< 
 
 v/ 
 
 
 
 ^ 
 
 
 
 
 
 
 \ 
 
 
 \ 
 
 

 ^a> 
 
THE ELECTRON 
 
THE UNIVERSITY OF CHICAGO PRESS 
 CHICAGO, ILLINOIS 
 
 THE BAKER & TAYLOR COMPANY 
 
 NEW YORK 
 
 THE CAMBRIDGE UNIVERSITY PRESS 
 
 LONDON AND EDINBURGH 
 
 THE MARUZEN-KABUSHIKI-KAISHA 
 
 TOKYO, OSAKA, KYOTO, FTTKUOKA, SENDAI 
 
 THE MISSION BOOK COMPANY 
 
 SHANGHAI 
 
THE ELECTRON 
 
 ITS ISOLATION AND MEASUREMENT AND THE 
 
 DETERMINATION OF SOME OF 
 
 ITS PROPERTIES 
 
 By 
 
 ROBERT ANDREWS MILLIKAN 
 
 Professor of Physics, the University of Chicago 
 
 THE UNIVERSITY OF CHICAGO PRESS 
 CHICAGO, ILLINOIS 
 
COPYRIGHT 1917 BY 
 THE UNIVERSITY OF CHICAGO 
 
 All Rights Reserved 
 
 Published August 1917 
 Second Impression February 1918 
 Third Impression November 1918 
 
 Composed and Printed By 
 
 The University of Chicago Press 
 
 Chicago, Illinois, U.S.A. 
 
 GIFT 
 
TO 
 
 ALBERT A. MICHELSON 
 
 AND 
 MARTIN A. RYERSON 
 
 THIS SMALL OUTGROWTH OF THEIR 
 INSPIRATION AND GENEROSITY 
 IS RESPECTFULLY DEDICATED 
 
PREFACE 
 
 It is hoped that this volume may be of some interest 
 both to the physicist and to the reader of somewhat less 
 technical training. It has been thought desirable for 
 the sake of both classes of readers, not to break the 
 thread of the discussion in the body of the book with 
 the detailed analyses which the careful student demands. 
 It is for this reason that all mathematical proofs have 
 been thrown into appendixes. If, in spite of this, the 
 general student finds certain chapters, such as vii and 
 viii, unintelligible, it is hoped that without them he may 
 yet gain some idea of certain phases at least of the 
 
 progress of modern physics. 
 
 R. A. MILLIKAN 
 May 18, 1917 
 
CONTENTS 
 
 INTRODUCTION . 
 
 I. EARLY VIEWS OF ELECTRICITY ....... 6 
 
 II. THE EXTENSION OF THE ELECTROLYTIC LAWS TO 
 CONDUCTION IN GASES ......... 25 
 
 III. EARLY ATTEMPTS AT THE DIRECT DETERMINATION 
 
 OF e .............. 43 
 
 IV. GENERAL PROOF OF THE ATOMIC NATURE OF ELEC- 
 TRICITY ............. 64 
 
 V. THE EXACT EVALUATION OF e .... . . 88 
 
 yi. THE MECHANISM OF IONIZATION OF GASES BY X-RAYS 
 
 AND RADIUM RAYS .......... 123 
 
 VII. BROWNIAN MOVEMENTS IN GASES . . ... 142 
 
 VIII. THE EXISTENCE OF A SUB-ELECTRON ? . . . . 155 
 
 IX. THE STRUCTURE OF THE ATOM ...... 179 
 
 X. THE NATURE OF RADIANT ENERGY ..... 217 
 
 APPENDIX A. ne FROM MOBILITIES AND DIFFUSION CO- 
 
 EFFICIENTS ............ 239 
 
 APPENDIX B. TOWNSEND'S FIRST ATTEMPT AT A DETERMI- 
 
 NATION OF e ....... ... 242 
 
 APPENDIX C. THE BROWNIAN-MOVEMENT EQUATION . . 245 
 
 APPENDIX D. THE ENERTIA OR MASS OF AN ELECTRICAL 
 
 CHARGE ON A SPHERE OF RADIUS a ..... 249 
 
 APPENDIX E. MOLECULAR CROSS -SECTION AND MEAN 
 
 FREE PATH ......... 252 
 
 xi 
 
xii CONTENTS 
 
 PAGE 
 
 APPENDIX F. NUMBER OF FREE POSITIVE ELECTRONS IN 
 THE NUCLEUS OF AN ATOM BY RUTHERFORD'S 
 METHOD 254 
 
 APPENDIX G. BOHR'S THEORETICAL DERIVATION OF THE 
 
 VALUE OF THE RYDBERG CONSTANT 259 
 
 APPENDIX H. THE ELEMENTS, THEIR ATOMIC NUMBERS, 
 
 ATOMIC WEIGHTS, AND CHEMICAL POSITIONS . . . 261 
 
 INDEXES 265 
 
INTRODUCTION 
 
 Perhaps it is merely a coincidence that the man who 
 first noticed that the rubbing of amber would induce 
 in it a new and remarkable state now known as the 
 state of electrification was also the man who first gave 
 expression to the conviction that there must be some 
 great unifying principle which links together all phe- 
 nomena and is capable of making them rationally intel- 
 ligible; that behind all the apparent variety and change 
 of things there is some primordial element, out of which 
 all things are made and the search for which must be 
 the ultimate aim of all natural science. Yet if this be 
 merely a coincidence, at any rate to Thales of Miletus 
 must belong a double honor. For he first correctly 
 conceived and correctly stated, as far back as 600 B.C., 
 the spirit which has actually guided the development 
 of physics in all ages, and he also first described, though 
 in a crude and imperfect way, the very phenomenon the 
 study of which has already linked together several of 
 the erstwhile isolated departments of physics, such as 
 radiant heat, light, magnetism, and electricity, and 
 has very recently brought us nearer to the primordial 
 element than we have ever been before. 
 
 Whether this perpetual effort to reduce the com- 
 plexities of the world to simpler terms, and to build up 
 the infinite variety of objects which present themselves 
 to our senses out of different arrangements or motions of 
 the least possible number of elementary substances, is a 
 
2 THE ELECTRON 
 
 modern heritage from Greek thought, or whether it is a 
 native instinct of the human mind may be left for the 
 philosopher and the historian to determine. Certain it 
 is, however, that the greatest of the Greeks aimed at 
 nothing less than the complete banishment of caprice 
 from nature and the ultimate reduction of all her pro- 
 cesses to a rationally intelligible and unified system. 
 And certain it is also that the periods of greatest progress 
 in the history of physics have been the periods in which 
 this effort has been most active and most successful. 
 
 Thus the first half of the nineteenth century is 
 unquestionably a period of extraordinary fruitfulness. 
 It is at the same time a period in which for the first time 
 men, under Dalton's lead, began to get direct, experi- 
 mental, quantitative proof that the atomic world which 
 the Greeks had bequeathed to us, the world of Leucippus 
 and Democritus and Lucretius, consisting as it did of an 
 infinite number and variety of atoms, was far more com- 
 plex than it needed to be, and that by introducing the 
 idea of molecules built up out of different combinations 
 and groupings of atoms the number of necessary elements 
 could be reduced to but about seventy. The importance 
 of this step is borne witness to by the fact that out of it 
 sprang in a very few years the whole science of modern 
 chemistry. 
 
 And now this twentieth century, though but sixteen 
 years old, has already attempted to take a still bigger 
 and more significant step. By superposing upon the 
 molecular and the atomic worlds of the nineteenth cen- 
 tury a third electronic world, it has sought to reduce the 
 number of primordial elements to not more than two, 
 namely, positive and negative electrical charges, Along 
 
INTRODUCTION 3 
 
 with this effort has come the present period of most 
 extraordinary development and fertility a period in 
 which new viewpoints and indeed wholly new phenomena 
 follow one another so rapidly across the stage of physics 
 that the actors themselves scarcely know what is happen- 
 ing a period too in which the commercial and industrial 
 world is adopting and adapting to its own uses with a 
 rapidity hitherto altogether unparalleled the latest prod- 
 ucts of the laboratory of the physicist and the chemist. 
 As a consequence, the results of yesterday's researches, 
 designed for no other purpose than to add a little more 
 to our knowledge of the ultimate structure of matter, are 
 today seized upon by the practical business world and 
 made to multiply tenfold the effectiveness of the tele- 
 phone or to extract six times as much light as was 
 formerly obtained from a given amount of electric power. 
 It is then not merely a matter of academic interest 
 that electricity has been proved to be atomic or granular 
 in structure, that the elementary electrical charge has 
 been isolated and accurately measured, and that it has 
 been found to enter as a constitutent into the making of 
 all the seventy-odd atoms of chemistry. These are 
 indeed matters of fundamental and absorbing interest to 
 the man who is seeking to unveil nature's inmost secrets, 
 but they are also events which are pregnant with mean- 
 ing for the man of commerce and for the worker in the 
 factory. For it usually happens that when nature's 
 inner workings have once been laid bare, man sooner or 
 later finds a way to put his brains inside the machine and 
 to drive it whither he wills. Every increase in man's 
 knowledge of the way in which nature works must, in 
 the long run, increase by just so much man's ability to 
 
4 THE ELECTRON 
 
 control nature and to turn her hidden forces to his own 
 account. 
 
 The purpose of this volume is to present the evidence 
 for the atomic structure of electricity, to describe some 
 of the most significant properties of the elementary elec- 
 trical unit, 'the electron, and to discuss the bearing of 
 these properties upon the two most important problems 
 of modern physics: the structure of the atom and the 
 nature of electromagnetic radiation. In this presenta- 
 tion I shall not shun the discussion of exact quantitative 
 experiments, for it is only upon such a basis, as Pythago- 
 ras asserted more than two thousand years ago, that any 
 real scientific treatment of physical phenomena is pos- 
 sible. Indeed, from the point of view of that ancient 
 philosopher, the problem of all natural philosophy is to 
 drive out qualitative conceptions and to replace them by 
 quantitative relations. And this point of view has been 
 emphasized by the farseeing throughout all the history of 
 physics clear down to the present. One of the greatest 
 of modern physicists, Lord Kelvin, writes: 
 
 When you can measure what you are speaking about and 
 express it in numbers, you know something about it, and when 
 you cannot measure it, when you cannot express it in numbers, 
 your knowledge is of a meagre and unsatisfactory kind. It may 
 be the beginning of knowledge, but you have scarcely in your 
 thought advanced to the stage of a science. 
 
 Although my purpose is to deal mostly with the 
 researches of which I have had most direct and intimate 
 knowledge, namely, those which have been carried on dur- 
 ing the past ten years in this general field in the Ryerson 
 Laboratory, I shall hope to be able to give a correct and 
 just review of the preceding work out of which these 
 
INTRODUCTION 5 
 
 researches grew, as well as of parallel work carried on in 
 other laboratories. In popular writing it seems to be 
 necessary to link every great discovery, every new theory, 
 every important principle, with the name of a single indi- 
 vidual. But it is an almost universal rule that develop- 
 ments in physics actually come about in a very different 
 way. A science, like a planet, grows in the main by a 
 process of infinitesimal accretion. Each research is 
 usually a modification of a preceding one; each new 
 theory is built like a cathedral through the addition by 
 many builders of many different elements. This is pre- 
 eminently true of the electron theory. It has been a 
 growth, and I shall endeavor in every case to trace the 
 pedigree of each research connected with it. 
 
CHAPTER I 
 
 EARLY VIEWS OF ELECTRICITY 
 I. GROWTH OF THE ATOMIC THEORY OF MATTER 
 
 There is an interesting and instructive parallelism 
 between the histories of the atomic conception of matter 
 and the atomic theory of electricity, for in both cases the 
 ideas themselves go back to the very beginnings of the 
 subject. In both cases too these ideas remained abso- 
 lutely sterile until the development of precise quantita- 
 tive methods of measurement touched them and gave 
 them fecundity. It took two thousand years for this 
 to happen in the case of the theory of matter and one 
 hundred and fifty years for it to happen in the case of 
 electricity; and no sooner had it happened in the case of 
 both than the two domains hitherto thought of as dis- 
 tinct began to move together and to appear as perhaps 
 but different aspects of one and the same phenomenon, 
 thus recalling again Thales' ancient belief in the essential 
 unity of nature. How this attempt at union has come 
 about can best be seen by a brief review of the histories 
 of the two ideas. 
 
 The conception of a world made up of atoms which 
 are in incessant motion was almost as clearly developed 
 in the minds of the Greek philosophers of the School of 
 Democritus (420 B.C.), Epicurus (370 B.C.), and Lucre- 
 tius (Roman, 50 B.C.) as it is in the mind of the modern 
 physicist, but the idea had its roots in one case in a mere 
 speculative philosophy; in the other case, like most of 
 
 6 
 
EARLY VIEWS OF ELECTRICITY 7 
 
 our twentieth-century knowledge, it rests upon direct, 
 exact, quantitative observations and measurement. Not 
 that the human eye has ever seen or indeed can ever see 
 an individual atom or molecule. This is forever impos- 
 sible, and for the simple reason that the limitations on our 
 ability to see small objects are imposed, not by the imper- 
 fections of our instruments, but by the nature of the eye 
 itself, or by the nature of the light-wave to which the 
 eye is sensitive. If we are to see molecules our biological 
 friends must develop wholly new types of eyes, viz., 
 eyes which are sensitive to waves one thousand times 
 shorter than those to which our present optic nerves can 
 respond. 
 
 But after all, the evidence of our eyes is about the 
 least reliable kind of evidence which we have. We are 
 continually seeing things which do not exist, even though 
 our habits are unimpeachable. It is the relations which 
 are seen by the mind's eye to be the logical consequences 
 of exact measurement which are for the most part 
 dependable. So far as the atomic theory of matter is 
 concerned, these relations have all been developed since 
 1800, so that both the modern atomic and the modern 
 kinetic theories of matter, in spite of their great an- 
 tiquity, are in a sense less than one hundred years old. 
 Indeed, nearly all of our definite knowledge about mole- 
 cules and atoms has come since 1851, when Joule 1 in 
 England made the first absolute determination of a 
 molecular magnitude, namely, the average speed with 
 which gaseous molecules of a given kind are darting 
 hither and thither at ordinary temperatures. This 
 
 1 Mem. of the Manchester Lit. and Phil. Soc. (1851; 2d series), 107; 
 Phil. Mag., XIV (1857), 211. 
 
8 THE ELECTRON 
 
 result was as surprising as many others which have 
 followed in the field of molecular physics, for it showed 
 that this speed, in the case of the hydrogen molecule, has 
 the stupendous value of about a mile a second. The 
 second molecular magnitude to be found was the mean 
 distance a molecule of a gas moves between collisions, 
 technically called the mean free path of a molecule. 
 This was computed first in 1860 by Clerk Maxwell. 1 It 
 was also 1860 before anyone had succeeded in making any 
 sort of an estimate of the number of molecules in a cubic 
 centimeter of a gas. When we reflect that we can now 
 count this number with probably greater precision than 
 we can attain in determining the number of people living 
 in New'York, in spite of the fact that it has the huge 
 value of 27.05 billion billion, one gains some idea of how 
 great has been our progress in mastering some at least 
 of the secrets of the molecular and atomic worlds. The 
 wonder is that we got at it so late. Nothing is more sur- 
 prising to the student brought up in the atmosphere of 
 the scientific thought of the present than the fact that the 
 relatively complex and intricate phenomena of light and 
 electromagnetism had been built together into moder- 
 ately consistent and satisfactory theories long before the 
 much simpler phenomena of heat and molecular physics 
 had begun to be correctly understood. And yet almost 
 all the qualitative conceptions of the atomic and kinetic 
 theories were developed thousands of years ago. Tyn- 
 dall's statement of the principles of Democritus, whom 
 Bacon considered to be "a man of mightier metal than 
 
 1 Phil. Mag., XIX (1860; 4th series), 28. Clausius had discussed 
 some of the relations of this quantity in 1858 (Pogg. Ann., CV [1858], 
 239), but Maxwell's magnificent work on the viscosity of gases first 
 made possible its evaluation. 
 
EARLY VIEWS OF ELECTRICITY 9 
 
 Plato or Aristotle, though their philosophy was noised and 
 celebrated in the schools amid the din and pomp of pro- 
 fessors/' will show how complete an atomic philosophy 
 had arisen 400 years B.C. "That it was entirely de- 
 stroyed later was not so much due to the attacks upon 
 it of the idealistic school, whose chief representatives were 
 Plato and Aristotle, as to the attacks upon all civiliza- 
 tion of Genseric, Attila, and the barbarians." That the 
 Aristotelian philosophy lasted throughout this period is 
 explained by Bacon thus: "At a time when all human 
 learning had suffered shipwreck these planks of Aris- 
 totelian and Platonic Philosophy, as being of a lighter 
 and more inflated substance, were preserved and came 
 down to us, while things more solid sank and almost 
 passed into oblivion." 
 
 Democritus' principles, as quoted by Tyndall, are as 
 follows : 
 
 1. From nothing comes nothing. Nothing that exists can be 
 destroyed. All changes are due to the combination and separation 
 of molecules. 
 
 2. Nothing happens by chance. Every occurrence has its 
 cause from which it follows by necessity. 
 
 3. The only existing things are the atoms and empty space; 
 all else is mere opinion. 
 
 4. The atoms are infinite in number and infinitely various in 
 form; they strike together and the lateral motions and whirlings 
 which thus arise are the beginnings of worlds. 
 
 5. The varieties of all things depend upon the varieties of 
 their atoms, in number, size, and aggregation. 
 
 6. The soul consists of fine, smooth, round atoms like those 
 of fire. These are the most mobile of all. They interpenetrate 
 the whole body and in their motions the phenomena of life arise. 
 
 These principles with a few modifications and omis- 
 sions might almost pass muster today. The great 
 advance which has been made in modern times is not so 
 
io THE ELECTRON 
 
 much in the conceptions themselves as in the kind of 
 foundation upon which the conceptions rest. The prin- 
 ciples enumerated above were simply the opinions of one 
 man or of a school of men. There were scores of other 
 rival opinions, and no one could say which was the better. 
 Today there is absolutely no philosophy in the field other 
 than the atomic philosophy, at least among physicists. 
 Yet this statement could not have been made even as 
 much as ten years ago. For in spite of all the multiple 
 relationships between combining powers of the elements, 
 and in spite of all the other evidences of chemistry and 
 nineteenth-century physics, a group of the foremost of 
 modern thinkers, until quite recently, withheld their 
 allegiance from these theories. The most distinguished 
 of this group was the German chemist and philosopher, 
 Wilhelm Ostwald. However, in the preface to a new 
 edition of his Outlines of Chemistry he now makes the 
 following clear and frank avowal of his present position 
 He says: 
 
 I am now convinced that we have recently become possessed 
 of experimental evidence of the discrete or grained nature of 
 matter for which the atomic hypothesis sought in vain for hun- 
 dreds and thousands of years". The isolation and counting of 
 gaseous ions on the one hand .... and on the other the agree- 
 ment of the Brownian movements with the requirements of the 
 kinetic hypothesis .... justify the most cautious scientist in 
 now speaking of the experimental proof of the atomic theory of 
 matter. The atomic hypothesis is thus raised to the position of 
 a scientifically well-founded theory. 
 
 II. GROWTH OF ELECTRICAL THEORIES 
 
 The granular theory of electricity, while unlike the 
 atomic and kinetic theories of matter in that it can boast 
 
EARLY VIEWS OF ELECTRICITY n 
 
 no great antiquity in any form, is like them in that the 
 first man who speculated upon the nature of electricity at 
 all conceived of it as having an atomic structure. Yet it 
 is only within very recent years twenty at the most 
 that the modern electron theory has been developed. 
 There are no electrical theories of any kind which go 
 back of Benjamin Franklin (1750). Aside from the dis- 
 covery of the Greeks that rubbed amber had the power 
 of attracting to itself light objects, there was no knowl- 
 edge at all earlier than 1600 A.D., when Gilbert, Queen 
 Elizabeth's surgeon, and a scientist of great genius and 
 insight, found that a glass rod and some twenty other 
 bodies, when rubbed with silk, act like the rubbed amber 
 of the Greeks, and he consequently decided to describe 
 the phenomenon by saying that the glass rod had become 
 electrified (amberized, electron being the Greek word for 
 amber), or, as we now say, had acquired a charge of 
 electricity. In 1733 Dufay, a French physicist, further 
 found that sealing wax, when rubbed with cat's fur, was 
 also electrified, but that it differed from the electrified 
 glass rod, in that it strongly attracted any electrified body 
 which was repelled by the glass, while it repelled any 
 electrified body which was attracted by the glass. He 
 was thus led to recognize two kinds of electricity, which 
 he termed " vitreous" and " resinous." About 1747 
 Benjamin Franklin, also recognizing these two kinds of 
 electrification, introduced the terms "positive" and 
 "negative," to distinguish them. Thus, he said, we will 
 arbitrarily call any body positively electrified if it is 
 repelled by a glass rod which has been rubbed with silk, 
 and we will call any body negatively electrified if it is 
 repelled by sealing wax which has been rubbed with cat's 
 
12 THE ELECTRON 
 
 fur. These are today our definitions of positive and nega- 
 tive electrical charges. Notice that in setting them up we 
 propose no theory whatever of electrification, but con- 
 tent ourselves simply with describing the- phenomena. 
 
 In the next place it was surmised by Franklin and 
 indeed asserted by him in the very use of the terms 
 "positive" and "negative," although the accurate proof 
 of the relation was not made until the time of Faraday's 
 ice-pail experiment in 1837, that when glass is positively 
 electrified by rubbing it with silk, the silk itself takes up 
 a negative charge of exactly the same amount as the 
 positive charge received by the glass, and, in general, 
 that positive and negative electrical charges always appear 
 simultaneously and in exactly equal amounts. 
 
 So far, still no theory. But in order to have a 
 rational explanation of the phenomena so far considered, 
 particularly this last one, Franklin now made the assump- 
 tion that something which he chose to call the electrical 
 fluid or "electrical fire" exists in normal amount as a con- 
 stituent of all matter in the neutral, or unelectrified state, 
 and that more than the normal amount in any body is 
 manifested as a positive electrical charge, and less than 
 the normal amount as a negative charge. Aepinus, pro- 
 fessor of physics at St. Petersburg and an admirer of 
 Franklin's theory, pointed out that, in order to account 
 for the repulsion of two negatively electrified bodies, it 
 was necessary to assume that matter, when divorced from 
 Franklin's electrical fluid, was self-repellent, i.e., that it 
 possessed properties quite different from those which are 
 found in ordinary unelectrified matter. In order, how- 
 ever, to leave matter, whose independent existence was 
 thus threatened, endowed with its familiar old properties, 
 
EARLY VIEWS OF ELECTRICITY 13 
 
 and in order to get electrical phenomena into a class by 
 themselves, other physicists of the day, led by Symmer, 
 1759, preferred to assume that matter in a neutral state 
 shows no electrical properties because it contains as con- 
 stituents equal amounts of two weightless fluids which they 
 called positive and negative electricity, respectively. From 
 this point of view a positively charged body is one in 
 which there is more of the positive fluid than of the nega- 
 tive, and a negatively charged body is one in which the 
 negative fluid is in excess. 
 
 Thus arose the so-called two-fluid theory a theory 
 which divorced again the notions of electricity and mat- 
 ter after Franklin had taken a step toward bringing them 
 together. This theory, in spite of its intrinsic difficulties, 
 dominated the development of electrical science for one 
 hundred years and more. This was because, if one did 
 not bother himself much with the underlying physical 
 conception, the theory lent itself admirably to the 
 description of electrical phenomena and also to mathe- 
 matical formulation. Further, it was convenient for the 
 purposes of classification. It made it possible to treat 
 electrical phenomena in a category entirely by them- 
 selves, without raising any troublesome questions as to 
 the relation, for example, between electrical and gravita- 
 tional or cohesive forces. But in spite of these advan- 
 tages it was obviously a makeshift. For the notion of 
 two fluids which could exert powerful forces and yet 
 which were absolutely without weight the most funda- 
 mental of physical properties and the further notion of 
 two fluids which had no physical properties whatever, 
 that is, which disappeared entirely when they were 
 mixed in equal proportions these notions were in a 
 
14 THE ELECTRON 
 
 high degree non-physical. Indeed, J. J. Thomson 
 remarked in his Silliman Lectures in 1903 that 
 
 the physicists and mathematicians who did most to develop the 
 fluid theories confined their attention to questions which involved 
 only the law of forces between electrified bodies and the simulta- 
 neous production of equal quantities of plus and minus electricity, 
 and refined and idealized their conception of the fluids themselves 
 until any reference to their physical properties was considered 
 almost indelicate. 
 
 From the point of view of economy in hypothesis, 
 Franklin's one-fluid theory, as modified by Aepinus, was 
 the better. Mathematically the two theories were iden- 
 tical. The differences may be summed up thus. The 
 modified one-fluid theory required that matter, when 
 divorced from the electrical fluid, have exactly the same 
 properties which the two-fluid theory ascribed to nega- 
 tive electricity, barring only the property of fluidity. 
 So that the most important distinction between the 
 theories was that the two-fluid theory assumed the exist- 
 ence of three distinct entities, named positive electricity, 
 negative electricity, and matter, while the one-fluid 
 theory reduced these three entities to two, which Franklin 
 called matter and electricity, but which might perhaps as 
 well have been called positive electricity and negative 
 electricity, unelectrified matter being reduced to a mere 
 combination of these two. 
 
 Of course, the idea of a granular structure for elec- 
 tricity was foreign to the two-fluid theory, and since this 
 dominated the development of electrical science, there 
 was seldom any mention in connection with it of an elec- 
 trical atom, even as a speculative entity. But with 
 Franklin the case was different. His theory was essen- 
 
EARLY VIEWS OF ELECTRICITY 15 
 
 tially a material one, and he unquestionably believed in 
 the existence of an electrical particle or atom, for he says : 
 "The electrical matter consists of particles extremely 
 subtle, since it can permeate common matter, even the 
 densest, with such freedom and ease as not to receive any 
 appreciable resistance." When Franklin wrote that, 
 however, he could scarcely have dreamed that it would 
 ever be possible to isolate and study by itself one of 
 the ultimate particles of the electrical fluid. The 
 atomic theory of electricity was to him what the 
 atomic theory of matter was to Democritus, a pure 
 speculation. 
 
 The first bit of experimental evidence which appeared 
 in its favor came in 1833, when Faraday found that the 
 passage of a given quantity of electricity through a solu- 
 tion containing a compound of hydrogen, for example, 
 would always cause the appearance at the negative 
 terminal of the same amount of hydrogen gas irrespec- 
 tive of the kind of hydrogen compound which had been 
 dissolved, and irrespective also of the strength of the 
 solution; that, further, the quantity of electricity 
 required to cause the appearance of one gram of hydro- 
 gen would always deposit from a solution containing 
 silver exactly 107 . i grams of silver. This meant, since 
 the weight of the silver atom is exactly 107 . i times the 
 weight of the hydrogen atom, that the hydrogen atom 
 and the silver atom are associated in the solution with 
 exactly the same quantity of electricity. When it was 
 further found in this way that all atoms which are 
 univalent in chemistry, that is, which combine with one 
 atom of hydrogen, carry precisely the same quantity of 
 electricity, and all atoms which are bivalent carry twice 
 
1 6 THE ELECTRON 
 
 this amount, and, in general, that valency, in chemistry, 
 is always exactly proportional to the quantity of elec- 
 tricity carried by the atom in question, it was obvious 
 that the atomic theory of electricity had been given very 
 strong support. 
 
 But striking and significant as were these discoveries, 
 they did not serve at all to establish the atomic hypothe- 
 sis of the nature of electricity. They were made at the 
 very time when attention began to be directed strongly 
 away from the conception of electricity as a substance 
 of any kind, and it was no other than Faraday himself 
 who, in spite of the brilliant discoveries just mentioned, 
 started this second period in the development of electrical 
 theory, a period lasting from 1840 to about 1900. In 
 this period electrical phenomena are almost exclusively 
 thought of in terms of stresses and strains in the medium 
 which surrounds the electrified body. Up to this time 
 a more or less definite something called a charge of elec- 
 tricity had been thought of as existing on a charged body 
 and had been imagined to exert forces on other charged 
 bodies at a distance from it in quite the same way in 
 which the gravitational force of the earth acts on the 
 moon or that of the sun on the earth. This notion of 
 action at a distance was repugnant to Faraday, and he 
 found in the case of electrical forces experimental reasons 
 for discarding it which had not then, nor have they as yet, 
 been found in the case of gravitational forces. These 
 reasons are summed up in the statement that the electri- 
 cal force between two charged bodies is found to depend 
 on the nature of the intervening medium, while gravita- 
 tional pulls are, so far as is known, independent of inter- 
 vening bodies. Faraday, therefore, pictured to himself 
 
EARLY VIEWS OF ELECTRICITY 17 
 
 the intervening medium as transmitting electrical force 
 in quite the same way in which an elastic deformation 
 started at one end of a rod is transmitted by the rod. 
 Further, since electrical forces act through a vacuum, 
 Faraday had to assume that it is the ether which acts as 
 the transmitter of these electrical stresses and strains. 
 The properties of the ether were then conceived of as 
 modified by the presence of matter in order to account 
 for the fact that the same two charges attract each other 
 with different forces according as the intervening medium 
 is, for example, glass, or ebonite, or air, or merely ether. 
 These views, conceived by Faraday and put into mathe- 
 matical form by Maxwell, called attention away from 
 the electrical phenomena in or on a conductor carrying 
 electricity and focused it upon the stresses and strains 
 taking place in the medium about the conductor. When 
 in T886 Heinrich Hertz in Bonn, Germany, proved by 
 direct experiment that electrical forces are indeed trans- 
 mitted in the form of electric waves, which travel through 
 space with the speed of light exactly as the Faraday- 
 Maxwell theory had predicted, the triumph of the 
 ether-stress point of view was complete. Thereupon 
 textbooks were written by enthusiastic, but none too 
 cautious, physicists in which it was asserted that an 
 electric charge is nothing more than a " state of strain 
 in the ether," and an electric current, instead of repre- 
 senting the passage of anything definite along the wire, 
 corresponds merely to a continuous "slip" or "break- 
 down of a strain" in the medium within the wire. 
 Lodge's book, Modern Views of Electricity, has been the 
 most influential disseminator and expounder of this 
 point of view. 
 
1 8 THE ELECTRON 
 
 Now what had actually been proved was not that 
 electricity is a state of strain, but that when any elec- 
 trical charge appears upon a body the medium about the 
 body does indeed become the seat of new forces which 
 are transmitted through the medium, like any elastic 
 forces, with a definite speed. Hence it is entirely proper 
 to say that the medium about a charged body is in a 
 state of strain. But it is one thing to say that the elec- 
 trical charge on the body produces a state of strain in the 
 surrounding medium, and quite another thing to say that 
 the electrical charge is nothing but a state of strain in the 
 surrounding medium, just as it is one thing to say that 
 when a man stands on a bridge he produces a mechanical 
 strain in the timbers of the bridge, and another thing to 
 say that the man is nothing more than a mechanical 
 strain in the bridge. The practical difference between 
 the two points of view is that in the one case you look 
 for other attributes of the man besides the ability to 
 produce a strain in the bridge, and in the other case you 
 do not look for other attributes. So the strain theory, 
 although not irreconcilable with the atomic hypothesis, 
 was actually antagonistic to it, because it led men to 
 think of the strain as distributed continuously about the 
 surface of the charged body, rather than as radiating from 
 definite spots or centers peppered over the surface of the 
 body. Between 1833 and 1900, then, the physicist was 
 in this peculiar position: when he was thinking of the 
 passage of electricity through a solution, he for the most 
 part, following Faraday, pictured to himself definite 
 specks or atoms of electricity as traveling through the 
 solution, each atom of matter carrying an exact multiple, 
 which might be anywhere between one and eight, of q 
 
EARLY VIEWS OF ELECTRICITY 19 
 
 definite elementary electrical atom, while, when he was 
 thinking of the passage of a current through a metallic 
 conductor, he gave up altogether the atomic hypothesis, 
 and attempted to picture the phenomenon to himself as 
 a continuous "slip" or "breakdown of a strain" in the 
 material of the wire. In other words, he recognized two 
 types of electrical conduction which were wholly distinct 
 in kind electrolytic conduction and metallic conduction ; 
 and since more of the problems of the physicist dealt with 
 metallic than with electrolytic conduction, the atomic 
 conception, as a general hypothesis, was almost, though 
 not quite, unheard of. Of course it would be unjust to 
 the thinkers of this period to say that they failed to 
 recognize and appreciate this gulf between current views 
 as to the nature of electrolytic and metallic conduction, 
 and simply ignored the difficulty. This they did not do, 
 but they had all sorts of opinions as to the causes. 
 Maxwell himself in his text on Electricity and Magnetism, 
 published in 1873, recognizes, in the chapter on "Elec- 
 trolysis," 1 the significance of Faraday's laws, and even 
 goes so far as to say that "for convenience in description 
 we may call this constant molecular charge (revealed by 
 Faraday's experiments) one molecule of electricity." 
 Nevertheless, a little farther on he repudiates the idea 
 that this term can have any physical significance by 
 saying that "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 obtained a secure basis on which 
 to form a true theory of electric currents and so become 
 independent of these provisional hypotheses." 
 
 1 I, 375-36. 
 
20 THE ELECTRON 
 
 And as a matter of fact, Faraday's experiments had 
 not shown at all that electrical charges on metallic con- 
 ductors consist of specks of electricity, even though they 
 had shown that the charges on ions in solutions have 
 definite values which are always the same for univalent 
 ions. It was entirely logical to assume, as Maxwell did, 
 that an ion took into solution a definite quantity of elec- 
 tricity because of some property which it had of always 
 charging up to the same amount from a charged plate. 
 There was no reason for assuming the charge on the elec- 
 trode to be made up of some exact number of electrical 
 atoms. 
 
 On the other hand, Wilhelm Weber, in papers written 
 in 187 1, 1 built up his whole theory of electromagnetism 
 on a basis which was practically identical with the modi- 
 fied Franklin theory and explained all the electrical 
 phenomena exhibited by conductors, including thermo- 
 electric and Peltier effects, on the assumption of two 
 types of electrical constituents of atoms, one of which was 
 very much more mobile than the other. Thus the hypo- 
 thetical molecular current, which Ampere had imagined 
 fifty years earlier to be continually flowing inside of 
 molecules and thereby rendering these molecules little 
 electromagnets, Weber definitely pictures to himself 
 as the rotation of light, positive charges about heavy 
 negative ones. His words are: 
 
 The relation of the two particles as regards their motions is 
 determined by the ratio of their masses e and e', on the assumption 
 that in e and e' are included the masses of the ponderable atoms 
 which are attached to the electrical atoms. Let e be the positive 
 electrical particle. Let the negative be exactly equal and opposite 
 
 See Werfc?, IV, 281. 
 
EARLY VIEWS OF ELECTRICITY 2t 
 
 and therefore denoted by e (instead of e'). But let a ponderable 
 atom be attracted to the latter so that its mass is thereby so 
 greatly increased as to make the mass of the positive particle 
 vanishingly small in comparison. The particle e may then be 
 thought of as at rest and the particle -\-e as in motion about the 
 particle e. The two unlike particles in the condition described 
 constitute then an Amperian molecular current. 
 
 It is practically this identical point of view which has 
 been elaborated and generalized by Lorenz and others 
 within the past decade in the development of the modern 
 electron theory, with this single difference, that we now 
 have experimental proof that it is the negative particle 
 whose mass or inertia is negligible in comparison with 
 that of the positive instead of the reverse. Weber even 
 went so far as to explain thermoelectric and Peltier 
 effects by differences in the kinetic energies in different 
 conductors of the electrical particles. 1 Nevertheless his 
 explanations are here widely at variance with our modern 
 conceptions of heat. 
 
 Again, in a paper read before the British Association 
 at Belfast in 1874, G. Johnstone Stoney not only stated 
 clearly the atomic theory of electricity, but actually went 
 so far as to estimate the value of the elementary electrical 
 charge, and he obtained a value which was about as 
 reliable as any which had been found until within quite 
 recent years. He got, as will be more fully explained in 
 the next chapter, .3Xio~ 10 absolute electrostatic units, 
 arid he got this result from the amount of electricity 
 necessary to separate from a solution one gram of hydro- 
 gen, combined with kinetic theory estimates as to the 
 number of atoms of hydrogen in two grams, i.e., in one 
 
 1 Op. cit. t p. 294. 
 
22 THE ELECTRON 
 
 gram molecule of that element. This paper was entitled, 
 "On the Physical Units of Nature," and though read in 
 1 8 74 it was not published in full until 1 88 1 .' After show- 
 ing that all physical measurements may be expressed in 
 terms of three fundamental units, he asserts that it would 
 be possible to replace our present purely arbitrary units 
 (the centimeter, the gram, and the second) by three 
 natural units, namely, the velocity of light, the coeffi- 
 cient of gravitation, and the elementary electrical charge. 
 With respect to the last he says: 
 
 Finally nature presents us with a single definite quantity of 
 electricity which is independent of the particular bodies acted on. 
 To make this clear, I shall express 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 electrolyte a certain 
 quantity of electricity traverses the electrolyte which is the same in 
 all cases. This definite quantity of electricity I shall call ,. If 
 we make this our unit of electricity, we shall probably have made 
 a very important step in our study of molecular phenomena. 
 
