the de- pendent discharge, again, where the ionisation is provided by an external agent, the current can never exceed a certain value, fixed by the number of ions supplied. When these are all engaged in conveying the current, a change in the potential fails to change the current. There exists, in fact, a "saturation current." This, as we shall see, is not the case in metals. Discharge through flames is a special form of gaseous discharge, and depends upon the natural ionisation produced by a high temperature. Heat also exerts an action upon the discharge from metals. It is found that a hot platinum wire is discharged more readily than a cold one. A nega- tively charged platinum wire is easiest discharged when surrounded by hydrogen ; that being a gas whose atoms lose their electrons easily. They surround the negative wire and pull out its elec- THE ELECTRIC DISCHARGE 83 trons. When a hot platinum cylinder is charged positively and hydrogen is made to diffuse out from it, the hydrogen atoms, with their positive charges, rapidly free the cylinder from its positive charge by conveying it into the surrounding space. 4. Discharge through Solid Conductors. In gases at ordinary pressure, or in a partial vacuum, we have to do with molecules possessing a certain free path, which, though very small (about rannnr cm.), yet gives them some little interval of undisturbed motion. In metals, on the other hand, the atoms are packed close together. How closely may be found by a simple calculation as follows. The mass of a copper atom is 70 x 10* 24 grammes. A cubic centimetre of copper weighs 8'9 grammes. That cubic centimetre therefore contains 0*127 x 10 24 atoms of copper, and each atom will have a volume of 7*9xlO~ 24 cc. to itself. If this volume is a small cube, its side will be 2 x 10~ 8 cm. This length is just the diameter of a molecule of hydrogen, so that if we fill up the small cubes with molecules of hydrogen, they will just fit tight. How, then, will the copper atoms fit ? We do not know the exact size of the atoms of copper, but can make a very close guess. We may take it that the diameter of a molecule of copper is not more than twice the diameter of a molecule of hydrogen, since we know that the mercury molecule is not more than 1*7 times as thick. Therefore the 84 THE ELECTRON THEORY copper atom is just about the size of the hydrogen molecule, and fits equally tight in the small cube. The copper atoms are therefore about as closely packed as they will go. Hence copper cannot be perceptibly compressed. But it also explains why the loose electrons attached to the copper atoms are practically free to obey outside electric forces. For they easily get into the neutral zone between neigh- bouring positive atoms, and are then under the influence of the outside force only. This happens, according to J. J. Thomson, about 40 million times per second to each electron. (In bismuth, at all events.) As a consequence, the whole of the loose electrons in a metal (I mean those electrons which can enter or leave the atom without producing a charge sufficient to stop the process) are every now and then set free to obey external electric forces. Their motion under the influence of those forces con- stitutes metallic conduction. From this simple fact the most important laws of metallic conduction may be immediately deduced. Schuster 1 has estimated that a metal contains from one to three mobile electrons for each atom. Copper contains about three mobile electrons for every two atoms. We must therefore imagine these electrons darting in and out among the atoms, and ready to obey the pull of an electric force whenever they happen to be free, which happens millions of 1 A. Schuster, Phil. Magazine, Feb. 1904. THE ELECTRIC DISCHARGE 85 times per second. The path of freedom increases as the metal cools and the atoms arrange themselves in larger aggregations. Hence the electrons in cold metals follow the electric force more readily than in hot metals. Now it may be asked whether the atoms themselves do not also obey electric forces. The answer is that they do so when they are linked to either more or less electrons than they contain in the neutral state. If linked to more electrons, they have a negative charge ; if to less, they have a positive charge. In the former case they tend to go the same way as the electrons, while in the latter case they tend to move in the opposite direction. But, being about a hundred thousand times more bulky than the electrons, they make little headway, and, except in extreme cases, their motion may be neglected, and we may take it that the electrons alone obey the pull of the electric force i.e. that it is they alone who form the " electric current " in metals. But it is evident that they move from the negative to the positive side, and, therefore, in the direction opposite to that in which an " electric current " has hitherto been supposed to flow. This fact constitutes a serious difficulty in the present state of transition of electrical terms. We cannot hope that people will at once revise all their elec- trical terms, and reverse all their previous notions. The textbooks alone would prevent that. It is, there- fore, imperative that we should use a term which 86 THE ELECTRON THEORY cannot possibly mislead any one. For this purpose I propose to use the term " electron current" for the movement of electrons. Whenever I speak of " the current" pure and simple, I shall mean the move- ment of electric charges without reference to their direction. When the direction from positive to nega- tive is to be understood, I shall speak of the " positive current." When the current is not conveyed by isolated electrons, but by "ions" i.e. larger aggregates of atoms containing a positive or negative charge there are two real displacements in opposite direc- tions, as in electrolysis. It will then be expedient to talk of a " positive current," denoting the flow of positively charged matter, and a " negative current/' to denote the flow of negatively charged matter. The total current is the sum of the two. Having settled these important matters of termin- ology, we may now proceed to unravel the mysteries of the electron current in metals. To simplify matters, we will take, as before, two infinite parallel plates, AC, BD, 1 cm. apart, and having a difference of potential such that it takes 1 " erg " of work ( = T^^V zro- and 1=_L_ T 66000 which agrees with the observations within the limits of error. 244 THE ELECTRON THEORY rise to various speculations ; but the smallness of the mass could not be accounted for, since no mass smaller than the hydrogen atom was known at that time. A further spectroscopic examination of the split lines showed that they consisted of circularly polar- ised light, the direction of rotation being in opposite directions in the two lines. A most important result was deduced from observing the direction of rotation in the two lines. Zeeman found that the electrons producing the longer wave-length were rotating clockwise, and the electrons producing the shorter and more refrangible waves were rotating anti-clockwise. This proved that the light-bearing rotations were those of negatively charged particles only. Indeed, we know from the laws of induction that the clockwise rotations are retarded by clockwise molecular electron currents, thus lengthening the waves and increasing the refrangibility, whereas the others are accelerated. So much for the phenomenon as observed along the lines of magnetic force. At right angles to the lines of force a triplet is observed instead of a doublet. The two circular vibrations we have been considering are seen end-on, and, therefore, appear plane - polarised, the plane of polarisation being parallel to the lines of force, and, therefore, at right angles to the vibrations of the electrons. There is the same difference of period as before, and, there- MAGNETO-OPTIC PHENOMENA 245 fore, the same separation. But in this case there are also the vibrations along the lines of force in- fluencing the eye, but suffering no influence from the magnetic field, since electrons are only affected by such a field when they cross the lines of magnetic force. There being no difference of period produced in this case, the original vibration remains, and a central line appears between the other two. Being due to vibrations along the lines of force, the rays are polarised in a plane at right angles to the lines I ; 1 I \ FIG. 31. of force. In this case there can be no doubt as to the direction of vibration of particles giving rise to polarised light, and an old optical controversy, already partly decided by Hertz's experiments, is thus finally set at rest. This is the famous Zeeman effect in jfts simplest form. The main phenomena are shown in the diagram (Fig. 31), where the solid line shows the ordinary D a line, the punctuated lines show the circularly polarised lines as seen along the lines of 246 THE ELECTRON THEORY force, and the shaded lines are the lines polarised in two different planes, as seen across the lines of force. But the effect is not in reality as simple as it would appear from the above description. The very fact that there are two different sodium lines shows that the electrons revolving round the sodium atom have two different natural periods, or that each atom has two electrons revolving round it, like two satellites with different periods. But affairs are still more complicated in the spectra of the heavier metals, some of which have hun- dreds of spectrum lines distributed apparently at random. This means a great number of electrons attached to each atom, or perhaps to a complicated group of atoms, and so much within each other's sphere of influence that they disturb each other's motion, and superpose extra vibrations of higher frequencies upon their fundamental periods. Ac- cordingly we find, notably in the magnetic metals, some very complicated Zeeman effects, lines being split up into four, five, seven, or even nine com- ponents. But, far from being a discouragement, this bewildering variety has been a valuable stimulus to research into the intimate structure of the chemical atom. The spectrum is, so to speak, the anatomical atlas of the chemical atom, and the index to this atlas is supplied by the Zeeman effect. For it has been found that the lines of each element can be grouped into several series which MAGNETO-OPTIC PHENOMENA 247 follow in harmonic succession, and where each series shows the same Zeeman effect in all its lines, but * where the effect alters from one series to another. Apart from this, there is a mathematical analysis of the atomic vibrations yet to come, and, perhaps, before very long, we shall have definite information concerning the number of electrons circulating round the atom of some element, and concerning the manner in which these revolving electrons give rise to its complicated spectrum. We may thus arrive at a knowledge of the atomic system as precise as is, on a much larger scale, our know- ledge of the motions and perturbations of the planets in the Solar System. (b) The Faraday Effect. The first magneto-optic effect discovered was that named the Faraday effect. When plane-polarised yellow light is sent through bisulphide of carbon contained in a mag- netic field of 5000 units, in the direction of the lines of force, the plane of polarisation is found to have been turned through an angle of three and a half degrees for every centimetre of the liquid traversed by the beam. The sense of the rotation is contrary to the direction of the electron currents constituting the magnet. In other words, it is in the same direction as the (positive) " current " which excites the magnet. This phenomenon admits of a simple explanation on the basis of the electron theory. 