 Hence we have very good reason to suppose that in V I} d, 
 and E 2 , we have three of a series of systematic units that in an 
 eminent sense are the units of nature, and stand in an intimate 
 relation with the work which goes on in her mighty laboratory. 
 
 Take one more illustration from prominent writers 
 of this period. In his Faraday lecture delivered at the 
 Royal Institution in 1881, Helmholtz spoke as follows: 
 
 Now the most startling result of Faraday's law is perhaps this, 
 if we accept the hypothesis that the elementary substances are 
 composed of atoms, we cannot avoid concluding that electricity 
 also, positive as well as negative, is divided into definite elementary 
 portions which behave like atoms of electricity. 2 
 
 1 Phil. Mag., XI (1881; sth series), 384. 
 
 2 Wissenschaftliche Abhatidlungen, III, 69. 
 
EARLY VIEWS OF ELECTRICITY 23 
 
 This looks like a very direct and unequivocal state- 
 ment of the atomic theory of electricity, and yet in the 
 same lecture Helm hoi tz apparently thinks of metallic 
 conduction as something quite different from electrolytic 
 when he says: 
 
 All these facts show that electrolytic conduction is not at all 
 limited to solutions of acids or salts. It will, however, be rather 
 a difficult problem to find out how far the electrolytic conduction 
 is extended, and I am not yet prepared to give a positive answer. 
 
 The context shows that "he thought of extending the 
 idea of electrolytic conduction to a great many insula- 
 tors. But there is no indication that he thought of 
 extending it to metallic conductors and imagining these 
 electrical atoms as existing as discrete individual things 
 on charged metals or as traveling along a wire carrying an 
 electrical current. Nevertheless, the statement quoted 
 above is one of the most unequivocal which can be found 
 anywhere up to about 1899 as to the atomic nature of 
 electricity. 
 
 The foregoing quotations are sufficient to show that 
 the atonlic theory of electricity, like the atomic theory 
 of matter, is not at all new so far as the conception alone 
 is concerned. In both cases there were individuals who 
 held almost exactly the modern point of view. In both 
 cases, too, the chief new developments have consisted in 
 the appearance of new and exact experimental data which 
 has silenced criticism and compelled the abandonment 
 of other points of view which up to about 1900 flourished 
 along with, and even more vigorously than, the atomic 
 conception. Even in 1897 Lord Kelvin, with a full 
 knowledge of all the new work which was appearing 
 on X-rays and cathode rays, could seriously raise the 
 
24 THE ELECTRON 
 
 question whether electricity might not be a " continuous 
 homogeneous liquid." He does it in these words: 
 
 Varley's fundamental discovery of the cathode rays, splendidly 
 confirmed and extended by Crookes, seems to me to necessitate the 
 conclusion that resinous electricity, not vitreous, is The Electric 
 Fluid, if we are to have a one-fluid theory of electricity. Mathe- 
 matical reasons prove that if resinous electricity is a continuous 
 homogeneous liquid it must, in order to produce the phenomena 
 of contact electricity, which you have seen this evening, be 
 endowed with a cohesional quality. It is just conceivable, though 
 it does not at present seem to me very probable, that this idea may 
 deserve careful consideration. I leave it, however, for the present 
 and prefer to consider an atomic theory of electricity foreseen as 
 worthy of thought by Faraday and Clerk-Maxwell, very definitely 
 proposed by Helmholtz in his last lecture to the Royal Institution, 
 and largely accepted by present-day workers and teachers. Indeed 
 Faraday's laws of electrolysis seem to necessitate something atomic 
 in electricity, . . . .* 
 
 What was the new experimental work which already 
 in 1897 was working this change in viewpoint ? Much 
 of it was at first little if at all more convincing than that 
 which had been available since Faraday's time. Never- 
 theless it set physicists to wondering whether stresses 
 and strains in the ether had not been a bit overworked, 
 and whether in spite of their undoubted existence elec- 
 tricity itself might not after all be something more 
 definite, more material, than the all-conquering Maxwell 
 theory had assumed it to be. 
 
 The result of the past fifteen years has been to bring 
 us back very close to where Franklin was in 1750, with 
 the single difference that our modern electron theory rests 
 upon a mass of very direct and very convincing evidence, 
 which it is the purpose of the next chapters to present. 
 
 1 Kelvin, "Contact Electricity and Electrolysis," Nature, LVI 
 (1897), 84. 
 
CHAPTER II 
 
 THE EXTENSION OF THE ELECTROLYTIC LAWS TO 
 CONDUCTION IN GASES 
 
 I. THE ORIGIN OF THE WORD "ELECTRON" 
 
 The word "electron" was first suggested in 1891 by 
 Dr. G. Johnstone Stoney as a name for the "natural unit 
 of electricity," gamely, that quantity of electricity which 
 must pass through a solution in order to liberate at one 
 of the electrodes one atom of hydrogen or one atom of 
 any univalent substance. In a paper published in 1891 
 he says: 
 
 Attention must be given to Faraday's Law of Electrolysis, 
 which is equivalent to the statement that hi electrolysis a definite 
 quantity of electricity, the same in all cases, passes for each chemi- 
 cal bond that is ruptured. The author called attention to this 
 form of the law in a communication made to the British Associa- 
 tion in 1874 and printed in the Scientific Proceedings of the Royal 
 Dublin Society of February, 1881, and in the Philosophical Maga- 
 zine for May, 1881, pp. 385 and 386 of the latter. It is there shown 
 that the amount of this very remarkable quantity of electricity is 
 
 about the twentiethet (that is -) of the usual electromagnetic 
 unit of electricity, i.e., the unit of the Ohm series. This is the 
 same as 3 eleventhets ( - ) of the much smaller C.G.S. electro- 
 static unit of quantity. A charge of this amount is associated in 
 the chemical atom with each bond. There may accordingly be 
 several such charges in one chemical atom, and there appear to be 
 at least two in each atom. These charges, which it will be con- 
 venient to call "electrons," cannot be removed from the atom, 
 but they become disguised when atoms chemically unite. If an 
 
 25 
 
26 THE ELECTRON 
 
 electron be lodged at the point P of the molecule which undergoes 
 the motion described in the last chapter, the revolution of this 
 charge will cause an electromagnetic undulation in the surrounding 
 ether. 1 
 
 It will be noticed from this quotation that the word 
 " electron" was introduced to denote simply a definite ele- 
 mentary quantity of electricity without any reference to 
 the mass or inertia which may be associated with it, and 
 Professor Stoney implies that every atom must contain 
 at least two electrons, one positive and one negative, 
 because otherwise it would be impossible that the atom 
 as a whole be electrically neutral. As a matter of fact 
 the evidence is now considerable that the hydrogen 
 atom does indeed contain just one positive and one 
 negative electron. 
 
 It is unfortunate that modern writers have not been 
 more careful to retain the original significance of the word 
 introduced by Professor Stoney, for it is obvious that a 
 word is needed which denotes merely the elementary unit 
 of electricity and has no implication as to where that 
 unit is found, to what it is attached, with what inertia 
 it is associated, or whether it is positive or negative in 
 sign; and it is also apparent that the word " electron" 
 is the logical one to associate with this conception. 2 
 
 1 Scientific Transactions of the Royal Dublin Society, IV (1891; ntl, 
 series), 563. 
 
 2 The most authoritative writers, Thomson, Rutherford, Campbell, 
 Richardson, etc., have in fact retained the original significance of the 
 word "electron" instead of using it to denote solely the free negative 
 
 electron or corpuscle of J. J. Thomson, the mass of which is - - of 
 
 that of the hydrogen atom. All of these writers in books or articles 
 written since 1913 have treated of positive as well as negative electrons, 
 although the mass associated with the former is never less than that of 
 the hydrogen atom. 
 
CONDUCTION IN GASES 27 
 
 J. J. Thomson's word " corpuscle " is a very appropriate 
 one to denote the very minute inertia with which the 
 negative electron is found associated in cathode rays. 
 
 e 
 
 II. THE DETERMINATION OF AND N FROM THE FACTS 
 
 m 
 
 OF ELECTROLYSIS 
 
 Faraday's experiments had of course not furnished 
 the data for determining anything about how much elec- 
 tricity an electron represents in terms of the standard 
 unit by which electrical charges are ordinarily measured 
 in the laboratory. This is called the coulomb, and 
 represents the quantity of electricity conveyed in 
 one second by one ampere. Faraday had merely shown 
 that a given current flowing in succession through 
 solutions containing different univalent elements like 
 hydrogen or silver or sodium or potassium would deposit 
 weights of these substances which are exactly propor- 
 tional to their respective atomic weights. This enabled 
 him to assert that one and the same amount of elec- 
 tricity is associated in the process of electrolysis with 
 an atom of each of these substances. He thought of this 
 charge as carried by the atom, or in some cases by a group 
 of atoms, and called the group with its charge an "ion," 
 that is, a "goer," or "traveler." Just how the atoms 
 come to be charged in a solution Faraday did not know, 
 nor do we know now with any certainty. Further, we 
 do not know how much of the solvent an ion associates 
 with itself and drags with it through the solution. But 
 we do know that when a substance like salt is dissolved 
 in water many of the neutral NaCl molecules are split 
 up by some action of the water into positively charged 
 
28 THE ELECTRON 
 
 sodium (Na) ions and negatively charged chlorine (Cl) 
 ions. The ions of opposite sign doubtless are all the 
 time recombining, but others are probably continually 
 forming, so that at each instant there are many uncom- 
 bined ions. Again, we know that when a water solution 
 of copper sulphate is formed many of the neutral CuSO 4 
 molecules are split up into positively charged Cu ions 
 and negatively charged S0 4 ions. In this last case too 
 we find that the same current which will deposit in a 
 given time from a silver solution a weight of silver eqnn 1 
 to its atomic weight will deposit from the copper-sulpha i 
 solution in the same time a weight of copper equal t< 
 exactly one-half its atomic weight. Hence we know that 
 the copper ion carries in solution twice as much elec- 
 tricity as does the silver ion, that is, it carries a charge of 
 two electrons. 
 
 But though we could get from Faraday's experiments 
 no knowledge about the quantity of electricity, e, repre- 
 sented by one electron, we could get very exact informa- 
 tion about the ratio of the ionic charge E to the mass 
 of the atom with which it is associated in a given solution. 
 
 For, if the whole current which passes through a 
 solution is carried by the ions and if it were not we 
 should not always find the deposits exactly proportional 
 to atomic weights then the ratio of the total quantity 
 of electricity passing to the weight of the deposit pro- 
 duced must be the same as the ratio of the charge E on 
 each ion to the mass m of that .ion. But by international 
 agreement one absolute unit of electricity has been 
 defined in the electromagnetic system of units as the 
 amount of electricity which will deposit from a silver 
 solution o.oiiiS grams of metallic silver. Hence if m 
 
CONDUCTION IN GASES 29 
 
 refers to the silver ion and E means the charge on the 
 ion, we have 
 
 for silver = - =80.44 electromagnetic units ; 
 m 0.01118 
 
 or if m refers to the hydrogen ion, since the atomic 
 
 weight of silver is - - - times that of hydrogen, 
 i.ooo 
 
 E i ,,107.88 
 for hydrogen -=-- = 9,573, 
 
 which is about io 4 electromagnetic units. 
 
 7^ 
 Thus in electrolysis varies from ion to ion, being 
 
 for univalent ions, for which E is the same and equal to 
 one electron e, inversely proportional to the atomic 
 weight of the ion. For polivalent ions E may be 2, 3, 
 4, or 5 electrons, but since hydrogen is at least 7 times 
 lighter than any other ion which is ever found in solution, 
 
 and its charge is but one electron, we see that the largest 
 17 
 
 value which ever has in electrolysis is its value for 
 m 
 
 hydrogen, namely, about io 4 electromagnetic units. 
 
 Ei 
 
 Although varies with the nature of the ion, there is 
 
 a quantity which can be deduced from it which is a uni- 
 versal constant. This quantity is denoted by Ne, where 
 e means as before an electron and N is the Avogadro con- 
 stant or the number of molecules in r6 grams of oxygen, 
 i.e., in one gram molecule. We can get this at once from 
 
 7^ 
 
 the value of -- by letting m refer to the mass of that 
 
 m J 
 
 imaginary univalent atom which is the unit of our 
 
30 THE ELECTRON 
 
 atomic weight system, namely, an atom which is exactly 
 1/16 as heavy as oxygen or 1/107.88 as heavy as silver. 
 For such an atom 
 
 E_e _ 107.88 _ 
 
 m m 0.01118 9 ' 5 
 
 Multiplying both numerator and denominator by N and 
 remembering that for this gas one gram molecule means 
 i gram, that is, Nm= i, we have 
 
 ^=9650 absolute electromagnetic units, (i) 
 
 and since the electromagnetic unit is equivalent to 
 3Xio 10 electrostatic units, we have 
 
 7Ve=28,95oXio 10 absolute electrostatic units. 
 
 Further, since a gram molecule of an ideal gas under 
 standard conditions, i.e., at o C. 76 cm. pressure, 
 occupies 22412 c.c., if w x represents the number of mole- 
 cules of such a gas per cubic centimeter at o C., 76 cm., 
 we have 
 
 nrf = =i .202Xio 10 electrostatic units. 
 
 22,412 
 
 Or if n represent the number of molecules per cubic 
 centimeter at 15 C. 76 cm., we should have to multiply 
 the last number by the ratio of absolute temperatures, 
 i.e., by 273/288 and should obtain then. 
 
 ne=i . 225X10 (2) 
 
 Thus, even though the facts of electrolysis give us no 
 information at all as to how much of a charge one electron 
 e represents, they do tell us very exactly that if we should 
 take e as many times as there are molecules in a gram 
 
CONDUCTION IN GASES 31 
 
 molecule we should get exactly 9,650 absolute electro- 
 magnetic units of electricity. This is the amount of 
 electricity conveyed by a current of i ampere in 10 sec- 
 onds. Until quite recently we have been able to make 
 nothing better than rough guesses as to the number of 
 molecules in a gram molecule, but with the aid of these 
 guesses, obtained from the Kinetic Theory, we have, of 
 course, been enabled by (i) to make equally good 
 guesses about e. These guesses, based for the most part 
 on quite uncertain computations as to the average radius 
 of a molecule of air, placed N anywhere between 2X io 2 
 and 2oXio 23 . It was in this way that G. Johnstone 
 Stoney in 1874 estimated e at .3Xio~ 10 E.S. units. In 
 O. E. Meyer's Kinetische Theorie der Gase (p. 335; 1899), 
 n, the number of molecules in a cubic centimeter is given 
 as 6X io 19 . This would correspond to e= 2X io~ 10 . In 
 all this e is the charge carried by a univalent ion in solu- 
 tion and N or n is a pure number, which is a characteristic 
 gas constant, it is true, but the analysis has nothing what- 
 ever to do with gas conduction. 
 
 III. THE NATURE OF GASEOUS CONDUCTION 
 
 The question whether gases conduct at all, and if so, 
 whether their conduction is electrolytic or metallic or 
 neither, was scarcely attacked until about 1895. Cou- 
 lomb in 1785 had concluded that after allowing for the 
 leakage of the supports of an electrically charged con- 
 ductor, some leakage must be attributed to the air itself, 
 and he explained this leakage by assuming that the air 
 molecules became charged by contact and were- then 
 repelled a wholly untenable conclusion, since, were it 
 true, no conductor in air could hold a charge long even 
 
32 THE ELECTRON 
 
 at low potentials, nor could a very highly charged con- 
 ductor lose its charge very rapidly when charged above 
 a certain potential and then when the potential fell below 
 a certain critical value cease almost entirely to lose it. 
 This is what actually occurs. Despite the erroneousness 
 of this idea, it persisted in textbooks written as late as 
 1900. 
 
 Warburg in 1872 experimented anew on air leakage 
 and was inclined to attribute it all to dust particles. The 
 real explanation of gas conduction was not found until 
 after the discovery of X-rays in 1895. The convincing 
 experiments were made by J. J. Thomson, or at his 
 instigation in the Cavendish Laboratory at Cambridge, 
 England. The new work grew obviously and simply out 
 of. the fact that X-rays, and a year or two later radium 
 rays, were found to discharge an electroscope, i.e., to 
 produce conductivity in a gas. Theretofore no agencies 
 had been known by which the electrical conductivity of 
 a gas could be controlled at will. Thomson and his 
 pupils found that the conductivity induced in gases 
 by X-rays disappeared when the gas was sucked 
 through glass wool. 1 It was also found to be reduced 
 when the air was drawn through narrow metal tubes. 
 Furthermore, it was removed entirely by passing the 
 stream of conducting gas between plates which were 
 maintained at a sufficiently large potential difference. 
 The first two experiments showed that the conduc- 
 tivity was due to something which could be removed 
 from the gas by filtration, or by diffusion to the walls of 
 a metal tube; the last proved that this something was 
 electrically charged. 
 
 1 J. J. Thomson and E. Rutherford, Phil. Mag., XLII (1896), 392. 
 
CONDUCTION IN GASES 33 
 
 When it was found, further, that the electric cur- 
 rent obtained from air existing between two plates 
 and traversed by X-rays, rose to a maximum as 
 the P.D. between the plates increased, and then 
 reached a value which was thereafter independent of this 
 potential difference; and, further, that this conductivity 
 of the air died out slowly through a period of several 
 seconds when the X-ray no longer acted, it was evident 
 that the qualitative proof was complete that gas con- 
 duction must be due to charged particles produced in the 
 air at a definite rate by a constant source of X-rays, and 
 that these charged particles, evidently of both plus and 
 minus signs, disappear by recombination when the rays 
 are removed. The maximum or saturation currents 
 which could be obtained when a given source was ionizing 
 the air between two plates whose potential difference 
 could be varied was obviously due to the fact that when 
 the electric field between the plates became strong enough 
 to sweep all the ions to the plates as fast as they were 
 formed, none of them being lost by diffusion or recom- 
 bination, the current obtained could, of course, not be 
 increased by further increase in the field strength. Thus 
 gas conduction was definitely shown about 1896 to be 
 electrolytic in nature. 
 
 IV. COMPARISON OF THE GASEOUS ION AND THE 
 ELECTROLYTIC ION 
 
 But what sort of ions were these that were thus 
 formed? We did not know the absolute value of the 
 charge on a univalent ion in electrolysis, but we did 
 know accurately ne. Could this be found for the ions 
 taking part in gas conduction ? That this question was 
 
34 THE ELECTRON 
 
 answered affirmatively was due to the extraordinary 
 insight and resourcefulness of J. J. Thomson and his 
 pupils at the Cavendish Laboratory in Cambridge, both 
 in working out new theoretical relations and in devising 
 new methods for attacking the new problems of gaseous 
 conduction. These workers found first a method of 
 expressing the quantity ne in terms of two measurable 
 constants, called (i) the mobility of gaseous ions and 
 (2) the coefficient of diffusion of these ions. Secondly, 
 they devised new methods of measuring these two 
 constants constants which had never before been deter- 
 mined. The theory of the relation between these con- 
 stants and the quantity ne will be found in Appendix A. 
 The result is 
 
 ne^P, (3) 
 
 in which P is the pressure existing in the gas and v and 
 D are the mobility and the diffusion coefficients respec- 
 tively of the ions at this pressure. 
 
 If then we can find a way of measuring the mobilities 
 v of atmospheric ions and also the diffusion coefficients 
 D, we can find the quantity ne, in which n is a mere num- 
 ber, viz., the number of molecules of air per cubic centi- 
 meter at 15 C., 76 cm. pressure, and e is the average 
 charge on an atmosphere ion. We shall then be in posi- 
 tion to compare this with the product we found in (2) on 
 p. 30, in which n had precisely the same significance as 
 here, but e meant the average charge carried by a uni- 
 valent ion in electrolysis. 
 
 The methods devised in the Cavendish Laboratory 
 between 1897 and 1903 for measuring the mobilities and 
 the diffusion coefficients of gaseous ions have been used 
 
CONDUCTION IN GASES 35 
 
 in all later work upon these constants. The mobilities 
 were first determined by Rutherford in 1897,* then more 
 accurately by another method in i8c}8. 2 Zeleny devised 
 a quite distinct method in igoo, 3 and Langevin still 
 another method in 1 903.4 These observers all agree 
 closely in finding the average mobility (velocity in unit 
 field) of the negative ion in dry air about i . 83 cm. per 
 second, while that of the positive ion was found but 
 1.35 cm. per second. In hydrogen these mobilities were 
 about 7.8 cm. per second and 6.1 cm. per second, 
 respectively, and in general the mobilities in different 
 gases, though not in vapors, seem to be roughly in the 
 inverse ratio of the square roots of the molecular weights. 
 The diffusion coefficients of ions were first measured 
 in 1900 by Townsend, now professor of physics in Oxford, 
 England, 5 by a method devised by him and since then 
 used by other observers in such measurements. If we 
 denote the diffusion coefficient of the positive ion by D+ 
 and that of the negative by D , Townsend's results in 
 dry air may be stated thus: 
 
 #+ = 0.028 
 
 D- =0.043. 
 
 These results are interesting in two respects. In the 
 first place, they seem to show that for some reason the 
 positive ion in air is more sluggish than the negative, 
 since it travels but about 0.7 (=1.35/1.81) as fast in a 
 given electrical field and since it diffuses through air but 
 about 0.7 (=28/43) as rapidly. In the second place, 
 
 ' Phil, Mag., XLIV (1898), 422. 
 
 3 Proc. Camb. Phil. Soc., IX, 401. 
 * Phil. Trans., A 195, p. 193. 
 
 4 Annale de Chimie el de Physique, XXVIII, 289. 
 
 5 Phil, Trans., A 193, p. 129. 
 
36 THE ELECTRON 
 
 the results of Townsend show that an ion is very much 
 more sluggish than is a molecule of air, for the coefficient 
 of diffusion of oxygen through air is 0.178, which is four 
 times the rate of diffusion of the negative ion through 
 air and five times that of the positive ion. This sluggish- 
 ness of ions as compared with molecules was at first uni- 
 versally considered to mean that the gaseous ion is not 
 a single molecule with an attached electrical charge, but 
 a cluster of perhaps from three to twenty molecules held 
 together by such a charge. If this is the correct inter- 
 pretation, then for some reason the positive ion in air 
 is a larger cluster than is the negative ion. 
 
 It has been since shown by a number of observers 
 that the ratio of the mobilities of the positive and nega- 
 tive ions is not at all the same in other gases as it is in 
 air. In carbon dioxide the two mobilities have very 
 nearly the same value, while in chlorine, water vapor, and 
 the vapor of alcohol the positive ion apparently has a 
 slightly larger mobility than the negative. There seems 
 to be some evidence that the negative ion has the larger 
 mobility in gases which are electro- positive, while the 
 positive has the larger mobility in the gases which 
 are strongly electro-negative. This dependence of the 
 ratio of mobilities upon the electro-positive or electro- 
 negative character of the gas has usually been considered 
 strong evidence in favor of the cluster-ion theory. 
 
 Very recently, however, Loeb, 1 who has worked at the 
 Ryerson Laboratory on mobilities in powerful electric 
 fields, and Wellish, 2 who, at Yale, has measured mobilities 
 
 1 Leonard B. Loeb, Proc, Nat. Acad., II (1916), 345, and Phys. 
 Rev., 1917. 
 
 * Wellish, Am. Jour, of Science, XXXIX (1915), 583. 
 
CONDUCTION IN GASES 37 
 
 at very low pressures, have concluded that their results 
 are not consistent with the cluster-ion theory, but must 
 rather be interpreted in terms of the so-called Atom-ion 
 Theory. This theory seeks to explain the relative 
 sluggishness of ions, as compared with molecules, by 
 the additional resistance which the gaseous medium 
 offers to the motion of a molecule through it when that 
 molecule is electrically charged. According to this hypoth- 
 esis, the ion would be simply an electrically charged 
 molecule. 
 
 Fortunately, the quantitative evidence for the elec- 
 trolytic nature of gas conduction is in no way dependent 
 upon the correctness of either one of the theories as to 
 the nature of the ion. It depends simply upon the com- 
 parison of the values of ne obtained from electrolytic 
 measurements, and those obtained from the substitution 
 in equation 3 of the measured values of v and D for 
 gaseous ions. 
 
 As for these measurements, results obtained by 
 Franck and Westphal, 1 who in 1908 repeated in Berlin 
 both measurements on diffusion coefficients and mobility 
 coefficients, agree within 4 or 5 per cent with the results 
 published by Townsend in 1900. According to both of 
 these observers, the value of ne for the negative ions pro- 
 duced in gases by X-rays, radium rays, and ultra-violet 
 light came out, within the limits of experimental error, 
 which were presumably 5 or 6 per cent, the same as the 
 value found for univalent ions in solutions, namely, 
 i. 23X10 absolute electrostatic units. This result 
 seems to show with considerable certainty that the 
 negative ions in gases ionized by X-rays or similar 
 
 1 Verh. der deutsch. phys. Ges., XI (1909), 146 and 276. 
 
38 THE ELECTRON 
 
 agencies carry on the average the same charge as that 
 borne by the univalent ion in electrolysis. When we 
 consider the work on the positive ion, our confidence in 
 the inevitableness of the conclusions reached by the 
 methods under consideration is perhaps somewhat 
 shaken. For Townsend found that the value of ne for 
 the positive ion came out about 14 per cent higher than 
 the value of this quantity for the univalent ion in elec- 
 trolysis, a result which he does not seem at first to have 
 regarded as inexplicable on the basis of experimental 
 uncertainties in his method. In 1908, however, 1 he 
 devised a second method of measuring the ratio of the 
 mobility and the diffusion coefficient and obtained this 
 time, as before, for the negative ion, ne i . 23 X io 10 , but 
 for the positive ion twice that amount, namely, 2 . 46 X io 10 . 
 From these last experiments he concluded that the 
 positive ions in gases ionized by X-rays carried on the 
 average twice the charge carried by the univalent ion in 
 electrolysis. Franck and Westphal, however, found in 
 their work that Townsend's original value for ne for the 
 positive ions was about right, and hence concluded that 
 only about 9 per cent of the positive ions could carry a 
 charge of value ie. Work which will be described later 
 indicates that neither Townsend's nor Franck and West- 
 phal's conclusions are correct, and hence point to errors 
 of some sort in both methods. But despite these diffi- 
 culties with the work on positive ions, it is nevertheless 
 fair to say that Townsend was the first to bring forward 
 strong quantitative evidence that the mean charge 
 carried by the negative ions in ionized gases is the same 
 as the mean charge carried by univalent ions in solu- 
 1 Proc. Roy. Soo., LXXX (1908), 207. 
 
CONDUCTION IN GASES 39 
 
 tions, and that the mean charge carried by the positive 
 ions in gases has not far from the same value. 
 
 But there is one other advance of fundamental impor- 
 tance which came with the study of the properties of 
 gases ionized by X-rays. For up to this time the only 
 type of ionization known was that observed in solution 
 and here it is always some compound molecule like 
 sodium chloride (NaCl) which splits up spontaneously 
 into a positively charged sodium ion and a negatively 
 charged chlorine ion. But the ionization produced in 
 gases by X-rays was of a wholly different sort, for it was 
 observable in pure gases like nitrogen or oxygen, or even 
 in monatomic gases like argon and helium. Plainly then 
 the neutral atom even of a monatomic substance must 
 possess minute electrical charges as constituents. Here 
 we had the first direct evidence (i) that an atom is a 
 complex structure, and (2) that electrical charges enter 
 into its make-up. With this discovery, due directly to the 
 use of the new agency, X-rays, the atom as an ultimate, 
 indivisible thing was gone, and the era of the study of the 
 constituents of the atom began. And with astonishing 
 rapidity during the past twenty years the properties of 
 the subatomic world have been revealed. 
 
 Physicists began at once to seek diligently and to find 
 at least partial answers to questions like these: 
 
 1. What are the masses of the constituents .of the 
 atoms torn asunder by X-rays and similar agencies ? 
 
 2. What are the values of the charges carried by 
 these constituents ? 
 
 3. How many of these constituents are there? 
 
 4. How large are they, i.e., what volumes do they 
 occupy ? 
 
40 THE ELECTRON 
 
 5. What are their relations to the emission and 
 absorption of light and heat waves, i.e., of electromag- 
 netic radiation ? 
 
 6. Do all atoms possess similar constituents? In 
 other words, is there a primordial subatom out of which 
 atoms are made ? 
 
 The partial answer to the first of these questions came 
 with the study of the electrical behavior of rarefied gases 
 in so-called vacuum tubes. J. J. Thomson 1 and Wie 
 chert 2 showed independently in 1897 that the value of 
 
 p 
 
 - for the negative ion in such exhausted tubes is about 
 m 
 
 i.SXio 7 electromagnetic units, or about 1,800 times the 
 
 o 
 
 value of for the hydrogen ion in solutions. Since the 
 
 approximate equality of ne in gases and solutions meant 
 that e was at least of the same order in both, the only 
 possible conclusion was that the negative ion which 
 appears in discharges in exhausted tubes has a mass, i.e., 
 an inertia only i/i,8ooth of the mass of the lightest 
 known atom, namely, the atom of hydrogen. 
 
 Furthermore, these and other experimenters have 
 
 shown that for the negative carrier is always the same 
 
 whatever be the nature of the residual gas in the dis- 
 charge tube. This was an indication of an affirmative 
 answer to the sixth question above an indication which 
 was strengthened by Zeeman's discovery in 1897 of the 
 splitting by a magnetic field of a single spectral line into 
 two or three lines; for this, when worked out quantita- 
 
 ' Phil. Mag., XLIV (1897), 298. 
 
 * Verh. der phys.-okon. Ges. zu Konigsberg, 1897. 
 
CONDUCTION IN GASES 41 
 
 lively, pointed to the existence within the atom of a 
 negatively charged particle which had approximately the 
 
 same value of . 
 m 
 
 The study of for the positive ions in exhausted tubes, 
 m 
 
 though first carried out quantitatively by Wien, 1 has been 
 most elaborately and most successfully dealt with by 
 J. J. Thomson. 2 The results of the work' of all observers 
 
 up to date seem to show quite conclusively that for a 
 
 positive ion in gases is never larger than its value for the 
 hydrogen ion in electrolysis, and that it varies with 
 different sorts of residual gases just as it is found to do 
 in electrolysis. 
 
 In a word, then, the act of ionization in gases appears 
 to consist in the detachment from a neutral atom of one 
 or more negatively charged particles, called by Thomson 
 corpuscles. The residuum of the atom is of course posi- 
 tively charged, and it always carries practically the 
 whole mass of the original atom. The detached cor- 
 puscle must soon attach itself, in a gas at ordinary pres- 
 sure, to a neutral atom, since otherwise we could not 
 account for the fact that the mobilities and the diffusion 
 coefficients of negative ions are usually of the same order 
 of magnitude as those of the positive ions. It is because 
 of this tendency of the parts of the dissociated atom to 
 form new attachments in gases at ordinary pressure that 
 the inertias of these parts had to be worked out in the 
 rarefied gases of exhausted tubes. 
 
 1 W. Wien, Wied. Ann., LXV (1898), 440. 
 
 2 Rays of Positive Electricity, London: Longmans, 1913. 
 
42 THE ELECTRON 
 
 The foregoing conclusions as to the masses of the 
 positive and negative constituents of atoms had all been 
 reached before 1900, mostly by the workers in the 
 Cavendish Laboratory, and subsequent investigation has 
 not modified them in any essential particulars. 
 
 The history of the development of our present knowl- 
 edge of the charges carried by the constituents will be 
 detailed in the next chapters. 
 
CHAPTER III 
 
 EARLY ATTEMPTS AT THE DIRECT DETER- 
 MINATION OF e 
 
 Although the methods sketched in the preceding 
 chapters had been sufficient to show that the mean 
 charges carried by ions in gases are the same or nearly 
 the same as the mean charges carried by univalent ions 
 in solution, in neither case had we any way of determin- 
 ing what the absolute value of that mean charge is, nor, 
 indeed, had we any proof even that all the ions of a given 
 kind, e.g., silver or hydrogen, carry the same charge. Of 
 course, the absolute value of e could be found from the 
 measured value of ne if only n, the number of molecules 
 in i c.c. of gas under standard conditions, were known. 
 But we had only rough guesses as to this number. These 
 guesses varied tenfold, and none of them were based 
 upon considerations of recognized accuracy or even 
 validity. 
 
 i. TOWNSEND'S WORK ON e 
 
 The first attempt at a direct determination of e was 
 published by Townsend in a paper read before the 
 Cambridge Philosophical Society on February 8, 1897. x 
 Townsend's method was one of much novelty and of no 
 little ingenuity. It is also of great interest because it 
 contains all the essential elements- of some of the sub- 
 sequent determinations. 
 
 1 Proceedings, IX (1897), 244. 
 
 43 
 
44 THE ELECTRON 
 
 It had been known, even to Laplace and Lavoisier a 
 hundred years before, that the hydrogen gas evolved 
 when a metal dissolves in an acid carries with it an elec- 
 trical charge. This " natural method'' of obtaining a 
 charge on a gas was scarcely studied at all, however, 
 until after the impulse to the study of the electrical 
 properties of gases had been given by the discovery in 
 1896 that electrical properties can be artificially imparted 
 to gases by X-rays. Townsend's paper appeared within 
 a year of that time. Enright 1 had indeed found that- 
 the hydrogen given off when iron is dissolving in sul- 
 phuric acid carries with it a positive charge, but Oliver 
 Lodge 2 had urged that it was not the gas itself which 
 carries the charge but merely the spray, for the frictional 
 electrification of spray was a well-known phenomenon. 
 Indeed, it has always been assumed that the gas mole- 
 cules which rise from the electrodes in electrolysis are 
 themselves neutral. Townsend, however, first showed 
 that some of these molecules are charged, although there 
 are indeed a million million neutral ones for every one 
 carrying a charge. He found that both the oxygen and 
 the hydrogen which appear at the opposite electrodes 
 when sulphuric acid is electrolyzed are positively charged, 
 while when the electrolyte is caustic potash both the oxy- 
 gen and the hydrogen given off are negative. Townsend's 
 electrolyzing currents were from 12 to 14 amperes. He 
 got in this way many more ions per cubic centimeter 
 than he could produce with X-rays, the total charge 
 per cubic centimeter being as large as 5Xio~ 3 electro- 
 static units. 
 
 1 Phil. Mag., XXIX (1890; sth series), 56. 
 
 2 Ibid., 292; Nature, XXXVI, 412. 
 
EARLY DETERMINATIONS OF e 45 
 
 When these charged gases were bubbled through 
 water they formed a cloud. This cloud could be com- 
 pletely removed by bubbling through concentrated sul- 
 phuric acid or any drying agent, but when the gas came 
 out again into the atmosphere of the room it again con- 
 densed moisture and formed a stable cloud. Townsend 
 says that "the process of forming the cloud in positive 
 or negative oxygen by bubbling through water, and 
 removing it again by bubbling through sulphuric acid, 
 can be gone through without losing more than 20 or 25 
 per cent of the original charge on the gas." This means 
 simply that the ions condense the water about them 
 when there is an abundance of moisture in the air, but 
 when the cloud is carried into a perfectly dry atmos- 
 phere, such as that existing in a bubble surrounded on 
 all sides by concentrated sulphuric acid, the droplets of 
 water evaporate and leave the charge on a molecule of 
 air as it was at first. The 20 or 25 per cent loss of charge 
 represents the fraction of the droplets with their charges 
 which actually got into contact with and remained in the 
 liquids through which the gas was being bubbled. 
 
 In order to find the charge on each ion, Townsend 
 took the following five steps: 
 
 1. He assumed that in saturated water vapor each 
 ion condensed moisture about it, so that the number of 
 ions was the same as the number of droplets. 
 
 2. He determined with the aid of a quadrant elec- 
 trometer the total electrical charge per cubic centimeter 
 carried by the gas. 
 
 3. He found the total weight of the cloud by passing 
 it through drying tubes and determining the increase in 
 weight of these tubes. 
 
46 THE ELECTRON 
 
 4. He found the average weight of the water droplets 
 constituting the cloud by observing their rate of fall 
 under gravity and computing their mean radius with 
 the aid of a purely theoretical law known as Stokes's 
 Law. 
 
 5. He divided the weight of the cloud by the average 
 weight of the droplets of water to obtain the number of 
 droplets which, if assumption i is correct, was the number 
 of ions, and he then divided the total charge per cubic 
 centimeter in the gas by the number of ions to find the 
 average charge carried by each ion, that is. to find e. 
 