248 THE ELECTRON THEORY Every plane-polarised beam may be considered as consisting of two beams circularly polarised in opposite directions. The beam circularly vibrating in the direction of the electron currents of the magnet is retarded, owing to molecular induction within the liquid, and the oppositely rotating beam is accelerated. When, therefore, the two beams combine again on emerging from the liquid, the plane has been turned in the direction of the faster rotation that is to say, in the direction opposed to the electron currents of the magnet. This is the explanation reduced to its simplest terms. But this effect, like the Zeeman effect, shows a variety of detail. The rotation per cm. in unit magnetic field (a quantity known as Verdet's constant) changes from one substance to another, and in a few rare cases even becomes negative. Thus in carbon bisulphide, it is 0*042 minutes of arc, in water 0'012, in glass 0*02 to 0*09, while in com- pressed air it is 0*0003, and increases with the pressure. To return to Drude's equation (p. 228). If the velocity of propagation is v y the refractive index n, the density of rotating electrons N, their " laxity " 0, the length of wave naturally emitted by them L, and the incident wave-length X, we have This equation shows that, as the natural period MAGNETO-OPTIC PHENOMENA 249 L increases, the velocity v diminishes that is to say, if the rotating electron is retarded by magnetic force or otherwise, it transmits the incident light with a smaller velocity. Now we know that the electron is retarded when it rotates in the same direction as the electrons producing the magnetic field. Hence the circularly polarised beam trans- mitted by the opposite rotation will be propagated more quickly. This supposes that X 2 is larger than L 2 . If it is not, the denominator and, therefore, also the whole fraction becomes negative, and the larger the natural wave-length the greater will be the velocity. This is then a case of anomalous dis- persion. It occurs when L 2 is larger than X 2 i.e. when the proper period of the electrons is in the infra-red. Normal dispersion occurs when the proper period of the electron is in the ultra-violet. These considerations explain why the Faraday effect is sometimes reversed. (c) The Kerr Effect. Kerr discovered that plane- polarised light reflected from the polished poles of an electro-magnet is elliptically polarised. Recent experiments have shown that this is simply a special case of the Faraday effect. All reflected light penetrates for some very small depth into the reflected surface. Light reflected from iron passes through a few molecular layers, and repasses them on being reflected. These two passages 2 SO THE ELECTRON THEORY amount to a transmission through the substance of iron. Now, iron has been examined in very thin transparent films produced by cathode dis- integration, and found to exert a very powerful Faraday effect. It is, therefore, not surprising that the passage of light even through the very thin films required for reflection should suffice to produce a very perceptible rotation of its plane of polarisation, more especially as the effect of both passages is in the same direction. Therein lies a fundamental difference from purely optical rotation. When a beam of light is sent through an " opti- cally active " substance, both going and returning, its plane is not rotated at all. Transmission in one direction is compensated by transmission in the reverse direction. In magneto-optic rotation the turning of the plane of polarisation is always in the direction of the (positive) magnetising current, and hence the rotation is proportional to the number of times the beam is transmitted either way. (d) Macaluso-CorUno Effect. Shortly after Zee- man's discovery, two Italian physicists, Macaluso and Corbino, announced that, on transmitting a plane-polarised yellow beam through sodium vapour placed in a magnetic field, there was a strong mag- neto-optic rotation in the neighbourhood of the absorption bands. This follows as a matter of course from the above facts and considerations. We have already seen that when X is very nearly MAGNETO-OPTIC PHENOMENA 2$ I equal to L, the third term in Drude's equation becomes enormous, and hence the velocity of trans- mission is powerfully affected when the wave-length of the incident sodium light is nearly the same as the wave-length of the period proper to the electrons rotating in the electric field. The whole chapter of magneto-optics, like that of the galvano-magnetic and thermo-magnetic effects to be dealt with next, still bristles with problems awaiting solution. But the electron theory has for the first time indicated the general lines along which a complete solution of outstanding questions may be looked for. CHAPTER XIV ELECTRICITY, HEAT, AND MAGNETISM THE relations between electricity and heat have already been dealt with in the chapter on Thermo- electricity (p. 121). As already stated, they involve the intimate structure of the chemical elements, and are therefore less definite than most of the other electrical properties of matter. When these relations are complicated by the presence of a magnetic field, their investigation becomes by no means easier; but the more multitudinous and complicated they are, the more information do they give us concerning the hidden structure of the chemical atom and the building up of solid substances. Let a thin metallic plate (Fig. 32) be traversed by a current from the battery B. According to the electron theory, this current consists mainly in the motion of electrons from the negative terminal to the positive terminal i.e. in the direction opposed to what is conventionally called the current. The positive atoms move in the opposite direction, but ELECTRICITY, HEAT, AND MAGNETISM 253 being hampered by their much greater size, the part which they contribute towards the convection of the current is insignificant. Now let the north-seeking pole, N, of an electro- magnet be brought under the plate. Then the following four phenomena are observed. FIG. 32. 1. A difference of potential between the sides. 2. A difference of temperature between the sides of the plate. 3. A change in the electrical conductivity of the plate. 4. A change in the conductivity for heat. If, instead of an electric current, a 'current of heat is directed through the plate in the same direction, as, for instance, by heating C to boiling point and keeping D cool, the same four pheno- 254 THE ELECTRON THEORY mena are observed. Thus we have eight galvano- magnetic and thermo-magnetic phenomena, which show an intimate connection between currents of heat, currents of electricity, and magnetism. Now it must be stated at once that these effects vary very much, both in quantity and direction, from one substance to another, and there is only one substance bismuth in which all the eight effects have as yet been measured. Such measure- ments are very difficult to carry out, on account of the many sources of error, and the decisive influ- ence of even slight impurities. Nevertheless, some valuable rules have been discovered, and the electron theory has shown itself well able to cope with these strange phenomena. In every case the effect is proportioned to the intensity of the electric current or heat current. This is readily understood. It is also inversely pro- portional to the thickness of the plate. This also is capable of a simple explanation. The transverse effects (1) and (2) and the cor- responding ones in the case of the heat current are proportional to the magnetic field. The changes of conductivity are supposed to be proportional to the square of the magnetic field, but are generally very feeble. Transverse Effects. The effects in bismuth may be summarised as follows : A current of heat pro- duces the same effects as a current of electrons. It is ELECTRICITY, HEAT, AND MAGNETISM 255 deflected by a magnetic field in the same direction as cathode rays are deflected. In a plate traversed by either a heat current or an electron current, a magnetic field increases the resistance and the COLD WARM 'HALL thermal conductivity. A deflection of the current of heat to one side is accompanied by a negative charge acquired by that side. The four transverse effects are shown diagram- matically in Fig. 33, where the circles with arrow- heads indicate the direction of revolution of the 256 THE ELECTRON THEORY electron currents which produce the magnetic field, and the long arrows represent the heat currents or electric currents. The Hall effect in bismuth is easily explained. The electrons constituting the electron current thread their laborious way through the crystalline agglomerations of bismuth atoms, and whenever they are free to follow the electric force they dart forward in the direction of the electron current i.e. from right to left. But while traversing their free path they are subject to deflection by the magnetic force. This will urge them towards the lower edge of the plate, and that edge, there- fore, acquires a negative charge. The upper edge, being drained of electrons, acquires a positive charge, and when the two edges are joined by a wire, a small but steady current passes through the wire. To understand the analogous effect of a heat current, it must be remembered that electrons are particles capable of conveying energy of motion, and that they therefore are just as capable of pro- pagating heat as the heavier atoms are. But in most substances heat has the effect of dissociating neutral atoms. More electrons are split off and set roaming at large. There is a greater number of free electrons in unit volume of the hot metal than in unit volume of the cold metal. To equalise this difference of density, electrons diffuse from the hot ELECTRICITY, HEAT, AND MAGNETISM 257 metal to the cold metal, and thus constitute an electron current which travels in the same direction as the heat current. The Nernst effect falls under this explanation. The electrons constituting part of the heat current are deflected in the same direction as those con- veying the electric current, and accumulate in the lower edge of the plate as before. No sooner is the difference of potential estab- lished between the opposite edges than a cross- current sets in to equalise it. But the rapidity with which this process of equalisation takes place depends upon the resistance of the plate, and this is the greater the thinner it is. It is, therefore, readily understood that the Hall and Nernst effects are inversely proportional to the thickness of the plate, as stated above. The Ettingshausen and Leduc effects are similarly explained. Though tabulated separately from the other two effects, they are really inseparable from them. The Hall and Ettingshausen effects occur together, the cold edge being positively charged and the warm edge negatively, and the Nernst and Leduc effects are similarly linked. The former are called " galvano-magnetic," and the latter " thermo-magnetic," effects. As