 A brief description of the way in which these experi- 
 ments were carried out is contained in Appendix B. 
 
 One of the interesting side results of this work was 
 the observation that clouds from negative oxygen fall 
 faster than those from positive oxygen, thus indicating 
 that the negative ions in oxygen act more readily than 
 do the positive ions as nuclei for the condensation of 
 water vapor. This observation was made at about the 
 same time in another way by C. T. R. Wilson, 1 also in the 
 Cavendish Laboratory, and it has played a rather impor- 
 tant role in subsequent work. Wilson's discovery was 
 that when air saturated with water vapor is ionized by 
 X-rays from radioactive substances and then cooled 
 by a sudden expansion, a smaller expansion is required 
 to make a cloud form about the negative than about the 
 positive ions. Thus when the expansion increased the 
 volume in a ratio between 1.25 and 1.3, only negative 
 ions acted as nuclei for cloudy condensation, while with 
 expansions greater than i . 3 both negatives and positives 
 were brought down. 
 
 1 Proc. Camb. Phil. Soc., IX (1897), 333. 
 
EARLY DETERMINATIONS OF e 47 
 
 Townsend first obtained by the foregoing method, 
 when he worked with positive oxygen, 
 
 e2 .8Xio~ 10 electrostatic units, 
 and when he worked with negative oxygen, 
 
 e =T ) . j x io~ 10 electrostatic units. 
 
 In later experiments 1 he obtained 2.4 and 2.9, respec- 
 tively, in place of the numbers given above, but in view 
 of the unavoidable errors, he concluded that the two 
 charges might be considered equal and approximately 
 3Xio~ 10 electrostatic units. Thus he arrived at about 
 the same value for e as that which was then current be- 
 cause of the kinetic theory estimates of n, the number of 
 molecules in a cubic centimeter of a gas. 
 
 The weak points in this first attempt at a direct 
 determination of e consisted in: (i) the assumption that 
 the number of ions is the same as the number of drops; 
 (2) the assumption of Stokes's Law of Fall which had 
 never been tested experimentally, and which from a 
 theoretical standpoint might be expected to be in error 
 when the droplets were small enough; (3) the assump- 
 tion that the droplets were all alike and fell at a uniform 
 rate wholly uninfluenced by evaporation or other causes 
 of change; (4) the assumption of no convection currents 
 in the gas when the rate of fall of the cloud was being 
 measured. 
 
 ii. SIR JOSEPH THOMSON'S WORK ON e 
 
 This first attempt to measure e was carried out in Pro- 
 fessor J. J. Thomson's laboratory. The second attempt 
 was made by Professor Thomson himself 2 by a method 
 
 1 Proc. Camb. Phil. Soc., IX (1897), 345. 
 * Phil. Mag., XL VI (1898), 528. 
 
48 THE ELECTRON 
 
 which resembled Townsend's very closely in all its essen- 
 tial particulars. Indeed, we may set down for Professor 
 Thomson's experiment precisely the same five elements 
 which are set down on p. 45 for Townsend's. The differ- 
 ences lay wholly in step 2, that is, in the way in which 
 the electrical charge per cubic centimeter carried by the 
 gas was determined, and in step 3, that is, in the way 
 in which the total weight of the cloud was obtained. 
 Thomson produced ions in the space A (Fig. i) by an 
 X-ray bulb which ran at a constant rate and measured 
 first the current which under the influence of a very weak 
 electromotive force E flows through A between the sur- 
 face of the water and the aluminum plate which closes 
 the top of the vessel. Then if n' is the whole number of 
 ions of one sign per cubic centimeter, u the velocity of 
 the positive and v that of the negative ion under unit 
 electric force, i.e., if u and v are the mobilities of the posi- 
 tive and negative ions, respectively, then the current/ 
 per unit area is evidently given by 
 
 I=n'e(u+v)E (4) 
 
 7 and E were easily measured in any experiment; 
 u-\-v was already known from Rutherford's previous 
 work, so that n'e, the charge of one sign per cubic centi- 
 meter of gas under the ionizing action of a constant 
 source of X-rays, could be obtained at once from (4). 
 This then simply replaces Townsend's method of obtain- 
 ing the charge per cubic centimeter on the gas, and in 
 principle the two methods are quite the same, the differ- 
 ence in experimental arrangements being due to the fact 
 that Townsend's ions are of but one sign while Thom- 
 son's are of both signs. 
 
EARLY DETERMINATIONS OF e 40 
 
 Having thus obtained n'e of equation (4), Thomson 
 had only to find n r and then solve for e. To obtain n' 
 he proceeded exactly as Townsend nad done in letting 
 the ions condense droplets of water about them and 
 weighing the cloud thus formed. But in order to form 
 the cloud, Thomson utilized C. T. R. Wilson's discovery 
 
 FIG. i 
 
 just touched upon above, that a sudden expansion and 
 consequent cooling of the air in A (Fig. i) would cause 
 the ions in A to act as nuclei for the formation of water 
 droplets. To produce this expansion the piston P is 
 suddenly pulled down so as to increase the volume of the 
 space above it. A cloud is thus formed about the ions 
 in A. Instead of measuring the weight of this cloud 
 directly, as Townsend had done, Thomson computed it 
 by a theoretical consideration of the amount of cooling 
 
50 THE ELECTRON 
 
 produced by the expansion and the known difference 
 between the densities of saturated water vapor at the 
 temperature of the room and the temperature resulting 
 from the expansion. This method of obtaining the 
 weight of the cloud was less direct and less reliable than 
 that used by Townsend, but it was the only one avail- 
 able with Thomson's method of obtaining an ionized gas 
 and of measuring the charge per cubic centimeter on that 
 gas. The average size of the droplets was obtained pre- 
 cisely as in Townsend's work by applying Stokes's Law 
 to the observed rate of fall of the top of the cloud in 
 chamber A. 
 
 The careful consideration of Thomson's experiment 
 shows that it contains all the theoretical uncertainties 
 involved in Townsend's work, while it adds considerably 
 to the experimental uncertainties. The most serious of 
 the theoretical uncertainties arise from (i) the assump- 
 tion of Stokes's Law, and (2) the assumption that the 
 number of ions is equal to the number of droplets. Both 
 observers sought for some experimental justification for 
 the second and most serious of these assumptions, but 
 subsequent work by H. A. Wilson, by Quincke, and 
 by myself has shown that clouds formed by C. T. R. 
 Wilson's method consist in general of droplets some of 
 which may carry one, some two, some ten, or almost any 
 number of unit charges, and I have never been able, 
 despite quite careful experimenting, to obtain conditions 
 in which it was even approximately true that each 
 droplet carried but a single unit charge. Quincke has 
 recently published results from which he arrives at the 
 same conclusion, 1 
 
 1 Verh. der deutsch. phys. Ges., XVI (1914), 422. 
 
EARLY DETERMINATIONS OF e 51 
 
 Again, when we compare the experimental uncer- 
 tainties in Townsend's and Thomson's work, it is at once 
 obvious that the assumption that the clouds are not 
 evaporating while the rate of fall is being determined is 
 even more serious in Thomson's experiment than in 
 Townsend's, for the reason that in the former case the 
 clouds are formed by a sudden expansion and a conse- 
 quent fall in temperature, and it is certain that during 
 the process of the return of the temperature to initial 
 conditions the droplets must be evaporating. Further- 
 more, this sudden expansion makes the likelihood of the 
 existence of convection currents, which would falsify 
 the computations of the radius of the drop from the ob- 
 served rate of fall, more serious in Thomson's work than 
 in Townsend's. The results which Thomson attained 
 in different experiments gave values ranging from 
 5.5Xio~ 10 to 8.4Xio~ 10 . He published as his final 
 value 6 . 5X io~ 10 . In 1903, however, 1 he published some 
 new work on e in which he had repeated the determina- 
 tion, using the radiation from radium in place of that 
 from X-rays as his ionizing agent and obtained the result 
 e 3.4Xio~ 10 . He explained the difference by the 
 assumption that in his preceding work the more active 
 negative ions had monopolized the aqueous vapor avail- 
 able and that the positive ions had not been brought 
 down with the cloud as he had before assumed was. the 
 case. He now used more sudden expansions than he 
 had used before, and concluded that the assumption 
 made in the earlier experiments tnat the number of ions 
 was equal to the number of particles, although shown to 
 be incorrect for the former case, was correct for these 
 
 1 Phil. Mag., V (1903; 6th series), 354. 
 
52 . THE ELECTRON 
 
 second experiments. As a matter of fact, if he had 
 obtained only half the ions in the first experiments and 
 all of them in the second, his second result should have 
 come out approximately one-half as great as the first, 
 which it actually did. Although Thomson's experiment 
 was an interesting and important modification of Town- 
 send 's, it can scarcely be said to have added greatly 
 to the accuracy of our knowledge of e. 
 
 The next step in advance in the attempt at the deter- 
 mination of e was made in 1903 by H. A. Wilson, 1 also 
 in the Cavendish Laboratory. 
 
 III. H. A. WILSON'S METHOD 
 
 Wilson's modification of Thomson's work consisted in 
 placing inside the chamber A two horizontal brass plates 
 3^ cm. in diameter and from 4 to 10 mm. apart and con- 
 necting to these plates the terminals of a 2,000- volt 
 battery. He then formed a negative cloud by a sudden 
 expansion of amount between 1.25 and 1.3, and 
 observed first the rate of fall of the top surface of this 
 cloud between the plates when no electrical field was 
 on; then he repeated the expansion and observed the 
 rate of fall of the cloud when the electrical field as well 
 as gravity was driving the droplets downward. If mg 
 represents the force of gravity acting on the droplets in 
 the top surface of the cloud and mg+Fe the force of 
 gravity plus the electrical force arising from the action 
 of the field F on the charge e, and if v t is the velocity 
 of fall under the action of gravity alone, and v 9 the 
 velocity when both gravity and the electrical field are 
 acting, then, if the ratio between the force acting and 
 
 l Op. dl., p. 47Q. 
 
EARLY DETERMINATIONS OF e 53 
 
 the velocity produced is the same when the particle is 
 charged as when it is uncharged, we have 
 
 l 
 mg+Fe 
 
 Combining this with the Stokes's Law equation which 
 runs 
 
 9 -n 
 
 in which a is the radius, a the density, t> x the velocity of 
 the drop under gravity #,. and 77 is the viscosity of the air, 
 and then eliminating m by means of 
 
 m = frra 3 o- ...... ,.....: ........ (7) 
 
 Wilson obtained after substituting for 17 and <j the appro- 
 priate values (not accurately known, it is true, for 
 saturated air at the temperature existing immediately 
 after the expansion), 
 
 (8) 
 
 Wilson's method constitutes a real advance in that it 
 eliminates the necessity of making the very awkward 
 assumption that the number of droplets is equal to the 
 number of negative ions, for since he observes only the 
 rate of fall of the top of the cloud, and since the more 
 heavily charged droplets will be driven down more 
 rapidly by the field than the less heavily charged ones, 
 his actual measurements would always be made upon 
 the least heavily charged droplets. All of the other dif- 
 ficulties and assumptions contained in either Town- 
 send's or Thomson's experiments inhere also in Wilson's, 
 and in addition one fresh and rather serious assumption 
 
54 THE ELECTRON 
 
 is introduced, namely, that the clouds formed in succes- 
 sive expansions are identical as to size of droplets. For 
 we wrote down the first equation of Wilson's method as 
 though the v t and v 2 were measurements made upon 
 the same droplet, when as a matter of fact the measure- 
 ments are actually made on wholly different droplets. 
 I have myself found the duplication of cloud conditions 
 in successive expansions a very uncertain matter. 
 Furthermore, Wilson's method assumes uniformity in the 
 field between the plates, an assumption which might be 
 quite wide of the truth. 
 
 Although the elimination of the assumption of 
 equality of the number of droplets and the number of 
 ions makes Wilson's determination of e more reliable as 
 to method than its predecessors, the accuracy actually 
 attained was not great, as can best be seen from his own 
 final summary of results. He made eleven different 
 determinations which varied from =2Xio~ 10 to 
 e=4.4Xio~ 10 . His eleven results are: 
 
 TABLE I 
 
 e e 
 
 2.3Xio~ 10 3.8X10-' 
 
 2.6 3.0 " 
 
 4-4 " 3-5 " 
 
 2.7 " 2.0 " 
 
 3-4 " 2.3 " 
 
 3-8 " 
 
 Mean 3.iXio~ 10 
 
 In 1906, being dissatisfied with the variability of these 
 results, the author repeated Wilson's experiment without 
 obtaining any greater consistency than that which the 
 latter had found. Indeed, the instability, distortion, and 
 indefiniteness of the top surface of the cloud were some- 
 
EARLY DETERMINATIONS OF e 55 
 
 what disappointing, and the results were not considered 
 worth publishing. Nevertheless, it was concluded from 
 these observations that the accuracy might be improved 
 by using radium instead of X-rays for the ionizing agent, 
 by employing stronger electrical fields, and thus increas- 
 ing the difference between Vj. and v 2 , which in Wilson's 
 experiment had been quite small, and by observing the 
 fall of the cloud through smaller distances and shorter 
 times in order to reduce the error due to the evapora- 
 tion of the cloud during the time of observation. 
 Accordingly, a 4,ooo-volt storage battery was built and 
 in the summer of 1908 Mr. Begeman and the author, 
 using radium as the ionizing agent, again repeated the 
 experiment and published some results which were some- 
 what more consistent than those reported by Wilson. 1 
 We gave as the mean of ten observations which varied 
 from 3. 66 to 4.37 the value e=4.o6Xio~ 10 . We stated 
 at the time that although we had not eliminated alto- 
 gether the error due to evaporation, we thought that we 
 had rendered it relatively harmless, and that our final 
 result, although considerably larger than either Wilson's 
 or Thomson's (3.1 and 3.4, respectively), must be con- 
 sidered an approach at least toward the correct value. 
 
 IV. THE BALANCED-DROP METHOD 
 
 Feeling, however, that the amount of evaporation of 
 the cloud was still a quite unknown quantity, I next 
 endeavored to devise a way of eliminating it entirely. 
 The plan now was to use an electrical field which was 
 strong enough, not merely to increase or decrease slightly 
 the speed of fall under gravity of the top surface of the 
 
 ' Phys. Rev., XXVI (1908), 198. 
 
56 THE ELECTRON 
 
 cloud, as had been done in all the preceding experiments, 
 but also sufficiently strong to hold the top surface of the 
 cloud stationary, so that the rate of its evaporation could 
 be accurately observed and allowed for in the computa- 
 tions. 
 
 This attempt, while not successful in the form in 
 which it had been planned, led to a modification of the 
 cloud method which seemed at the time, and which has 
 actually proved since, to be of far-reaching importance. 
 // made it for the first time possible to make all the measure- 
 ments on individual droplets, and thus not merely to 
 eliminate ultimately all of the questionable assumptions 
 and experimental uncertainties involved in the cloud 
 method of determining e, but, more important still, it 
 made it possible to examine the properties of individual 
 isolated electrons and to determine whether different 
 ions actually carry one and the same charge. That is 
 to say, it now became possible to determine whether 
 electricity in gases and solutions is actually built up out 
 of electrical atoms, each of which has exactly the same 
 value, or whether the electron which had first made its 
 appearance in Faraday's experiments on solutions and 
 then in Townsend's and Thomson's experiments on gases 
 is after all only a statistical mean of charges which are 
 themselves greatly divergent. This latter view had been 
 strongly urged up to and even after the appearance of 
 the work which is now. under consideration. It will be 
 given further discussion presently. 
 
 The first determination which was made upon the 
 charges carried by individual droplets was carried out 
 in the spring of 1909. A report of it was placed upon 
 the program of the British Association meeting at Winni- 
 
EARLY DETERMINATIONS OF e 57 
 
 peg in August, 1909, as an additional paper, was printed 
 in abstract in the Physical Review for December, 1909, 
 and in full in the Philosophical Magazine for February, 
 1910, under the title "A New Modification of the Cloud 
 Method of Determining the Elementary Electrical 
 Charge and the Most Probable Value of That Charge. 7 ' 1 
 The following extracts from that paper show clearly what 
 was accomplished in this first determination of the 
 charges carried by individual droplets. 
 
 THE BALANCING OF INDIVIDUAL CHARGED DROPS BY AN 
 ELECTROSTATIC FIELD 
 
 My original plan for eliminating the evaporation error was to 
 obtain, if possible, an electric field strong enough exactly to balance 
 the force of gravity upon the cloud and then by means of a sliding 
 contact to vary the strength of this field so as to hold the cloud 
 balanced throughout its entire life. In this way it was thought 
 that the whole evaporation-history of the cloud might be recorded, 
 and that suitable allowances might then be made in the observa- 
 tions on the rate of fall to eliminate entirely the error due to 
 evaporation. It was not found possible to balance the cloud, as 
 had been originally planned, but it was found possible to do some- 
 thing much better: namely, to hold individual charged drops sus- 
 pended by the field for periods varying from 30 to 60 seconds. 
 I have never actually timed drops which lasted more than 45 
 seconds, although I have several times observed drops which in 
 my judgment lasted considerably longer than this: The drops 
 which it was found possible to balance by an electrical field always 
 carried multiple charges, and the difficulty experienced in balan- 
 cing such drops was less than had been anticipated. 
 
 The procedure is simply to form a cloud and throw on the 
 field immediately thereafter. The drops which have charges of 
 the same sign as that of the upper plate or too weak charges of the 
 opposite sign rapidly fall, while those which are charged with too 
 many multiples of the sign opposite to that of the upper plate are 
 
 1 Phil. Mag., XIX (1910), 209. 
 
58 THE ELECTRON 
 
 jerked up against gravity to this plate. The result is that after 
 a lapse of 7 or 8 seconds the field of view has become quite clear 
 save for a relatively small number pf drops which have just the 
 right ratio of charge to mass to be held suspended by the electric 
 field. These appear as perfectly distinct bright points. I have 
 on several occasions obtained but one single such "star" in the 
 whole field and held it there for nearly a minute. For the most 
 part, however, the observations recorded below were made with 
 a considerable number of such points in view. Thin, flocculent 
 clouds, the production of which seemed to be facilitated by keep- 
 ing the water-jackets /i and 7 2 (Fig. 2) a degree or two above the 
 temperature of the room, were found to be particularly favorable 
 to observations of this kind. 
 
 Furthermore, it was found possible so to vary the mass of a 
 drop by varying the ionization, that drops carrying in some cases 
 two, in some three, in some four, in some five, and in some six, 
 multiples could be held suspended by nearly the same field. The 
 means of gradually varying the field which had been planned were 
 therefore found to be unnecessary. If a given field would not 
 hold any drops suspended it was varied by steps of 100 or 200 
 volts until drops were held stationary, or nearly stationary. When 
 the P.D. was thrown off it was often possible to see different drops 
 move down under gravity with greatly different speeds, thus show- 
 ing that these drops had different masses and correspondingly 
 different charges. 
 
 The life-history of these drops is as follows: If they are a 
 little too heavy to be held quite stationary by the field they begin 
 to move slowly down under gravity. Since, however, they slowly 
 evaporate, their downward motion presently ceases, and they 
 become stationary for a considerable period of time. Then the 
 field gets the better of gravity and they move slowly upward. 
 Toward the end of their life in the space between the plates, this 
 upward motion becomes quite rapidly accelerated and they are 
 drawn with considerable speed to the upper plate. This, taken 
 in connection with the fact that their whole life between plates 
 only 4 or 5 mm. apart is from 35 to 60 seconds, will make it obvious 
 that during a very considerable fraction of this time their motion 
 must be exceedingly slow. I have often held drops through a 
 
EARLY DETERMINATIONS OF e 59 
 
 period of from 10 to 15 seconds, during which it was impossible to 
 see that they were moving at all. Shortly after an expansion I 
 have seen drops which at first seemed stationary, but which then 
 began to moveslowly down in the direction of gravity, then become 
 stationary again, then finally began to move slowly up. This is 
 probably due to the fact that large multiply charged drops are not 
 in equilibrium with smaller singly charged drops near them, and 
 hence, instead of evaporating, actually grow for a time at the 
 expense of their small neighbors. Be this as it may, however, it 
 is by utilizing the experimental fact that there is a considerable 
 period during which the drops are essentially stationary that it 
 becomes possible to make measurements upon the rate of fall in 
 which the error due to evaporation is wholly negligible hi compari- 
 son with the other errors of the experiment. Furthermore, in 
 making measurements of this kind the observer is just as likely 
 to time a drop which has not quite reached its stationary point as 
 one which has just passed through that point, so that the mean of 
 a considerable number of observations would, even from a theo- 
 retical standpoint, be quite free from an error due to evaporation. 
 
 THE METHOD OF OBSERVATION 
 
 The observations on the rate of fall were made with a short- 
 focus telescope T (see Fig. 2) placed about 2 feet away from the 
 plates. In the eyepiece of this telescope were placed three equally 
 spaced cross-hairs, the distance between those at the extremes cor- 
 responding to about one-third of the distance between the plates. 
 A small section of the space between the plates was illuminated by 
 a narrow beam from an arc light, the heat of the arc being absorbed 
 by three water cells in series. The air between the plates was 
 ionized by 200 mg. of radium, of activity 20,000, placed from 
 3 to 10 cm. away from the plates. A second or so after expansion 
 the radium was removed, or screened off with a lead screen, and the 
 field thrown on by hand by means of a double-throw switch. If 
 drops were not found to be held suspended by the field, the P.D. 
 was changed or the expansion varied until they were so held. The 
 cross-hairs were set near the lower plate, and as soon as a stationary 
 drop was found somewhere above the upper cross-hair, it was 
 watched for a few seconds to make sure that it was not moving, 
 
6o 
 
 THE ELECTRON 
 
 and then the field was thrown off and the plates short-circuited 
 by means of the double-throw switch, so as to make sure that they 
 retained no charge. The drop was then timed by means of an 
 accurate stop watch as it passed across the three ^ross-hairs, one 
 of the two hands of the watch being stopped at the instant of 
 
 FIG. 
 
 passage across the middle cross-hair, the other at the instant of 
 passage across the lower one. It will be seen that this method 
 of observation furnishes a double check upon evaporation; for if 
 the drop is stationary at first, it is not evaporating sufficiently to 
 influence the reading of the rate of fall, and if it begins to evaporate 
 appreciably before the reading is completed, the time required to 
 pass through the second space should be greater than that required 
 
EARLY DETERMINATIONS OF e 61 
 
 to pass through the first space. It will be seen from the observa- 
 tions which follow that this was not, in general, the case. 
 
 It is an exceedingly interesting and instructive experiment to 
 watch one of these drops start and stop, or even reverse its direc- 
 tion of motion, as the field is thrown off and on. I have often 
 caught a drop which was just too light to remain stationary and 
 moved it back and forth in this way four or five times between the 
 same two cross-hairs, watching it first fall under gravity when the 
 field was thrown off and then rise against gravity when the field 
 was thrown on. The accuracy and certainty with which the 
 instants of passage of the drops across the cross-hairs can be deter- 
 mined are precisely the same as that obtainable in timing the 
 passage of a star across the cross-hairs of a transit instrument. 
 
 Furthermore, since the observations upon the quantities 
 occurring in equation (4) [see (8) p. 53 of this volume] are all 
 made upon the same drop, all uncertainties as to whether condi- 
 tions can be exactly duplicated in the formation of successive 
 clouds obviously disappear. There is no theoretical uncertainty 
 whatever left in the method unless it be an uncertainty as to 
 whether or not Stokes's Law applies to the rate of fall of these 
 drops under gravity. The experimental uncertainties are reduced 
 to the uncertainty in a time determination of from 3 to 5 seconds, 
 when the object being timed is a single moving bright point. This 
 means that when the time interval is say 5 seconds, as it is in some 
 of the observations given below, the error which a practiced 
 observer will make with an accurate stop watch in any particular 
 observation will never exceed 2 parts in 50. The error in the mean 
 of a considerable number of concordant observations will obviously 
 be very much less than this. 
 
 Since in this form of observation the v 3 of equation (5) [(8) of 
 this volume] is zero, and since F is negative in sign, equation (5) 
 reduces to the simple form: 
 
 y 
 
 X-(*>i)* ................. (6)' 
 
 X I had changed the constant in Wilson's equation from 3.1 to 
 3.422 because of careful measurements on the temperature existing in 
 the cloud chamber about 10 seconds after expansion and because of new 
 measurements on the viscosity of the saturated air. 
 
62 
 
 THE ELECTRON 
 
 It will perhaps be of some interest to introduce two 
 tables from this paper to show the exact nature of these 
 
 SERIES i (BALANCED POSITIVE 
 WATER DROPS) 
 
 Distance between plates . 545 cm. 
 Measured distance of fall .155 cm. 
 
 TABLE II 
 
 SERIES 
 
 2 (BALANCED POSITIVE 
 WATER DROPS) 
 
 Distance between plates . 545 cm. 
 Measured distance of fall .155 cm. 
 
 Volts 
 
 Time 
 i Space 
 
 Time 
 2 Spaces 
 
 2, 28^. . 
 
 2 . 4 sec. 
 
 4 8 sec. 
 
 2,281?. . 
 
 2.4 
 
 4 8 
 
 2,27<\ . . 
 
 2.4 
 
 4.8 
 
 2 32S 
 
 2 4, 
 
 4. 8 
 
 2 32"? 
 
 2 6 
 
 4 8 
 
 2,32^ 
 
 2 2 
 
 4 8 
 
 2,36^ . . 
 
 2 4 
 
 4 8 
 
 
 
 
 2 312 
 
 2 4 
 
 4 8 
 
 
 
 
 Mean time for .155 cm. = 4. 
 
 14.14 
 = 13.77x10-10 
 
 Therefore 6=13. 85X10-1' 
 =4.59X10-10. 
 
 sec. 
 I 
 
 Volts 
 
 Time 
 i Space 
 
 Time 
 2 Spaces 
 
 2,36^ . 
 
 i 8 sec. 
 
 4 O sec. 
 
 2,365 
 
 2,365 
 
 1.8 
 2 . 2 
 
 4.0 
 3.8 
 
 2,^6< 
 
 i 8 
 
 4O 
 
 2,3Q< . 
 
 2 O 
 
 4- O 
 
 2,^qr 
 
 2 O 
 
 4 
 
 2,395 . . 
 
 2 .O 
 
 3 8 
 
 2 ?6<C 
 
 I 8 
 
 4O 
 
 2 36^ 
 
 I 8 
 
 4O 
 
 2,365; . 
 
 i 8 
 
 4 O 
 
 
 
 
 2,374 
 
 1 .90 
 
 ^.06 
 
 
 
 
 Mean time for .155 cm. = 3. 91 sec. 
 
 = 18.25X10-10 
 Therefore 6 = 18.25-7-4 
 
 = 4.56X1010. 
 
 TABLE III 
 
 Series 
 
 Charge 
 
 Value of e 
 
 Weight 
 Assigned 
 
 I 
 
 ~\e 
 
 4 59 
 
 7 
 
 2 
 
 40 
 
 4- 56 
 
 7 
 
 
 ie 
 
 4 64 
 
 6 
 
 4" 
 
 Cg 
 
 4 83 
 
 4 
 
 f . . 
 
 2g 
 
 4.87 
 
 i 
 
 6 
 
 6e 
 
 4 60 
 
 j 
 
 
 
 
 
 Simple mean 6 = 4.70X10 I0 
 Weighted mean 6=4.65X10-10 
 
EARLY DETERMINATIONS OF e 63 
 
 earliest measurements on the charges carried by indi- 
 vidual particles. 
 
 In connection with these experiments I chanced to 
 observe a phenomenon which interested me very much 
 at the time and suggested quite new possibilities. While 
 working with these " balanced drops " I noticed on sev- 
 eral occasions on which I had failed to screen off the rays 
 from the radium that now and then one of them would 
 suddenly change its charge and begin to move up or 
 down in the field, evidently because it had captured in 
 the one case a positive, in the other a negative, ion. This 
 opened up the possibility of measuring with certainty., 
 not merely the charges on individual droplets as I had 
 been doing, but the charge carried by a single atmos- 
 pheric ion. For by taking two speed measurements on the 
 same drop, one before and one after it had caught an ion, I 
 could obviously eliminate entirely the properties of the drop 
 and of the medium and deal with a quantity which was pro- 
 portional merely to the charge on the captured ion itself. 
 
 Accordingly, in the fall of 1909 there was started the 
 series of experiments described in the succeeding chapter. 
 
 The problem had already been so nearly solved by 
 the work with the water droplets that there seemed no 
 possibility of failure. It was only necessary to get a 
 charged droplet entirely free from evaporation into the 
 space between the plates of a horizontal air condenser 
 and then, by alternately throwing on and off an electrical 
 field, to keep this droplet pacing its beat up and down 
 between the plates until it could catch an atmospheric 
 ion in just the way I had already seen the water droplets 
 do. The change in the speed in the field would then be 
 exactly proportional to the charge on the ion captured. 
 
CHAPTER IV 
 
 GENERAL PROOF OF THE ATOMIC NATURE OF 
 ELECTRICITY 
 
 Although the " balanced-droplet method'' just de- 
 scribed had eliminated the chief sources of uncertainty 
 which inhered in preceding work on e and had made it 
 possible to assert with much confidence that the unit 
 charge was' a real physical entity and not merely a 
 " statistical mean," it was yet very far from an exact 
 method of studying the properties of gaseous ions. The 
 sources of error or uncertainty which still inhered in it 
 arose from (i) the lack of stagnancy in the air through 
 which the drop moved ; (2) the lack of perfect uniformity 
 of the electrical field used; (3) the gradual evaporation 
 of the drops, rendering it impossible to hold a given drop 
 under observation for more than a minute or to time a 
 drop as it fell under gravity alone through a period of 
 more than five or six seconds; and (4) the assumption 
 of the validity of Stokes's Law. 
 
 The method which was devised to replace it was not 
 only entirely free from all of these limitations, but it 
 constituted an entirely new way of studying ionization 
 and one which at once yielded important results in a 
 considerable number of directions. This chapter deals 
 with some of these by-products of the determination of 
 e which are of even more fundamental interest and 
 importance than the mere discovery of the exact size of 
 the electron. 
 
 6 4 
 
ATOMIC NATURE OF ELECTRICITY 65 
 
 I. ISOLATION OF INDIVIDUAL IONS AND MEASUREMENT 
 OF THEIR RELATIVE CHARGES 
 
 In order to compare the charges on different ions, the 
 procedure adopted was to blow with an ordinary com- 
 mercial atomizer an oil spray into the chamber C (Fig. 3). 
 
 FIG. 3 
 
 The air with which this spray was blown was first ren- 
 dered dust-free by passage through a tube containing 
 glass wool. The minute droplets of oil constituting the 
 spray, most of them having a radius of the order of a 
 one- thousandth of a millimeter, slowly fell in the cham- 
 ber C, and occasionally one of them would find its way 
 
66 THE ELECTRON 
 
 through the minute pinhole p in the middle of the circular 
 brass plate M, 22 cm. in diameter, which formed one of 
 the plates of the air condenser. The other plate, N, was 
 held 16 mm. beneath it by three ebonite posts a. By 
 means of the switch 5* these plates could be charged, the 
 one positively and the other negatively, by making them 
 the terminals of a 10,000- volt storage battery B, while 
 throwing the switch the other way (to the left) short- 
 circuited them and reduced the field between them to zero. 
 The oil droplets which entered at p were illuminated by a 
 powerful beam of light which passed through diametri- 
 cally opposite windows in the encircling ebonite strip c. 
 As viewed through a third window in c on the side toward 
 the reader, it appeared as a bright star on a black back- 
 ground. These droplets which entered p were found in 
 general to have been strongly charged by the frictional 
 process involved in blowing the spray, so that when the 
 field was thrown on in the proper direction they would 
 be pulled up toward M . Just before the drop under 
 observation could strike M the plates would be short- 
 circuited and the drop allowed to fall under gravity until 
 it was close to N, when the direction of motion would 
 be again reversed by throwing on the field. In this way 
 the drop would be kept traveling back and forth between 
 the plates. The first time the experiment was tried an 
 ion was caught within a few minutes, and the fact of its 
 capture was signaled to the observer by the change 
 in the speed with which it moved up when the field was 
 on. The significance of the experiment can best be 
 appreciated by examination of the complete record of 
 one of the early experiments when the timing was done 
 merely with a stop watch. 
 
ATOMIC NATURE OF ELECTRICITY 67 
 
 The column headed t g gives the successive times which 
 the droplet required to fall between two fixed cross-hairs 
 in the observing telescope whose distance apart corre- 
 sponded in this case to an actual distance of fall of 
 .5222 cm. It will be seen that these numbers are all the 
 same within the limits of error of a stop-watch measure- 
 ment. The column marked t F gives the successive times 
 
 TABLE IV 
 
 tg tv 
 
 13-6 12.5 
 
 13.8 12.4 
 
 13.4 21.8 
 13-4 34-8 
 13.6 84.5 
 13-6 85.5 
 13-7 34-6 
 13-5 34-8 
 
 13.5 16.0 
 13-8 34-8 
 13-7 34-6 
 13.8 21.9 
 13-6 
 
 13-5 
 13-4 
 13-8 
 13-4 
 
 Mean 13.595 
 
 which the droplet required to rise under the influence of 
 the electrical field produced by applying in this case 
 5,051 volts of potential difference to the plates M and N. 
 It will be seen that after the second trip up, the time 
 changed from 12.4 to 21.8, indicating, since in this case 
 the drop was positive, that a negative ion had been 
 caught from the air. The next time recorded under //?, 
 namely, 34.8, indicates that another negative ion had 
 been caught. The next time, 84 . 5, indicates the capture 
 
68 THE ELECTRON 
 
 of still another negative ion. This charge was held 
 for two trips, when the speed changed back again to 
 34.6, showing that a positive ion had now been caught 
 which carried precisely the same charge as the negative 
 ion which before caused the inverse change in time, i.e., 
 that from 34.8 to 84.5. 
 
 In order to obtain some of the most important con- 
 sequences of this and other similar experiments we 
 need make no assumption further than this, that the 
 velocity with which the drop moves is proportional to 
 the force acting upon it and is independent of the elec- 
 trical charge which it carries. Fortunately this assump- 
 tion can be put to very delicate experimental test, as will 
 presently be shown, but introducing it for the time being 
 as a mere assumption, as Townsend, Thomson, and 
 Wilson had done before, we get 
 
 ^1 nig mg ( , ^ 
 
 = -=^(i> x +%) ......... (9) 
 
 V 2 Fe n mg Fvj 
 
 The negative sign is used in the denominator because v 2 
 will for convenience be taken as positive when the drop 
 is going up in the direction of F t while z> x will be taken 
 as positive when it is going down in the direction of g. 
 e n denotes the charge on the drop, and must not be con- 
 fused with the charge on an ion. If now by the capture 
 of an ion the drop changes its charge from e n to e n *, then 
 the value of the captured charge et is 
 
 ei=e n >-e n =~(v' 2 -v 2 ) ........... (10) 
 
 and since ^ is a constant for this drop, any charge 
 rVi 
 
 which it may capture will always be proportional to 
 
ATOMIC NATURE OF ELECTRICITY 
 
 69 
 
 (v' 2 v 2 ), that is, to the change produced in the velocity 
 in the field F by the captured ion. The successive values 
 of v 2 and of (v 2 v 2 ) are shown in Table V. 
 
 TABLE V 
 
 "=.04196 
 12.45 
 
 --=.02390 
 
 2i-5 
 
 5222 
 
 34-7 
 
 5222 
 
 85-o 
 
 5222 
 
 34-7 
 
 5222 
 
 16. o 
 
 5222 
 34-7 
 
 5222 
 21.85 
 
 = 01505 
 
 = .006144 
 
 = 01505 
 
 = .03264 
 
 = .01505 
 
 02390 
 
 018064-2= .00903 
 
 .0088 5-7-1=. 0088 5 
 
 .008914-1= .00891 
 
 .008914-1= .00891 
 
 .017594-2= . 00880 
 
 .017594-2= .00880 
 
 .00891 
 
 00891 
 
 It will be seen from the last column that within the 
 limits of error of a, stop-watch measurement, all the 
 charges captured have exactly the same value save in 
 three cases. In all of these three the captured charges 
 were just twice as large as those appearing in the other 
 changes. Relationships of exactly this sort have been 
 found to hold absolutely without exception, no matter 
 in what gas the drops have been suspended or what sort 
 of droplets were used upon which to catch the ions. In 
 many cases a given drop has been held under observation 
 
70 THE ELECTRON 
 
 for five or six hours at a time and has been seen to 
 catch not eight or ten ions, as in the above experiment, 
 but hundreds of them. Indeed, I have observed, all 
 told, the capture of many thousands of ions in this way, 
 and in no case have I ever found one the charge of which, 
 when tested as above, did not have either exactly the 
 value of the smallest charge ever captured or else a very 
 small multiple of that value. Here, then, is direct, unim- 
 peachable proof that the electron is not a "statistical mean,''' 
 but that rather the electrical charges found on ions all have 
 either exactly the same value or else small exact multiples of 
 that value. 
 
 H. PROOF THAT ALL STATIC CHARGES BOTH ON CON- 
 DUCTORS AND INSULATORS ARE BUILT UP OF 
 ELECTRONS 
 
 The foregoing experiment leads, however, to results 
 of much more fundamental importance than that men- 
 tioned in the preceding section. The charge which the 
 droplet had when it first came under observation had 
 been acquired, not by the capture of ions from the air, 
 but by the ordinary frictional process involved in blow- 
 ing the spray. If then ordinary static charges are built 
 up of electrons, this charge should be found to be an 
 exact multiple of the ionic charge which had been found 
 from the most reliable measurement shown in Table V 
 to be proportional to the velocity .00891. This initial 
 charge e n on the drop is seen from equations (9) and (10) 
 to bear the same relation to (v l -}-v 2 ) which the ionic 
 charge^' e n bears to (v' 2 v 2 ). Now, v^= .5222/13.595 
 = .03842, hence v l -\-v 2 = .03842+. 04196= .08038. Di- 
 viding this by 9 we obtain . 00893 r > which is within about 
 
ATOMIC NATURE OF ELECTRICITY 71 
 
 one-fifth of i per cent of the value found in the last 
 column of Table V as the smallest charge carried by an 
 ion. Our experiment has then given us for the first time 
 a means of comparing a frictional charge with the ionic 
 charge, and the frictional charge has in this instance been 
 found to contain exactly 9 electrons. A more exact means 
 of making this comparison will be given presently, but 
 suffice it to say here that experiments like the foregoing 
 have now been tried on thousands of drops in different 
 media, some of the drops being made of non-conductors 
 like oil, some of semi-conductors like glycerin, some of 
 excellent metallic conductors like mercury. In every 
 case, without a single exception, the initial charge placed 
 upon the drop by the frictional process, and all of the 
 dozen or more charges which have resulted from the 
 capture by the drop of a larger or smaller number of 
 ions, have been found to be exact multiples of the small- 
 est charge caught from the air. Some of these drops 
 have started with no charge at all, and one, two, three, 
 four, five, and six elementary charges or electrons have 
 been picked up. Others have started with seven or 
 eight units, others with twenty, others with fifty, others 
 with a hundred, others with a hundred and fifty elemen- 
 tary units, and have picked up in each case a dozen or 
 two of elementary charges on either side of the starting- 
 point, so that in all drops containing every possible num- 
 ber of electrons between one and one hundred and fifty 
 have been observed and the number of electrons which 
 each drop carried has been accurately counted by the 
 method described. When the number is less than fifty 
 there is not a whit more uncertainty about this count 
 than there is in counting one's own fingers and toes. It 
 
72 THE ELECTRON 
 
 is not found possible to determine with certainty the 
 number of electrons in a charge containing more than 
 one hundred or two hundred of them, for the simple 
 reason that the method of measurement used fails to 
 detect the difference between 200 and 201, that is, we 
 cannot measure v' 2 v a with an accuracy greater than 
 one-half of i per cent. But it is quite inconceivable that 
 large charges such as are dealt with in commercial appli- 
 cations of electricity can be built up in an essentially 
 different way from that in which the small charges whose 
 electrons we are able to count are found to be. Further- 
 more, since it has been definitely proved that an electrical 
 current is nothing but the motion of an electrical charge 
 over or through a conductor, it is evident that the 
 experiments under consideration furnish not only the 
 most direct and convincing of evidence that all electrical 
 charges are built up out of these very units which we 
 have been dealing with as individuals in these experi- 
 ments, but that all electrical currents consist merely in 
 the transport of these electrons through the conducting 
 bodies. 
 
 In order to show the beauty and precision with which 
 these multiple relationships stand out in all experiments 
 of this kind, a table corresponding to much more precise 
 measurements than those given heretofore is here intro- 
 duced (Table VI). The time of fall and rise shown in 
 the first and second columns were taken with 'a Hipp 
 chronoscope reading to one- thousandths of a second. 
 The third column gives the reciprocals of these times. 
 These are used in place of the velocities v 2 in the field, 
 since distance of fall and rise is always the same. The 
 fourth column gives the successive changes in speed due 
 
ATOMIC NATURE OF ELECTRICITY 
 
 73 
 
 to the capture of ions. These also are expressed merely 
 as time reciprocals. For reasons which will be explained 
 in the next section, each one of these- changes may corre- 
 spond to the capture of not merely one but of several dis- 
 tinct ions. The numbers in the fifth column represent 
 
 TABLE VI 
 
 Sic. 
 
 tp 
 Sec. 
 
 I 
 tp 
 
 (NJ 
 
 ' 
 
 i<') 
 
 ( + i) 
 
 n 
 
 &4) 
 
 11.848 
 
 80 . 708 
 
 .01236 1 
 
 
 
 
 .09655 
 
 18 
 
 005366 
 
 11.890 
 
 22.366 
 
 
 
 03234 
 
 6 
 
 005390 
 
 
 
 
 11.908 
 
 22.390 
 
 
 . 04470 
 
 
 
 
 .12887 
 
 24 
 
 005371 
 
 11.904 
 
 22.368 
 
 
 
 03751 
 
 7 
 
 005358 
 
 
 
 
 11.882 
 i i . 906 
 11.838 
 
 140.565 
 79 . 600 
 34.748 
 
 
 .007192! ' 
 -01254 /v 
 
 005348 
 .Ol6l6 
 
 i 
 3 
 
 005348 
 005387 
 
 .09138 
 .09673 
 
 17 
 18 
 
 -005375 
 005374 
 
 11.816 
 
 34.762 
 
 
 .02870 ' 
 
 
 
 
 .11289 
 
 21 
 
 .005376 
 
 11.776 
 
 34-846 
 
 
 
 
 
 
 
 
 
 i i . 840 
 r i . 904 
 
 29.286 
 29.236 
 
 
 03414 I 
 
 .026872 
 
 5 
 
 005375 
 
 . H833 
 
 22 
 
 005379 
 
 11.870 
 11.952 
 
 137.308 
 34-638 
 
 .007 268P 
 
 .02884 K 
 
 .021572 
 
 4 
 
 005393 
 
 .09146 
 -II303 
 
 17 
 21 
 
 .005380 
 .005382 
 
 11.860 
 
 
 , 
 
 .01623 
 
 3 
 
 .005410 
 
 
 
 
 11.846 
 ii .912 
 
 22.104\ 
 22.268) 
 
 .04507 i 
 
 .04307 
 
 8 
 
 .005384 
 
 .12926 
 
 24 
 
 .005386 
 
 11.910 
 
 500. I 
 
 .002000 ' 
 
 
 
 
 .08619 
 
 16 
 
 005387 
 
 11.918 
 11.870 
 11.888 
 11.894 
 11.878 
 
 19.704! 
 
 I9.668J 
 77.630\ 
 77. 806 / 
 42.302 
 
 05079 1 
 
 .01285 I 
 .02364 / 
 
 .04879 
 03874 
 .OI079 
 
 9 
 7 
 
 2 
 
 .005421 
 .005401 
 
 , .005395 
 
 .13498 
 .09704 
 10783 
 
 25 
 18 
 
 20 
 
 005399 
 
 .005390 
 .005392 
 
 ii 880 
 
 
 
 Means 
 
 
 -005386 
 
 - 
 
 
 005384 
 
 Duration of exp. =45 min. 
 
 Plate distance 
 Fall distance 
 Initial volts 
 Final volts 
 
 Temperature 
 
 16 mm. 
 = 10.21 mm. 
 = 5,088.8 
 = 5,081.2 
 
 = 22.82 C. 
 
 Pressure 
 Oil density 
 Air viscosity 
 Radius (a) 
 
 = 75.62 cm. 
 = .9199 
 = 1,824X10 -i 
 .000276 cm. 
 = 034 
 
 1=4.991X10 
 
 Speed of fall = 08584 cm./sec. 
 
 simply the small integer by which it is found that the 
 numbers in the fourth column must be divided in order 
 to obtain the numbers in the sixth column. These will 
 be seen to be exactly alike within the limits of error of the 
 experiment. The mean value at the bottom of the sixth 
 column represents, then, the smallest charge ever caught 
 
74 
 
 THE ELECTRON 
 
 from the air, that is, it is the elementary ionic charge. 
 The seventh column gives the successive values of v l -\-v 2 
 expressed as reciprocal times. These numbers, then, rep- 
 resent the successive values of the total charge carried by 
 the droplet. The eighth column gives the integers by 
 which the numbers in the seventh column must be 
 divided to obtain the numbers in the last column. These 
 also will be seen to be invariable. The mean at the 
 bottom of the last column represents, then, the electrical 
 unit out of which the frictional charge on the droplet was 
 built up, and it is seen to be identical with the ionic charge 
 represented by the number at the bottom of the sixth column. 
 It may be of interest to introduce one further table 
 (Table VII) arranged in a slightly different way to show 
 
 TABLE VII 
 
 n 
 
 4.pi7X 
 
 Observed 
 Charge 
 
 
 
 4.QI7XW 
 
 Observed 
 Charge 
 
 I 
 
 4 QI7 
 
 
 IO 
 
 40 1 7 
 
 4Q 41 
 
 2 . 
 
 834 
 
 
 II . 
 
 1:4 OQ 
 
 K3 OI 
 
 
 lA. 7C 
 
 
 12 
 
 ZQ OO 
 
 CQ 12 
 
 4 
 
 IQ.66 
 
 19 66 
 
 I"? . . 
 
 63 92 
 
 63 68 
 
 
 24.59 
 
 24. 60 
 
 14 
 
 68.84 
 
 68 65 
 
 6 
 
 20 ^O 
 
 20 62 
 
 ir 
 
 737 s ; 
 
 
 7 
 
 34 42 
 
 34 47 
 
 16 
 
 78 67 
 
 78 34 
 
 8 . . : . 
 
 }Q -24 
 
 30 38 
 
 17 . 
 
 83 so 
 
 83 22 
 
 
 44 2"\ 
 
 44 42 
 
 18 
 
 88.51 
 
 
 
 
 
 
 
 
 how infallibly the atomic structure of electricity follows 
 from experiments like those under consideration. 
 
 In this table 4.917 is merely a number obtained 
 precisely as above from the change in speed due to the 
 capture of ions and one which is proportional in this 
 experiment to the ionic charge. The column headed 
 4.917X7* contains simply the whole series of exact mul- 
 
ATOMIC NATURE OF ELECTRICITY 75 
 
 tiples of this number from i to 18. The column headed 
 " Observed Charge " gives the successive observed values 
 of (i+a). It will be seen that during the time of obser- 
 vation, about four hours, this drop carried all possible 
 multiples of the elementary charge from 4 to 18, save only 
 15. No more exact or more consistent multiple relationship 
 is found in the data which chemists have amassed on the 
 combining powers of the elements and on which the atomic 
 theory of matter rests than is found in the foregoing numbers. 
 Such tables as these and scores of them could be 
 given place beyond all question the view that an 
 electrical charge wherever it is found, whether on an 
 insulator or a conductor, whether in electrolytes or in 
 metals, has a definite granular structure, that it consists 
 of an exact number of specks of electricity (electrons) all 
 exactly alike, which in static phenomena are scat- 
 tered over the surface of the charged body and in current 
 phenomena are drifting along the conductor. Instead 
 of giving up, as Maxwell thought we should some day do, 
 the " provisional hypothesis of molecular charges," we 
 find ourselves obliged to make all our interpretations of 
 electrical phenomena, metallic as well as electrolytic, in 
 terms of it. 
 
 III. MECHANISM OF CHANGE OF CHARGE OF A DROP 
 
 All of the changes of charge shown in Table IV were 
 spontaneous changes, and it has been assumed that all 
 of these changes were produced by the capture of ions 
 from the air. When a negative drop suddenly increases 
 its speed in the field, that is, takes on a larger charge of 
 its own kind than it has been carrying, there seems to be 
 no other conceivable way in which the change can be 
 
76 THE ELECTRON 
 
 produced. But when the charge suddenly decreases there 
 is no a priori reason for thinking that the change may not 
 be due as well to the direct loss of a portion of the charge 
 as to the neutralization of this same amount of electricity 
 by the capture of a charge of opposite sign. That, how- 
 ever, the changes do actually occur, when no X-rays or 
 radioactive rays are passing between the plates, only by 
 the capture of ions from the air, was rendered probable by 
 the fact that drops not too heavily charged showed the 
 same tendency on the whole to increase as to decrease in 
 charge. This should not have been the case if there were 
 two causes tending to decrease the charge, namely, direct 
 loss and the capture of opposite ions, as against one tend- 
 ing to increase it, namely, capture of like ions. The 
 matter was very convincingly settled, however, by mak- 
 ing observations when the gas pressures were as low as 
 2 or 3 mm. of mercury. Since the number of ions present 
 in a gas is in general directly proportional to the pressure, 
 spontaneous changes in charge should almost never occur 
 at these low pressures; in fact, it was found that drops 
 could be held for hours at a time without changing. The 
 frequency with which the changes occur decreases regu- 
 larly with the pressure, as it should if the changes are 
 due to the capture of ions. For the number of ions 
 formed by a given ionizing agent must vary directly as 
 the pressure. 
 
 Again, the changes do not, in general, occur when the 
 electrical field is on, for then the ions are driven instantly 
 to the plates as soon as formed, at a speed of, say, 
 10,000 cm. per second, and so do not have any oppor- 
 tunity to accumulate in the space between them. When 
 the field is off, however, they do so accumulate, until, in 
 
ATOMIC NATURE OF ELECTRICITY 77 
 
 ordinary air, they reach the number of, say, 20,000 per 
 cubic centimeter. These ions, being endowed with the 
 kinetic energy of agitation characteristic of the tempera- 
 ture, wander rapidly through the gas and become a part 
 of the drop as soon as they impinge upon it. It was thus 
 that all the changes recorded in Table IV took place. 
 
 It is possible, however, so to control the changes as 
 to place electrons of just such sign as one wishes, and of 
 just such number as one wishes, within limits, upon a 
 given drop. If, for example, it is desired to place a posi- 
 tive electron upon a given drop the latter is held with 
 the aid of the field fairly close to the negative plate, say 
 the upper plate; then an ionizing agent- -X-rays or 
 radium is arranged to produce dniform ionization in 
 the gas between the plates. Since now all the positive 
 ions nibve up while the negatives move down, the drop 
 is in a shower of positive ions, and if the ionization is 
 intense enough the drop is sure to be hit. In this way 
 a positive charge of almost any desired strength may be 
 placed upon the drop. 
 
 Similarly, in order to throw a negative ion or ions 
 upon the drop it is held by the field close to the lower, 
 i.e., to the positive, plate in a shower of negative ions 
 produced by the X-rays. It was in this way that most 
 of the changes shown in Table VI were brought about. 
 This accounts for the fact that they correspond in some 
 instances to the capture of as many as six electrons. 
 
 When X-rays are allowed to fall directly upon the 
 drop itself the change in charge may occur, not merely 
 because of the capture of ions, but also because the rays 
 eject beta particles, i.e., negative electrons, from the 
 molecules of the drop. That changes in charge were 
 
78 THE ELECTRON 
 
 actually produced in this way in our experiments was 
 proved conclusively in 1910 by the fact that when the 
 pressure was reduced to a very low value and X-rays 
 were allowed to pass through the air containing the drop, 
 the latter would change readily in the direction of increas- 
 ing positive or decreasing negative charge, but it could 
 almost never be made to change in the opposite direc- 
 tion. This is because at these low pressures the rays 
 can find very few gas molecules to ionize, while they 
 detach negative electrons from the drop as easily as at 
 atmospheric pressure. This experiment proved directly 
 that the charge carried by an ion in gases is the same as the 
 charge on the beta or cathode-ray particle. 
 
 When it was desired to avoid the direct loss of nega- 
 tive electrons by the drop, we arranged lead screens so 
 that the drop itself would not be illuminated by the rays, 
 although the gas underneath it was ionized by them. 1 
 
 IV. DIRECT OBSERVATION OF THE KINETIC ENERGY OF 
 AGITATION OF A MOLECULE 
 
 I have already remarked that when a drop carries 
 but a small number of electrons it appears to catch ions 
 of its own sign as rapidly as those of opposite signs a 
 result which seems strange at first, since the ions of 
 opposite sign must be attracted, while those of like sign 
 must be repelled. Whence, then, does the ion obtain the 
 energy which enables it to push itself up against this 
 electrostatic repulsion and attach itself to a drop already 
 strongly charged with its own kind of electricity ? It 
 cannot obtain it from the field, since the phenomenon of 
 capture occurs when the field is not on. It cannot 
 
 < See Phil. Mag., XXI (1911), 757. 
 
ATOMIC NATURE OF ELECTRICITY 79 
 
 obtain it from any explosive process which frees. the ion 
 from the molecule at the instant of ionization, since 
 in this case, too, ions would be caught as well, or 
 nearly as well, when the field is on as when it is off. Here, 
 then, is an absolutely direct proof that the ion must be 
 endowed with a kinetic energy of agitation which is 
 sufficient to push it up to the surface of the drop against 
 the electrostatic repulsion of the charge on the drop. 
 
 This energy may easily be computed as follows : Let 
 us take a drop, such as was used in one of these experi- 
 ments, of radius .000197 cm - The potential at the sur- 
 face of a charged sphere can be shown to be the charge 
 divided by the radius. The value of the elementary 
 electrical charge obtained from the best observations of 
 this type, is 4.774Xio~ 10 absolute electrostatic units. 
 Hence the energy required to drive an ion carrying the 
 elementary charge e up to the surface of a charged sphere 
 of radius r, carrying 16 elementary charges, is 
 
 i6X(4.774Xio- 10 ) 2 
 =i.95Xio~ 14 ergs. 
 .000197 L 
 
 Now, the kinetic energy of agitation of a molecule as 
 deduced from the value of e herewith obtained, and the 
 kinetic theory equation, p = ^nmc 2 , is 5.75Xio~ 14 ergs. 
 According to the Maxwell-Boltzmann Law of the parti- 
 tion of energy, which certainly holds in gases, this should 
 also be the kinetic energy of agitation of an ion. It will 
 be seen that the value of this energy is approximately 
 three times that required to push a single ion up to the 
 surface of the drop in question. Hence the electrostatic 
 forces due to 16 electrons on the drop are too weak to 
 exert much influence upon the motion of an approaching 
 
8o THE ELECTRON 
 
 ion. But if it were possible to load up a drop with 
 negative electricity until the potential energy of its 
 charge were about three times as great as that computed 
 above for this drop, then the phenomenon here observed 
 of the catching of new negative ions by such a negatively 
 charged drop should not take place, save in the excep- 
 tional case in which an ion might acquire an energy 
 of agitation considerably larger than the mean value. 
 Now, as a matter of fact, it was regularly observed that 
 the heavily charged drops had a very much smaller tend- 
 ency to pick up new negative ions than the more lightly 
 charged drops, and, in one instance, we watched for four 
 hours another negatively charged drop of radius 
 .000658 cm., which carried charges varying from 126 to 
 150 elementary units, and which therefore had a poten- 
 tial energy of charge (computed as above on the assump- 
 tion of uniform distribution) varying from 4. 6X io~ 14 to 
 5 . 47 X io~ 14 . In all that time this drop picked up but one 
 single negative ion when the field was off, and that 
 despite the fact that the ionization was several times 
 more intense than in the case of the drop of Table I. 
 Positive ions too were being caught at almost every trip 
 down under gravity. (The strong negative charge on 
 the drop was maintained by forcing on negative ions by 
 the field as explained above.) 
 
 V. POSITIVE AND NEGATIVE ELECTRONS EXACTLY EQUAL 
 
 The idea has at various times been put forth in con- 
 nection with attempts to explain chemical and cohesive 
 forces from the standpoint of electrostatic attractions 
 that the positive and negative charges in a so-called 
 neutral atom may not after all be exactly equal, in other 
 
ATOMIC NATURE OF ELECTRICITY 8 1 
 
 words, that there is really no such thing as an entirely 
 neutral atom or molecule. As a matter of fact, it is 
 difficult to find decisive tests of this' hypothesis. The 
 present experiments, however, make possible the follow- 
 ing sort of test. I loaded a given drop first with negative 
 electrons and took ten or twelve observations of rise and 
 fall, then with the aid of X-rays, by the method indicated 
 in the last section, I reversed the sign of the charge on 
 the drop and took a corresponding number of observa- 
 tions of rise and fall, and so continued observing first the 
 value of the negative electron and then that of the posi- 
 tive. Table VIII shows a set of such observations taken 
 in air with a view to subjecting this point to as rigorous a 
 test as possible. Similar, though not quite so elaborate, 
 observations have been made in hydrogen with the same 
 result. The table shows in the first column the sign of 
 the charge; in the second the successive values of the 
 time of fall under gravity; in the third the successive 
 times of rise in the field F; in the fourth the number of 
 electrons carried by the drop for each value of //?; and in 
 the fifth the number, characteristic of this drop, which 
 is proportional to the charge of one electron. This num- 
 ber is obtained precisely as in the two preceding tables 
 by finding the greatest common divisor of the successive 
 values of (fli+fl 2 ) and then multiplying this by an 
 arbitrary constant which has nothing to do with the 
 present experiment and hence need not concern us here 
 (see chap. v). 
 
 It will be seen that though the times of fall and of 
 rise, even when the same number of electrons is carried 
 by the drop, change a trifle because of a very slight 
 evaporation and also because of the fall in the potential 
 
THE ELECTRON 
 TABLE VIII 
 
 Sign of Drop 
 
 4. 
 
 *P 
 Sec. 
 
 n 
 
 e 
 
 
 63.118 
 
 
 
 
 
 63 . 050 
 
 
 
 
 
 63.186 
 
 41.728! 
 
 
 
 
 63.332 
 
 41 590/ 
 
 
 
 
 
 62.328 
 
 
 
 
 
 62.728 
 
 25.740] 
 
 
 ^ = 6.713 
 
 
 62.926 
 
 25.798 
 
 f i 
 
 
 
 62.900 
 
 
 a 
 
 
 
 63-214 
 
 25io6J 
 
 
 
 
 Mean=62.976 
 
 
 
 
 
 63-538 
 
 22.694! 
 
 
 
 
 63.244 
 
 22.830; 
 
 12 
 
 
 
 63.114 
 
 25.870] 
 
 
 
 
 63 . 242 
 
 25. 876 [ 
 
 II 
 
 
 
 63.362 
 
 25.484] 
 
 
 
 + 
 
 63.136 
 63.226 
 
 10.830 
 10.682 
 
 
 ^ = 6.692 
 
 
 63 764 
 
 10.756 > 
 
 
 
 
 63.280 
 
 10.778 
 
 22 
 
 
 
 63-530 
 
 10.672 
 
 
 
 
 63 . 268 
 
 10.646 
 
 
 
 
 63-642 
 
 
 
 
 
 63 . 020 
 
 71.664! 
 
 
 
 
 62.820 
 
 71-248; 
 
 
 
 
 63-5I4 
 
 52.668] 
 
 
 
 -j- 
 
 63.312 
 
 52.800! 
 
 
 
 
 63.776 
 
 52 496] 
 
 7 
 
 61 = 6.702 
 
 
 63.300 
 
 52.860] 
 
 
 
 
 63.156 
 
 71.708 
 
 6 
 
 
 
 63.126 
 
 
 
 
 
 Mean = 63 . 407 
 
 
 
 
ATOMIC NATURE OF ELECTRICITY 
 
 TABLE VIII Continued 
 
 Sign of Drop 
 
 4 
 
 *P 
 
 Sec. 
 
 w 
 
 e 
 
 
 63.228 
 63 . 294 
 63.184 
 
 42.006 
 41.920 
 
 42. 1 08 
 
 . 
 
 8 
 
 
 - 
 
 63. 260 
 63-478 
 63 . 074 
 63.306 
 
 53-210 
 52.922 
 53 034 
 53-438> 
 
 1 
 
 7 
 
 ei = 6.686 
 
 
 63-414 
 63-450 
 63 - 446 
 63-556 
 
 12.888 
 12.812 
 12.748 
 12.824 
 
 
 iQ 
 
 
 Mean = 63. 335 
 
 Duration of experiment i hr. 40 min. Mean + = 6.697 
 
 Initial volts =1723.5 Mean e = 6 . 700 
 
 Final volts = 1 702 . i 
 Pressure = 53 ; 48 cm. 
 
 of the battery, yet the mean value of the positive elec- 
 tron, namely, 6.697, agrees with the mean value of the 
 negative electron, namely, 6 . 700, or to within less than 
 i part in 2,000. Since this is about the limit of the 
 experimental error (the probable error by least squares 
 is i part in 1,500), we may with certainty conclude that 
 there are no differences of more than this amount between 
 the values of the positive and negative electrons. This is 
 the best evidence I am aware of for the exact neutrality 
 of the ordinary molecules of gases. Such neutrality, if 
 it is actually exact, would seem to preclude the possi- 
 bility of explaining gravitation as a result of electrostatic 
 forces of any kind. The electromagnetic effect of mov- 
 ing charges might, however, still be called upon for 
 this purpose. 
 
84 THE ELECTRON 
 
 VI. RESISTANCE OF MEDIUM TO MOTION OF DROP THROUGH 
 
 IT THE SAME WHEN DROP IS CHARGED AS WHEN 
 
 UNCHARGED 
 
 A second and equally important conclusion can be 
 drawn from Table VIII. It will be seen from the column 
 headed "n" that during the whole of the time corre- 
 sponding to the observations in the third group from 
 the top the drop carried either 6 or 7 electrons, while, 
 during the last half of the time corresponding to the 
 observations in the second group from the top, it 
 carried three times as many, namely, 22 electrons. 
 Yet the mean times of fall under gravity in the two 
 groups agree to within about one part in one thousand. 
 The time of fall corresponding to the heavier charge 
 happens in this case to be the smaller of the two. 
 We may conclude, therefore, that in these experiments the 
 resistance which the medium offers to the motion of a body 
 through it is not sensibly increased when the body becomes 
 electrically charged. This demonstrates experimentally the 
 exact validity for this work of the assumption made on 
 p. 68 that the velocity of the drop is strictly propor- 
 tional to the force acting upon it, whether it is charged or 
 uncharged. 
 
 The result is at first somewhat surprising since, 
 according to Sutherland's theory of the small ion, the 
 small mobility or diffusivity of charged molecules, as 
 compared with uncharged, is due to the additional resist- 
 ance which the medium offers to the motion through it 
 of a charged molecule. This additional resistance is 
 due to the fact that the charge on a molecule drags 
 into collision with it more molecules than would other- 
 wise hit it. But with oil drops of the sizes here used 
 
ATOMIC NATURE OF ELECTRICITY 85 
 
 (a=5oXio~ 6 ) the total number of molecular collisions 
 against the surface of the drop is so huge that even 
 though the small number of charges on it might produce 
 a few more collisions, their number would be negligible 
 in comparison with the total number. At any rate the 
 experiment demonstrates conclusively that the charges 
 on our oil drops do not influence the resistance of the 
 medium to the motion of the drop. This conclusion 
 might also have been drawn from the data contained in 
 Table VI. The evidence for its absolute correctness has 
 been made more convincing still by a comparison of 
 drops which carried but i charge and those which 
 carried as many as 68 unit charges. Further, I have 
 observed the rate of fall under gravity of droplets 
 which were completely discharged, and in every case 
 that I have ever tried I have found this rate pre- 
 cisely the same, within the limits of error of the 
 time measurements, as when it carried 8 or 10 unit 
 charges. 
 
 VII. DROPS ACT LIKE RIGID SPHERES 
 
 It was of very great importance for the work, an ac- 
 count of which will be given in the next chapter to deter- 
 mine whether the drops ever suffer either because of 
 their motion through a resisting medium, or because of 
 the electrical field in which they are placed any appre- 
 ciable distortion from the spherical form which a freely 
 suspended liquid drop must assume. The complete 
 experimental answer to this query is contained in the 
 agreement of the means at the bottom of the last and 
 the third from the last columns in Table VI and in 
 similar agreements shown in many other tables, which 
 
86 THE ELECTRON 
 
 may be found in the original articles. 1 Since - is in this 
 
 i g 
 
 experiment large compared to , the value of the greatest 
 
 IF 
 
 common divisor at the bottom of the last column of 
 Table VI is determined almost wholly by the rate of fall 
 of the particle under gravity when there is no field at all 
 between the plates, while the velocity at the bottom of 
 the third from the last column is a difference between two 
 velocities in a strong electrical field. If, therefore, the 
 drop were distorted by the electrical field, so that it 
 exposed a larger surface to the resistance of the medium 
 than when it had the spherical form, the velocity due to 
 a given force, that is, the velocity given at the bottom of 
 the third from the last column, would be less than that 
 found at the bottom of the last column, which corre- 
 sponds to motions when the drop certainly was spherical. 
 
 Furthermore, if the drops were distorted by their 
 motion through the medium, then this distortion would 
 be greater for high speeds than for low, and consequently 
 the numbers in the third from the last column would be 
 consistently larger for high speeds than for low. No 
 such variation of these numbers with speed is apparent 
 either in Table VI or in other similar tables. 
 
 We have then in the exactness and invariableness of 
 the multiple relations shown by successive differences in 
 speed and the successive sums of the speeds in the third 
 from the last and the last columns of Table VI complete 
 experimental proof that in this work the droplets act 
 under all circumstances like undeformed spheres. It is 
 of interest that Professor Hadamard, 2 of the University of 
 
 1 Phys. Rev., Series i, XXXII (1911), 349; Series 2, II (1913), 109. 
 
 2 Comptes r endus (1911), 1735. 
 
ATOMIC NATURE OF ELECTRICITY 87 
 
 Paris, and Professor Lunn, 1 of the University of Chicago, 
 have both shown from theoretical considerations that 
 this would be the case with oil drops as minute as those 
 with which these experiments deal, so that the conclu- 
 sion may now be considered as very firmly established 
 both by the experimentalist and the theorist. 
 
 < Phys. Rev., XXXV (1912), 227. 
 
CHAPTER V 
 
 THE EXACT EVALUATION OF e 
 I. DISCOVERY OF THE FAILURE OF STOKES's LAW 
 
 Although complete evidence for the atomic nature of 
 electricity is found in the fact that all of the charges 
 which can be placed upon a body as measured by the 
 sum of speeds fli-f-z> 2 , and all the changes of charge which 
 this body can undergo as measured by the differences of 
 speed (v' 2 v 2 ) are invariably found to be exact multiples 
 of a particular speed, yet there is something still to be 
 desired if we must express this greatest common divisor 
 of all the observed series of speeds merely as a velocity 
 which is a characteristic constant of each particular drop 
 but which varies from drop to drop. We ought rather 
 to be able to reduce this greatest common divisor to 
 electrical terms by finding the proportionality factor 
 between speed and charge, and, that done, we should, of 
 course, expect to find that the charge came out a uni- 
 versal constant independent of the size or kind of drop 
 experimented upon. The attempt to do this by the 
 method which I had used in the case of the water drops 
 (p. 53), namely, by the assumption of Stokes's Law, 
 heretofore taken for granted by all observers, led to the 
 interesting discovery that this law is not valid. 1 Accord- 
 
 1 Cunningham (Proc. Roy. Soc., LXXXIII [1910], 357) and the 
 author came independently to the conclusion as to the invalidity of 
 Stokes's Law, he from theoretical considerations developed at about the 
 same time, I from my experimental work. 
 
 88 
 
THE EXACT EVALUATION OF e 89 
 
 ing to this law the rate of fall of a spherical drop under 
 gravity, namely, v tj is given by 
 
 * = %(*- p) .' .............. (n) 
 
 9*7 
 
 in which rj is the viscosity of the medium, a the radius 
 and o- the density of the drop, and p the density of the 
 medium. This last quantity was neglected in (6), p. 53, 
 because, with the rough measurements there possible, it 
 was useless to take it into account, but with our oil drops 
 in dry air all the other factors could be found with great 
 precision. 
 
 When we assume the foregoing equation of Stokes and 
 combine it with equation (5) on p. 53, an equation whose 
 exact validity was proved experimentally in the last 
 chapter, we obtain, after substitution of the purely geo- 
 metrical relation 7^=4/3 a 3 (<r p), the following expres- 
 sion for the charge e n carried by a drop loaded with n 
 electrons which we will assume to have been counted by 
 the method described: 
 
 _4/9> 
 
 According to this equation the elementary charge e^ 
 should be obtained by substituting in this the greatest 
 common divisor of all the observed series of values o'f 
 (fli~H 2 ) or of (v' 2 v 2 ). Thus, if we call this (0i+%) , we 
 have 
 
 But when this equation was tested out upon different 
 drops, although it yielded perfectly concordant results 
 
go THE ELECTRON 
 
 so long as the different drops all fell with about the same 
 speed, when drops of different speeds, and, therefore, of 
 different sizes, were used, the values of d obtained were 
 consistently larger the smaller the velocity under gravity. 
 For example, d for one drop for which Vi= . 01085 cm. per 
 second came out 5 . 49 X io~ 10 , while for another of almost 
 the same speed, namely, v^= .01176, it came out 5.482; 
 but for two drops whose speeds were five times as large, 
 namely, .0536 and .0553, e t came out 5.143 and 5.145, 
 respectively. This could mean nothing save that 
 Stokes's Law did not hold for drops of the order of mag- 
 nitude here used, something like a= .0002 cm. (see Sec- 
 tion IV below), and it was surmised that the reason for 
 its failure lay in the fact that the drops were so small that 
 they could no longer be thought of as moving through 
 the air as they would through a continuous homogeneous 
 medium, which was the situation contemplated in the 
 deduction of Stokes's Law. This law ought to begin to 
 fail as f soon as the inhomogeneities in the medium i.e., 
 the distances between the molecules began to be at all 
 comparable with the dimensions of the drop. Further- 
 more, it is easy to see that as soon as the holes in the * 
 medium begin to be comparable with the size of the 
 drop, the latter must begin to increase its speed, for it 
 may then be thought of as beginning to reach the stage 
 in which it can fall freely through the holes in the 
 medium. This would mean that the observed speed of 
 fall would be more and more in excess of that given by 
 Stokes's Law the smaller the drop became. But the 
 apparent value of the electronic charge, namely, e^ is 
 seen from equation (13) to vary directly with the speed 
 fe+fl 2 ) imparted by a given force. Hence e^ should 
 
I 
 THE EXACT EVALUATION OF c 91 
 
 come out larger and larger the smaller the radius of the 
 drop, that is, the smaller its velocity under gravity. Now, 
 this was exactly the behavior shown consistently by all 
 the oil drops studied. Hence it looked as though we had 
 discovered, not merely the failure of Stokes J s Law, but 
 also the line of approach by means of which it might be 
 corrected. 
 
 In order to be certain of our ground, however, we 
 were obliged to initiate a whole series of new and some- 
 what elaborate experiments. 
 
 These consisted, first, in finding very exactly what 
 is the coefficient of viscosity of air under conditions in 
 which it may be treated as a homogeneous medium, and. 
 second, in finding the limits within which Stokes's Law 
 may be considered valid. 
 
 II. THE COEFFICIENT OF VISCOSITY OF AIR 
 
 The experiments on the coefficient of viscosity of 
 air were carried out in the Ryerson Laboratory by 
 Dr. Lachen Gilchrist, now of Toronto Unfversity, and 
 Dr. I. M. Rapp, now of the University of Oklahoma. 
 Dr. Gilchrist used a method 1 which was in many respects 
 new and which may fairly be said to be freer from theo- 
 retical uncertainties than any method which has ever 
 been used. He estimated that his results should not be 
 in error by more than . T or . 2 of i per cent. Dr. Rapp 
 used a form of the familiar capillary- tube method, but 
 under conditions which seemed to adapt it better to an 
 absolute evaluation of rj for air than capillary-tube 
 arrangements have ordinarily been. 
 
 hys. Rev., I, N.S. (1913), 124. 
 
92 THE ELECTRON 
 
 These two men, as the result of measurements which 
 were in progress for more than two years, obtained final 
 means which were in very close agreement with one 
 another as well as with the most careful of preceding 
 determinations. It will be seen from Table IX that 
 
 TABLE IX 
 
 *, for Air 
 
 .00018227 Rapp, Capillary-tube method, 1913 
 (Phys. Rev., II, 363). 
 
 .00018257 Gilchrist, Constant deflection method, 
 1913 (Phys. Rev., I, 124). 
 
 .00018229 Hogg, Damping of oscillating cylin- 
 ders, 1905 (Proc. Am. Acad., XL, 6n). 
 
 .00018258 Tomlinson, Damping of Swinging Pendu- 
 lum, 1886 (Phil. Trans., CLXXVII, 
 767). 
 