before, the equalisation of temperatures between the opposite edges depends upon the intervening conductivity for heat. B 258 THE ELECTRON THEORY Effects similar in every respect, but much feebler, are presented by carbon and nickel. Of the four effects described, the Hall effect was the first dis- covered, and it is always the easiest to observe, since no measurements of temperature are involved. Even with very thin plates and strong fields, the E.M.F. between the edges does not exceed a few thousandths of a volt. But that is well within our powers of measurement. It is by far the largest in bismuth, being 400 times greater than in nickel, which comes next in order. It is smallest in tin and lead. The Hall effect depends upon a difference in the mobilities of the positive and negative carriers of electricity, and its existence in metals confirms the supposition that metallic conduction is carried on mainly by electrons. In liquids, the effect has been looked for in vain, for two reasons. The ions in liquids are much more thinly scattered than in metals, and their mobilities are much more nearly equal. It may be roughly esti- mated that in most ordinary metals the mobility of the electron exceeds that of the positive atoms 100 or 200 times. In electrolytes, no ion ever has a mobility more than about 10 times that of another ion. Hence it is clear that the Italian physicists who started in search of the Hall effect in liquids attempted practically an impossible task. ELECTRICITY, HEAT, AND MAGNETISM 259 Owing to the fact that free electrons have a great tendency to condense water about them, and to form heavier negative ions, they do not act as carriers in liquids. In gases, on the other hand, they are present in large numbers, and gaseous conduc- tion is carried on mainly by electrons and positive atoms. Hence there is quite a per- ceptible Hall effect in gases, especially hot gases, where the ionisation is great. The Hall effect has been proved to exist in flames without much difficulty. Longitudinal Effects. The longitudinal effects are not re- versed by reversing the magnetic field. They simply depend upon the state of things at the ends of the plate, and are in- dependent of the charge or temperature of the sides. The four effects are shown diagrammatically in Fig. 34. The electron currents are deflected in the direction in which the arrows are bent, and the heat currents are deflected in the same direction when electrons are diverted towards the lower edge of the plate, instead of making straight for the left- FIG. 34. 260 THE ELECTRON THEORY hand edge ; the left-hand edge will naturally be less negatively charged than before. It will, in fact, rise in positive potential, and will become comparatively more positive than the right-hand edge that is to say, the original difference of potential is increased. The same thing would happen if the plate were made either longer or thinner. It amounts to this, then : that the magnetic field increases the resistance of the bismuth. The increase in a field of 10,000 units amounts to as much as one-third of the original resistance. This property is so constant and reliable that it has been used for measuring the strength of magnetic fields. All that is re- quired is a small coil of bismuth and a resistance- box. The resistance of the coil of bismuth indicates the strength of the magnetic field at the place where it happens to be. It can even be used for alternating magnetic fields; but these must not be too rapid, as otherwise the electrons have no time to get deflected out of their paths, and then the resistance remains constant. The fourth longitudinal effect is a direct in- crease of the " thermal resistance," or a diminution of the conductivity for heat. The cool end of the plate becomes cooler than before as soon as the magnet is excited. It gives up less heat to the cooling water than it did before. Again the effect is as if the plate had been lengthened. It is due, as before, to the deflection of the elec- ELECTRICITY, HEAT, AND MAGNETISM 26 1 trons which constitute the largest part of the heat current. The other two effects are reciprocal effects of currents of heat and of electricity. The heat current consisting mainly of electrons, any deflec- tion of it implies a deflection of (negative) elec- tricity, and wherever there is an accumulation of heat there is also an accumulation of electrons in other words, a negative electrification. The eight effects may be combined into a single diagram (Fig. 35), where the arrows show the direction and de- flection of a current, which may be either a heat current or an electron current. Reversed E/ects. It appears from the above details that the elec- tron theory of metallic conduction suffices for explaining all the manifold relations between heat, electricity, and magnetism as far as bismuth is concerned. But in other metals the transverse effects are different, while the longitudinal effects are, as a rule, too small to be observed. In antimony, cobalt, and tellurium the direct (Hall and Leduc) effects are reversed, and in iron they are all reversed. This means that the laws of metallic conduction are modified by other -f 262 THE ELECTRON THEORY influences. The effects in cobalt are too small to draw any conclusions from them ; but in antimony and tellurium the reversal of the two effects indicates a structure which allies those metals to the non-metallic elements. There is probably very little direct dissociation into positive atoms and electrons. The dissociation is probably more like what we have in electrolytic dissociation, each elec- tron gathering neutral atoms round it to form heavier ions. The electron, thus weighted, has no advantage of mobility over the positive ions, and may even be inferior in mobility to the latter. That the reciprocal effects hold good shows that heat produces a splitting-off of electrons, as in bismuth. This does not appear to be the case in iron, where it is known that heat does not produce a spontaneous evolution of free electrons. We know from the strong magnetic properties of iron that the molecules of iron are quite free to place them- selves in any direction they choose, and that they do place their magnetic axes into coincidence with the axis of a magnetic field. This indicates a great freedom of the ponderable material of iron. Its treble valency also shows that one positive atom can bind several electrons. It may therefore well happen that most of the electrons are bound up with atoms, while a large number of positive atoms are roaming free, and although they have not the great mobility of the electrons, they make up for ELECTRICITY, HEAT, AND MAGNETISM 263 that by their superior numbers. The same con- siderations will explain the reversal of the Thomson effect in iron, without having recourse to the as- sumption of free positive electrons, which are not indicated by any other phenomenon. CHAPTER XV RADIO-ACTIVITY A NEW branch has been added to physical science within the last ten years. The phenomena of radio-activity are impossible on the basis of the older atomic theory of chemistry, though they add new proofs of the atomic structure of matter. They are largely electrical phenomena, and are quite inconsistent with the view, sometimes tentatively put forward, that electricity, like heat, is a mode of motion. The phenomena of radio-activity have confirmed the atomic structure of matter, but have abolished the dogma of the indestructibility of the atom. They have created a new department of chemistry by giving us access to the hidden re- cesses of the atom itself. They have also defi- nitely established the atomic structure of electricity, substituting the indivisible and indestructible elec- tron for the chemical atom, now no longer considered either indivisible or indestructible. That, surely, is a tremendous revolution, a re- volution for which the closing years of the nine- teenth century will be for ever memorable. This is not the place to give a detailed account 264 RADIO-ACTIVITY 265 of the phenomena presented by the radio-active substances. I shall restrict myself to those phe- nomena which have an immediate bearing upon the electron theory. In the course of the present sketch of the chief facts of electricity and magnetism in the light of the electron theory, I have only incidentally referred to radio-activity, preferring to establish the theory first in regions more familiar to the student. I think I can claim to have shown that in the more ordinary electric phenomena, the electron theory not only explains observed facts much better than any other theory hitherto accepted, but unifies all facts in a manner hitherto unapproached, and forms a firm and fruitful basis for further research. In pro- ceeding, however, to radio-activity, we find that the electron theory becomes paramount and indispens- able, and that it seems likely to annex the greater part of physics and the whole of chemistry. The radio-active bodies hitherto investigated are uranium, thorium, radium, actinium, and polonium. Of these uranium and thorium were well known to chemists before the discovery of radio-activity. The others were discovered by their radio-active properties. Radio-activity a term invented by Madame Curie, now Professor of Chemistry at Paris University consists in the spontaneous emission of cathode rays, canal rays, or Rontgen rays that is to say, 266 THE ELECTRON THEORY of electrons, positive atoms, or ether-pulses, or of several of these at the same time. The " positive atoms " emitted are, however, not atoms of the substance itself, but atoms of a very much lighter substance, consisting of either hydro- gen or helium, probably the latter. This is the most astounding fact of the whole new range of phenomena. A well-defined chemical atom, with a characteristic spectrum of its own, splits into two, one of them an atom of a gas found in the sun and the earth, the other a substance which undergoes further decomposition by giving off more atoms of helium and electrons, and finally, perhaps, trans- forms itself into some other known " element." The substance showing the greatest number of radio-active phenomena, and those in the fullest detail, is radium, discovered by Prof, and Madame Curie in 1898. It is supposed to be " descended" from uranium, and it develops into lead after six intermediate changes. Each change takes a defi- nite time to complete itself in a given weight of the substance. As Rutherford says, 1 " There can be no doubt that in the radio-elements we are wit- nessing the spontaneous transformation of matter, and that the different products which arise mark the stages as halting-places in the process of trans- formation, where the atoms are able to exist for a 1 " Radio-activity." By E. Rutherford : Cambridge University Press, 1905. RADIO-ACTIVITY 267 short time before again breaking up into new systems." Radium is a metal closely allied to barium in its chemical properties. Its atomic weight is 225, and is only exceeded by the two radio-active elements uranium (240) and thorium (232*5). The atoms of radium are in imperfect equilibrium ; but the break- up of an atom occurs so rarely that only one atom in ten thousand million breaks up every second in one gramme of pure radium. Since a gramme of pure radium contains about 4xl0 21 atoms, this means that one gramme of pure radium spon- taneously breaks