 .00018232 Grindley and Gibson, Flow through pipe, 
 1908 (Proc. Roy. Soc., LXXX, 114). 
 
 Mean... .00018240 
 
 every one of the five different methods which have been 
 used for the absolute determination of 77 for air leads to 
 a value that differs by less than one part in one thousand 
 from the following mean value, 1723= . 00018240. It was 
 concluded, therefore, that we could depend upon the 
 value of T} for the viscosity of air under the conditions of 
 our experiment to at least one part in one thousand. 
 Very recently Dr. E. Harrington 1 has improved still 
 further the apparatus designed by Dr. Gilchrist and the 
 authcTr and has made with it in the Ryerson Laboratory 
 a determination of 77 which is, I think, altogether unique 
 in its reliability and precision. I give to it alone greater 
 
 1 Phys. Rev., December, 1916. 
 
THE EXACT EVALUATION OF e 93 
 
 weight than to all the other work of the past fifty years 
 in this field taken together. The final value is 
 
 7723 =.000182 2 6 ' 
 
 and the error can scarcely be more than one part in two 
 thousand. 
 
 III. LIMITS OF VALIDITY OF STOKES's LAW 
 
 In the theoretical derivation of Stokes's Law the 
 following five assumptions are made: (i) that the 
 inhomogeneities in the medium are small in comparison 
 with the size of the sphere; (2) that the sphere falls as 
 it would in a medium of unlimited extent; (3) that the 
 sphere is smooth and rigid; (4) that there is no slipping 
 of the medium over the surface of the sphere; (5) that 
 the velocity with which the sphere is moving is so small 
 that the resistance to the motion is all due to the vis- 
 cosity of the medium and not at all due to the inertia 
 of such portion of the media as is being pushed forward 
 by the motion of the sphere through it. 
 
 If these conditions were all realized then Stokes's 
 Law ought to hold. Nevertheless, there existed up to 
 the year 1910 no experimental work which showed that 
 actual experimental results may be accurately predicted 
 by means of the unmodified law, and Dr. H. D. Arnold 
 accordingly undertook in the Ryerson Laboratory to test 
 how accurately the rates of fall of minute spheres through 
 water and alcohol might be predicted by means of it. 
 
 His success in these experiments was largely due to 
 the ingenuity which he displayed in producing accurately 
 spherical droplets of rose-metal. This metal melts at 
 about 82 C. and is quite fluid at the temperature of 
 
94 THE ELECTRON 
 
 boiling water. Dr. Arnold placed some of this metal in 
 a glass tube drawn to form a capillary at one end and 
 suspended the whole of the capillary tube in a glass 
 tube some 70 cm. long and 3 cm. in diameter. He then 
 filled the large tube with water and applied heat in such 
 a way that the upper end was kept at about 100 C., 
 while the lower end was at about 60. He then forced 
 the molten metal, by means of compressed air, out 
 through the capillary into the hot water. It settled in 
 the form of spray, the drops being sufficiently cooled by 
 the time they reached the bottom to retain their spherical 
 shape. This method depends for its success on the 
 relatively slow motion of the spheres and on the small 
 temperature gradient of the water through which they 
 fall. The slow and uniform cooling tends to produce 
 homogeneity of structure, while the low velocities allow 
 the retention of very accurately spherical shape. In this 
 way Dr. Arnold obtained spheres of radii from . 002 cm. to 
 .1 cm., which, when examined under the microscope, were 
 found perfectly spherical and practically free from surface 
 irregularities. He found that the slowest of these drops 
 fell in liquids with a speed which could be computed from 
 Stokes's Law with an accuracy of a few tenths of i per 
 cent, and he determined experimentally the limits of 
 speed through which Stokes's Law was valid. 
 
 Of the five assumptions underlying Stokes's Law, 
 the first, third, and fourth were altogether satisfied in 
 Dr. Arnold's experiment. The second assumption he 
 found sufficiently realized in the case of the very small- 
 est drops which he used, but not in the larger ones. The 
 question, however, of the effect of the walls of the vessel 
 upon the motion of drops through the liquid contained 
 
THE EXACT EVALUATION OF e 95 
 
 in the vessel had been previously studied with great 
 ability by Ladenburg, 1 who, in working with an exceed- 
 ingly viscous oil, namely Venice turpentine, obtained 
 a formula by which the effects of the wall on the motion 
 might be eliminated. If the medium is contained in a 
 cylinder of circular cross-section of radius R and of 
 length L, then, according to Ladenburg, the simple 
 Stokes formula should be modified to read 
 
 2 ga 2 (<r-p) 
 
 Arnold found that this formula held accurately in all of 
 his experiments in which the walls had any influence on 
 the motion. Thus he worked under conditions under 
 which all of the first four assumptions underlying 
 Stokes's Law were taken care of. This made it possible 
 for him to show that the law held rigorously when the 
 fifth assumption was realized, and also to find by experi- 
 ment the limits within which this last assumption might 
 be considered as valid. Stokes had already found from 
 theoretical considerations 2 that the law would not hold 
 unless the radius of the sphere were small in comparison 
 
 with -- , in which p is the density of the medium, rj its 
 
 viscosity, and v the velocity of the sphere. This radius 
 is called the critical radius. But it was not known how 
 near it was possible to approach to the critical radius. 
 Arnold's experiments showed that the inertia of the 
 medium has no appreciable effect upon the rate of 
 
 ' Ann. der Phys., XXII (1907), 287; XXIII (190$), 447- 
 2 Math, and Phys. Papers, III, 59. 
 
g6 THE ELECTRON 
 
 motion of a sphere so long as the radius of that sphere 
 is less than . 6 of the critical radius. 
 
 Application of this result to the motion of our oil 
 drops established the fact that even the very fastest 
 drops which we ever observed fell so slowly that not 
 even a minute error could arise because of the inertia of 
 the medium. This meant that the fifth condition neces- 
 sary to the application of Stokes's Law was fulfilled. 
 Furthermore, our drops were so small that the second 
 condition was also fulfilled, as was shown by the work of 
 both Ladenburg and Arnold. The third condition was 
 proved in the last chapter to be satisfied in our experi- 
 ments. Since, therefore, Arnold's work had shown very 
 accurately that Stokes's Law does hold when all of the 
 .five conditions are fulfilled, the problem of finding a 
 formula for replacing Stokes's Law in the case of our 
 oil-drop experiments resolved itself into finding in just 
 what way the failure of assumptions i and 4 affected the 
 motion of these drops. 
 
 IV. CORRECTION OF STOKES'S LAW FOR INHOMOGE- 
 NEITIES IN THE MEDIUM 
 
 The first procedure was to find how badly Stokes's 
 Law failed in the case of our drops. This was done by 
 plotting the apparent value of the electron e x against the 
 observed speed under gravity. This gave the curve 
 shown in Fig. 4, which shows that though for very small 
 speeds z varies rapidly with the change in speed, for 
 speeds larger than that corresponding to the abscissa 
 marked 1,000 there is but a slight dependence of e t on 
 speed. This abscissa corresponds to a speed of . i cm. 
 per second. We may then conclude that for drops which 
 
THE EXACT EVALUATION OF * 
 
 97 
 
 are large enough to fall at a rate of i cm. in ten seconds 
 or faster, Stokes's Law needs but a small correction, 
 because of the inhomogeneity of the air. 
 
 To find an exact expression for this correction we may 
 proceed as follows: The average distance which a gas 
 molecule goes between two collisions with its neighbors, 
 a quantity well known and measured with some approach 
 
98 THE ELECTRON 
 
 to precision in physics and called "the mean free path" 
 of a gas molecule, is obviously a measure of the size of 
 the holes in a gaseous medium. When Stokes 's Law 
 begins to fail as the size of the drops diminish, it must 
 be because the medium ceases to be homogeneous, as 
 looked at from the standpoint of the drop, and this 
 means simply that the radius of the drop has begun to 
 be comparable with the mean size of the holes -a quan- 
 tity which we have decided to take as measured by the 
 mean' free path /. The increase in the speed of fall over 
 that given by Stokes's Law, when this point is reached, 
 
 must then be some function of -. In other words, the 
 
 correct expression for the speed v x of a drop falling 
 through a gas, instead of being 
 
 as Arnold showed that it was when the holes were neg- 
 ligibly small as the latter are when the drop falls 
 through a liquid should be of the form 
 
 If we were in complete ignorance of the form of the func- 
 tion / we could still express it in terms of a series of 
 undetermined constants A, B, C, etc., thus 
 
 and so long as the departures from Stokes's Law were 
 small as Fig. 4 showed them to be for most of our drops, 
 
THE EXACT EVALUATION OF e 99 
 
 we could neglect the second-order terms in - and have 
 therefore 
 
 Using this corrected form of Stokes's Law to combine 
 with (9) (p. 68), we should obviously get the charge e n 
 in just the form in which it is given in (13), save that 
 wherever a velocity appears in (13) we should now have 
 
 v 
 to insert in place of this velocity L And since the 
 
 T.~\~A.~ 
 
 a 
 
 velocity of the drop appears in the 3/2 power in (13), if 
 we denote now by e the absolute value of the electron 
 and by e I} as heretofore, the apparent value obtained 
 from the assumption of Stokes's Law, that is, from the 
 use of (13), we obtain at once 
 
 e= , l ,. . . ..(16) 
 
 In this equation e x can always be obtained from (13), 
 while / is a known constant, but e, A, and a are all 
 unknown. If a can be found our observations permit 
 at once of the determination of both e and A , as will be 
 shown in detail under Section VI (see p. 103). 
 
 However, the possibility of determining e if we know 
 a can be seen in a general way without detailed analysis. 
 For the determination of the radius of the drop is 
 equivalent to finding its weight, since its density is 
 known. That we can find the charge on the drop as 
 soon as we can determine its weight is clear from the 
 simple consideration that the velocity under gravity is 
 proportional to its weight, while the velocity in a given 
 
ioo THE ELECTRON 
 
 electrical field is proportional to the charge which it 
 carries. Since we measure these two velocities directly, 
 we can obtain either the weight, if we know the charge, 
 or the charge, if we know the weight. (See equation 9, 
 p. 67.) 
 
 V. WEIGHING THE DROPLET 
 
 The way which was first used for finding the weight 
 of the drop was simply to solve Stokes's uncorrected 
 equation (n) (p. 89) for a in the case of each drop. 
 Since the curve of Fig. 4 shows that the departures from 
 Stokes's Law are small except for the extremely slow 
 drops, and since a appears in the second power in (n), it 
 is clear that, if we leave out of consideration the very 
 slowest drops, (n) must give us very nearly the correct 
 values of a. We can then find the approximate value 
 of A by the method of the next section, and after it is 
 found we can solve (15) for the correct value of a. This 
 is a method of successive approximations which theo- 
 retically yields a and A with any desired degree of pre- 
 cision. As a matter of fact the whole correction term, 
 
 A - is a small one, so that it is never necessary to make 
 
 more than two approximations to obtain a with much 
 more precision than is needed for the exact evaluation 
 of e. 
 
 As soon as e was fairly accurately known it became 
 possible, as indicated above, to make a direct weighing 
 of extraordinarily minute bodies with great certainty 
 and with a very high degree of precision. For we have 
 already shown experimentally that the equation 
 
THE EXACT EVALUATION OF e 101 
 
 is a correct one and it involves no assumption whatever 
 as to the shape, or size, or material of the particle. If 
 we solve this equation for the weight mg of the particle 
 we get 
 
 In this equation e n is known with the same precision as e, 
 for we have learned how to count n. It will presently be 
 shown that e is probably now known with an accuracy 
 of one part in a thousand, hence mg can now be deter- 
 mined with the same accuracy for any body which can 
 be charged up with a counted number n of electrons and 
 then pulled up against gravity by a known electrical 
 field, or, if preferred, simply balanced against gravity 
 after the manner used in the water-drop experiment and 
 also in part of the oil-drop work. 1 This device is simply 
 an electrical balance in place of a mechanical one, and it 
 will weigh accurately and easily to one ten-billionth of a 
 milligram. 
 
 Fifty years ago it was considered the triumph of 
 the instrument-maker's art that a balance had been 
 made so sensitive that one could weigh a piece of 
 paper, then write his name with a hard pencil on the 
 paper and determine the difference between the new 
 weight and the old that is, the weight of the name. 
 This meant determining a weight as small as one-tenth 
 or possibly one-hundredth of a milligram (a milligram is 
 about 1/30,000 of an ounce). Some five years ago 
 Ramsay and Spencer, in London, by constructing a 
 balance entirely out of very fine quartz fibers and placing 
 it in a vacuum, succeeded in weighing objects as small 
 
 1 See Phil. Mag., XIX (1860), 216; XXI (1862), 757. 
 
102 THE ELECTRON 
 
 as one-millionth of a milligram, that is, they pushed the 
 limit of the weighable down about ten thousand times. 
 The work which we are now considering pushed it down 
 at least ten thousand times farther and made it possible 
 to weigh accurately bodies so small as not to be visible 
 at all to the naked eye. For it is only necessary to 
 float such a body in the air, render it visible by reflected 
 light in an ultra-microscope arrangement of the sort we 
 were using, charge it electrically by the capture of ions, 
 count the number of electrons in its charge by the method 
 described, and then vary the potential applied to the 
 plates or the charge on the body until its weight is just 
 balanced by the upward pull of the field. The weight 
 of the body is then exactly equal to the product of the 
 known charge by the strength of the electric field. We 
 made all of our weighings of our drops and the deter- 
 mination of their radii in this way as soon as we had 
 located e with a sufficient degree of precision to warrant 
 it, 1 Indeed, even before e is\ery accurately known it 
 is possible to use such a balance for a fairly accurate 
 evaluation of the radius of a spherical drop. For when 
 we replace m in (18) by 4/^ma 3 (orp) and solve for a 
 we obtain 
 
 r g( <r P) 
 
 The substitution in this equation of an approximately 
 correct value of e yields a with an error but one-third as 
 great as that contained in the assumed value of e, for a 
 is seen from this equation to vary as the cube root of e. 
 This is the method which, in view of the accurate evalua- 
 
 1 Phys. Rev., II (1913), 117. This paper was read before the 
 Deutsche physikalische Geseilschaft in Berlin in June, 1912. 
 
THE EXACT EVALUATION OF e 103 
 
 tion of e, it is now desirable to use for the determination 
 of the weight or dimensions of any minute body, for the 
 method is quite independent of the nature of the body 
 or of the medium in which it is immersed. Indeed, it 
 constitutes as direct and certain a weighing of the body 
 as though it were weighed on a mechanical balance. 
 
 VI. THE EVALUATION OF 6 AND A 
 I 
 
 With e,. and - known, we can easily determine e and 
 
 d 
 
 A from the equation 
 
 for if we write this equation in the form 
 
 = *i. ..(20) 
 
 and then plot the observed values of e^ as ordinates and 
 the corresponding values of - as abscissae we should get 
 
 a straight line, provided our corrected form of Stokes's 
 Law (15) (p. 99) is adequate for the correct representa- 
 tion of the phenomena of fall of the droplets within the 
 
 range of values of - in which the experiments lie. If no 
 
 such linear relation is found, then an equation of the form 
 of (15) is not adequate for the description of the phe- 
 nomena within this range. As a matter of fact, a linear 
 relation was found to exist for a much wider range of 
 
 values of - than was anticipated would be the case. The 
 a 
 
IO4 
 
 THE ELECTRON 
 
THE EXACT EVALUATION OF e 
 
 I0 5 
 
 
 
 
 o 
 
 o 
 
 
io6 THE ELECTRON 
 
 intercept of this line on the axis of ordinates, that is, the 
 value of 0i when -=o is seen from (20) to be e*, and we 
 
 have but to raise this to the 3/2 power to obtain the 
 absolute value of e. Again, A is seen from (20) to be 
 merely the slope of this line divided by the intercept on 
 the es axis. 
 
 In order to carry this work out experimentally it is 
 
 necessary to vary - and find the corresponding values 
 
 of 61. This can be done in two ways. First, we may 
 hold the pressure constant and choose smaller and 
 smaller drops with which to work, or we may work with 
 drops of much the same size but vary the pressure of 
 the gas in which our drops are suspended, for the mean 
 free path / is evidently inversely proportional to the 
 pressure. 
 
 Both procedures were adopted, and it was found that 
 a given value of e t always corresponded to a given value 
 
 of - , no matter whether / was kept constant and a 
 
 reduced to, say, one-tenth of its first value, or a kept about 
 the same and / multiplied tenfold. The result of one 
 somewhat elaborate series of observations which was 
 first presented before the Deutsche physikalische Gesell- 
 schaft in June, 1912, and again before the British Asso- 
 ciation at Dundee in September, 191 2, 1 is shown in 
 Figs. 5 and 6. The numerical data from which these 
 curves are plotted are given fairly fully in Table IX. 
 [t will be seen that this series of observations embraces 
 a study of 58 drops. These drops represent all of those 
 studied for 60 consecutive days, no single one being 
 
 Phys. Rev., II (1913), 136- 
 
THE EXACT EVALUATION OF e 
 
 107 
 
 8*1-19 
 
 2* SSSSSffSS 8 2^8 S o S 83 H J?K o'S'SS S?$ 
 
 OOOOOOOOOOOOOOOOOOOOOOOOOOOOO 
 
 O<NWO 
 OOO t^- O 
 
 O n o r 
 
 O O CO W ** 
 O 00 ro f-O W 
 
 S'SS'SS 
 
 -IS, 
 
 WOO 00 OvOO M 
 
 \ H T- lOO Ov O H 
 
 ioiOtoio ir>\O O 
 
 Ov O H H H H 
 
 j'tw ^ to ON^O 
 't O O N O O 
 
 
 00 VO OO CO ON N H OvO OO t- O Oi 
 
 O r-~ 
 O> H 
 
 O H O 
 CO lOOO e 
 
 rO^t^->oir>r)ioio ioO O O O O O r^O 00 OO 10 O O O ioO 't 't v oc 
 OOOOOOOOOOOOOOOOOOOOOHMOQOOM 
 
 t^O 
 cooo o M 
 
 O O O O O O O O O O O H O O O O O H w M 
 
 cOO 
 O H 
 
 ro N WOO POOOONQrOWWO OiOO WO 
 O O\ O WO OO ^O TfO OO O^ 
 CO * 0> t-0 00 0> w w to H 
 
 Q^ 
 
 fe> 
 
 o > O o H M co w w w woo oooooooo ow o. wro-tro 
 
 MWMMMMMMWIHMl-IMHCNM CO * CO M IH OO M 
 
 OOOOco<NioOoOO> ir>\o O * t^.00 CO O co CO "*OO WOO O O W O O J 
 O CN O O ^OO OV^OCOMOOO CM t^t^OO O<OO*H O O 100 r^ t^ ^- *> 
 MWHMOOOWMOOOOOOMOOOOOOOOOWWMO 
 W u? W W W W O W W W W W W W W W W W W W W W W W * ^f OU? 
 
 >OOO f* O^O t>- 10 H O O O^oO^O fO^oOoO W\OvOOO OcO O O 
 00 O 00 t^ 1000 oiOOOOcot^OCOO\OOt^MC>MMOO 
 
 O I--00 O O M CN ro "t W\O 1^00 Ov O M 1 O *t WO t^OO O 
 
io8 
 
 THE ELECTRON 
 
 8i - i9 = ireaj^ 
 
 O 00 <N co O r- tf) coo O O i^ * u~. O O O cooO <N 10 -*O cooO 04 M t- rf 
 
 OcOWM<MOOMt^OO<NOOt>COMN<SOOOcOMH<NMOOM 
 MMMMMMMMMOMOMOMMMMMMOMMMMMMQM 
 
 OOOOOOOOOOOOOOOOOOOOOOOOOOOOO 
 
 .00 co oo co ggg .....'. ICli r^'rl t.i oo oo > o?ojoo^oj 
 
 SIH 
 
 OOOO ioO *O 1000 rOO OO O *O Ol rooO OO OO 
 
 O O 100 O O <N t^ r^ M 00 OOO M O * "5 cooO OOOOMJ^MTJ-OO 
 Ot^-OOOO N <N Tt 10 t^oo O MOO O co co -*O t- O 1000 O M M M 
 
 .n OI 
 l^ o 
 
 OO tCOO t^ 1000 
 
 O >0 t- COOO Tj-oO Tj- co 10 OOO f00 O M O TJ- O O 'tO O ^00 co it O 
 \r> co <M O <O t^ "too <N 00 t>.O OO 10 iOO OO r^oO 10 r 10 M O t^oo O 
 
 HMCtMMCO M M CSC4 MMM 
 
 M M r>.OWOCO fOH rooO ^w t^C4 rJ-roO<N ro t^O t^ 
 
 ?H O O M ^t ^- uo rOOO OO O *^ ^ O t^- t^ roO M fO ^O O 
 wOOwOOOOOGOOOOOOOOwOOi-i 
 oooooooooooooooooooooo 
 
 M OO MIMINOOMlOO't'tOfOl^t^MOl'! t^O M IO r~O O OO 
 
 MMOOOOOOOOOOOOOOOOOOO<NOO 
 
 OOOOO 
 
 OOOOOOOOt^OOOOt^O TfO OMO cOO^O Ot^ 'too fO 
 
 CO t^O C* MO t^^tOlOCOO ^O M t^-O OWOO IOW O t^<N 1OIO*>-CO 
 
 00-*OOwoOOOOMOfOOMt^ OOO CO OO O'tfCM <M O ^-co 
 O 00 4oO 00 O O w O O 1-1 4oO coOO>o<N M 'ti-i O O <r>o4oto4 
 
 MCOMIHCO MMMMINI-IIHMNMMCOMHIHIOCOMW MM 
 
 O OO t^O O MO TJ- O O >0 -<toO * t^ M co O 
 wOOOOOOOOOOOOOMO OOO 0000 
 
 a E 
 
 sjya 
 
 'o'o 
 g 
 
 
 IOO 1^00 O O M CO ^ >OO ^0 
 
 --- 
 
THE EXACT EVALUATION OF e 
 
 109 
 
 omitted. 
 
 They represent a thirty-fold variation in - 
 
 (from .016, drop No. i, to .444, drop No. 58), a seven- 
 teen-fold variation in the pressure p (from 4.46 cm., 
 drop No. 56, to 76.27 cm., drop No. 10), a twelvefold 
 variation in a (from 4.69Xio~ 5 cm., drop No. 28, to 
 58.56Xio~ 5 cm., drop No. i), and a variation in the 
 
 FIG. 7 
 
 number of free electrons carried by the drop from i on 
 drop No. 28 to 136 on drop No. 56. 
 
 The experimental arrangements are shown in Fig. 7. 
 The brass vessel D was built for work at all pressures up 
 to 15 atmospheres, but since the present observations 
 have to do only with pressures from 76 cm. down, these 
 were measured with a very carefully made mercury ma- 
 nometer m, which at atmospheric pressure gave precisely 
 
no THE ELECTRON 
 
 the same reading as a standard barometer. Complete 
 stagnancy of the air between the condenser plates M 
 and N was attained, first, by absorbing all of the heat 
 rays from the arc A by means of a water cell w, 80 cm. 
 long, and a cupric chloride cell d, and, secondly, by 
 immersing the whole vessel D in a constant temperature 
 bath G of gas-engine oil (40 liters), which permitted, in 
 general, fluctuations of not more than . 02 C. during an 
 observation. This, constant-temperature bath was found 
 essential if such consistency of measurement as is shown 
 here was to be obtained. A long search for causes of 
 slight irregularity revealed nothing so important as this, 
 and after the bath was installed all of the irregularities 
 vanished. The atomizer A was blown by means of a 
 puff of carefully dried and dust-free air introduced 
 through cock e. The air about the drop p was ionized 
 when desired, or electrons discharged directly from the 
 drop, by means of Rontgen rays from X, which readily 
 passed through the glass window g. To the three win- 
 dows g (two only are shown) in the brass vessel D corre- 
 spond, of course, three windows in the ebonite strip c, 
 which encircles the condenser plates M and N. Through 
 the third of these windows, set at an angle of about 28 
 from the line Xpa and in the same horizontal plane, the 
 oil drop is observed through a short-focus telescope hav- 
 ing a scale in the eyepiece to make possible the exact 
 measurement of the speeds of the droplet-star. 
 
 In plotting the actual observations I have used the 
 
 reciprocal of the pressure - in place of /, for the reason 
 that / is a theoretical quantity which is necessarily pro- 
 portional to - , while p is the quantity actually measured. 
 
THE EXACT EVALUATION OF e ' in 
 
 This amounts to writing the correction- term to Stokes's 
 
 Law in the form ( H ) instead of in the form i-\-A - and 
 
 \ pa/ a 
 
 considering b the undetermined constant which is to be 
 evaluated, as was A before, by dividing the slope of our 
 line by its ^-intercept. 
 
 Nevertheless, in view of the greater ease of visualiza- 
 tion of - all the values of this quantity corresponding 
 to successive values of are given in Table IX. Fig. 5 
 shows the graph obtained by plotting the values of e t 
 against for the first 51 drops of Table IX, and Fig. 6 
 shows the extension of this graph to twice as large values 
 
 of and i. It will be seen that there is not the slightest 
 pa 
 
 indication of a departure from a linear relation between 
 
 e-i and -'- up to the value = 620. 2, which corresponds 
 pa pa 
 
 to a value of - of .4439 (see drop No. 58, Table IX). 
 
 Furthermore, the scale used in the plotting is such that 
 a point which is one division above or below the line in 
 Fig. 5 represents in the mean an error of 2 in 700. // 
 will be seen from Figs. 5 and 6 thai there is but one drop 
 in the 58 whose departure from the line amounts to as 
 much as o . 5 per cent. It is to be remarked, too, that this 
 is not a selected group of drops, but represents all of the 
 drops experimented upon during 60 consecutive days, dur- 
 ing which time the apparatus was taken down several 
 times and set up anew. It is certain, then, that an 
 equation of the form (15) holds very accurately up to 
 
112 THE ELECTRON 
 
 - = . 4. The last drop of Fig. 6 seems to indicate the 
 
 beginning of a departure from this linear relationship. 
 Since such departure has no bearing upon the evaluation 
 of e, discussion of it will not be entered into here, although 
 it is a matter of great interest for the molecular theory. 
 Attention may also be called to the completeness of 
 the answers furnished by Figs. 5 and 6 to the question 
 raised in chap, iv as to a possible dependence of the drag 
 which the medium exerts on the drop upon the amount 
 of the latter 's charge; also, as to a possible variation of 
 the density of the drop with its radius. Thus drops 
 
 Nos. 27 and 28 have practically identical values of , 
 
 but while No. 28 carries, during part of the time, but 
 i unit of charge (see Table IX), drop No. 27 carries 
 29 times as much and it has about 7 times as large a 
 diameter. Now, if the small drop were denser than the 
 large one, or if the drag of the medium upon the heavily 
 charged drop were greater than its drag upon the one 
 lightly charged, then for both these reasons drop No. 27 
 would move more slowly relatively to drop No. 28 
 than would otherwise be the case, and hence e t for drop 
 No. 27 would fall below e^ for drop No. 28. Instead of 
 this the two d fall so nearly together that it is impossible 
 to represent them on the present scale by two separate 
 dots. Drops Nos. 52 and 56 furnish an even more 
 striking confirmation of the same conclusion, for both 
 
 / 
 drops have about the same value for - and both are 
 
 exactly on the line, though drop No. 56 carries at one 
 time 68 times as heavy a charge as drop No. 52 and has 
 three times as large a radius. In general, the fact that 
 
THE EXACT EVALUATION OF e 113 
 
 Figs. 5 and 6 show no tendency whatever on the part of 
 either the very small or the very large drops to fall above 
 or below the line is experimental proof of the joint cor- 
 rectness of the assumptions of constancy of drop-density 
 and independence of drag of the medium on the charge 
 on the drop. 
 
 The values of e} and b obtained graphically from the 
 ^-intercept and the slope in Fig. 5 are e ! = 6i. i3Xio~ 8 
 and b= .000625, p being measured, for the purposes of 
 Fig. 5 and of this computation in centimeters of Hg at 
 23 C. and a being measured in centimeters. The value 
 of A in equations 15 and 16 (p. 99) corresponding to this 
 value of b is .874. 
 
 Instead, however, of taking the result of this graphical 
 evaluation of e, it is more accurate to reduce each of the 
 observations on e T to e by means of the foregoing value 
 of b and the equation 
 
 . b 
 
 The results of this reduction are contained in the last 
 column of Table IX. These results illustrate very 
 clearly the sort of consistency obtained in these observa- 
 tions. The largest departure from the mean value found 
 anywhere in the table amounts to 0.5 per cent and "the 
 probable error" of the final mean value computed in the 
 usual way is 16 in 61,000. 
 
 Instead, however, of using this final mean value as 
 the most reliable evaluation of e, it was thought prefer- 
 able to make a considerable number of observations at 
 atmospheric pressure on drops small enough to make t g 
 determinable with great accuracy and yet large enough 
 so that the whole correction term to Stokes's Law 
 
H4 THE ELECTRON 
 
 amounted to but a small percentage, since in this case, 
 even though there might be a considerable error in the 
 correction-term constant b, such error would influence 
 the final value of e by an inappreciable amount. The 
 first 23 drops of Table IX represent such observations. 
 It will be seen that they show slightly greater consistency 
 than do the remaining drops in the table and that the 
 correction-term reductions for these drops all lie between 
 i . 3 per cent (drop No. i) and 5 . 6 per cent (drop No. 23) , 
 so that even though b were in error by as much as 3 per 
 cent (its error is actually not more than i . 5 per cent), e 
 would be influenced by that fact to the extent of but 
 o. i per cent. The mean value of e* 3 obtained from the 
 first 23 drops is 61 . 12X io~ 8 , a number which differs by 
 i part in 3,400 from the mean obtained from all the 
 drops. 
 
 When correction is made for the fact that the num- 
 bers in Table IX were obtained on the basis of the 
 assumption 77=. 0001825, instead of 77=. 0001824 (see 
 Section II), which was the value of 7723 chosen in 1913 
 when this work was first published, the final mean value 
 of e obtained from the first 23 drops is 6i.o85Xio~ 8 . 
 This corresponds to 
 
 e=4.774Xio~ 10 electrostatic units. 
 
 I have already indicated that as soon as e is known it 
 becomes possible to find with the same precision which 
 has been attained in its determination the exact number 
 of molecules in a given weight of any substance, the 
 absolute weight of any. atom or molecule, the average 
 kinetic energy of agitation of an atom or molecule at 
 any temperature, and a considerable number of other 
 
THE EXACT EVALUATION OF e 115 
 
 important molecular and radioactive constants. In 
 addition, it has recently been found that practically all 
 of the important radiation constants like the wave- 
 lengths of X-rays, Planck's h, the Stefan-Boltzmann 
 constant o-, the Wien constant c 2) etc:, depend for their 
 most reliable evaluation upon the value of e. In a word, 
 e is increasingly coming to be regarded, not only as the 
 most fundamental of physical or chemical constants, but also 
 the one of most supreme importance for the solution of the 
 numerical problems of modern physics. It seemed worth 
 while, therefore, to drive the method herewith developed 
 for its determination to the limit of its possible precision. 
 Accordingly, I built two years ago a new condenser 
 having surfaces which were polished optically and made 
 flat to within two wave-lengths of sodium light. These 
 were 22 cm. in diameter and were separated by 3 pieces 
 of echelon plates, 14 . 91 74 mm. thick, and all having opti- 
 cally perfect plane-parallel surfaces. The dimensions of 
 the condenser, therefore, no longer introduced an uncer 
 tainty of more than about i part in 10,000. The volts 
 were determined after -each reading in terms of a Weston 
 standard cell and are uncertain by no more than i part 
 in 3,000. The times were obtained from an exception- 
 ally fine printing chronograph built by William Gaertner 
 & Co. It is controlled by a standard astronomical 
 clock and prints directly the time to hundred ths of a 
 second. All the other elements of the problem were 
 looked to with a care which was the outgrowth of .five 
 years of experience with measurements of this kind. 
 The present form of the apparatus is shown in diagram 
 in Fig. 8, and in Fig. 9 is shown a photograph taken 
 before the enclosing oil tank had been added. This work 
 
n6 
 
 THE ELECTRON 
 
THE EXACT EVALUATION OF e 
 
 117 
 
n8 THE ELECTRON 
 
 was concluded in August, 1916, and occupied the better 
 part of two years of time. The final table of results and 
 the corresponding graph are given in Table X and in 
 Fig. 10. The final value of e* computed on the basis 
 7/23= .0001824 is seen to be now 6i.i26Xio~ 8 instead 
 of 61.085, or -7 P er cent higher than the value found 
 in 1913. But Dr. Harrington's new value of rj 23) namely, 
 .00018226, is more reliable than the old value and is 
 lower than it by . 07 per cent. Since rj appears in the 
 first power in e*, it will be seen that the new value 1 of e, 
 determined with new apparatus and with a completely 
 new determination of all the factors involved, comes out 
 to the fourth place exactly the same as the value pub- 
 lished in 1913, namely, 
 
 e=4.774Xio~ 10 absolute electrostatic units. 
 
 The corresponding values of b and A are now .000617 
 and .863, respectively. 
 
 Since the value of the Faraday constant has now been 
 fixed virtually by international agreement 2 at 9,650 abso- 
 lute electromagnetic units, and since this is the number N 
 of molecules in a gram molecule times the elementary 
 electrical charge, we have 
 
 Although the probable error in this number computed by 
 the method of least squares from Table X is but one part 
 in 4,000, it would be erroneous to infer that e and N are 
 now known with that degree of precision, for there are 
 
 'For full details see Millikan, Phil. Mag., June, 1917. 
 
 2 At. wt. of Ag. = io7.88; electrochem. eq't. of Ag.= 0.01188. 
 
THE EXACT EVALUATION OF e 
 
 four constant factors entering into all of the results in 
 Table X and introducing uncertainties as follows : The 
 coefficient of viscosity 77 which appears in the 3/2 power 
 introduces into e and N a maximum possible uncertainty 
 of less than o. i per cent, say 0.07 per cent. The cross- 
 hair distance which is uniformly duplicatable to one 
 part in two thousand appears in the 3/2 power and 
 introduces an uncertainty of no more than 0.07 per 
 cent. All the other factors, such as the volts and the 
 distance between the condenser plates, introduce errors 
 which are negligible in comparison. The uncertainty in 
 e and A^ is then that due to two factors, each of which 
 introduces a maximum possible uncertainty of about 
 0.07 per cent. Following the usual procedure, we may 
 estimate the uncertainty in e and N as the square root 
 of the sum of the squares of these two uncertainties, 
 that is, as about one part in 1000. We have then: 
 
 6=4. 774=*= .oosXio" 10 
 
 Perhaps these numbers have little significance to the 
 general reader who is familiar with no electrical units save 
 those in which his monthly light bills are rendered. If 
 these latter seem excessive, it may be cheering to reflect 
 that the number of electrons contained in the quantity of 
 electricity which courses every second through a common 
 sixteen-candle-power electric-lamp filament, and for 
 which we pay 1/100,000 of i cent, is so large that if all 
 the two and one-half million inhabitants of Chicago were 
 to begin to count out these electrons and were to keep on 
 counting them out each at the rate of two a second, and 
 if no one of them were ever to stop to eat, sleep, or die, 
 
I2O 
 
 THE ELECTRON 
 
 *> too N- M Qi O 1-1 >o HI t^vo M O* ~- -*OO O 
 
 MO-*i^ro^.(r>oiHO*o i-^oo 
 
 WMIO<NOOC>HHIWI^I-IHO> OVCO 
 fOtorO^t*t>OiO00 VOO t- t^ 
 
 ir^mfssf&SsHSHS!?! 
 
 -i* 
 
 ^ t^ ^O OMWvOO\t^OO ^O^O Ot^-WMi-i 
 10 vo\O CO O> O O O O O IOMD \r> Q Q Msocp M 
 
 
 rCO t^Tj-fOtOM M HI top lOCO NTj-MWXOVO<Op<OCO O 1 ^ 
 
 tOOO 
 CS <M 
 O I^ 
 
 o o i o o o ! o o o o o o o o o o o o o 
 
 
 
 
 
 
 Oi 
 >O < 
 
 _ ro rO tO CO to 
 
 
THE EXACT EVALUATION OF 
 
 121 
 
122 THE ELECTRON 
 
 it would take them just twenty thousand years to finish 
 the task. 
 
 Let us now review, with Figs. 5 and 10 before us, the 
 essential elements in the measurement of e. We dis- 
 cover, first, that electricity is atomic, and we measure the 
 electron in terms of a characteristic speed for each drop- 
 let. To reduce these speed units to electrical terms, and 
 thus obtain an absolute value of e, it is necessary to know 
 how in a given medium and in a given field the speed due 
 to a given charge on a drop is related to the size of the 
 drop. This we know accurately from Stokes's theory 
 and Arnold's experiments when the holes in the medium, 
 
 that is, when the values of - are negligibly small, but 
 
 when - is large we know nothing about it. Consequently 
 
 there is but one possible way to evaluate e, namely, to find 
 experimentally how the apparent value of e, namely, e t 
 
 varies with - or , and from the graph of this relation to 
 * i 
 
 find what value -Ci approaches as - or approaches zero. 
 
 a pa 
 
 So as to get a linear relation we find by analysis that we 
 
 must ploj e^ instead of e l against - or . We then get 
 
 a pa 
 
 e from the intercept of an experimentally determined 
 straight line on the y-axis of our diagram. This whole 
 procedure amounts simply to reducing our drop- 
 velocities to what they would be if the pressure were so 
 
 large or so small that the holes in the medium were all 
 pa 
 
 closed up. For this case and for this case alone we know 
 both from Stokes 's and Arnold's work exactly the law of 
 motion of the droplet. 
 
CHAPTER VI 
 
 THE MECHANISM OF IONIZATION OF GASES BY 
 X-RAYS AND RADIUM, RAYS 
 
 I. EARLY EVIDENCE 
 
 Up to the year 1908 the only experiments which threw 
 any light whatever upon the question as to what the act 
 of ionization of a gas consists in were those performed 
 by Townsend 1 in 1900. He had concluded from the 
 theory given on p. 34 and from his measurements on the 
 diffusion coefficients and the mobilities of gaseous ions 
 that both positive and negative ions in gases carry unit 
 charges. This conclusion was drawn from the fact that 
 
 the value of ne in the equation ne-j^ came out about 
 
 i . 23 X io 10 electrostatic units, as it does in the electrolysis 
 of hydrogen. 
 
 In 1908, however, Townsend 2 devised a method of 
 
 measuring directly the ratio j-: and revised his original 
 
 conclusions. His method consisted essentially in driving 
 ions by means of an electric field from the region between 
 two plates A and B (Fig. n), where they had been pro- 
 duced by the direct action of X-rays, through the gauze 
 in B, and observing what fraction of these ions was driven 
 by a field established between the plates B and C to the 
 central disk D and what fraction drifted by virtue of 
 diffusion to the guard-ring C. 
 
 1 Phil. Trans., CXCIII (1900), 129. 
 3 Proc. Roy. Soc., LXXX (1908), 207. 
 123 
 
124 THE ELECTRON 
 
 By this method Townsend found that ne for the 
 negative ions was accurately i.23Xio 10 , but for the 
 positive ions it was 2.4iXio 10 . From these results 
 the conclusion was drawn that in X-ray ionization all of 
 the positive ions are bivalent, i.e., presumably, that the 
 act of ionization by X-rays consists in the detachment 
 from a neutral molecule of two elementary electrical 
 charges. 
 
 Townsend accounted for the fact that his early experi- 
 ments had not shown this high value of ne for the 
 positive ions by the assumption that by the time the 
 
 A 
 
 FIG. ii 
 
 doubly charged positive ions in these experiments had 
 reached the tubes in which D was measured, most of 
 them had become singly charged through drawing to 
 themselves the singly charged negative ions with which 
 they were mixed. This hypothesis found some justifica- 
 tion in the fact that in the early experiments the mean 
 value of ne for the positive ions had indeed come out 
 some 15 or 20 per cent higher than i.23Xio 10 a dis- 
 crepancy which had at first been regarded as attributable 
 to experimental errors, and which in fact might well be 
 attributed to such errors in view of the discordance 
 between the observations on different gases. 
 
MECHANISM OF IONIZATION OF GASES 125 
 
 Franck and Westphal, 1 however, in 1909 redeter- 
 mined ne by a slight modification of Townsend's original 
 method, measuring both v and D independently, and 
 not only found, when the positive and negative ions are 
 separated by means of an electric field so as to render 
 impossible such recombination as Tpwnsend suggested, 
 that D was of exactly the same value as when they were 
 not so separated, but also that ne for the positive ions pro- 
 duced by X-rays was but i . 4X io 10 instead of 2 . 41 X io 10 . 
 Since this was in fair agreement with Townsend's original 
 mean, the authors concluded that only a small fraction 
 about 9 per cent of the positive ions formed by X-rays 
 are doubles, or other multiples, and the rest singles. In 
 their experiments on the ionization produced by a-rays, 
 /3-rays, and 7-rays, they found no evidence for the 
 existence of doubly charged ions. 
 
 In summarizing, then, the work of these observers 
 it could only be said that, although both Townsend and 
 Franck and Westphal drew the conclusion that doubly 
 charged ions exist in gases ionized by X-rays, there were 
 such contradictions and uncertainties in their work as 
 to leave the question unsettled. In gases ionized by 
 other agencies than X-rays no one had yet found any 
 evidence for the existence of ions carrying more than a 
 single charge. 
 
 II. OIL-DROP EXPERIMENTS ON VALENCY IN 
 GASEOUS IONIZATION 
 
 The oil-drop method is capable of furnishing a direct 
 and unmistakable answer to the question as to whether 
 the act of ionization of a gas by X-rays or other agencies 
 
 1 Verh. deutsch. phys. Ges., March 5, 1909. 
 
126 THE ELECTRON* 
 
 consists in the detachment of one, of several, or of many 
 electrons from a single neutral molecule. For it makes 
 it possible to catch the residue of such a molecule prac- 
 tically at the instant at which it is ionized and to count 
 directly the number of charges carried by that residue. 
 The initial evidence obtained from this method seemed 
 to favor the view that the act of ionization may consist 
 in the detachment of quite a number of electrons from a 
 single molecule, for it was not infrequently observed 
 that a balanced oil drop would remain for several seconds 
 unchanged in charge while X-rays were passing between 
 the plates, and would then suddenly . assume a speed 
 which corresponded to a change of quite a number of 
 electrons in its charge. 
 
 It was of course recognized from the first, however, 
 that it is very difficult to distinguish between the prac- 
 tically simultaneous advent upon a drop of two or three 
 separate ions and the advent of a doubly or trebly 
 charged ion, but a consideration of the frequency with 
 which ions were being caught in the experiments under 
 consideration, a change occurring only once in, say, 10 
 seconds, seemed at first to render it improbable that the 
 few double, or treble, or quadruple catches observed when 
 the field was on could represent the simultaneous advent 
 of separate ions. It was obvious, however, that the ques- 
 tion could be conclusively settled by working with 
 smaller and smaller drops. For the proportion of double 
 or treble to single catches made in a field of strength 
 between 1,000 and 6,000 volts per centimeter should be 
 independent of the size of the drops if the doubles are 
 due to the advent of doubly charged ions, while this 
 proportion should decrease with the square of the radius 
 
MECHANISM OF IONIZATION OF GASES 127 
 
 of the drop if the doubles are due to the simultaneous 
 capture of separate ions. 
 
 Accordingly, Mr. Harvey Fletcher and the author, 1 
 suspended, by the method detailed in the preceding 
 chapter, a very small positively charged drop in the 
 upper part of the field between M and N (Fig. 12), 
 adjusting either the charge upon the drop or the field 
 strength until the drop was nearly balanced. We then 
 produced beneath the drop a sheet of X-ray ionization. 
 With the arrangement shown in the figure, in which M 
 
 Edrtf\ 
 
 FIG. 12 
 
 and N are the plates of the condenser previously de- 
 scribed, and L and L f are thick lead screens, the positive 
 ions- are thrown practically at the instant of formation 
 to the upper plate. When one of them strikes the drop 
 it increases the positive charge upon it, and the amount 
 of the charge added by the ion to the drop can be com- 
 puted from the observed change in the speed of the drop. 
 For the sake of convenience in the measurement of 
 successive speeds a scale containing 70 equal divisions 
 was placed in the eyepiece of the observing cathetometer 
 telescope, which in these experiments produced a 
 
 1 Phil. Mag., XXIII (1911), 753. 
 
128 THE ELECTRON 
 
 magnification of about 15 diameters. The method of pro- 
 cedure was, in general, first, to get the drop nearly 
 balanced by shaking off its initial charge by holding a 
 little radium near the observing chamber, then, with a 
 switch, to throw on the X-rays until a sudden start in 
 the drop revealed the fact that an ion had been caught, 
 then to throw off the rays and take the time required 
 for it to move over 10 divisions, then to throw on the 
 rays until another sudden quickening in speed indicated 
 the capture of another ion, then to measure this speed 
 and to proceed in this way without throwing off the field 
 at all until the drop got too close to the.upper plate, when 
 the rays were thrown off and the drop allowed to fall 
 under gravity to the desired distance from the upper 
 plate. In order to remove the excess of positive charge 
 which the drop now had because of its recent captures, 
 some radium was brought near the chamber and the 
 field thrown off for a small fraction of a second. As 
 explained in preceding chapters, ions are caught by the 
 drop many times more rapidly when the field is off than 
 when it is on. Hence it was in general an easy matter 
 to bring the positively charged drop back to its balanced 
 condition, or indeed to any one of the small number of 
 working speeds which it was capable of having, and then 
 to repeat the series of catches described above. In this 
 way we kept the same drop under observation for hours 
 at a time, and in one instance we recorded 100 successive 
 captures of ions by a given drop, and determined in each 
 case whether the ion captured carried a single or a 
 multiple charge. 
 
 The process of making this determination is exceed- 
 ingly simple and very reliable. For, since electricity is 
 
MECHANISM OF IONIZATION OF GASES 129 
 
 atomic in structure, there are only, for example, three 
 possible speeds which a drop can have when it carries 
 i, 2, or 3 elementary charges, and it is a perfectly simple 
 matter to adjust conditions so that these speeds are of 
 such different values that each one can be recognized 
 unfailingly even without a stop-watch measurement. 
 Indeed, the fact that electricity is atomic is in no way 
 more beautifully shown than by the way in which, as 
 reflected in Table XI, these relatively few possible work- 
 ing speeds recur. After all the possible speeds have 
 been located it is only necessary to see whether one of 
 them is ever skipped in the capture of a new ion in 
 order to know whether or not that ion was a double. 
 Table XI represents the results of experiments made 
 with very hard X-rays produced by means of a powerful 
 1 2 -inch Scheidel coil, a mercury- jet interrupter, and a 
 Scheidel tube whose equivalent spark-length was about 
 5 inches. No attempt was made in these experiments to 
 make precise determinations of speed, since a high degree 
 of accuracy of measurement was not necessary for the 
 purpose for which the investigation was undertaken. 
 Table XI is a good illustration of the character of the 
 observations. The time of the fall under gravity recorded 
 in the column headed '%" varies slightly, both because 
 of observational errors and because of Brownian move- 
 ments. Under the column headed 'V are recorded the 
 various observed values of the times of rise through 10 
 divisions of the scale in the eyepiece. A star (*) after an 
 observation in this column signifies that the drop Was 
 moving with gravity instead of against it. The pro- 
 cedure was in general to start with the drop either 
 altogether neutral (so that it fell when the field was on 
 
130 
 
 THE ELECTRON 
 
 with the same speed as when the field was off) , or having 
 one single positive charge, and then to throw on positive 
 
 TABLE XI 
 
 Plate Distance 1.6 cm. Distance of Fall .0975 cm. Volts 1,015. 
 Temperature 23 C. Radius of Drop . 000063 cm. 
 
 fr 
 
 If 
 
 No. of 
 Charges on 
 Drop 
 
 No. of 
 Charges on 
 Ion Caught 
 
 < 
 
 tp 
 
 No. of 
 
 Charges on 
 Drop 
 
 No. of 
 
 Charges on 
 Ion Caught 
 
 19.0 
 
 IOO.O 
 
 16.0 
 8.0 
 
 I P 
 2P 
 3? 
 
 IP 
 IP 
 
 2 O.O 
 
 IO.O* 
 2 O.O* 
 IOO.O 
 
 i N 
 
 
 
 i P 
 
 P 
 P 
 
 N 
 
 
 
 
 
 
 2 O.O* 
 
 
 
 
 20.0 
 
 16.0 
 8.0 
 
 2 P 
 3? 
 
 I P 
 
 
 IOO.O 
 
 16.0 
 
 IP 
 2 p 
 
 P 
 P 
 i P 
 
 
 
 
 
 
 8.0 
 
 3? 
 
 
 
 IOO.O 
 
 i P 
 
 
 
 
 
 
 
 17.0 
 
 8.2 
 
 6.0 
 
 2 P 
 3? 
 4? 
 
 I P 
 IP 
 IP 
 
 
 104.0 
 15.0 
 9.0 
 
 i P 
 2 P 
 3? 
 
 i P 
 i P 
 
 T P 
 
 
 
 
 
 
 6.0 
 
 4? 
 
 I JL 
 
 
 7-0* 
 
 2 N 
 
 T) 
 
 
 
 
 
 
 7^o* 
 
 iN 
 2 N 
 
 I if 
 
 iN 
 
 
 IO.O* 
 
 2 N 
 i N 
 
 I P 
 I P 
 
 
 
 
 
 
 20. O* 
 
 o 
 
 TJ 
 
 21.0 
 
 20.0* 
 
 95-o 
 16-5 
 8.0 
 
 o 
 iP 
 2 P 
 3? 
 
 iP 
 iP 
 i P 
 
 T P 
 
 
 IOO.O 
 
 15.5 
 
 8.0 
 6.0 
 
 iP 
 2 P 
 3? 
 4P 
 
 I P 
 iP 
 I P 
 I P 
 
 
 6.0 
 
 4? 
 
 I A 
 
 
 
 
 
 
 
 
 
 
 IOO.O 
 
 iP 
 
 T P 
 
 
 IOO.O 
 
 iP 
 
 T P 
 
 
 16.5 
 
 2 P 
 
 1 -L 
 
 
 16.0 
 
 2 P 
 
 1 A 
 T) 
 
 
 
 
 
 
 8-4 
 
 3? 
 
 I r 
 
 
 20.0* 
 
 o 
 
 I P 
 
 
 
 
 
 
 IOO.O 
 
 i P 
 
 T P 
 
 20. O 
 
 106.0 
 16.0 
 8.4 
 
 iP 
 2 P 
 3? 
 
 IP 
 IP 
 
 
 16.6 
 
 8.8 
 5-7' 
 
 2 P 
 
 11 
 
 I -t 
 I P 
 IP 
 
 
 IO.O* 
 
 i N 
 
 i P 
 
 
 IOO.O 
 
 * 
 
 I P 
 
 i N 
 
 
 2O. 0* 
 IOO.O 
 
 16.0 
 
 o 
 iP 
 2 P 
 
 IP 
 i P 
 
 
 2O. 0* 
 IO.O* 
 
 20. o* 
 
 O 
 
 iN 
 
 
 
 iN 
 iP 
 
 
 IOO.O 
 
 i P 
 
 i P 
 
 
 44 catches, all singles 
 
 
 16.0 
 
 2 P 
 
 i P 
 
 
 
 
 8.0 
 
 3? 
 
 
 
 
MECHANISM OF IONIZATION OF GASES 131 
 
 charges until its speed came to the 6.0 second value, 
 then to make it neutral again with the aid of radium, 
 and to begin over again. 
 
 It will be seen from Table XI that in 4 cases out of 44 
 we caught negatives, although it would appear from the 
 arrangement shown in Fig. 12 that we could catch only 
 positives. These negatives are doubtless due to second- 
 ary rays which radiate in all directions from the air 
 molecules when these are subjected to the primary X-ray 
 radiation. 
 
 Toward the end of Table XI is an interesting series 
 of catches. At the beginning of this series, the drop 
 was charged with 2 negatives which produced a speed 
 in the direction of gravity of 6 . 5 seconds. It caught in 
 succession 6 single positives before the field was thrown off. 
 The corresponding times were 6.5*, 10*, 20*, 100, 15.5, 
 8.0, 6.0. The mean time during which the X-rays had 
 to be on in order to produce a " catch" was in these 
 experiments about six seconds, though in some instances 
 it was as much as a minute. The majority of the times 
 recorded in column tp were actually measured with a 
 stop watch as recorded, but since there could be no 
 possibility of mistaking the ico-second speed, it was 
 observed only four or five tirnes. It will be seen from 
 Table XI that out of 44 catches of ions produced by 
 every hard X-ray there is not a single double. As a 
 result of observing from 500 to i ,000 catches in the man- 
 ner illustrated in Table XI, we came to the conclusion 
 that, although we had entered upon the investigation 
 with the expectation of proving the existence of valency 
 in gaseous ionization, we had instead obtained direct, 
 unmistakable evidence that the act of ionization of air 
 
132 THE ELECTRON 
 
 molecules by both primary and secondary X-rays of widely 
 varying degrees of hardness, as well as by /3- and y-rays, 
 uniformly consists , under all the conditions which we were 
 able to investigate, in the detachment from a neutral molecule 
 of one single elementary electrical charge. 
 
 III. RECENT EVIDENCE A$ TO NATURE OF IONIZATION 
 PRODUCED BY ETHER WAVES 
 
 Although Townsend and Franck and Westphal dis- 
 sented from the foregoing conclusion, all the evidence 
 which has appeared since has tended to confirm it. Thus 
 Salles, 1 using a new method due to Langevin of measuring 
 
 directly the ratio f-^j of the mobility to the diffusion 
 
 coefficient, concluded that when the ionization is produced 
 by 7-rays there are no ions bearing multiple charges. 
 Again, the very remarkable photographs (see plate 
 opposite p. 187) taken by C. T. R. Wilson in the 
 Cavendish Laboratory of the tracks made by the passage 
 of X-rays through gases show no indication of a larger 
 number of negatively than of positively charged droplets. 
 Such an excess is to be expected if the act of ionization 
 ever consists in these experiments in the detachment of 
 two or more negative electrons from a neutral molecule. 
 Further, if the initial act of ionization by X-rays ever 
 consists in the ejection of two or more corpuscles from 
 a single atom, there should appear in these Wilson pho- 
 tographs a rosette consisting of a group of zigzag lines 
 starting from a common point. A glance at the plate 
 opposite p. 189 shows that this is not the case, each 
 zigzag line having its own individual starting-point. 
 
 1 Le Radium, X (1913), 113, 119. 
 
MECHANISM OF IONIZATION OF GASES 133 
 
 There are two other types of experiments which 
 throw light on this question. 
 
 When in the droplet experiments the X-rays are 
 allowed to fall directly upon the droplet, we have seen 
 that they detach negative electrons from it, and if the 
 gas is at so low a pressure that there is very little chance 
 of the capture of ions by the droplet, practically all of 
 its changes in charge have this cause. ' Changes produced 
 under these conditions appear, so far as I have yet been 
 able to discover, to be uniformly unit changes, though 
 I have not yet made a systematic or exhaustive study of 
 this point. Also, when the changes are produced by the 
 incidence on the droplet of ultra-violet light, so far as 
 experiments carried out in the Ryerson Laboratory go, 
 they usually, though not always, have appeared to cor- 
 respond to the loss of one single electron. The same 
 seems to have been true in the experiments reported by 
 A. Joffe, 1 who has given this subject careful study. 
 Meyer and Gerlach, however, 2 seem very often to 
 observe changes corresponding to the simultaneous loss 
 of several electrons. 
 
 It is to be noted, however, that their drops are gen- 
 erally quite heavily charged, carrying from 10 to 30 
 electrons. Under such conditions the loss of a single 
 electron makes but a minute change in speed, and is 
 therefore likely not only to be unnoticed, but to be almost 
 impossible to detect until the change has become more 
 pronounced through the loss of several electrons. This 
 question, then, can be studied reliably only when the field is 
 powerful enough to hold the droplet balanced with only one 
 
 1 Sitzungsber. d. k. Bayerischen Akad. d. Wiss. (1913), p. 19. 
 Ann. d. Phys., XLV, 177; XL VII, 227. 
 
134 THE ELECTRON 
 
 or two free electrons upon it. I do not consider, therefore, 
 that the experiments of Meyer and Gerlach contain any 
 evidence that the act of ionization by ultra-violet light 
 detaches more than one electron from a single atom. 
 Nor indeed do they claim that it does, while the evidence 
 accumulated in the Ryerson Laboratory, though not yet 
 complete, points strongly the other way. 
 
 Table XII contains one series of observations taken 
 with my apparatus by Mr. P. I. Pierson. The first 
 column gives the volts applied to the plates of the con- 
 denser shown in Fig. 7, p. 109. These were made variable 
 so that the drop might always be pulled up with a slow 
 speed even though its positive charge were continually 
 increasing. The second and third columns give the times 
 required to move i cm. under gravity and under the 
 field respectively. The fourth column gives the time 
 intervals required for the drop to experience a change in 
 charge under the influence of a constant source of ultra- 
 violet light a quartz mercury lamp. The fifth column 
 gives the total charge carried by the drop computed from 
 equation (12), p. 89. The sixth column shows the change 
 in charge computed from equation (10), p. 68. This is 
 seen to be as nearly a constant as could be expected in 
 view of Brownian movements and the inexact measure- 
 ments of volts and times. The mean value of ^ is seen 
 to be 5. iXio~ 10 which yields with the aid of equation 
 (16), p. 99, after the value of A found for oil drops has 
 been inserted, = 4. 77X10"", which is in better agree- 
 ment with the result obtained with oil drops than we 
 had any right to expect. In these experiments the light 
 was weak /so that the changes come only after an average 
 interval of 29 seconds and it will be seen that they are all 
 
MECHANISM OF IONIZATION OF GASES 135 
 
 unit changes. When the light was more intense we 
 sometimes appeared to get double and in one case treble 
 
 TABLE XII 
 
 MERCURY DROPLET OF RADIUS o = 8Xio-s CM. DISCHARGING ELEC- 
 TRONS UNDER THE INFLUENCE OF ULTRA- VlOLET LlGHT 
 
 Volts 
 
 Drop No. i 
 Per Cm. 
 
 tp Sec. 
 per Cm. 
 
 Time Interval 
 between 
 Discharges 
 in Seconds 
 
 n Xio 
 
 Change 
 in c 
 
 Change 
 in n 
 
 2,260 
 -i 070 
 
 II. O 
 
 no 
 
 I2OO 
 -4- 32 8 
 
 \ 
 
 49-4 
 
 CQ ir 
 
 I 
 
 
 1, 060. . 
 
 II O 
 
 IQ4 
 
 II 
 
 "?4.4 
 
 4-4 
 
 I 
 
 I 060 
 
 
 ~\~ IQO 
 
 12.8 
 
 60 8 
 
 6 4 
 
 I 
 
 1,820 
 I 600 
 
 II. 2 
 
 + 22O 
 + 23O 
 
 23 
 
 40 
 
 65.0 
 60 8 
 
 4-2 
 
 4 8 
 
 I 
 
 I 
 
 I, ceo. . 
 
 
 + 332 
 
 15.2 
 
 7^. i 
 
 c.3 
 
 I 
 
 3,040 
 
 2 CAO 
 
 Drop No. i 
 10.4 
 
 + 98 
 + 2OO 
 
 5-6 
 
 43-5 
 
 4.0 4. 
 
 t Q 
 
 I 
 
 2,230. . 
 
 
 + 3OO 
 
 18.6 
 
 ct 2 
 
 5-8 
 
 I 
 
 2,230. . 
 
 
 + 76 
 
 3-5-0 
 
 60.7 
 
 5-5 
 
 I 
 
 1,030. . 
 
 
 -1- 200 
 
 42 
 
 6e; o 
 
 4 3 
 
 I 
 
 1,810 
 
 
 + 176 
 
 54 
 
 69.6 
 
 4-6 
 
 I 
 
 i,6co. . 
 
 ' 
 
 + 2 <?o 
 
 70 
 
 7C 2 
 
 5-6 
 
 I 
 
 1,520 
 
 
 4- soo 
 
 45 
 
 70.4 
 
 4-2 
 
 I 
 
 I.C2O. . 
 
 
 no 
 
 9-8 
 
 85 i 
 
 e. c 
 
 I 
 
 
 
 
 
 
 
 
 
 
 Mean. . 
 
 29 
 
 Mean. . 
 
 S-i 
 
 
 changes, but since these uniformly appear with less and 
 less frequency both as the charge diminishes and as the 
 
136 THE ELECTRON 
 
 interval between the changes is made larger, the inference 
 is inevitable that when multiple changes appear fre- 
 quently, as they do in Meyer and Gerlach's work, it is 
 because some of the changes in speed escape the notice 
 of the observer. 
 
 So long, then, as we are considering the ionization of 
 neutral atoms through the absorption of an ether wave 
 of any kind, the evidence at present available indicates 
 that the act always consists in the detachment from the 
 atom of one single negative electron, the energy with 
 which this electron is ejected from the atom depending, as 
 we shall see in chap, x, in a very definite and simple way 
 upon the frequency of the ether wave which. ejects it. 
 
 IV. IONIZATION BY /3-RAYS 
 
 When the ionization is due to the passage of /3-rays 
 through matter, the evidence of the oil-drop experiments 
 as well as that of C. T. R. Wilson's experiments (see 
 chap. IX) on the photographing of the tracks of the 
 /3-rays is that here, too, the act consists in the detachment 
 of one single electron from a single atom. This experi- 
 mental result is easy to understand in the case of the 
 /3-rays, when it is remembered that Wilson's photo- 
 graphs prove directly the fact, long known from other 
 types of evidence, that a /3-ray, in general, ionizes but a 
 very minute fraction of the number of atoms through 
 which it shoots before its energy is expended. If, then, 
 its chance, in shooting through an atom, of coming near 
 enough to one of the electronic constituents of that atom 
 to knock it out is only one in one thousand, or one in 
 one million, then its chance of getting near enough to 
 two electronic constituents of the same atom to knock 
 
MECHANISM OF IONIZATION OF GASES 137 
 
 them both out is likely to be negligibly small. The 
 argument here rests, however, on the assumption that 
 the corpuscles within the atom are independent of one 
 another, which is not necessarily the case, so that the 
 matter must be decided after all solely by experiment. 
 The difference between the act of ionization when 
 produced by a /3-ray and when produced by an ether 
 wave seems, then, to consist wholly in the difference in 
 the energy with which the two agencies hurl the electron 
 from its mother atom. Wilson's photographs show that 
 0-rays do not eject electrons from atoms with appre- 
 ciable speeds^ while ether waves may eject them with 
 tremendous energy. Some of Wilson's photographs 
 showing the effect of passing X-rays through air are 
 shown in the most interesting plate opposite p. 189. 
 The original X-rays have ejected electrons with great 
 speeds from a certain few of the atoms of the gas, 
 and it is the tracks of these electrons as they shoot 
 through the atoms of the gas, ionizing here and there as 
 they go, which constitute the wiggly lines shown in the 
 photograph. Most of the ionization, then, which is pro- 
 duced by X-rays is a secondary effect due to the negative 
 electrons, i.e., the /3-rays which the X-rays eject. If 
 these /3-rays could in turn eject electrons with ionizing 
 speeds, each of the dots in one of these /3-ray tracks 
 would be the starting-point of a new wiggly line like the 
 original one. But such is not the case. We may think, 
 then, of the /3~rays as simply shaking loose electronic 
 dust from some of the atoms through which they pass 
 while we think of the X-rays as taking hold in some way 
 of the negative electrons within an atom and hurling 
 them out with enormous energy. 
 
138 THE ELECTRON 
 
 V. IONIZATION BY a-RAYS 
 
 But what happens to the electronic constituents of 
 an atom when an a-particle, that is, a helium atom, 
 shoots through it? Some of Bragg's experiments and 
 Wilson's photographs show that the a-particles shoot 
 in straight lines through from 3 to 7 cm. of air before 
 they are brought to rest. We must conclude, then, that 
 an atom has so loose a structure that another atom, if 
 endowed with enough speed, can shoot straight through it 
 without doing anything more than, in some instances, to 
 shake off from that atom an electron or two. The tracks 
 shown in Figs. 14 and 15, p. 186, are Wilson's photographs 
 of the tracks of the a-particles of radium. They ionize 
 so many of the atoms through which they pass that the 
 individual droplets of water which form about the ions 
 produced along the path of the ray, and which are the 
 objects really photographed, are not distinguishable 
 as individuals. The sharp changes in the direction of 
 the ray toward the end of the path are convincing 
 evidence that the a-particle actually goes through 
 the atoms instead of pushing them aside as does a 
 bullet. For if one solar system, for example, endowed 
 with a stupendous speed, were to shoot straight 
 through another similar system, but without an actual 
 impact of their central bodies, the deflection from its 
 straight path which the first system experienced might 
 be negligibly small if its speed were high enough, and that 
 for the simple reason that the two systems would not be 
 in one another's vicinity long enough to produce a 
 deflecting effect. In technical terms the time inte- 
 gral of the force would be negligibly small. The slower 
 the speed, however, the longer this time, and hence 
 
MECHANISM OF IONIZATION OF GASES 139 
 
 the greater the deflection. Thus it is only when the 
 a-particle shown in Fig. 15 has lost most of its velocity 
 i.e., it is only toward the end of its path that the nuclei 
 of the atoms through which it passes, are able to deflect 
 it from its straight path. If it pushed tne molecules 
 aside as a bullet does, instead of going through them, 
 the resistance to its motion would be greatest when the 
 speed is highest. Now, the facts are just the opposite of 
 this. The a-particle ionizes several times more violently 
 toward the end of its path than toward the beginning, 
 and it therefore loses energy more rapidly when it is going 
 slowly than when it is going rapidly. Further, it is 
 deflected more readily then, as the photograph shows. 
 All of this is just as it should be if the a-particle shoots 
 straight through the molecules in its path instead of 
 pushing them aside. 
 
 These photographs of Wilson's are then the most 
 convincing evidence that we have that the atom is a sort 
 of miniature stellar system with constituents which are 
 unquestionably just as minute with respect to the total 
 volume occupied by the atom as are the sun and planets 
 and other constituents of the solar system with respect 
 to the whole volume inclosed within the confines of this 
 system. When two molecules of a gas are going as 
 slowly as they are in the ordinary motion of thermal 
 agitation, say a mile a second, when their centers come 
 to within a certain distance about o. 2 JJL/JL (million ths of 
 a millimeter) they repel one another and so the two 
 systems do not inter-penetrate. This is the case of an 
 ordinary molecular collision. But endow one of these 
 molecules with a large enough energy and it will shoot 
 right through the other, sometimes doubtless without so 
 
140 THE ELECTRON . 
 
 much as knocking out a single electron. This is the case 
 of an a-particle shooting through air. 
 
 But the question to which we are here seeking an 
 answer is, does the a-particle ever knock more than one 
 electron from a single atom or molecule through which 
 it passes, so as to leave that atom doubly or trebly 
 charged? The oil-drop method used at low pressures 
 has just given a very definite negative answer to this 
 question. In no gas or vapor which we can find, and 
 many, including mercury compounds, have been tried, 
 does an a-ray ever knock more than one electron from a 
 single atom. 
 
 J. J. Thomson has, however, brought forward evi- 
 dence 1 that the positive residues of atoms which shoot 
 through discharge tubes in a direction opposite to that 
 of the cathode rays do sometimes detach several electrons 
 from certain kinds of atoms. Indeed, he thinks that he 
 has evidence that the ionization of a mercury atom con- 
 sists either in the detachment of i negative electron or 
 else in the detachment of 8. This evidence, too, seems 
 to me quite convincing, and indeed a slow-moving 
 positive ray may well do more damage to an atom 
 through which it passes than a high-speed a-ray. 
 
 VI. SUMMARY 
 
 The results of the studies reviewed in this chapter 
 may be summarized thus : 
 
 i. The act of ionization by /3-rays seems to consist 
 in the shaking off without any appreciable energy of one 
 single electron from an occasional molecule through 
 
 1 Rays of Positive Electricity, 1913, p. 46. I 
 
MECHANISM OF IONIZATION OF GASES ,141 
 
 which the 0-ray passes. The faster the /3-ray the less 
 frequently does it ionize. 
 
 2. The act of ionization by ether waves, i.e., by 
 X-rays or light, seems to consist in the hurling out with 
 an energy which may be very large, but which depends 
 upon the frequency of the incident ether wave, of one 
 single electron from an occasional molecule over which 
 this wave passes. 
 
 3. The act of ionization by rapidly moving a-particles 
 consists in the shaking loose of one single electron from 
 the atom through which it passes 1 , but a slow-moving 
 positive ray appears in some cases to be able to detach 
 several electrons from a single atom. 
 
 1 See Gottschalk and Kelly, Phys. Rev., 1917. 
 
CHAPTER VII 
 
 BROWNIAN MOVEMENTS IN GASES 
 I. HISTORICAL SUMMARY 
 
 In 1827 the English botanist, Robert Brown, first 
 made mention of the fact that minute particles of dead 
 matter in suspension in liquids can be seen in a high- 
 power microscope to be endowed with irregular wiggling 
 motions which strongly suggest "life." 1 Although this 
 phenomenon was studied by numerous observers and 
 became known as the phenomenon of the Brownian 
 movements, it remained wholly unexplained for just 
 fifty years. The first man to suggest that these motions 
 were due to the continual bombardment to which these 
 particles are subjected because of the motion of thermal 
 agitation of the molecules of the surrounding medium 
 was the Belgian Carbonelle, whose work was first pub- 
 lished by his collaborator, Thirion, in i88o, 2 although 
 three years earlier Delsaulx 3 had given expression to views 
 of this sort but had credited Carbonelle with priority in 
 adopting them. In 1881 Bodoszewski 4 studied the 
 Brownian movements of smoke particles and other sus- 
 pensions in air and saw in them "an approximate image 
 of the movements of the gas molecules as postulated by 
 the kinetic theory of gases." Others, notably Gouy, 5 
 
 *Phtt. Mag., IV (1828), 161. 
 
 3 Revue des questions sdentifiques, Louvain, VII (1880), 5. 
 3 Ibid., II (1877), 319. 
 
 < Dinglers polyL Jour., CCXXXIX (1881), 325. 
 s Jour, de Phys., VII (1888), 561; Comptes rendus, CIX (1889), 102. 
 142 
 
BROWNIAN MOVEMENTS IN GASES 143 
 
 urged during the next twenty years the same interpre- 
 tation, but it was not until 1905 that a way was found 
 to subject the hypothesis to a quantitative test. Such 
 a test became possible through the brilliant theoretical 
 work of Einstein 1 of Bern, Switzerland, who, starting 
 merely with the assumption that the mean kinetic 
 energy of agitation of a particle suspended in a fluid 
 medium must be the same as the mean kinetic energy 
 of agitation of a gas molecule at the same temperature, 
 developed by unimpeachable analysis an expression for 
 the mean distance through which such a particle should 
 drift in a given time through a given medium because 
 of this motion of agitation. This distance could be 
 directly observed and compared with the theoretical 
 value. Thus, suppose one of the wiggling particles is 
 observed in a microscope and its position noted on a 
 scale in the eyepiece at a particular instant, then noted 
 again at the end of r (for example, 10) seconds, and 
 the displacement A# in that time along one particular 
 axis recorded. Suppose a large number of such displace- 
 ments A# in intervals all of length T are observed, each one 
 of them squared, and the mean of these squares taken 
 and denoted by A#* : Einstein showed that the theoretical 
 value of Ar 2 should be 
 
 in which R is the universal gas constant per gram mole- 
 cule, namely, 83i.5Xio s de C g^ es , T the temperature on 
 the absolute scale, N the number of molecules in one 
 gram molecule, and K a resistance factor depending 
 
 Ann. d. Phys. (4), XVII (1905), 5495 XIX (1906), 371; XXII 
 (1907), 569. 
 
144 THE ELECTRON 
 
 upon the viscosity of the medium and the size of the 
 drop, and representing the ratio between the force ap- 
 plied to the particle in any way and the velocity pro- 
 duced by that force. If Stokes's Law, namely, F=6Trrjai^ 
 held for the motion of the particle through the medium, 
 
 F 
 
 then K= would have the value 67n?a, so that Ein- 
 
 v 
 stein's formula would become 
 
 (22) 
 
 This was the form which Einstein originally gave to 
 his equation, a very simple derivation of which has been 
 given by Langevin. 1 The essential elements of this 
 derivation will be found in Appendix C. 
 
 The first careful test of this equation was made on 
 suspensions in liquids by Perrin, 2 who used it for finding 
 N the number of molecules in a gram molecule. He 
 obtained the mean value ./V=68. 2Xio 22 , which, in view 
 of the uncertainties in the measurement of both K and 
 ir 2 , may be considered as proving the correctness of 
 Einstein's equation within the limits of error of Perrin 's 
 measurements, which differ among themselves by as 
 much as 30 per cent. 
 
 II. QUANTITATIVE MEASUREMENTS IN GASES 
 
 Up to 1909 there had been no quantitative work 
 whatever on Brownian movements in gases. Bodoszewski 
 had described them fully and interpreted them correctly 
 
 1 Comptes rendus, CXLVI (1908), 530. 
 
 3 Ibid., p. 967; CXLVII (1908), 475, 530, 5945 CLII (1911), 1380, 
 1569; see also Perrin, Brownian Movements and Molecular Reality, 
 Engl. tr. by Soddy, 1912. 
 