up 4 x 1 11 of its atoms every second. The break-up of the atoms results in the projection of a positively charged helium atom with a velocity in many cases approaching the velocity of light. These charged particles are the so-called (st- rays, whose nature was a mystery until their deflection by a magnet was clearly established by using a very strong field. The proportion between radium atoms present and radium disintegrated is very constant, and quite independent of heat or any other physical or chemical agent. The more the radium is disin- tegrated, the more slowly will the remainder disin- tegrate. The rate of disintegration, as, well as the intensity of the a-rays, decreases, as they say, accord- ing to an exponential law. The most convenient way of stating the stability of such a body as radium is to state the time a gramme of the substance would 268 THE ELECTRON THEORY take to transform or disintegrate half its atoms. This time, T, is 1300 years in the case of radium. We therefore see that if pure radium has a certain radio-activity to-day, that activity will have fallen to half its present value in A.D. 3206. Meanwhile, what becomes of the products of disintegration ? The helium atoms fly off into the surrounding gas and ionise its molecules by collision. They are stopped in 3 cm. of air at atmospheric pressure ; but not before they have produced about 86,000 ions for each helium atom stopped. Now a billion helium atoms do not give much helium, certainly not a measurable quantity. But that quantity becomes discoverable by spectroscopy when it is multiplied about 100 million times, and this takes about 100 million seconds, or about four years. Helium has actually been observed by Ramsay and Soddy in the spectrum of a tube containing radium after a considerable lapse of time. More- over, helium is found occluded in all radium minerals in proportion to the amount of radium present, having been accumulated there since the radium was formed. What remains of the radium atom after the helium atom is split off forms an atom of an inert gas resembling argon. This gas emanates from the radium mineral, and can be drawn off in a current of air and condensed at a temperature of 150 C. It is called Radium Emanation. Its atomic weight RADIO-ACTIVITY 269 is 221, since that of the helium atom is 4, and of the radium atom 225. The atom of emanation gives off another a- particle or helium atom, which goes to swell the amount of helium evolved direct from radium, and what then remains is no longer a gas, but a solid, which deposits itself on the walls of the vessel, and is called radium A, with an atomic weight of 217. This change is much more rapid than that of the radium into emanation. The emanation is much more unstable than the radium itself. While radium takes 1300 years to transmute itself by half, the same process is accomplished in radium emanation in 3*8 days. If, therefore, the emanation is drawn off into a separate tube, half of it is precipitated on the walls within 3*8 days, with evolution of helium. If now the helium and the remaining emanation is drawn off by a current of gas, we have a deposit of radium A on the walls of the tube far too minute to be seen or weighed, but discoverable by its radio-activity. For radium A also decomposes. It is soluble in strong acids, which, however, do not affect its rate of disintegration. It can be volatilised at 1000 C.,but again without affecting its rate of inevitable decay. Its disintegration is accompanied by another expul- sion of a helium atom the third so far and the remainder forms another solid deposit called radium 2/O THE ELECTRON THEORY B. This conversion completes itself half in three minutes, and is the most rapid of all radium trans- formations. Radium B volatilises at 700 C. It disintegrates in turn, transforming itself by half in 2 1 minutes. But this transformation is not accom- panied by any expulsion, and probably consists in some rearrangement of material within the atom. The next stage is radium C, another solid sub- stance, which volatilises at 1000 C., and makes up for the absence of rays in radium B by emitting no less than three different kinds of rays. Each atom of radium C which decomposes throws off a helium atom and an electron, and gives rise to an electro- magnetic wave-pulse or Rontgen ray. Its time of half-decay, T, is 28 minutes. Radium B was dis- covered solely through the initial irregularity of the curves of decay of radium C. These three pro- ducts, radium A, B, and C, together form the active deposit due to radium emanation. But after their disintegration, which, we have seen, does not take many minutes, they give rise to three further pro- ducts, called radium D, E, and F respectively, which together form the " permanent " active deposit. T is about 40 years in the case of radium D, and the change is another rayless one. T for radium E is six days. It is non-volatile, but gives off electrons and Rontgen rays. The final product is radium F, whose T is 143 days. It gives off helium atoms (a-rays) only, and is deposited on bismuth from RADIO-ACTIVITY 271 solution. This radium F is an exceedingly in- teresting body. All its properties are identical with those of another radio-active body discovered independently by Madame Curie, and called by her " Polonium," in honour of her native country, and also by Marckwald in Germany, who found it associated with tellurium, and therefore styled it " radio-tellurium." The credit of accomplishing the long and laborious researches for tracing the parent- age of polonium belongs to Rutherford, of Montreal. Here is the full pedigree : Radium gives off helium atoms. Emanation .1 Radium A Radium B no rays. Radium C helium atoms, electrons, and X-rays. Radium D no rays. Radium E electrons and X-rays. Radium F helium atoms. = Polonium = radio-tellurium. It will be remembered that all these changes, except the evolution of helium, are undiscoverable by chemical or even spectroscopic means. The sub- stances only identify themselves by their radiations, and the manner in which that radiation decays. The radiations may be observed in different ways ; but the most convenient method is by the ionisa- tion of air, whereby a delicate electroscope is dis- 272 THE ELECTRON THEORY charged. For aught we know, many more changes may be continually going on, not only in radio- active bodies, but in ordinary matter. The a-rays or helium atoms cease to produce ionisation when their velocity falls below the enormous figure of 10 9 cm. per second, or one-thirtieth of that of light. Con- sequently, it is quite possible that all matter may be gradually disintegrating, but not with the ex- plosive violence of the radio-active bodies, and there- fore unperceived. Many indications go to show that polonium itself eventually changes into either lead or bismuth. Uranium, thorium, and actinium show a some- what similar life-history ; but in their case the first product formed is not an emanation, but a solid. Uranium gives rise to " Uranium X," and any further change is at present unknown. Uranium takes about 600 million years to transform itself by half. Each atom which disintegrates gives off an a-particle (helium atom), and leaves behind an atom of a new substance, which disintegrates much more easily. This new substance is called uranium X. It was for some time considered to be the sole active constituent of uranium. Its discovery is described by Kutherford as follows : "The experiments of Mme. Curie show that the radio-activity of uranium and radium is an atomic phenomenon. The activity of any uranium compound depends only on the amount of that KADIO- ACTIVITY 273 element present, and is unaffected by its chemical combination with other substances, and is not appreciably affected by wide variations of tempe- rature. It would thus seem probable, since the activity of uranium is a specific property of the element, that the activity could not be separated from it by chemical agencies. In 1900, however, Sir William Crookes showed that, by a single chemical operation, uranium could be obtained photographically inactive, while the whole of the activity could be concentrated in a small residue free from uranium. This residue, to which he gave the name of ' Ur X,' was many hundred times more active photographically, weight for weight, than the uranium from which it had been separated. The method employed for this separation was to pre- cipitate a solution of the uranium with ammonium carbonate. On dissolving the precipitate in an excess of the reagent a light precipitate remained behind. This was filtered, and constituted the Ur X. The active substance Ur X was probably present in a very small quantity, mixed with im- purities derived from the uranium. No new lines were observed in the spectrum. A partial separa- tion of the activity of uranium was also effected by another method. Crystallised uranium nitrate was dissolved in ether, when it was found that the uranium divided itself between the ether and water present in two unequal fractions. The small part S 2/4 THE ELECTRON THEORY dissolved in the water layer was found to contain practically all the activity when examined by the photographic method, while the other fraction was almost inactive. These results, taken by them- selves, pointed very strongly to the conclusion that the activity of uranium was not due to the element itself, but to some other substance associated with it, which had distinct chemical properties. " Results of a similar character were observed by Becquerel. It was found that barium could be made photographically very active by adding barium chloride to the uranium solution and precipitating the barium as sulphate. By a succession of preci- pitations the uranium was rendered photographi- cally almost inactive, while the barium was strongly active. "The inactive uranium and the active barium were laid aside; but, on examining them a year later, it was found that the uranium had completely regained its activity, while that of the barium had completely disappeared. The loss of activity of uranium was thus only temporary in character/ 7 The obvious explanation of this peculiar be- haviour was that uranium continually evolves some substance much more active than itself, which can be chemically separated from it. This new sub- stance, Uranium X, decays to half- value in 22 days, instead of hundreds of millions of years. The original uranium can only be identified by a feeble RADIO-ACTIVITY 275 radio-activity consisting in the expulsion of helium atoms. Thorium and actinium give rise to similar pro- ducts called thorium X and actinium X respec- tively. From these a gas or emanation is developed, which, however, is extremely unstable and takes only a few seconds to decay by half. Thorium emana- tion gives rise to two successive decomposition products called thorium A and thorium B. They form a deposit on bodies and are concentrated on the cathode in an electric field. Thorium A is more volatile than thorium B. Lastly, actinium emanation gives rise to actinium A and actinium B, which are deposited on bodies concentrated on the cathode in an electric field, and are soluble in ammonia and strong acids : they are volatilised at the boiling-point of water. Actinium A can be separated from actinium B by electrolysis. Both thorium B and actinium B emit three sorts of rays, while their " parents " emit none. Their life period counts by minutes. These are all the radio-active bodies and disin- tegration products hitherto known. The list will, no doubt, soon be extended possibly into the region of well-known bodies like lead, mercury, and gold. Research is busy with the momentous question as to whether any artificial method can accelerate or retard this process of disintegration. This is a question not at all easy of solution. The 276 THE ELECTRON THEORY effect of heat may not be to accelerate or retard decay, but to make the presence or absence of a given substance either more or less evident to us, as they differ in melting-point or volatility. The fact that uranium shows the same activity in liquid air and at ordinary temperatures goes to show that the activity resides within the atom itself, P. Curie also found that the luminosity of radium and its power of exciting fluorescence in bodies were retained at the temperature of liquid air. If a radium com- pound is heated in an open vessel, it is found that the activity, measured by the a-rays, falls to about 25 per cent, of its original value. This, however, is explained by Rutherford as not being due to a change in the radio-activity, but to the release of the radium-emanation, which is stored in the radium. No alteration is observed if the radium is heated in a closed vessel, from which none of the radio-active products are able to escape. Of all the radio-active materials mentioned, radium possesses the most striking properties. It is two million times more active than uranium, and a few milligrammes suffice to produce strong photographic action, to discharge electroscopes, to give a brilliant luminosity to a fluorescent screen, and to produce dangerous and painful effects on the skin. All radium compounds shine in the dark, especially when dry. A small quantity has been known to give light enough to read by in a RADIO-ACTIVITY 277 dark room, though that practice is by no means to be recommended. But it is not the purest pre- parations of radium salt that give most light. A strong admixture of barium increases the lumi- nosity, which is by no means so well-defined a property as the radio-activity. A radium preparation usually a few milli- grammes of radium bromide mounted between thin glass plates gives out a-rays, /3-rays (which are identical with projected electrons and cathode rays), and the so-called y-rays, or ether pulses, which do not consist of any kind of projected particles. The a-rays are, as mentioned above, in all probability atoms of helium, and are, there- fore, very much bulkier than electrons. The latter have, indeed, a hundred times more power of pene- tration than the former, and can pass through a sheet of aluminium half a millimetre thick. But this power of penetration is surpassed over a hun- dred times by the y-rays, the most penetrating radiation known, which can pierce through 3 in. of aluminium and J in. of lead ! That these three radiations are simultaneously emitted by the radium preparation is readily understood if we consider that the preparation contains not only the original radium, wKich slowly evolves helium atoms, but also the emanation and the active deposits, including radium C, which gives off all those classes of rays. 278 THE ELECTRON THEORY The three radiations are readily separated by a strong magnetic field. If a thin line of radium is placed along the lines of force in a narrow hori- zontal trough, the y-rays shoot straight upwards, while the /3-rays, being electrons, are bent over to one side, and the a-rays deflected to a very much slighter extent towards the other side. Those electrons that are projected in a line at right angles to the trough describe complete circles if free to do so, and it is possible to make them record their presence on a photographic film at any point in the circumference. Such tracings of the path of the electrons projected by radium are capable of great delicacy. Kaufmann succeeded in showing both their magnetic and electric de- flection simultaneously, and was thus enabled to determine the ratio of the charge to the mass. It turned out to be exactly the same as the value deduced from cathode rays and from the Zeeman effect, and thus furnished a striking proof of the fundamental importance and identity of electrons. A remarkable phenomenon, first observed by Curie, is that radium maintains itself steadily at a temperature about 3 above its surroundings. This heat is most due to the expulsion of helium atoms. It has been calculated that 1 gramme of radium gives off 100 gramme-calories of heat per hour. This would mean that during its whole " life " it RADIO-ACTIVITY 279 would give off 1/6 X 10 9 gramme-calories, or about a million times more energy, weight for weight, than was hitherto known in any chemical reaction. This fact enables us to realise the vast forces which may become available once we can control the rate of disintegration of the atom. It confirms what was said in the initial chapters with regard to the vast stores of energy perceptible in the most elementary electrical phenomena as soon as we deal with them on a molecular scale. CHAPTER XVI CONSTITUTION OF THE ELECTRON WE have seen that practically all the known pheno- mena of electricity and magnetism can be explained by assuming that 1. The electric current consists in the motion of very small electric particles called electrons, having a definite and constant charge, and a definite mass which is constant, but becomes larger at very high velocities. 2. These electrons are usually associated with atoms of ordinary matter, round which they de- scribe circular or elliptical orbits, with periods approaching those of visible light-waves. 3. That there is a force of attraction between the atoms and the electrons belonging to it which continues to act when they are separated, but rapidly decreases with increasing distance. 4. That atoms deprived of electrons repel each other. 5. That electrons mutually repel each other. 6. That electrons moving side by side through the ether attract each other with a force propor- 280 CONSTITUTION OF THE ELECTRON 28 1 tional to their speed, and inversely proportional to the square of their distance apart. 7. A change of momentum of an electron pro- duces a change of momentum in every other electron in the opposite direction. These assumptions and their corollaries embrace nearly all the facts hitherto accumulated. They are few in number surprisingly few considering the vast array of facts they cover and certainly fewer than those which form the basis of any of the older theories. But the human mind is never satisfied to take things, even simple things, for granted. These things must be " explained " in their turn that is to say, they must be reduced to other and fewer and more familiar ideas. Such curiosity is legitimate so long as there are any facts remaining unaccounted for. But if it should be found that all facts are satisfactorily explained by the assumptions of the electron theory, then the science of electricity will be complete, and further research into the cause and reasonableness of the fundamental assumptions will add nothing new to electrical science. They may add to our knowledge, indeed ; but that new knowledge will constitute a new science. This is made evident by a glance at mathematical astronorfiy. All its facts are accounted for by Newton's law of gravita- tion, which states that two heavenly bodies attract each other with a force proportional to the product 282 THE ELECTRON THEORY of their masses, and inversely proportional to the square of their distance apart. Further research into the nature of gravitational force will not amplify mathematical astronomy, nor will it enable us to predict astronomical events with greater accuracy than before. If, however, the law of gravitation should be found to be subject to ex- ceptions, the theory will have to be recast, and this will mean, not a retrogression, but an advance towards new and more general truths. As J. J. Thomson says, the electron is at present better known than the atom. It is likely, there- fore, that an electron theory of the chemical atom will shortly come into being. Such a theory is made necessary by the facts of radio-activity where atoms are found throwing off electrons and positive particles. These electrons and positive particles must therefore have been constituents of the atom. The atom, with its detachable electrons, is some- times compared to the solar system. The analogy is somewhat far-reaching, and deserves to be pointed out, if only to assist the memory and the imagina- tion. If the solar system is an atom on a large scale, the sun must be regarded as the positive nucleus, and the planets as the electrons. It is actually found that the sun has a positive charge, and the earth a negative charge. But these charges are comparatively infinitesimal, and do not perceptibly CONSTITUTION OF THE ELECTRON 283 influence the force between them. In this point, therefore, the analogy fails. On the other hand, the ratio of the masses is very instructive. That of Jupiter is about one- thousandth of that of the sun, and approaches the mass of an electron in comparison with a hydrogen atom. The mass of the earth is ^TO-THF f that f the sun an( ^ this ratio is nearly the same as that of an electron to the atoms of the heavy metals. We may say, therefore, that in the solar system we have ex- amples of the various actual ratios of mass as between an electron and its positive nucleus, though in the case of atoms it is the atoms themselves, and not the electrons, which vary in mass. The solar system may be regarded as a magnetic molecule. The charge of the earth is at the very least 2 5 million coulombs or " armies " of electrons. This charge passes round the sun once every year, so that the current represented by the earth's motion is 25 million coulombs per annum, or just about 1 ampere (O'l " electro-magnetic " unit of current). The magnetic moment (see p. 167) of the system sun-earth may be obtained by multiplying the current by the area round which it circulates. The area of the earth's orbit is about 10 27 square centimetres, so that the magnetic moment of the system sun-earth is 1 26 c.g.s. units. This moment is too small to exert any measurable effect outside 284 THE ELECTRON THEORY the solar system, not to speak of influencing the orientation of the planetary orbits of other stars. Hence we see, as before, that magnetic and electric forces play no appreciable part in the motions of the heavenly bodies. It may well be, however, that the sun's positive electric charge just balances the negative charges of the planets, in which case the solar system would represent a neutral atom of matter. If, under such circumstances, another neutral solar system were to approach ours sufficiently closely to entice Neptune from its allegiance to our own sun, we should have an illustration of two atoms combining, and then separating with opposite charges, our solar system being positively charged, and the foreign system negatively, having captured one " electron/' Neptune, from us. Thus we should represent, say, a mercury atom, and the foreign solar system, say, a chlorine atom. As matters stand, the solar systems of the visible universe do not seem to approach together so closely as to interfere with each other's planets. The visible universe thus represents a gas rather than a liquid or solid, except that portion called the Milky Way, which appears to have a con- sistency capable of giving it a metallic appearance if it could, by some magic means, be reduced to tangible dimensions. The visible stars number quite a thousand million. CONSTITUTION OF THE ELECTRON 285 Now, the smallest object visible in a microscope contains at least a hundred million atoms. We may take it for granted, then, that the visible uni- verse, whose outer edge is the Milky Way, if reduced in the same proportion that an electron bears to the earth, would resemble something rather like a human blood corpuscle, and would contain about the same number of atoms. A blood corpuscle is too small to observe indi- vidually its electric and magnetic properties, not to speak of examining the properties of its individual atoms and electrons. A large number of universes would have to be taken together, and the results would be average values. If we can imagine a giant of this new Brobdingnag endeavouring to arrive at some measurements of the masses, veloci- ties, and electric charges of the stars and planets " atoms " and " electrons " he would call them he might very well find the same average value for each million of them which he might pick out at random. He might find that the ratio of the charge to the mass of each detachable planet was the same, and that the charge of each planet ap- proached a standard value within the limits of hi powers of measurement. He would naturally arrive at the same conclusion as we do with regard to the electrons viz. that they are absolutely constant and equal bodies, constituting the physical units and vehicles of electricity. 