BROWNIAN MOVEMENTS IN GASES 145 
 
 in 1 88 1. In 1906 Smoluchowski 1 had computed how 
 large the mean displacements in air for particles of 
 radius a= io~ 4 ought to be, and in 1907 Ehrenhaft 2 had 
 recorded displacements of the computed order with 
 particles the sizes of which he made, however, no attempt 
 to measure, so that he knew nothing at all about the 
 resistance factor K. There was then nothing essentially 
 quantitative about this work. 
 
 In March, 1908, De Broglie, in Paris, 3 made the 
 following significant advance. He drew the metallic 
 dust arising from the condensation of the vapors coming 
 from an electric arc or spark between metal electrodes 
 (a phenomenon discovered by Hemsalech and De Watte- 
 ville 4 ) into a glass box and looked down into it through 
 a microscope upon the particles rendered visible by a 
 beam of light passing horizontally through the box and 
 illuminating thus the Brownian particles in the focal 
 plane of the objective. His addition consisted in placing 
 two parallel metal plates in vertical planes, one on either 
 side of the particles, and in noting that upon applying a 
 potential difference to these plates some of the particles 
 moved under the influence of the field toward one plate, 
 some remained at rest, while others moved toward the 
 other plate, thus showing that a part of these particles 
 were positively electrically charged and a part negatively. 
 In this paper he promised a study of the charges on these 
 particles. In May, 1909, in fulfilling this promise 5 he 
 
 1 Ann. der Phys., IV (1906), 21, 756. 
 
 2 Wiener Berichte, CXVI (1907), II, 1175. 
 
 * Comples rendus, CXLVI (1908), 624, 1010. 
 Ibid., CXLIV (1907), 1338. 
 >Ibid., CXLVIII (1909), 1316. 
 
146 THE ELECTRON 
 
 
 
 made the first quantitative study of Brownian move- 
 ments in gases. The particles used were minute droplets 
 of water condensed upon tobacco smoke. The average 
 rate at which these droplets moved in Broglie's horizontal 
 electric field was determined. The equation for this 
 motion was 
 
 Fe=Kv (23) 
 
 The mean Ax 2 was next measured for a great many 
 particles and introduced into Einstein's equation: 
 
 2RT 
 
 A r 2 T 
 
 ~NK T ' 
 
 From these two equations K was eliminated and e 
 obtained in terms of N. Introducing Perrin's value of 
 N, De Broglie obtained from one series of measurements 
 =4.5Xio~ 10 ; from another series on larger particles 
 he got a mean value several times larger -a result which 
 he interpreted as indicating multiple charges on the 
 larger particles. Although these results represent merely 
 mean values for many drops which are not necessarily all 
 alike, either in radius or charge, yet they may be con- 
 sidered as the first experimental evidence that Einstein's 
 equation holds approximately, in gases, and they are the 
 more significant because nothing has to be assumed about 
 the size of the particles, if they are all alike in charge 
 and radius, or about the validity of Stokes's Law in 
 gases, the ^-factor being eliminated. 
 
 The development of the oil-drop method made it 
 possible to subject the Brownian-movement theory to a 
 more accurate and convincing experimental test than 
 had heretofore been attainable, and that for the following 
 reasons : 
 
BROWNIAN MOVEMENTS IN GASES 147 
 
 1. It made it possible to hold, with the aid of the 
 vertical electrical field, one particular particle under 
 observation for hours at a time and to measure as many 
 displacements as desired on it alone instead of assuming 
 the identity of a great number of particles, as had been 
 done in the case of suspensions in liquids and in De 
 BroghVs experiments in gases. 
 
 2. Liquids are very much less suited than are 
 gases to convincing tests of any kinetic hypothesis, 
 for the reason that prior to Brownian-movement 
 work we had no satisfactory kinetic theory of liquids 
 at all. 
 
 3. The absolute amounts of the displacements of a 
 given particle in air are 8 times greater and in hydrogen 
 15 times greater than in water. 
 
 4. By reducing the pressure to low values the dis- 
 placements can easily be made from 50 to 200 times 
 greater in gases than in liquids. 
 
 5. The measurements can be made independently 
 of the most troublesome and uncertain factor involved 
 in Brownian-movement work in liquids, namely, the 
 factor K, which contains the radius of the particle and 
 the law governing its motion through the liquid. 
 
 Accordingly, there was begun in the Ryerson Lab- 
 oratory, in 1910, a series of very careful experiments in 
 Brownian movements in gases. Svedberg, 1 in reviewing 
 this subject in 1913, considers this "the only exac.t 
 investigation of quantitative Brownian movements in 
 gases." A brief summary of the method and results 
 was published by the author. 2 A fyll account was 
 
 1 Jahrbuch der Radioaktimtiit und Elektronik, X (1913), 513. 
 
 2 Science, February 17, 1911. 
 
148 THE ELECTRON 
 
 published by Mr. Harvey Fletcher in May, 191 1, 1 and 
 further work on the variation of Brownian movements 
 with pressure was presented by the author the year 
 following. 2 The essential contribution of this work as 
 regards method consisted in the two following particulars : 
 i. By combining the characteristic and fully tested 
 equation of the oil-drop method, namely, 
 
 (24) 
 
 with the Einstein Brownian-movement equation, namely, 
 -r- 2RT 
 
 it was possible to obtain the product Ne without any 
 reference to the size of the particle or the resistance of 
 the medium to its motion. This quantity could then 
 be compared with the same product obtained with great 
 precision from electrolysis. The experimental procedure 
 consists in balancing a given droplet and measuring, as 
 in any Brownian-movement work, the quantity Ax 2 , then 
 unbalancing it and measuring F, v t and (^i+v 2 ) ; the 
 combination of (24) and (25) then gives 
 
 
 Ne 
 
 Since it is awkward to square each displacement A# 
 before averaging, it is preferable to modify by sub- 
 stituting from the Maxwell distribution law, which holds 
 
 * Phys. Zeitschr., XII (1911), 202-8; see also Phys. Rev., XXXIII 
 (IQTT), 81. 
 
 a Phys. Rev., I, N.S. (1913), 218. 
 
BROWNIAN MOVEMENTS IN GASES 149 
 
 for Brownian displacements as well as for molecular 
 velocities, the relation 
 
 We obtain thus 
 
 or 
 
 
 * 
 
 The possibility of thus eliminating the size of the 
 particle and with it the resistance of the medium to its 
 motion can be seen at once from the simple consideration 
 that so long as we are dealing with one and the same 
 particle the ratio K between the force acting and the 
 velocity produced by it must be the same, whether the 
 acting force is due to gravity or an electrical field, as in 
 the oil-drop experiments, or to molecular impacts as 
 in Brownian-movement work. De Broglie might have 
 made such an elimination and calculation of Ne in his 
 work, had his Brownian displacements and mobilities 
 in electric fields been made on one and the same particle, 
 but when the two sets of ' measurements are made on 
 different particles, such elimination would involve the 
 very uncertain assumption of identity of the particles in 
 both charge and size. Although De Broglie did actually 
 make this assumption, he did not treat his data in the 
 manner indicated, and the first publication of this 
 method of measuring Ne as well as the first actual deter- 
 mination was made in the papers mentioned above. 
 
150 THE ELECTRON 
 
 Some time later E. Weiss reported similar work to 
 the Vienna Academy. 1 
 
 2. Although it is possible to make the test of Ne in 
 just the method described and although it was so made 
 in the case of one or two drops, Mr. Fletcher worked out 
 a more convenient method, which involves expressing 
 the displacements Ax in terms of the fluctuations in the 
 time required by the particle to fall a given distance 
 and thus dispenses with the necessity of balancing the 
 drop at all. I shall present another derivation which 
 is very simple and yet of unquestionable validity. 
 
 In equation (28) let T be the time required by the 
 particle, if there were no Brownian movements, to fall 
 between a series of equally spaced cross-hairs whose 
 distance apart is d. In view of such movements the 
 particle will have moved up or down a distance Ax in 
 the time T. Let us suppose this distance to be up. 
 Then the actual time of fall will be r+AJ, in which At 
 is now the time it takes the particle to fall the distance 
 Ax. If now A/ is small in comparison with r, that is, if 
 Ax is small in comparison with d (say i/io or less), then 
 we shall introduce a negligible error (of the order i/ioo 
 at the most) if we assume that Ax = ViAt in which ^ is 
 the mean velocity under gravity. Replacing then in 
 (28) (AxY byv l 2 (AtY, in which (KtY is the square of the 
 average difference between an observed time of fall and 
 the mean time of fall t g , that is, the square of the average 
 
 1 It was read before the Academy on July 6 : Wiener Berichte, CXX 
 (1911), II, 1021, but appeared first in print in the August ist number 
 of the Phys. Zeitschr. (1911), p. 63. Fletcher's article is found in brief 
 in an earlier number of the same volume of the Phys. Zeitschr., p. 203, 
 and was printed in full in the July, number of Le Radium, VIII 
 (1911), 279. 
 
BROWNIAN MOVEMENTS IN GASES 151 
 
 fluctuation in the time of fall through the distance d, 
 we obtain after replacing the ideal time T by the mean 
 time t\ 
 
 tRTdt+vJJ, 
 
 -~~ .............. (29) 
 
 In any actual work A/ will be kept considerably less 
 than i/io the mean time t g if the irregularities due to 
 the observer's errors are not to mask the irregularities 
 due to the Brownian movements, so that (29) is sufficient 
 for practically all working conditions. 1 
 
 The work of Mr. Fletcher and of the author was done 
 by both of the methods represented in equations (28) 
 and (29). The 9 drops reported upon in Mr. Fletcher's 
 paper in i9ii 2 yielded the results shown below in which 
 n is the number of displacements used in each case in 
 determining Ax or A/. 
 
 TABLE XIII 
 
 1.68 125 
 1 . 67 136 
 1.645 321 
 
 . 695 2O2 
 
 73 171 
 
 .65 20O 
 
 .66 84 
 
 .785 411 
 
 65 85 
 
 When weights are assigned proportional to the num- 
 ber of observations taken, as shown in the last column 
 
 1 No error is introduced here if, as assumed, A/ is small in comparison 
 with tg. However, for more rigorous equations see Fletcher, Phys. Rev., 
 IV (1914), 442; also Smoluchowski, Phys. Zeitschr., XVI (1915), 321. 
 
 1 Le Radium, VIII (1911), 279; Phys. Rev., XXXIII (1911), 107. 
 
152 THE ELECTRON 
 
 of Table XIII, there results for the weighted mean value 
 which represents an average of 1,735 displacements, 
 l / A^=i.698Xio 7 or Ne=2.SSXio 14 electrostatic units, 
 as against 2.896Xio 14 , the value found in electroly- 
 sis. The agreement between theory and experiment is 
 then in this case about as good as one-half of i per cent, 
 which is well within the limits of observational error. 
 
 This work seemed to demonstrate, with considerably 
 greater precision than had 'been attained in earlier 
 Brownian-movement work and with a minimum of 
 assumptions, the correctness of the Einstein equation, 
 which is in essence merely the assumption that a particle 
 in a gas, no matter how big or how little it is or out of 
 what it is made, is moving about with a mean translatory 
 kinetic energy which is a universal constant dependent 
 only on temperature. To show how well this conclusion 
 has been established I shall refer briefly to a few later 
 researches. 
 
 In 1914 Dr. Fletcher, assuming the value of K which 
 I had published 1 for oil drops moving through air, made 
 new and improved Brownian-movement measurements 
 in this medium and solved for N the original Einstein 
 equation, which, when modified precisely as above by 
 
 replacing A# 2 by (AJ) and (5#) =Vj. 2 (At) becomes 
 
 (30) 
 
 He took, all told, as many as 18,837 A/'s, n t ^ ess than 
 5, 900 on a single drop, and obtained ./V=6o. 3X10" =*= 1.2. 
 This cannot be regarded as an altogether indepen- 
 dent determination of N, since it involves my value 
 
 1 Phys. Rev., I (1913), 218. 
 
BROWNIAN MOVEMENTS IN GASES 153 
 
 of K. Agreeing, however, as well as it does with my 
 value of N ', it does show with much conclusiveness that 
 both Einstein's equation and my corrected form of 
 Stokes's equation apply accurately to the motion of oil 
 drops of the size here used, namely, those of radius from 
 2.79Xio~ s cm. to 4.iXio~ s cm. (280400 /z^u). 
 
 In 1915 Mr. Carl Eyring tested by equation (29) the 
 value of Ne on oil drops, of about the same size, in 
 hydrogen and came out within . 6 per cent of the value 
 found in electrolysis, the probable error being, however, 
 some 2 per cent. 
 
 Precisely similar tests on substances other than oils 
 were made by Dr. E. Weiss 1 and Dr. Karl Przibram. 2 
 The former worked with silver particles only half 
 as large as the oil particles mentioned above, namely, 
 of radii between i and 2.3Xio~ 5 cm. and obtained 
 Ne= 10,700 electromagnetic units instead of 9,650. as 
 in electrolysis. This is indeed n per cent too high, but 
 the limits of error in Weiss's experiments were in his 
 judgment quite as large as this. K. Przibram worked 
 on suspensions in air of five or six different substances, 
 the radii varying from 200 ju/z to 600 juju, and though his 
 results varied among themselves by as much as 100 per 
 cent, his mean value came within 6 per cent of 9,650. 
 Both of the last two observers took too few displacements 
 on a given drop to obtain a reliable mean displacement, 
 but they used so many drops that their mean Ne still 
 has some significance. 
 
 It would seem, therefore, that the validity of Ein- 
 stein's Brownian-movement equation had been pretty 
 
 ' Sitzungsber. d. k. Akad. d. Wiss. in Wien, CXX (1911), II, 1021. 
 1 Ibid., CXXI (1912), II, 950. 
 
154 THE ELECTRON 
 
 thoroughly established in gases. In liquids too it has 
 recently been subjected to much more precise test than 
 had formerly been attained. Nordlund, 3 in 1914, using 
 minute mercury particles in water and assuming Stokes's 
 Law of fall and Einstein's equations, obtained 
 N=S9- iXio 21 . While in 1915 Westgren at Stockholm 4 
 by a very large number of measurements on colloidal 
 gold, silver, and selenium particles, of diameter from 
 65 HIJL to 130 up (6.5 to 13 X io~ 6 cm.), obtained a result 
 which he thinks is correct to one-half of i per cent, this 
 value is N = 60 . 5 X i o 22 =*= . 3 X i o 22 , which agrees per- 
 fectly with the value which I obtained from the measure- 
 ments on the isolation and measurement of the electron. 
 It has been because of such agreements as the fore- 
 going that the last trace of opposition to the kinetic and 
 atomic hypotheses of matter has disappeared from the 
 scientific world, and that even Ostwald has been willing 
 to make such a statement as that quoted on p. 10 above. 
 
 3 Ztschr.f. Phys. Ckem., LXXXVII (1914), 40. 
 
 4 Die Brown'sche Bewegung besonders als Mittel zur Bestimmung der 
 Avogadroschen Konstante, inaugural dissertation. Upsala: Almquist & 
 Wiksells Boktryckeri, 1915. 
 
CHAPTER VIII 
 THE EXISTENCE OF A SUB-ELECTRON? 
 
 It would not be in keeping with the ntethod of modern 
 science to make any dogmatic assertion as to the indi- 
 visibility of the electron. Such assertions used to be 
 made in high-school classes with respect to the atoms of 
 the elements, but the far-seeing among physicists, like 
 Faraday, were always careful to disclaim any belief in 
 the necessary ultimateness of the atoms of chemistry, and 
 that simply because there existed until recently no basis 
 for asserting anything about the insides of the atom. 
 We knew that there was a smallest thing which took part 
 in chemical reactions and we named that thing the atom, 
 leaving its insides entirely to the future. 
 
 Precisely similarly the electron was denned as the 
 smallest quantity of electricity which ever was found to 
 appear in electrolysis, and nothing was then said or is 
 now said about its necessary ultimateness. Our experi- 
 ments have, however, now shown that this quantity is 
 capable of isolation and exact measurement, and that all 
 the kinds of charges which we have been able to investi- 
 gate are exact multiples of it. Its value is 4. 774X io~ 10 
 electrostatic units. 
 
 I. A SECOND METHOD OF OBTAINING e 
 
 I have presented one way of measuring this charge, 
 but there is an indirect method of arriving at it which 
 was worked out independently by Rutherford and Geiger 1 
 
 1 Proc. Roy. Soc., A LXXXI (1908), 141, 161. 
 155 
 
156 THE ELECTRON 
 
 and Regener. 1 The unique feature in this method con- 
 sists in actually counting the number of a-particles shot 
 off per second by a small speck of radium or polonium 
 through a given solid angle and computing from this the 
 number of these particles emitted per second by one gram 
 of the radium or polonium. Regener made his determi- 
 nation by counting the scintillations produced on a dia- 
 mond screen in the focal plane of his observing microscope. 
 He then caught in a condenser all the a-particles emitted 
 per second by a known quantity of his polonium and 
 determined the total quantity of electricity delivered to 
 the condenser by them. This quantity of electricity 
 divided by the number of particles emitted per second 
 gave the charge on each particle. Because the a-particles 
 had been definitely proved to be helium atoms 2 and the 
 
 value of -- found for them showed that if they were 
 m 
 
 helium they ought to carry double the electronic charge, 
 Regener divided his result by 2 and obtained 
 
 He estimated his error at 3 per cent. Rutherford and 
 Geiger made their count by letting the a-particles from 
 a speck of radium C shoot into a chamber and produce 
 therein sufficient ionization by collision to cause an 
 electrometer needle to jump every time one of them 
 entered. These authors measured the total charge as 
 Regener did and, dividing by 2 the charge on each 
 a-particle, they obtained 
 
 =4.65X10-'. 
 
 *Sitzungsber. d. k. Preuss. Akad., XXXVIII (1909), 948. 
 2 Rutherford and Royds, Phil. Mag., XVII (1909), 281. 
 
THE EXISTENCE OF A SUB-ELECTRON ? 157 
 
 All determinations of e from radioactive data involve 
 one or the other of these two counts, namely, that of 
 Rutherford and Geiger or that of Regener. Thus, 
 Boltwood and Rutherford 1 measured the total weight of 
 helium produced in a second by a known weight of 
 radium. Dividing this by the number of a-particles 
 (helium atoms) obtained from Rutherford and Geiger's 
 count, they obtain the mass of one atom of helium from 
 which the number in a given weight, or volume since the 
 gas density is known, is at once obtained. They pub- 
 lished for the number n of molecules in a gas per cubic 
 centimeter at o?76 cm., w=2.6gXio 19 , which corre- 
 sponds to 
 
 This last method, like that of the Brownian movement, 
 is actually a determination of N, rather than of e, since 
 e is obtained from it only through the relation ^=9,650 
 electromagnetic units. Indeed, this is true of all 
 methods of estimating e, so far as I am aware, except the 
 oil-drop method and the Rutherford-Geiger-Regener 
 method, and of these two the latter represents the 
 measurement of the mean charge on an immense number 
 of a-particles. 
 
 Thus a person who wished to contend that the unit 
 charge appearing in electrolysis is only a mean charge 
 which may be made up of individual charges which vary 
 widely among themselves, in much the same way in 
 which the atomic weight assigned to neon has recently 
 been shown to be a mean of the weights of at least two 
 different elements inseparable chemically, could not be 
 gainsaid, save on the basis of the evidence contained in 
 
 1 Phil Mag. (6), XXII (IQII), 599. 
 
158 THE ELECTRON 
 
 the oil-drop experiments; for these constitute the only 
 method which has been found of measuring directly the 
 charge on each individual ion. It is of interest and sig- 
 nificance for the present discussion, however, that the 
 mean charge on an a-particle has been directly measured 
 and that it comes out, within the limits of error of the 
 measurement, at exactly' two electrons -as it should 
 
 s> 
 
 according to the evidence furnished by measurements 
 on the a-particles. 
 
 II. THE EVIDENCE FOR THE EXISTENCE OF A SUB- 
 ELECTRON 
 
 Now, the foregoing contention has actually been made 
 recently, and evidence has been presented which purports 
 to show that electric charges exist which are much 
 smaller than the electron. Since this raises what may 
 properly be called the most fundamental question of 
 modern physics, the evidence needs very careful con- 
 sideration. This evidence can best be appreciated 
 through a brief historical review of its origin. 
 
 The first measurements on the mobilities in electric 
 fields of swarms of charged particles of microscopically 
 visible sizes were made by H. A. Wilson 1 in 1903, as 
 detailed in chap. iii. These measurements were repeated 
 with modifications by other observers, including our 
 selves, during the years immediately following. De 
 Broglie's modification, published in 1908,* consisted in 
 sucking the metallic clouds discovered by Hemsalech 
 and De Watteville, 3 produced by sparks or arcs between 
 
 -Phil. Mag. (6), V (1903), 429- 
 
 2 Com pies rendus, CXLVI (1908), 624, 1010. 
 
 3/Wtf., CXLIV (1907), 1338. 
 
THE EXISTENCE OF A SUB-ELECTRON? 159 
 
 metal electrodes, into the focal plane of an ultra- 
 microscope and observing the motions of the individual 
 particles in this cloud in a horizontal electrical field pro- 
 duced by applying a potential difference to two vertical 
 parallel plates in front of the objective of his microscope. 
 In this paper De Broglie first commented upon the fact 
 that some of these particles were charged positively, 
 some negatively, and some not at all, and upon the 
 further fact that holding radium near the chamber 
 caused changes in the charges of the particles. He 
 promised quantitative measurements of the charges 
 themselves. One year later he fulfilled the promise, 1 
 and at practically the same time Ehrenhaft 2 published 
 similar measurements made with precisely the arrange- 
 ment described by De Broglie a year before. Both men, 
 as Ehrenhaft clearly pointed out, 3 while observing indi- 
 vidual particles, obtained only a mean charge, since the 
 different measurements entering into the evaluation of e 
 were made on different particles. So far as concerns e, 
 these measurements, as everyone agrees, were essentially 
 cloud measurements like Wilson's. 
 
 In the spring and summer of 1909 I isolated indi- 
 vidual water droplets and determined the charges car- 
 ried by each one, 4 and in April, 1910, I read before the 
 American Physical Society the full report on the oil-drop 
 work in which the multiple relations between charges were 
 established, Stokes's Law corrected, and e accurately 
 
 *Ibid. t CXLVIII (1909), 1316. 
 3 Phys. Zeitschr., X (1909), 308. 
 
 3 Ibid., XI (1910), 619. 
 
 4 This paper was published in abstract in Phys. Rev., XXX (1909), 
 560, and Phil. Mag., XIX (1910), 209. 
 
:6o THE ELECTRON 
 
 determined. 1 In the following month (May, 1910) 
 Ehrenhaft, 2 having seen that a vertical condenser 
 arrangement made possible, as shown theoretically and 
 experimentally in the 1909 papers mentioned above, the 
 independent determination of the charge on each indi- 
 vidual particle, read the first paper in which he had used 
 this arrangement in place of the De Broglie arrange- 
 ment which he had used theretofore. He reported re- 
 sults identical in all essential particulars with those 
 which I had published on water drops the year before, 
 save that where I obtained consistent and simple multiple 
 relations between charges carried by different particles 
 he found no such consistency in these relations. The 
 absolute values of these charges obtained on the as- 
 sumption of Stokes's Law fluctuated about values con- 
 siderably lower than 4.6Xio~ 10 . Instead, however, of 
 throwing the burden upon Stokes's Law or upon wrong 
 assumptions as to the density of his particles, he re- 
 marked in a footnote that Cunningham's theoretical cor- 
 rection to Stokes's Law, 3 which he (Ehrenhaft) had just 
 seen, would make his values come still lower, and hence 
 that no failure of Stokes's Law could be responsible 
 for his low values. He considered his results therefore 
 as opposed to the atomic theory of electricity altogether, 
 and in any case as proving the existence of charges much 
 smaller than that of the electron. 4 
 
 1 This paper was published in abstract in Phys. Rev., XXXI (1910), 
 92; Science, XXXII (1910), 436; Phys. Zeilschr., XI (1910), 1097. 
 
 2 Wien. Ber., CXIX (1910), II, 809. This publication was appar- 
 ently not issued before December, 1910, for it is not noted in Naturae 
 Novitales before this date. 
 
 3 Proc. Roy. Soc., LXXXIII (1910), 360. 
 
 " These results were presented and discussed at great length in the 
 fall of 1910; see Phys. Zeilschr., XI (1910), 619, 940. 
 
THE EXISTENCE OF A SUB-ELECTRON? 161 
 
 The apparent contradiction between these results and 
 mine was explained when Mr. Fletcher and myself 
 showed 1 experimentally that Brownian movements pro- 
 duced just such apparent fluctuations as Ehrenhaft 
 observed when the e is computed, as had been done in 
 his work, from one single observation of a speed under 
 gravity and a corresponding one in an electric field. We 
 further showed that the fact that his values fluctuated 
 about too low an average value meant simply that his 
 particles of gold, silver, and mercury were less dense 
 because of surface impurities, oxides or the like, than he 
 had assumed. The correctness of this explanation 
 would be well-nigh demonstrated if the values of Ne 
 computed by equations (28) or (29) in chap, vii from a 
 large number of observations on Brownian movements 
 always came out as in electrolysis, for in these equations 
 no assumption has to be made as to the density of the 
 particles. As a matter of fact, all of the nine particles 
 studied by us and computed by Mr. Fletcher 2 showed 
 the correct value of Ne, while only six of them as com- 
 puted by me fell on, or close to, the line which pictures 
 the law of fall of an oil drop through air (Fig. 5, p. 104). 
 This last fact was not published in 1911 because it took 
 me until 1913 to determine with certainty the complete 
 law of fall of a droplet through air; in other words, to 
 extend curves of the sort given in Fig. 5 to as large 
 
 values of - as correspond to particles small enough to 
 
 show large Brownian movements. As soon as I had 
 done this I computed all the nine drops which gave cor- 
 
 1 Phys. Zeitschr., XII (1911), 161; Phys. Rev., XXXII (1911), 394- 
 2 Le Radium, VIII (1911), 279; Phys. Rev., XXXIII (1911), 107. 
 
162 THE ELECTRON 
 
 rect values of Ne and found that two of them fell way 
 below the line, one more fell somewhat below, while one 
 fell considerably above it. This meant obviously that 
 these four particles were not spheres of oil alone, two of 
 them falling much too slowly to be so constituted and 
 one considerably too rapidly. There was nothing at all 
 surprising about this result, since I had explained fully 
 in my first paper on oil drops 1 that until I had taken 
 great precaution to obtain dust-free air "the values of e l 
 came out differently, even for drops showing the same 
 velocity under gravity." In the Brownian-movement 
 work no such precautions to obtain dust-free air had 
 been taken because we wished to test the general validity 
 of equations (28) and (29) . That we actually used in this 
 test two particles which had a mean density very much 
 smaller than that of oil and one which was considerably 
 too heavy, was fortunate since it indicated that our 
 result was indeed independent of the material used. 
 
 It is worthy of remark that in general, even with oil 
 drops, almost all of those behaving abnormally fall too 
 slowly, that is, they fall below the line of Fig. 5 and 
 only rarely does one fall above it. This is because the 
 dust particles which one is likely to observe, that is, those 
 which remain long in suspension in the air, are either in 
 general lighter than oil or else expose more surface and 
 hence act as though they were lighter. When one works 
 with particles made of dense metals this behavior will 
 be still more marked, since all surface impurities of what- 
 ever sort will diminish the density. The possibility, 
 however, of freeing oil-drop experiments from all such 
 sources of error is shown by the fact that although during 
 
 ' Phys. Rev., XXXIII (1911), 366, 367. 
 
THE EXISTENCE OF A SUB-ELECTRON? 163 
 
 the past year I have studied altogether as many as three 
 hundred drops, there has not been a single case that I 
 can recall which did not fall within less than i per cent 
 of the line of Fig. 5. It will be shown, too, in this 
 chapter, that in spite of the failure of the Vienna experi- 
 menters, it is possible to obtain mercury drops which 
 behave, even as to law of fall, in practically all cases with 
 perfect consistency and normality. 
 
 When E. Weiss in Prag and K. Przibram in the 
 Vienna laboratory itself, as explained in chap, vii, had 
 found that Ne for all the substances which they worked 
 with, including silver particles like those used by 
 Ehrenhaft, gave about the right value of .Ne, although 
 yielding much too low values of e when the latter was 
 computed from the law of fall of silver particles, the 
 scientific world practically universally accepted our 
 explanation of Ehrenhaft's results and ceased to concern 
 itself with the idea of a sub-electron. 1 
 
 In 1914 and 1915, however, Professor Ehrenhaft 2 and 
 two of his pupils, F. Zerner 3 and D. Konstantinowsky, 4 
 published new evidence for the existence of such a sub- 
 electron. This evidence appears to be but little under- 
 stood and therefore calls for some comment. These 
 authors make three contentions. The first is essentially 
 that they have now determined Ne for their particles by 
 equation (29) ; and although in many instances it comes 
 .out as in electrolysis, in some instances it comes out from 
 
 1 See R. Pohl, Jahrbuch der Radioactimtat und Elektronik, VIII 
 (1912), 431. 
 
 8 Wien. Sitzungsber., CXXIII (1914), 53-155; Ann. d. Pkys., XLIV 
 (1914), 657. 
 
 a Phys. Zeitschr., XVI (1915), 10. 
 
 * Ann. d. Phys., XL VI (1915), 261. 
 
164 THE ELECTRON 
 
 20 per cent to 50 per cent too low, while in a few cases 
 it is as low as one-fourth or one-fifth of the electrolytic 
 value. Their procedure is in general to publish, not the 
 value of Ne, but, instead, the value of e obtained from 
 Ne by inserting Perrin's value of N (joX io 22 ) in (29) and 
 then solving for e. This is their method of determining 
 e "from the Brownian movements.' 7 
 
 Their second contention is the same as that originally 
 advanced, namely, that, in some instances, when e is 
 determined with the aid of Stokes 's Law of fall (equa- 
 tion 12, p. 89), even when Cunningham's correction or 
 my own (equation 15, p. 99) is employed, the result 
 comes out very much lower than 4.77Xio~ 10 . Their 
 third claim is that the value of e, determined as just 
 explained from the Brownian movements, is in general 
 higher than the value computed from the law of fall, 
 and that the departures become greater and greater the 
 smaller the particle. These observers conclude therefore 
 that we at the Ryerson Laboratory failed to detect sub- 
 electrons because our droplets were too big to be able to 
 reveal their existence. The minuter particles which they 
 study, however, seem to them to bring these sub- 
 electrons to light. In other words, they think the value 
 of the smallest charge which can be caught from the air 
 actually is a function of the radius of the drop on which 
 it is caught, being smaller for small drops than for large 
 ones. 
 
 Ehrenhaft and Zerner even analyze our reports on oil 
 droplets and find that these also show in certain instances 
 indications of sub-electrons, for they yield in these 
 observers' hands too low values of e, whether computed 
 from the Brownian movements or from the law of fall. 
 
THE EXISTENCE OF A SUB-ELECTRON ? 165 
 
 When the computations are made in the latter way e is 
 found, according to them, to decrease with decreasing 
 radius, as is the case in their experiments on particles of 
 mercury and gold. 
 
 III. CAUSES OF THE DISCREPANCIES 
 
 Now, the single low value of Ne which these authors 
 find in the oil-drop work is obtained by computing Ne 
 from some twenty-five observations on the times of fall, 
 and an equal number on the times of rise, of a particle 
 which, before we had made any Ne computations at all, 
 we reported upon 1 for the sake of showing that the 
 Brownian movements would produce just such fluctua- 
 tions as Ehrenhaft had observed when the conditions 
 were those under which he worked. When I compute 
 Ne by equation (29), using merely the twenty-five times 
 of fall, I find the value of Ne comes out 26 per cent low, 
 just as Zerner finds it to do. If, however, I omit the 
 first reading it comes out but 1 1 per cent low. In other 
 words, the omission of one single reading changes the 
 result by 15 per cent. Furthermore, Fletcher 2 has just 
 shown that these same data, though treated entirely 
 legitimately, but with a slightly different grouping than 
 that used by Zerner, can be made to yield exactly the 
 right value of Ne. This brings out clearly the futility 
 of attempting to test a statistical theorem by so few 
 observations as twenty-five, which is nevertheless more 
 than Ehrenhaft usually uses on his drops. Furthermore, 
 I shall presently show that unless one observes under 
 carefully chosen conditions, his own errors of observation 
 
 1 Phys. Zeitschr., XII (1911), 162. 
 
 2 Ibid., XVI (1915), 316. 
 
1 66 THE ELECTRON 
 
 and the slow evaporation of the drop tend to make Ne 
 obtained from equation (29) come out too low, and these 
 errors may easily be enough to vitiate the result entirely. 
 There is, then, not the slightest indication in any work 
 which we have thus far done on oil drops that Ne comes 
 out too small. 
 
 Next consider the apparent variation in e when it is 
 computed from the law of fall. Zerner computes e from 
 my law of fall in the case of the nine drops published by 
 Fletcher, in which Ne came out as in electrolysis, and 
 finds that one of them yields e = 6.66Xio"~ 10 , one 
 tf=3.97Xio~ 10 , one e=i.32Xio~ 10 , one e=i.'jXio~ 10 , 
 while the other five yield about the right value, namely, 
 4. 8X io~ 10 . In other words (as stated on p. 162 above), 
 five of these drops fall exactly on my curve (Fig. 5), one 
 falls somewhat above it, one somewhat below, while two 
 are entirely off and very much too low. These two, there- 
 fore, I concluded were not oil at all, but dust particles. 
 Since Zerner computes the radius from the rate of fall, 
 these two dust particles which fall much too slowly, and 
 therefore yield too low values of e, must, of course, yield 
 correspondingly low values of a. Since they are found 
 to do so, Zerner concludes that our oil drops, as well as 
 Ehrenhaft's mercury particles, yield decreasing values of 
 e with decreasing radius. His own tabulation does not 
 show this. It merely shows three erratic values of e, 
 two of which are very low and one rather high. But a 
 glance at all the other data which I have published on 
 oil drops shows the complete falsity of this position, 1 for 
 these data show that after I had eliminated dust all of my 
 particles yielded exactly the same value of li e" whatever their 
 
 ' Phys. Rev., II (1913), 138- 
 
THE EXISTENCE OF A SUB-ELECTRON? 167 
 
 size. 1 The only possible interpretation then which could 
 be put on these two particles which yielded correct values 
 of Ne, but too slow rates of fall, was that which I put 
 upon them, namely, that they were not spheres of oil. 
 
 As to the Vienna data on mercury and gold, Ehren- 
 haft publishes, all told, data on just sixteen particles and 
 takes for his Brownian-movement calculations on the 
 average fifteen times of fall and fifteen of rise on each, the 
 smallest number being 6 and the largest 2J. He then com- 
 putes his statistical average (A/) 2 from observations of 
 this sort. Next he assumes Perrin's value of N, namely, 
 yoXio 22 , which corresponds to = 4.1, and obtains 
 instead by the Brownian-movement method, i.e., the 
 Ne method, the following values of e, the exponential 
 term being omitted for the sake of brevity: 1.43, 2. 13, 
 i . 38, 3 . 04, 3 . 5, 6 . 92, 4 . 42, 3 . 28, .84. Barring the first 
 three and the last of these, the mean value of e is just 
 about what it should be, namely, 4.22 instead of 4. i. 
 Further, the first three particles are the heaviest ones, 
 the first one falling between his cross-hairs in 3 . 6 seconds, 
 and its fluctuations in time of fall are from 3.2 to 3.85 
 seconds, that is, three-tenths of a second on either side 
 of the mean value. Now, these fluctuations are only 
 slightly greater than those which the average observer will 
 make in timing the passage of a uniformly moving body 
 across equally spaced cross-hairs. This means that in 
 these observations two nearly equally potent causes were 
 operating to produce fluctuations. The observed A/'s 
 were, of course, then, larger than those due to Brownian 
 movements alone, and might easily, with but a few 
 observations, be two or three times as Jarge. Since 
 
 1 See Phys. Rev., II (1913), 134-35- 
 
i68 THE ELECTRON 
 
 (A/) 2 appears in the denominator of equation (29), it will 
 be seen at once that because of the observer's timing 
 errors a series of observed A/'s will always tend to be 
 larger than the A/ due to Brownian movements alone, 
 and hence that the Brownian-movement method always 
 tends to yield too low a value of Ne, and accordingly 
 too low a value of e. It is only when the observer's mean 
 error is wholly negligible in comparison with the Brownian- 
 movement fluctuations that this method will not yield too 
 low a value of e. The overlooking of this fact is, in my 
 judgment, one of the causes of the low values of e 
 recorded by Ehrenhaft. 
 