286 THE ELECTRON THEORY Further, our giant might be able to sort the various solar systems according to their masses, and establish certain " chemical " affinities between systems of different mass. He might find that the masses, which he would call " atomic weights," showed a certain constancy, and a determining influ- ence upon the affinity and chemical characteristics, and would thus be led to discover a large-scale " periodic law/' He might, by compression or chemical treatment, bring the solar systems closer together, and enable a certain number of planets to roam at large among the fixed stars. He would thus have produced a " conductor." Finally, he might succeed in turning the ecliptics of the various solar systems into the same plane, and thus would produce a " magnet " of stupendous magnitude. We thus see that much insight into molecular physics may be gained by considerations of astro- nomical phenomena happening on a much larger scale. The scale by which we must reduce the visible universe to get it down to microscopic dimensions is 10 22 to 1. The radius of the solar system is, roughly, 10 U cm. This, on dividing by 10 22 , be- comes 10~ 8 cm., the radius of an atom. Neptune, one of the most " detachable " planets we have, may be likened to a detachable electron. Its radius is about 10 9 cm., and this, reduced in the CONSTITUTION OF THE ELECTRON 287 same proportion, becomes 10~ 13 cm., the radius of an electron. The mass of Neptune bears about the same ratio to that of the solar system as that of an electron bears to that of a lithium or oxygen atom, so that the analogy still holds good. The distance between the sun and the nearest fixed star is about 10 18 cm., and this, divided by 10 22 , becomes 10~ 4 cm., or 0*001 mm., which is the mean free path of a molecule of air on a high mountain. If, besides reducing the linear dimensions from 10 22 to 1, we suppose the present velocities of the heavenly bodies to be maintained, we obtain some very interesting and suggestive results. Since Nep- tune takes some 220 years to revolve once round the sun, its " frequency " of revolution (i.e. revolutions per second) is 1*5 x 10~ 10 . Since the path is reduced 10 22 times, the frequency of describing it will be increased in the same proportion, and will become 1'5 x 10 12 . This is the frequency of some infra- red waves of light. The frequency of the planet Mercury will become 1*25 x 10 15 , which lies in the ultra-violet. All the other planets will produce spectrum lines intermediate between these i.e. lying in the visible spectrum. The asteroids will produce a broad band instead of a line, and there will be certain extra lines due to perturbations of the planets by each other. The solar system will, therefore, present a spectrum much resembling the spec- trum of a chemical element. This is a striking feature 288 THE ELECTRON THEORY of the analogy between an atom and a planetary system. We may also, of course, reverse the process by taking the Lilliput world of the atom and the elec- tron, and enlarging it by the factor 10 22 , leaving all its velocities as they were. An atom of, say, oxygen would thus become of the same size as the solar system, and its two detachable electrons would closely resemble Uranus and Neptune as regards size, distance from the sun, and period of revolution. One of the electrons more closely bound up with the atom, and assisting in producing the phenomena of magnetism and radiation, but not of conduction, might resemble the earth in size, and distance from the sun, and might revolve round the latter in one sidereal year. We naturally expect an electron, when enlarged to the size of the earth, to be a perfectly smooth sphere. At least, so we are accus- tomed to find it described. But such a sphere is, in reality, absolutely inconceivable ; nor is it necessary to imagine it to be so. An electron may have a structure resembling that of the earth in every par- ticular, and yet not only could that make no differ- ence to its electrical or astronomical properties, but the fact of its having such a structure would remain for ever unknown to us, considering the scale of phenomena which are accessible to our senses. We may therefore, without in the least interfering with the efficiency of the electron as a universal vehicle of CONSTITUTION OF THE ELECTRON 289 electrical manifestations, imagine it to be a veritable microcosm, a world in which life might not very materially differ from life on our earth. Indeed, considering that time and space would be reduced in the same constant and uniform proportion, it is doubtful whether our present instruments, thus suddenly transformed, would be able to indicate the occurrence of any fundamental change. This is but another illustration of the well-known principle that size and length of time are purely relative, and depend upon comparison with standards. If all dimensions, including the standards, were reduced in the same proportion, or if all things were accele- rated or retarded in the same proportion, we should be absolutely unaware that anything had happened. On the other hand, if any intelligent being could be transferred from the microcosm to our present world, and could keep up some connection with the microcosm, his busy life here would appear to the inhabitants of the microcosm to be a changeless eternity, since any change measurable by them would take millions of their years to accomplish itself. We here enter upon the region of pure specula- tion, and it is not the function of a scientific work to deal with occult problems of that kind. But since the electron theory promises to guide us further into the mysteries of matter than anything attempted hitherto, it is necessary to discuss the T 2QO THE ELECTRON THEORY general prospect even cursorily. To sum up, we find in the fruitful and suggestive astronomico-chemical analogy a boundless vista of worlds within worlds, which, while rightly preventing us from setting a limit to the multiplicity of possible phenomena, comforts us with the reflection that for our purposes, and as far as our present senses are concerned, the multiplicity of phenomena has an absolute limit, which makes it possible to look forward to the eventual formulation of a theory embracing all phenomena accessible to our senses. CHAPTEE XVII DIMENSIONS OF ELECTRICAL QUANTITIES THE discovery that electricity has an atomic struc- ture, that its carriers are discrete particles, brings the desirability of recasting our dimensional formulae into renewed prominence. We find that electricity is as fundamental as mass, perhaps, indeed, more fundamental, and all indications point to the ad- vantage of recognising electricity as a fundamental natural quantity. The other fundamental quanti- ties so far recognised are length, mass, and time. They are called fundamental quantities because, while none of them can be measured in terms of the rest of them, the three quantities are capable of measuring other more complex quantities. Thus, we require no fundamental unit for velocity. We measure it in terms of our units of space and time, as cm. per second, or miles per hour. Neither do we require a separate fundamental unit for work, which can be expressed in foot-pounds * or horse- power-hours. There is nothing to prevent us adopt- ing a special unit for it, such as the erg ; but this unit is not fundamental, as it can be reduced to mass, space, and time. 291 2Q2 THE ELECTRON THEORY A formula which expresses the manner in which the three fundamental units enter into the com- position of derived units is called a dimensional formula. These formulae are very useful in giving us an analysis of the structure of a physical quan- tity, much as chemical formulae reveal to us the structure of the chemical molecule. They are also useful for converting quantities from one system of measurement to another. The fundamental quantities mass, length, and time are denoted by the symbols M, L, and T re- spectively. Of these, L is the most fundamental of all, since M and T are often measured as lengths on a scale referred to the dimensions of the earth. T is referred to the time of rotation of the earth about its axis. M is referred to L and T by the stipulation that the unit of mass is the mass of water contained in one cubic centimetre when at its greatest density. Thus we see that size and rotation of the earth as a whole give us our standards of space and time, and that a peculiar chemical sub- stance water gives us the standard of mass. This again illustrates the less fundamental character of mass. The measurement of an area requires two inde- pendent measurements of length, the results being multiplied together. Denoting each measurement by L, the measurement of an area may, therefore, be denoted by L 2 , and the measurement of a volume DIMENSIONS OF ELECTRICAL QUANTITIES 293 by L 3 . The last formula also indicates that when the linear scale is altered in any ratio, the numerical result will be altered in the third power of that ratio, since the three results of the separate measure- ments of length are affected in the same manner. The measurement of a velocity involves the simul- taneous measurement of a length and a time. The velocity increases with the length, and decreases with the time taken to describe it. The dimensional formula of velocity is, therefore, ^, or, as it is more usually written, LT' 1 . In measuring acceleration, we measure the velocity acquired in a certain time. There are, therefore, two independent measures of time involved in the same determination, and the dimensional formula becomes LT~ 2 . Force is measured by the mass moved and the velocity it acquires in unit time. Its dimensional formula is MLT" 2 . Work or energy, measured by the product of force into distance, is represented by ML 2 T- 2 , and so on. It has sometimes been proposed to eliminate M from the dimensional calculus and to reduce it to L and T, as these are more fundamental. This can be done as soon as we can obtain an equation from which M may be evolved in terms of L apd T. For this purpose we must find another permanent and universal property of mass besides that of always acquiring the same velocity under a given impulse. If, for instance, all bodies were equally dense, mass 294 THE ELECTRON THEORY would become identical with volume, and its furmula would be L 3 . This, of course, is not by any means the case. But there is another universal property of mass, discovered by Newton. It is that the force of attraction between two masses is directly pro- portional to the product of the masses and inversely proportional to the square of the distance between them. This force may therefore be put = -= or M 2 L" 2 . A force, as we may have seen above, has the dimensional formula M L T" 2 . Hence we have MLT- 2 = M 2 L- 2 which cannot be true unless either (a) some other quantity, such as the density of the ether, is left out of account, or (&) mass is expressible in terms of L and T. For it is obvious that the dimensional formulae must be the, same on both sides of the equation. We can never equate a length with a time, since they are two essentially different quantities. It would be like saying, for instance, that three horses equal three dogs. Adopting the alternative (6), and dividing both sides by M, we obtain L T- 2 = M L- 2 or M = L 3 T- 2 which may be regarded as the product of a length into the square of a velocity. Since, however, we are as yet in entire ignorance of what that supposed velocity and length may signify, the gain is trifling. We might, indeed, measure the masses of different DIMENSIONS OF ELECTRICAL QUANTITIES 295 bullets of the same size by the depth to which they penetrate into wood when fired with a given velocity ; but the new method would be clumsy in comparison with the usual weighing methods. Besides, the discarding of M would make us lose a definite and useful physical conception which appeals directly to our muscular sense. Now, all the arguments in favour of retaining mass as a fundamental quantity also tell in favour of recognising electric quantity as a fundamental quantity. And it has a natural unit, the electron, of a much more prevailing and universal kind. Electric quantity may be measured by any one of the many sets of phenomena in which the amount of it present plays a decisive part. We have already described the two chief systems of measuring electricity, one derived from electro- static repulsion (p. 38), and the other from electro- dynamic or magnetic force (p. 148). To these may be added the chemical system, which furnishes the most accurate method, though usually based upon the electro-magnetic system. The electrostatic system derives its unit of electricity from the re- pulsion of two quantities of the same sign placed at unit distance apart. This is like deducing the unit of mass from its gravitational attraction. The equation is MLT-2=E 2 L- 2 where E is the quantity of electricity. If we wish 296 THE ELECTRON THEORY to reduce E to M, L, and T, we must solve the above equation for E. We obtain This dimensional formula for E is very complicated, and its interpretation is made difficult owing to the fractional index of M, which seems irrational. And even if we adopt it we do not know what pro- perties of the medium we are leaving out of account. Besides, we obtain a different dimensional formula for E when we deduce it from some other property, such as magnetic force. It is, therefore, more advisable to consider quantity of electricity a funda- mental quantity, and to refer it to the electron as a standard, or to any of its measurable effects. By doing this we obtain a uniform, simple, and rational system of dimensional formulae, as will be seen in what follows. The fundamental units are M mass, L length, T time, and E electricity. We obtain the following dimensional formulae : Electric quantity, E. Surface density of electricity, or quantity of elec- tricity per sq. cm., EL" 2 . Electric current, quantity of electricity passing a given surface in one second, E T" 1 . Current density, current per sq. cm. of section across conductor, E T" 1 L~ 2 . Electric force, same formula as force, M L T" 2 . DIMENSIONS OF ELECTRICAL QUANTITIES 297 Electrostatic field, force exerted on unit quantity of electricity, M L T' 2 E" 1 . Electric potential, work done on unit quantity, M L 2 T- 2 E- 1 . Dielectric constant, (density of electrons) X (dis- placement in unit field), E 2 M" 1 Ir 3 T 2 . Resistance, by Ohm's law, E.M.F. / current, ML 2 T -l E -2 Resistivity or specific resistance, resistance of 1 cm. cube, M L 3 T- 1 E~ 2 . Conductivity (specific), inverse of resistivity, M- 1 L- 3 T E 2 . This last admits of a simple interpretation in accordance with the electron theory (see p. 108). We may write it E_ L E L 3 " T ' MLT- 2 ' Or (electrons per c.c.) x (velocity of electrons) x ( g-r^ ) That is to say, the specific conductivity is measured by the number of free electrons per cubic cm., multiplied by the steady speed which each free electron acquires in a unit field. We also get the following magnetic formulae : Magnetic moment, current multiplied by area round which it circulates, E T" 1 L 2 . Magnetic pole-strength, magnetic moment per unit length, ET- 1 !,. Magnetic force, same as force. 298 THE ELECTRON THEORY Magnetic potential, work per unit magnet pole, M -I LT -I E -I. Magnetic field, force per unit magnet pole, E -i MT -i Intensity of magnetisation, magnetic moment per unit volume, ET" 1 L~ 1 , which means the current circulating round unit length of the magnet. Strength of a magnetic shell, E T' 1 ( = current circulating round it), Magnetic flux, field multiplied by area, E -1 MT -1 L 2 Magnetic susceptibility, intensity of magnetisation acquired in unit field, E 2 M' 1 L' 1 . Finally, for inductance, or the coefficient of self- induction, being the E.M.F. induced in a circuit by unit charge of current per second, we obtain M L 2 T- 2 E" 1 , or M L* E~ 2 . The above dimensional formulae exhibit at a glance the structure and derivation of the various electric and magnetic quantities, and their con- nection with the unit of electricity. Practical Units. The natural unit of electricity is the electron. But it is so excessively small that it would be necessary to adopt a large multiple of it in practice say, a trillion electrons, or 0*112 coulomb sufficient to pass 0'126 milligrammes of silver through an electrolytic cell. This, however, is at present impossible, since the charge of an electron DIMENSIONS OF ELECTRICAL QUANTITIES 299 is not known with, sufficient accuracy. In any case, it would be unwise to dislocate electrical engineer- ing by displacing the present units unless some very great advantage would accrue therefrom. The practical unit of electricity is the coulomb, which contains 8*79 trillion electrons. This unit I have sometimes called an " army " of electrons, not in order to displace the word coulomb, but to empha- sise the atomic structure of electricity, and also to distinguish it from the much smaller electrostatic unit or "company" (see p. 38). The ratio of the two units is 3 x 10 10 , or the figure representing the velocity of light. The magnetic attraction between two electrons moving side by side through the ether just balances their electrostatic repulsion when their velocity reaches that figure. The practical unit of current strength is the amp&re, consisting in the passage of one coulomb per second through any cross-section of the con- ductor. If a current of one amp&re is sent through an electrolytic cell or voltameter consisting of silver electrodes immersed in a solution of silver nitrate, the current deposits 1-118 milligrammes of silver per second. This is the legal definition of current strength. It may also be arrived at through mag- netic attraction (see p. 153), and that* is how the unit of current was originally fixed. But the " electro-magnetic " unit of current is ten times the value of the ampere. 3OO THE ELECTRON THEORY The next most important unit is that of differ- ence of potential. To bring a quantity of electricity from a point at low potential to a point at high potential requires an expenditure of work. This work per unit quantity measures the difference of potential between the two points. We might define unit difference of potential as existing between two points when it requires one " erg " of work to bring one " company " or electrostatic unit of electrons from one to the other. This is the electrostatic unit of difference of potential. The practical unit is the volt, which is ^^-th part of this. To take one coulpmbjbhrough a difference o_f potential of one volt requires an expenditure of 10 million ergs, a quan- tity which has been called one "joule," after Joule, the discoverer of the law of heating in current- bearing wires. Conversely, when one coulomb falls through one volt, one joule of work may be derived _from it. As a rule, it is represented by the heat in the wire, generated by the stoppages of the electrons. The most obvious way of defining conductivity would be to ascribe unit conductivity to a substance containing one free electron per cubic cm., capable of acquiring a steady speed of one cm. per second, under the influence of a field of one volt per cm., or to stipu- late that in such a field one electron per second should pass through every square cm. of the cross-section. But in practice the conductivity is derived from DIMENSIONS OF ELECTRICAL QUANTITIES 30 1 the resistance, and this is derived from the current and voltage. A conductor has a unit resistance of one " ohm " if a current of one ampere flows through it on applying a difference of potential of one volt to its ends. The work done by a current is measured in joules. The rate of work or " power " is measured by the product of current and voltage, the unit being the watt, consisting of one joule per second. Many practical electricians measure the work in watt- seconds or kilowatt-hours rather than in joules. One kilowatt-hour is 3,600,000 joules, or 3'6 X 10 13 ergs. It has already been stated (p. 168) that unit magnetic pole is possessed by a long thin magnet of 1 sq. cm. sectional area if the current circulating round it amounts to one .electro-magnetic unit (=10 amperes) per cm. le'ngth. In this case the practical unit (the ampere) is not adopted, and the same may be said of the other magnetic quantities, which were originally based upon the repulsion between two similar magnet poles. The most im- portant of these are the magnetic moment (length multiplied by pole strength), the magnetic field (force per unit pole), intensity of magnetisation (mag- netic moment per unit volume), and the magnetic susceptibility (magnetisation in unit field). The magnetic " permeability " is the total field existing in the interior of a substance when immersed in 302 THE ELECTRON THEORY unit field. It is measured by 1 + 4?rK, where K is the magnetic susceptibility. The " induction " B is the product of the permeability and the field strength. It represents the actual internal mag- netic field of the substance. /This magnetic " induction " must be carefully distinguished from the electro-magnetic induction which gives rise to induced currents, and also from the electrostatic induction or "influence," which gives rise to charges in bodies when brought into an electric field. It is unfortunate that this word has acquired three different meanings. / When a current through a conductor changes, the inertia of the moving electrons, whether due to their own motion or to the reaction of surrounding electrons, represents a store of energy which is expended in resisting the change, and this store of energy per unit quantity in motion may be measured in volts. When the current either decreases or increases at the rate of one ampere per second, and the E.M.F. thus induced in the circuit is one volt, the conductor is said to have unit inductance. This unit of inductance is called one henry. It is 10 9 times the unit derived from theoretical con- siderations of the E.M.F. induced in a conductor traversed by lines of force, where the inductance is defined as the number of lines of force added to or subtracted from those traversing the circuit owing to the change of current (see p. 189). DIMENSIONS OF ELECTRICAL QUANTITIES 303 The development of electrical science has suffered much by the existence of three different systems of electrical units, called the electrostatic, electro- magnetic, and the practical units respectively. This multiplicity of systems was due to ignorance as to the real nature of magnetism, and to the prevalence of false analogies between electric and magnetic phenomena. We now see that magnetism is re- ducible to the revolution of electrons. It has sometimes been urged as an objection to this view that there would have to be some gyroscopic action due to the innumerable minute molecular gyro- scopes constituted by the revolving electrons. But this objection leaves out of account the extreme shortness of the period of revolution, a shortness which enables the electron to follow a rotation much as a high-frequency galvanometer needle gives a dead-beat reading. The electron theory, with its logical corollary the recognition of electricity as a fundamental quantity gives a consistent and comprehensive view of all the facts of electricity and magnetism hitherto accumulated. Within the next few years we shall, no doubt, witness its application to every detail of electrical science. EEFERENCES To some of the Principal Papers dealing with Electrons, arranged alphabetically according to Authors. ABRAHAM, MAX : Dynamics of the Electron (Annalen der PhysiJc 10, pp. 105-179, 1903). ARRHENIUS, S. : lonisation (Textbook of Electro-chemistry). BECQUEREL, HENRI : Uranium Radiation, &c. (Oomptes Rendus 122, pp. 301, 359, 420, 501, 559, 689, 762, 1086, 1896 ; 129, p. 996, 1899). CROOKES, Sir WILLIAM: Radiant Matter (British Association, Sheffield, 1879). CURIE, P. and S. : Radium (Comptes Rendus 127, p. 1215, 1898). DRUDE, P. : Electron Theory of Metals (Annalen der Physik 1, p. 566, 1900 ; 3, p. 369, 1900). Optics (Lehrbuch der Optik). ELSTER and GEITEL : Atmospheric Electricity (Physikalische Zeit- schrift 1, p. 11, 1899; p. 245, 1900; 2, p. 116, 1900; p. 590, 1901 ; 3, p. 305, 1902). FLEMING, J. A. : Electronic Theory (Popular Science Monthly, May 1902). GIESE, W. : Corpuscular Theory of Conduction (Wiedemann's An- nalen 37, p. 576, 1889). HERTZ, H. : Influence of Ultra-violet Light on the Electric Dis- charge (Wied. Ann. 31, p. 983, 1887). KAUFMANN, W. : Electro-Magnetic Mass of the Electron (Gottinyer Nachrichten, p. 90, 1903). 305 U 306 REFERENCES LANGEVIN, P. : Mobility of Ions in the Atmosphere (Oomptes Rendus 134, p. 646, 1902). - Theory of Magnetism (Journal de Physique, October 1905). LARMOR, JOSEPH : " Ether and Matter." LENARD, P. : Cathode Rays in the Open Air ( Wied. Ann. 51, p. 225, 1894). LODGE, Sir OLIVER : On Electrons (Electrician, 1903). LORENTZ, H. A.: Propagation of Light (Wied. Ann. 9, 1880). - Zeeman Effect (Paris Congress, 1900, Report, vol. iii. p. 1). - Metallic Absorption and Emission (Proceedings Amsterdam Academy , 1902-3, p. 666). MCCLELLAND, J. A. : Conductivity of Flame Gases (Philosophical Magazine 46, p. 29, July 1898). MARX, ERICH : Hall Effect in Flame Gases (Physikalische Zeitschrift 2, p. 412, 1901). , H. : Dynamics of the Electron (Comptes Rendus 140, p. 1504, 1905). RlECKE, E. : Electron Theory (Annalen der Physilc 4, p. 378, 1901 ; 7, p. 401, 1902 ; Physikalische Zeitschrift 2, p. 182, 1901). RUTHERFORD, E. : Uranium Rays (Phil. Mag. 47, p. 109, 1899). - Radium Rays (Phil. Mag. 5, p. 177, 1903). - and SODDY: Disintegration Products of Radium (Phil. Mag., p. 576, 1903). SCHUSTER, ARTHUR : Discharge through Gases (Proceedings Royal Society 47, p. 526, 1890). - Metallic Conduction (Phil. Mag. 38, p. 151, 1904). SIMON, S. : Ratio of Charge to Mass (Wied. Ann. 69, p. 589, 1899). STARK, J. : lonisation by Shock (Annalen der Physilc 7, p. 417, 1902; PhysiJcal. Zeitschr. 5, p. 51, 1903). STONEY, G. JOHNSTONE: Elementary Quantity of Electricity (British Association, Belfast Report, 1874 ; Transactions Royal Dublin Society 4, p. 563, 1891). REFERENCES 307 THOMSON, J. J. : Electric and Magnetic Effect of Moving Electrified Bodies (Phil. Mag. 11, p. 229, 1881). THOMSON, J. J., and E. RUTHEKFOED: Passage of Electricity through Ionised Gases (Phil. Mag. 42, p. 392, 1896). Cathode Rays (Phil. Mag. 44, p. 293, 1897). Electric Charge Transported by Ions (Phil. Mag. 4.6, p. 528, 1898 ; 5, p. 346, 1903). Theory of Gaseous Conductivity (Phil. Mag. 47, p. 253, 1899). lonisation by Discharge (Phil. Mag. 50, p. 278, 1900). TOWNSBND, J. S. : Gaseous Conductivity produced by Shock (Phil. Mag. 1, p. 198, 1901). Diffusion of Ions in a Gas (Philosophical Transactions Royal Society 193A, p. 129, 1900). WIECHEBT, E. : Velocity and Magnetic Deflection of Cathode Rays (Wied. Ann. 69, p. 739, 1899). WIEN, W. : Electric Discharge in Gases ( Wied. Ann. 65, p. 440, 1898). Electro- Magnetic Foundation of Mechanics (ArcMves Neer- landaises, 5, p. 96). WILSON, C. T. R. : Condensation Nuclei (Phil. Trans. Royal Society 192A, p. 403, 1899). WILSON, H. A. : Charge of Gaseous Ions (Phil. Mag. 5, p. 429, 1903). NOTE. Most of the above papers are reprinted in Les Quantites JElemcntaires d' Jtllectricite : Ions, Electrons, Corpmcules, published by the French Physical Society in 1905 (Gauthiers Villars, Paris). INDEX ABEAHAM, 22 Absorption of light, 204, 233 Actinium, 272 Ampere unit, 91 definitions of, 155 "Army" of 8'79 trillion elec- trons, 91 Arrhenius, 99, 104 Astronomical analogy, 282 Atoms in 1 cc. copper, 28 BECQUEEEL, 21, 127, 214 Bucherer, 22 CANAL rays, 119 Capacity, 51 Cathode rays, Circuit, 98 Circular polarisation, 202 Clausius, vii Colour, 205, 228 " Company" of 2930 million electrons, 38 Condensers, 52 Conduction in liquids and solids, difference, 101 metallic, nature of, 84 Conductivity, 297 elements of, 107 Conductors, nature of, 35 Constitution of the electron, 280 Contact electrification, 134 Corpuscle, 219 Coulomb's magnetic law, 174 Coulomb unit, 91 Crookes, 81, 273 Curie, 21 Madame, 265 DAEK space, 79 d'Arsonval, 211 Dependent discharge, 77 Detachable electrons, 28 Diamagnetism, 160, 204 Dielectrics, 225 Dielectric strength, 67 Dimensions of electric quanti- ties, 291 Direction of flow of current, 9 Discharge in general, 69 through insulators, 72 through gases, 75 through solid conductors, 83 through liquids, 98 through a vacuum, 114 Dispersion, 228 Dissociation, 99 Distribution of free charges, 35 Double refraction, 235 Drude, 21,228 ELECTEICITY a fundamental quantity, 295 Electro-dynamics, 146 Electrolysis, 98 Electro-magnetic waves, 196, 227 Electrometers, 60 Electro-motive force, 97 Electron at rest, 23 charge of, tf '4 x 10" 10 elec- trostatic units, 37 mass of, 0-61 x 10' 37 gr., 23 name, 219 properties of, 23 radius of, 10- 13 cm., 23 theory of gravitation, 30 309 INDEX Electrons and matter, 25 Electrostatic machines, 65 Elster and Geitel, 139 Emanation, 268 Equipotential surface, 46 Erg, 86 Ettingshausen effect, 257 Ewing, 162 FAEADAY, 5, 180 effect, 247 Faraday's laws of electrolysis, 110, 112 Ferro-magnetism, 160 Fluid theory, 7 Franklin, 3, 7, 220 Frequency of revolution, 32 Frictional electrification, 65, 142 Fuechtbauer, 138 GALVANIC cell, 143 Galvano-magnetic effects, 252 Galvanometer, 156 Glow discharge. 79 Gramme-molecule, 102 HALL effect, 16, 256 Hankel series, 140 Heating effect of current, 92 Helium, 268 Helmholtz on "Atoms of Elec- tricity," 13 Hertz, 139 Hydrated atoms, 103 IMAGES, electric, 50 Independent discharge, 77 Induced currents, 176 Inductance, 189, 298 Induction, 302 Infinite series, 41 Influence, 37 Insulators, 53 Intensity of magnetisation, 161 Internal resistance, 97 lonisation, 68, 71, 76, 86, 147 JOULE'S law, 92, 150 Joule unit, 300 KAUFMANN, 21, 214, 278 Kayser and Runge, xvi Kerr effect, 249 Kilowatt hours, 301 Kinetic energy, 177 Kirchhoff's laws, 95 LANGEVIN, 22, 160 Larmor, 22 Lecher wire system, 198 Leduc effect, 257 Lenard, 19, 214 Leyden jar, 57 Liebenow, 129 Lines of force, 4, 5, 180 Lodge, 22 Longitudinal magneto - thermal effects, 259 Lorentz, 21, 228, 239 MACALUSO and Corbino, 250 Magnetic flux, 185 force, 147 moment, 167 pole, 160 repulsion, 174 shell, strength of, 298 susceptibility, 298, 301 Magnetism, 159 Magneto-optics, 237 Maxwell, x Maxwell-Bartol's pressure, 120 Maxwell's ' ' Atom of Electri city," 14 Mean free path, xi Measurements concerning elec- trons, 206 Molecular magnets, 161 NEGATIVE atoms, 103 Nernst effect, 257 OHM'S law, 92 Ohm unit, 98 Optical rotation, 235 Orbital velocity of electrons, 32 Osmotic pressure, 113 INDEX PARAMAGNETISM, 159^, Peltier effect, 124 Permeability, 301 Photo-electric current, 140 Plane -polarised vibrations, 202 Point discharge, 78 Polarisation of light, 234 Pole-strength, 167 Polonium, 271 Positive atoms, 27, 31, 36, 38 and negative, 9, 65 Potential, 39, 46 Power, 301 Practical units, 298 Propagation of electric force, 193, 200 of waves, 226 RADIANT matter, 15, 81 Radiation, 190 Radio-activity, 264 Radio- tellurium, 271 Radium, 267 products, 269 Rate of decay, 268 Reflection, 233 Refraction, 224 Repulsion, mutual, of two elec- trons, 23 Residual magnetism, 166 Resistance, definition, 90 Resistivity of electrolytes, 109 Riecke, 21 Rontgen rays, 88, 11* Rotation, optical, 235 Rutherford, 21, 266 Rydberg, xvi SATURATION current, 82 Schuster, A., 19, 21, 84, 222, 228 Seebeck's discovery, 126 Self-induction, 189 Semi-permeable membranes, 113 Simon, 21, 214 Solar system a magnetic mole- cule, 283 Solenoid, 156 Sommerfeld, 22 Spark, electric, 77 Specific inductive capacity, 62 Stark, 139 Stoney, G. Johnstone, 14, 219 Symmer, 9 THERMO-ELECTRICITY, 121 Thermo-magnetic effects, 252 Thompson, Silvanus, 186 Thomson, J. J., 21, 37, 84, 181, 209, 214, 217 Thomson effect, 132 Thorium, 272 Townsend, 21 ULTRA-VIOLET light, discharg- ing effect of, 116 Unit of current, 91, 153 Units, fundamental, 292 Uranium, 272 VACUUM an insulator, 34 Velocity of cathode rays, 116 Volt, 300 Voltaic electricity, 134 Volta series, 140 WATERSTON, vii Watt unit, 301 Wave-lengths, 32 Weber's molecular currents, 12 Wiechert, 211, 214 Wien, 22, 119 Wilson, 21, 217 ZEEMAN, 20, 228, 278 effect, 237 . Printed by BALLANTYNE, HANSON & Co. Edinburgh &> London UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. DEC 3 1947 FEB 7- 1955 JAN I 11955 r\ OCT 3 1362 REC'D LC OCT 2 '63-12 LD 21-100m-9,'47(A5702sl6)476 VB 095^6 \ < Foamier