 Again, in the original work on mercury droplets 
 which I produced both by atomizing liquid mercury and 
 by condensing the vapor from boiling mercury, 1 1 noticed 
 that such droplets evaporated for a time even more 
 rapidly than oil, and other observers who have since 
 worked with mercury have reported the same behavior. 2 
 The amount of this effect may be judged from the fact 
 that one particular droplet of mercury recently under 
 observation in this laboratory had at first a speed of 
 i cm. in 20 seconds, which changed in half an hour to 
 i cm. in 56 seconds. The slow cessation, however, of 
 this evaporation indicates that the drop slowly becomes 
 coated with some sort of protecting film. Now, if any 
 evaporation whatever is going on while successive times 
 of fall are being observed and as a matter of fact 
 changes due to evaporation or condensation are always 
 taking place to some extent the apparent (A/) 2 will be 
 larger than that due to Brownian movements, even 
 
 ' Phys. Rev., XXXII (1911), 389. 
 
 2 See Schidlof et Karpowicz, Comples rendus, CLVIII (1914), 1912. 
 
THE EXISTENCE OF A SUB-ELECTRON ? 169 
 
 though these movements are large enough to prevent the 
 observer from noticing, in taking twenty or thirty read- 
 ings, that the drop is continually changing. These 
 changes combined with the fluctuations in t due to the 
 observer's error are sufficient, I think, to explain all of the 
 low values of e obtained by Ehrenhaft by the Brownian- 
 movement method. Indeed, I have myself repeatedly 
 found Ne coming out less than half of its proper value 
 until I corrected for the evaporation of the drop, and this 
 was true when the evaporation was so slow that its rate 
 of fall changed but i or 2 per cent in a half-hour. But 
 it is not merely evaporation which introduces an error 
 of this sort. The running down of the batteries, the 
 drifting of the drop out of focus, or anything which 
 causes changes in the times of passage across the equally 
 spaced cross-hairs tends to decrease the apparent value 
 of Ne. There is, then, so far as I can see, no evidence 
 at all in any of the data published to date that the 
 Brownian-movement method actually does yield too 
 low a value of e, and very much positive evidence that 
 it does not was given in the preceding chapter. 
 
 Konstantinowsky's data are very much like Ehren- 
 haft's in the possibility which they permit of too low 
 values of Ne due to observational error, evaporation, and 
 drifting out of focus, but they emphasize one further 
 source of error which apparently leads the author en- 
 tirely astray. He publishes Ne observations on only n 
 particles, 1 five of which yield values of e between 3 . 3 and 
 4.2Xio~ 10 , or roughly correct values when the fact is 
 considered that his chosen value of N is yoXio 22 ; three 
 of the others yield about 2Xio~ 10 , two more about 
 
 1 Ann. d. Phys., XL VI (1915), 292. 
 
i yo THE ELECTRON 
 
 i X io~ 10 , while one yields . 5 X io~ 10 . His determination 
 of the series of multiple relationships by which he gets 
 the greatest common divisor (fli+fl 2 ) (see equation (29) ) is 
 however so unreliable that he raises a question as to 
 whether there is any greatest common divisor at all, in 
 spite of the fact that all other observers, a dozen of us 
 now at least, including Ehrenhaft himself, now find these 
 exact multiple relations invariably to hold. But an 
 uncertainty in ( x +%) (see equation (29) ) means an equal 
 uncertainty in Ne. Konstantinowsky's very low values 
 of Ne (one-tenth of the normal value) are, then, in my 
 judgment, due to the fact that he chooses the wrong 
 value of (fli+z^o- But with apparatus of his dimensions 
 and particles as minute as he uses it is not at all sur- 
 prising that he cannot find the greatest common divisor 
 of the series of speeds. // would take more observations 
 than he usually makes on a particle to locate it with cer- 
 tainty where the Brownian movements are as large as those 
 which his particles ought to show, and where the field 
 strengths are as small as those which he uses (nine volts 
 only in some cases on condenser plates 2 mm. apart), and 
 hence where the drops are relatively heavily charged. 
 
 That e and a computed from the law of fall become 
 farther and farther removed from the values of e and a 
 computed from the Brownian movements, the smaller 
 these particles appear to be, is just what would be 
 expected if the particles under consideration have surface 
 impurities or non-spherical shapes or else are not mer- 
 cury at all. Again, the fact that these data are all taken 
 when the observers are working with the exceedingly 
 dense substances, mercury and gold, volatilized in an 
 electric arc, and when, therefore, anything not mercury or 
 
THE EXISTENCE OF A SUB-ELECTRON? 171 
 
 gold, but assumed to be, would yield very low values of 
 e and a, is in itself a very suspicious circumstance. The 
 further fact that Ehrenhaft implies that normal values 
 of e very frequently appear in his work, 1 while these 
 low erratic drops represent only a part of the data taken, 
 is suggestive. When one considers, too, that in place of 
 the beautiful consistency and duplicability shown in the 
 oil-drop work, Ehrenhaft and his pupils never publish 
 data on any two particles which yield the same value 
 of e, but instead find only irregularities and erratic 
 behavior, 2 just as they would expect to do with non- 
 uniform particles, or with particles having dust specks 
 attached to them, one wonders why any explanation 
 other than the foreign-material one, which explains all 
 the difficulties, has ever been thought of. As a matter 
 of fact, in our work with mercury droplets at the Ryerson 
 Laboratory, we have found that the initial rapid evapo- 
 ration gradually ceases, just as though the droplets had. 
 become coated with some foreign film which prevents 
 further loss. Schidlof and Karpowicz find that the 
 behavior of their mercury drops as regards evaporation 
 is the same in the purest nitrogen as it is in air. Ehren- 
 haft himself, in speaking of the Brownian movements of 
 his metal particles, comments on the fact that they seem 
 at first to show large movements which grow smaller with 
 
 1 " Die bei grosseren Partikeln unter gewissen Umstanden bei 
 gleicher Art der Erzeugung haufig wiederkehrenden hoheren Qu'anten 
 waren dann etwa als stabilere raumliche Gleichgewichtsverteilungen 
 dieser Sub-electron anzusehen, die sich unter gewissen Umstanden 
 ergeben." Wien. Ber., CXXIII, 59. 
 
 2 Their whole case is summarized in the tables in Ann. d. Phys., 
 XLIV (1914), 693, and XLVI (1915), 292, and it is recommended that 
 all interested in this discussion take the time to glance at the data on 
 these pages, for the data themselves are so erratic as to render dis- 
 cussion needless. 
 
172 THE ELECTRON 
 
 time. 1 This is just what would happen if the radius were 
 increased by the growth of a foreign film. 
 
 Now what does Ehrenhaft say to these very obvious 
 suggestions as to the cause of his troubles ? Merely that 
 he has avoided all oxygen, and hence that an oxide film is 
 impossible. Yet he makes his metal particle by striking 
 an electric arc between metal electrodes. This, as everyone 
 knows, brings out all sorts of occluded gases. Besides, 
 chemical activity in the electric arc is tremendously 
 intense, so that there is opportunity for the formation of 
 all sorts of higher nitrites, the existence of which in the 
 gases coming from electric arcs has many times actually 
 been proved. Ehrenhaft says further that he photographs 
 big mercury droplets and finds them spherical and free 
 from oxides. But the fact that some drops are pure mer- 
 cury is no reason for assuming that all of them are, and it 
 is only the data on those which are not which he publishes. 
 Further, because big drops which he can see and measure 
 are of mercury is no justification at all for assuming that 
 sub-microscopic particles are necessarily also spheres of 
 pure mercury. In a word, Ehrenhaft's tests as to 
 sphericity and purity are all absolutely worthless as 
 applied to the particles in question, which according to 
 him have radii of .the order io~ 6 cm. a figure a hundred 
 times below the limit of sharp resolution. 
 
 IV. THE BEARING OF THE VIENNA WORK ON THE QUES- 
 TION OF THE EXISTENCE OF A SUB-ELECTRON 
 
 But let us suppose that these observers do actually 
 work with particles of pure mercury and gold, as they 
 
 1 "Wie ich in meinen friiheren Publikationen erwahnt habe zeigen 
 die ultramikroskopischen Metallpartikel, unmittelbar nach der Erzeu- 
 gung beobachtet eine viel lebhaftere Brownsche Bewegung als nach 
 einer halben Stunde." Phys. Zeiischr., XII, 98. 
 
THE EXISTENCE OF A SUB-ELECTRON? 173 
 
 think they do, and that the observational and evapo ra- 
 tional errors do not account for the low values of Ne. 
 Then what conclusion could legitimately be drawn from 
 their data? Merely this and nothing more, that 
 (i) Einstein's Brownian-movement equation is not uni- 
 versally applicable, and (2) that the law of motion of 
 their very minute charged particles through air is not 
 yet fully known. So long as they find exact multiple 
 relationships, as Ehrenhaft now does, between the 
 charges carried by a given partible when its charge is 
 changed by the capture of ions or the direct loss of elec- 
 trons, the charges on these ions must be the same as the 
 ionic charges which I have accurately and consistently 
 measured and found equal to 4.77Xio~ 10 electrostatic 
 units; for they, in their experiments, capture exactly the 
 same sort of ions, produced in exactly the same way as 
 those which I captured and measured in my experiments. 
 That these same ions have one sort of a charge when 
 captured by a big drop and another sort when captured 
 by a little drop is obviously absurd. // they are not the 
 same ions which are caught, then in order to reconcile the 
 results with the existence of the exact multiple relationship 
 found by Ehrenhaft as well as ourselves, it would be neces- 
 sary to assume that there exist in the air an infinite number 
 of different kinds of ionic charges corresponding to the 
 infinite number of possible radii of drops, and that when 
 a powerful electric field drives all of these ions toward a 
 given drop this drop selects in each instance just the charge 
 which corresponds to its particular radius. Such an 
 assumption is not only too grotesque for serious con- 
 sideration, but it is directly contradicted by my experi- 
 ments, for I have repeatedly pointed out that with a 
 
174- THE ELECTRON 
 
 given value of - I obtain exactly the same value of e ly 
 whether I work with big drops or with little ones. 
 
 V. NEW PROOF OF THE CONSTANCY OF 6 
 
 For the sake of subjecting the constancy of c to the 
 most searching test, I have recently made new measure- 
 ments of the same kind as those heretofore reported, but 
 using now a range of sizes which overlaps that in which 
 Ehrenhaft works. I have also varied through wide 
 limits the nature and^ density of both the gas and the 
 drops. Fig. 13 (I) contains new oil-drop data taken in air ; 
 Fig. 13 (II) similar data taken in hydrogen. The radii of 
 these drops, computed by the very exact method given 
 in the Physical Review, 1 vary tenfold, namely, from 
 .000025 cm. to .00023 cm. Ehrenhaft's range is from 
 .000008 cm. to .000025 cm. It will be seen that these 
 drops fall in every instance on the lines of Fig. 13, 
 I and II, and hence that they all yield exactly the same 
 value of e l , namely, 6i.iXio~ 8 . The details of the 
 measurements, which are just like those previously given, 
 will be entirely omitted, but sample data on four of the 
 drops in hydrogen are given in Tables I, II, III, and IV, 
 above. There is here not a trace of an indication that the 
 value of "e" becomes smaller as "a" decreases. The points 
 on these two curves represent consecutive series of obser- 
 vations, not a single drop being omitted in the case of 
 either the air or the hydrogen. This shows the complete 
 uniformity and consistency which we have succeeded in 
 obtaining in the work with oil drops. 
 
 That mercury drops show a similar behavior was 
 somewhat imperfectly shown in the original observations 
 
 'II (1913), 117. 
 
THE EXISTENCE OF A SUB-ELECTRON ? 175 
 
176 THE ELECTRON 
 
 which I published on mercury. 1 I have since fully con- 
 firmed the conclusions there reached. That mercury 
 drops can with suitable precautions be made to behave 
 practically as consistently as oil is shown in Fig. 13 (III), 
 which represents data obtained by blowing into the 
 observing chamber above the pinhole in the upper plate a 
 cloud of mercury droplets formed by the condensation 
 of the vapor arising from boiling mercury. These results 
 have been obtained in the Ryerson Laboratory with 
 my apparatus by Mr. John B. Derieux. Since the 
 pressure was here always atmospheric, the drops 
 progress in the order of size from left to right, the 
 largest having a diameter about three times that of 
 the smallest, the radius of which is .00003244 cm. 
 The original data may be found in the Physical 
 Review, December, 1916. In Fig. 13 (IV) is found 
 precisely similar data taken with my apparatus by 
 Dr. J. Y. Lee on solid spheres of shellac falling 
 in air. 2 
 
 These results establish with absolute collusiveness the 
 correctness of the assertion that the apparent value of the 
 electron is not in general a function of the gas in which the 
 par tide falls, of the materials used, or of the radius of the drop 
 on which it is caught, even when that drop is of mercury, 
 and even when it is as small as some of those with which 
 Ehrenhaft obtained his erratic results. If it appears to 
 
 l Phys. Rev., CCC (1911), 389-90. 
 
 a The results shown in Fig. 13 do not lay claim to the precision 
 reached in those recorded in Table X and Fig. 10. No elaborate pre- 
 cautions were here taken in the calibration of the Hipp chronoscope and 
 the voltmeter, and it is due to slight errors discovered later in these 
 calibrations that the slope of line I in Fig. 13 is not quite in agreement 
 with the slope in Fig. 10. 
 
THE EXISTENCE OF A SUB -ELECTRON ? 177 
 
 be so with his drops, the cause cannot possibly be found 
 in actual fluctuations in the charge of the electron with- 
 out denying completely the validity df my results. But 
 these results have now been checked, in their essential 
 aspects, by scores of observers, including Professor 
 Ehrenhaft himself. Furthermore, it is not my results 
 alone with which Ehrenhaft 's contention clashes. The 
 latter is at variance also with all experiments like those 
 of Rutherford and Geiger and Regener on the measure- 
 ment -of the charges carried by a- and /3-particles, for 
 these are infinitely smaller than any particles used by 
 Ehrenhaft; and if, as he contends, the value of the unit 
 out of which a charge is built up is smaller and smaller 
 the smaller the capacity of the body on which it is found, 
 then these a-particle charges ought to be extraordinarily 
 minute in comparison with the charges on our oil drops. 
 Instead of this, the charge on the a-particle comes out 
 exactly twice the charge which I measure in my oil-drop 
 experiments. 
 
 While then it would not be in keeping with the spirit 
 or with the method of modern science to make any dog- 
 matic assertion about the existence or non-existence of a 
 sub-electron, it can be asserted with entire confidence 
 that there is not in Ehrenhaft's experiments a scrap of 
 evidence for the existence of charges smaller than the 
 electron. If all of his assumptions as to the nature of 
 his particles are correct, then his experiments mean 
 simply that Einstein's Brownian-movement equation is 
 not of universal validity and that the law of motion of 
 minute charged particles is quite different from that 
 which he has assumed. It is very unlikely that either 
 of these results can be drawn from his experiments, for 
 
178 THE ELECTRON 
 
 Nordlund 1 and Westgren 2 have apparently verified the 
 Einstein equation in liquids with very much smaller par- 
 ticles than Ehrenhaft uses; and, on the other hand, while 
 I have worked with particles as small as 2X io~ s cm. and 
 
 with values of - as large as 135, which is very much 
 
 larger than any which appear in the work of Ehrenhaft 
 and his pupils, I have thus far found no evidence of a 
 law of motion essentially different from that which I 
 published in 1913. 
 
 There has then appeared up to the present time no evi- 
 dence whatever of the existence of a sub-electron. 
 
 1 Zeit.fiir Phys. Chem., LXXXVII (1914), 40. 
 
 2 Inaugural Dissertation von Arne Westgren, Untersuchungen uber 
 Brownsche Bewegung, Stockholm, 1915. 
 
CHAPTER IX 
 THE STRUCTURE OF THE ATOM 
 
 We have shown in the preceding chapters how within 
 the last two decades there has been discovered beneath 
 the nineteenth-century world of molecules and atoms a 
 wholly new world of electrons, the very existence of 
 which was undreamed of twenty years ago. We have 
 seen that these electrons, since they can be detached by 
 X-rays from all kinds of neutral atoms, must be con- 
 stitu tents of all atoms. Whether or not they are the sole 
 constituents we have thus far made no attempt to deter- 
 mine. We have concerned ourselves with studying the 
 properties of these electrons themselves and have 
 found that they are of two kinds, negative and positive, 
 which are, however, exactly alike in strength of charge 
 but wholly different in inertia or mass, the negative being 
 commonly associated with a mass which is but 1/1,845 
 of that of the lightest known atom, that of hydrogen, 
 while the positive appears never to be associated with 
 a mass smaller than that of the hydrogen atom. We 
 have found how to isolate and measure accurately the 
 electronic charge and have found that this was the key 
 which unlocked the door to many another otherwise 
 inaccessible physical magnitude. It is the purpose of 
 this chapter to consider certain other fields of exact 
 knowledge which have been opened up through the 
 measurement of the electron, and in particular to discuss 
 what the physicist, as he has peered with his newly dis- 
 covered agencies, X-rays, radioactivity, ultra-violet 
 
 179 
 
iSo THE ELECTRON 
 
 light, etc., into the insides of atoms, has been able to 
 discover regarding the numbers and sizes and relative 
 positions of these electronic constituents, and to show 
 how far he has gone in answering the question as to 
 whether the electrons are the sole building-stones of 
 the atoms. 
 
 I. THE SIZES OF ATOMS 
 
 One of the results of the measurement of the electronic 
 charge was to make it possible to find the quantity which 
 is called the diameter of an atom with a definiteness and 
 precision theretofore altogether unattained. 
 
 It was shown in chap, v that the determination of e 
 gave us at once a knowledge of the exact number of 
 molecules in a cubic centimeter of a gas. Before this 
 was known we had fairly satisfactory information as to 
 the relative diameters of different molecules, for we 
 have known for a hundred years that different gases 
 when at the same temperature and pressure possess the 
 same number of molecules per cubic centimeter (Avo- 
 gadro's rule). From this it is at once evident that, as 
 the molecules of gases eternally dart hither and thither 
 and ricochet against one another and the walls of the 
 containing vessel, the average distance through which 
 one of them will go between collisions with its neighbors 
 will depend upon how big it is. The larger the diameter 
 the less will be the mean distance between collisions a 
 quantity which is technically called "the mean free path." 
 Indeed, it is not difficult to see that in different gases the 
 mean free path / is an inverse measure of the molecular 
 cross-section. The exact relation is easily deduced (see 
 Appendix E). It is 
 
 ..(31) 
 
THE STRUCTURE OF THE ATOM 181 
 
 in which d is the molecular diameter and n is the number 
 of molecules per cubic centimeter of the gas. Now, we 
 have long had methods of measuring /, for it is upon 
 this that the coefficient of viscosity of the gas largely 
 depends. When, therefore, we have measured the 
 viscosities of different gases we can compute the corre- 
 sponding Ts, and then from equation (31) the relative 
 diameters d, since n is the same for all gases at the same 
 temperature and pressure. But the absolute value of 
 d can be found only after the absolute value of n is 
 known. If we insert in equation (31) the value of n 
 found from e by the method presented in chap, v, it is 
 found that the average diameter of the atom of the 
 monatomic gas helium is 2Xio~ 8 cm., that of the dia- 
 tomic hydrogen molecule is a trifle more, while the diam- 
 eters of the molecules of the diatomic gases, oxygen and 
 nitrogen, are 50 per cent larger. 1 This would make the 
 diameter of a single atom of hydrogen a trifle smaller, 
 and that of a single atom of oxygen or nitrogen a trifle 
 larger than that of helium. By the average molecular 
 diameter we mean the average distance to which the 
 centers of two molecules approach one another in such 
 impacts as are continually occurring in connection with 
 the motions of thermal agitation of gas molecules this 
 and nothing more. 
 
 As will presently appear, the reason that two mole- 
 cules thus rebound from one another when in their 
 motion of thermal agitation their centers of gravity ap- 
 proach to a distance of about 2X io" 8 cm. is presumably 
 that the atom is a system with negative electrons in its 
 outer regions. When these negative electrons in two 
 
 ' R. A. Millikan, Phys. Rev., XXXII (1911), 397. 
 
182 THE ELECTRON 
 
 different systems which are coming into collision ap- 
 proach to about this distance, the repulsions between 
 these similarly charged bodies begin to be felt, although 
 at a distance the atoms are forceless. With decreasing 
 distance this repulsion increases very rapidly until it 
 becomes so great as to overcome the inertias of the 
 systems and drive them asunder. 
 
 II. THE RADIUS OF THE ELECTRON FROM THE ELECTRO- 
 MAGNETIC THEORY OF THE ORIGIN OF MASS 
 
 The first estimates of the volume occupied by a 
 single one of the electronic constituents of an atom were 
 obtained from the electromagnetic theory of the origin 
 of mass, and were therefore to a pretty large degree 
 speculative, but since these estimates are strikingly in 
 accord with results which follow from direct experiments 
 and are independent of any theory, and since, further, 
 they are of extraordinary philosophic as well as historic 
 interest, they will briefly be presented here. 
 
 Since Rowland proved that an electrically charged 
 body in motion is an electrical current the magnitude 
 of which is proportional to the speed of motion of the 
 charge, and since an electric current, by virtue of the 
 property called its self-induction, opposes any attempt 
 to increase or diminish its magnitude, it is clear that an 
 electrical charge, as such, possesses the property of 
 inertia. But inertia is the only invariable property 
 of matter. It is the quantitative measure of matter, 
 and matter quantitatively considered is called mass. It 
 is clear, then, theoretically, that an electrically charged 
 pith ball must possess more mass than the same pith 
 ball when uncharged. But when we compute how much 
 
THE STRUCTURE OF THE ATOM 183 
 
 the mass of a pith ball is increased by any charge which 
 we can actually get it to hold, we find that the increase 
 is so extraordinarily minute as to be 'hopelessly beyond 
 the possibility of experimental detection. However, 
 the method of making this computation, which was first 
 pointed out by Sir J. J. Thomson in i88i, x is of unques- 
 tioned validity, so that we may feel quite sure of the 
 correctness of the result. Further, when we combine 
 the discovery that an electric charge possesses the dis- 
 tinguishing property of matter, namely, inertia, with 
 the discovery that all electric charges are built up out 
 of electrical specks all alike in charge, we have made it 
 entirely legitimate to consider an electric current as the 
 passage of a definite, material, granular substance along 
 the conductor. In other words, the two entities, elec- 
 tricity and matter, which the nineteenth century tried 
 to keep distinct, bjegin to look like different aspects of 
 one and the same thing. 
 
 But, though we have thus justified the statement 
 that electricity is material, have we any evidence as yet 
 that all matter is electrical that is, that, all inertia is 
 of the same origin as that of an electrical charge ? The 
 answer is that we have evidence, but as yet no proof. 
 The theory that this is the case is still a speculation, 
 but one which rests upon certain very significant facts. 
 These facts are as follows: 
 
 If a pith ball is spherical and of radius a, then the 
 mass m due to a charge E spread uniformly over its sur- 
 face is given, as is shown in Appendix D by, 
 
 2E 2 
 
 m ~ a ; ( 3 2 ) 
 
 1 J. J. Thomson, Phil. Mag., XI (1881), 229. 
 
184 THE ELECTRON 
 
 The point of especial interest in this result is that the 
 mass is inversely proportional to the radius, so that the 
 smaller the sphere upon which we can condense a given 
 charge E the larger the mass of that charge. If, then, we 
 had any means of measuring the minute increase in mass 
 of a pith ball when we charge it electrically with a known 
 quantity of electricity E, we could compute from equation 
 (32) the size of this pith ball, even if we could not see 
 it or measure it in any other way. This is much the sort 
 of a position in which we find ourselves with respect to 
 the negative electron. We can measure its mass, and it is 
 found to be accurately 1/1,845 of that of the hydrogen 
 atom. We have measured accurately its charge and 
 hence can compute the radius a of the equivalent sphere, 
 that is, the sphere over which e would have to be uni- 
 formly distributed to have the observed mass, provided 
 we assume that the observed mass of the electron is all 
 due to its charge. 
 
 The justification for such an assumption is of two 
 kinds. First, since we have found that electrons are 
 constituents of all atoms and that mass is a property 
 of an electrical charge, it is of course in the interests 
 of simplicity to assume that all the mass of an atom is 
 due to its contained electrical charges, rather than that 
 there are two wholly different kinds of mass, one of 
 electrical origin and the other of some other sort of an 
 origin. Secondly, if the mass of a negative electron 
 is all of electrical origin, then we can show from electro- 
 magnetic theory that this mass ought to be independent 
 of the speed with which the electron may chance to be 
 moving unless that speed approaches close to the speed 
 of light. But from one-tenth the speed of light up to 
 
THE STRUCTURE OF THE ATOM 185 
 
 that speed the mass ought to vary with speed in a 
 definitely predictable way. 
 
 Now, it is a piece of rare good fortune for the testing 
 of this theory that radium actually does eject negative 
 electrons with speeds which can be accurately measured 
 and which do vary from three-tenths up to ninety-eight 
 hundredths of that of light. // is further one of the 
 capital discoveries of the twentieth century* that within 
 these limits the observed rate of variation of the mass 
 of the negative electron with speed agrees accurately with 
 the rate of variation computed on the assumption that this 
 mass is all of electrical origin. This leaves no room for a 
 mass of any other kind to be associated with the free 
 negative electron. Such is the experimental argument 
 for the electrical origin of mass. 
 
 Solving then equation (32) for a, we find that the 
 radius of the sphere over which the charge e of the 
 negative electron would have to be distributed to have 
 the observed mass is but 2X io~ 13 cm., or but one fifty- 
 thousandth of the radius of the atom (io~ 8 cm.). From 
 this point of view, then, the negative electron represents a 
 charge of electricity which is condensed into an exceed- 
 ingly minute volume. In fact, its radius cannot be 
 larger in comparison with the radius of the atom than 
 is the radius of the earth in comparison with the radius 
 of her orbit about the sun. 
 
 In the case of the positive electron there is no direct 
 experimental justification for the assumption that the 
 mass is also wholly of electrical origin, for we cannot 
 impart to the positive electrons speeds which approach 
 the speed of light, nor have we as yet found in nature 
 
 1 Bucherer, Annalen der Physik, XXVIII (1909), 513. 
 
i86 THE ELECTRON 
 
 any of them which are endowed with speeds greater than 
 about one-tenth that of light. But in view of the experi- 
 mental results obtained with the negative electron, the 
 carrying over of the same assumption to the positive elec- 
 tron is at least natural. Further, if this step be taken, 
 it is clear from equation (32), since m for the positive is 
 nearly two thousand times larger than m for the negative, 
 that a for the positive can be only 1/2,000 of what it is 
 for the negative. In other words, the size of the positive 
 electron would be to the size of the negative as a sphere 
 having a two-mile radius would be to the size of the 
 earth. From the standpoint; then, of the electromagnetic 
 theory of the origin of mass, the dimensions of the 
 negative and positive constituents of atoms in com- 
 parison with the dimensions of the atoms themselves are 
 like the dimensions of the planets and asteroids in com- 
 parison with the size of the solar system. All of these 
 computations, whatever their value, are rendered pos- 
 sible by the fact that e is now known. 
 
 Now we know from methods which have nothing to 
 do with the electromagnetic theory of the origin of 
 mass, that the excessive minuteness predicted by that 
 theory for both the positive and the negative constitu- 
 ents of atoms is in fact correct, though we have no evi- 
 dence as to whether the foregoing ratio is right. 
 
 III. DIRECT EXPERIMENTAL PROOF OF THE EXCESSIVE 
 
 MINUTENESS OF THE ELECTRONIC CONSTITUENTS 
 
 OF ATOMS 
 
 For more than ten years we have had direct experi- 
 mental proof 1 that the fastest of the a-particles, or 
 
 ' Bragg, Phil. Mag., VIII (1904), 719, 726; X (1905), 318; XI 
 (1906), 617. 
 
FIG. 14 
 
 FIG. 15 
 
 PHOTOGRAPHS OF THE TRACKS OF CI-PARTICLES 
 SHOOTING THROUGH AIR 
 
FIG. 16 
 
 FIG. 17 
 
 PHOTOGRAPHS OF THE TRACKS OF /S-PARTICLES 
 SHOOTING THROUGH AIR 
 
THE STRUCTURE OF THE ATOM 187 
 
 helium atoms, which are ejected by radium, shoot in 
 practically straight lines through as much as 7 cm. of 
 air at atmospheric pressure before being brought to rest. 
 Some a-par tides which have a range of 11.3 cm. have 
 just been found. 1 Figs. 14 and 15 show actual photo- 
 graphs of the tracks of such particles. We know too, 
 for the reasons given on p. 138, that these a-par tides do 
 not penetrate the air after the manner of a bullet, namely, 
 by pushing the molecules of air aside, but rather that 
 they actually shoot through all the molecules of air which 
 they encounter. The number of such passages through 
 molecules which an a-particle would have to make in 
 traversing seven centimeters of air would be about half 
 a million. 
 
 Further, the very rapid /3-particles, or negative 
 electrons, which are shot out by radium have been 
 known for a still longer time to shoot in straight lines 
 through much greater distances in air than 7 cm., and 
 even to pass practically undeflected through appreciable 
 thicknesses of glass or metal. 
 
 We saw in chap, vi that the tracks of both the a- and 
 the /3-particles through air could be photographed 
 because they ionize some of the molecules through which 
 they pass. These ions then have the property of con- 
 densing water vapor about themselves, so that water 
 droplets are formed which can be photographed by 
 virtue of the light which they reflect. Fig. 17 shows the 
 track of a very high-speed /3-ray. A little to the right of 
 the middle of the photograph a straight line can be 
 drawn from bottom to top which will pass through a 
 dozen or so of pairs of specks. These specks are the 
 
 1 Rutherford and Wood, Phil. Mag., XXXI (1916), 379. 
 
1 88 THE ELECTRON 
 
 water droplets formed about the ions which were pro- 
 duced at these points. Since we know the size of a 
 molecule and the number of molecules per cubic centi- 
 meter, we can compute, as in the case of the a-particle, 
 the number of molecules through which a /3-particle 
 must pass in going a given distance. The extraordinary 
 situation revealed by this photograph is that this par- 
 ticular particle shot through on an average as many as 
 10,000 atoms before it came near enough to an elec- 
 tronic constituent of any one of these atoms to detach 
 it from its system and form an ion. This shows con- 
 clusively that the electronic or other constituents of atoms 
 can occupy but an exceedingly small fraction of the space 
 inclosed within the atomic system. Practically the whole 
 of this space must be empty to an electron going with 
 this speed. 
 
 The left panel in the lower half of the plate (Fig. 16) 
 shows the track of a negative electron of much slower 
 speed, and it will be seen, first, that it ionizes much 
 more frequently, and, secondly, that instead of continu- 
 ing in a straight line it is deflected at certain points 
 from its original direction. The reason for both of these 
 facts can readily be seen from the considerations on 
 p. 138, which it may be worth while to extend to the case 
 in hand as follows. 
 
 If a new planet or other relatively small body were 
 to shoot with stupendous speed through our solar sys- 
 tem, the time which it spent within our system might 
 be so small that the force between it and the earth or 
 any other member of the solar system would not have 
 time either to deflect the stranger from its path or to 
 pull the earth out of its orbit. If the speed of the strange 
 
FIG. 18 
 
 FIG. 19 
 
 FIG. 20 
 
 PHOTOGRAPHS OF THE TRACKS OF /S-PARTICLES EJECTED 
 BY X-RAYS FROM MOLECULES OF AlR 
 
THE STRUCTURE OF THE ATOM 189 
 
 body were smaller, however, the effect would be more 
 disastrous both to the constituents of our solar system 
 and to the path of the strange body, for the latter 
 would then have a much better chance of pulling one 
 of the planets out of our solar system and also a 
 much better chance of being deflected from a straight 
 path itself. The slower a negative electron moves, 
 then, the more is it liable to deflection and the more 
 frequently does it ionize the molecules through which 
 it passes. 
 
 This conclusion finds beautiful experimental con- 
 firmation in the three panels of the plate opposite this 
 page, for the speed with which X-rays hurl out negative 
 electrons from atoms has long been known to be much 
 less than the speed of /3-rays from radium, and the zigzag 
 tracks in these photographs are the paths of these cor- 
 puscles. It will be seen that they bend much more often 
 and ionize much more frequently than do the rays shown 
 in Figs. 1 6 and 17. 
 
 But the study of the tracks of the a-particles (Figs. 14 
 and 15, opposite p. 186) is even more illuminating as 
 to the structure of the atom. For the a-particle, being 
 an atom of helium eight thousand times more massive 
 than a negative electron, could no more be deflected by 
 one of the latter in an atom through which it passes 
 than a cannon ball could be deflected by a pea.. Yet 
 Figs. 14 and 15 show that toward the end of its path 
 the a-particle does in general suffer several sudden 
 deflections. Such deflections could be produced only 
 by a very powerful center of force within the atom 
 whose mass is at least comparable with the mass of the 
 helium atom. 
 
THE ELECTRON 
 
 These sharp deflections, which occasionally amount 
 to as much as 150 to 180, lend the strongest of support 
 to the view that the atom consists of a heavy positively 
 charged nucleus about which are grouped enough elec- 
 trons to render the whole atom neutral. But the fact 
 that in these experiments the a-particle goes through 
 500,000 atoms without approaching near enough to this 
 central nucleus to suffer appreciable deflection more 
 than two or three times constitutes the most convincing 
 evidence that this central nucleus which holds the nega- 
 tive electrons within the atomic system occupies an 
 excessively minute volume, just as we computed from 
 the electromagnetic theory of the origin of mass that 
 the positive electron ought to do. Indeed, knowing as 
 he did by direct measurement the speed of the a-particle, 
 Rutherford, who is largely responsible for the nucleus- 
 atom theory, first computed, 1 with the aid of the inverse 
 square law, which we know to hold between charged 
 bodies of dimensions which are small compared with their 
 distances apart, how close the a-particle would approach 
 to the nucleus of a given atom like that of gold before 
 it would be turned back upon its course (see Appendix F). 
 The result was in the case of gold, one of the heaviest 
 atoms, about io~" cm., and in the case of hydrogen, the 
 lightest atom, about io" 13 cm. These are merely upper 
 limits for the dimensions of the nuclei. 
 
 However uncertain, then, we may feel about the 
 sizes of positive and negative electrons computed from 
 the electromagnetic theory of the origin of the mass, we 
 may regard it as fairly well established by such direct 
 experiments as these that the electronic constituents 
 
 ' Phil. Mag., XXI (1911), 669. 
 
THE STRUCTURE OF THE ATOM 191 
 
 of atoms are as small, in comparison with the dimensions 
 of the atomic systems, as are the sun and planets in 
 comparison with the dimensions of the solar system. 
 Indeed, when we reflect that we can shoot helium atoms 
 by the billion through a thin-walled highly evacuated 
 glass tube without leaving any holes behind, i.e., without 
 impairing in the slightest degree the vacuum or percep- 
 tibly weakening the glass, we see from this alone that 
 the atom itself must consist mostly of "hole"; in other 
 words, that an atom, like a solar system, must be an 
 exceedingly loose structure whose impenetrable portions 
 must be extraordinarily minute in comparison with the 
 penetrable portions. The notion that an atom can 
 appropriate to itself all the space within its boundaries 
 to the exclusion of all others is then altogether exploded 
 by these experiments. A particular atom can certainly 
 occupy the same space at the same time as any other 
 atom if it is only endowed with sufficient kinetic energy. 
 Such energies as correspond to the motions of thermal 
 agitation of molecules are not, however, sufficient to 
 enable one atom to penetrate the boundaries of another, 
 hence the seeming impenetrability of atoms in ordinary 
 experiments in mechanics. That there is, however, a 
 portion of the atom which is wholly impenetrable to the 
 alpha particles is definitely proved by experiments of 
 the sort we have been considering; for it occasionally 
 happens that an alpha particle hits this nucleus "head 
 on," and, when it does so, it is turned straight back 
 upon its course. As indicated above, the size of this 
 impenetrable portion, which may be defined as the size 
 of the nucleus, is in no case larger than i/ 10,000 the 
 diameter of the atom. 
 
iy2 THE ELECTRON 
 
 IV. THE NUMBER OF ELECTRONS IN AN ATOM 
 
 If it be considered as fairly conclusively established 
 by the experiments just described that an atom consists 
 of a heavy but very minute positively charged nucleus 
 which holds light negative electrons in some sort of a 
 configuration about it, then the number of negative 
 electrons outside the nucleus must be such as to have a 
 total charge equal to the free positive charge of the 
 nucleus, since otherwise the atom could not be neutral. 
 
 But the positive charge on the nucleus has been 
 approximately determined as follows: With the aid of 
 the knowledge, already obtained through the determina- 
 tion of e, of the exact number of atoms in a given weight 
 of a given substance, Sir Ernest Rutherford 1 first com- 
 puted the chance that a single helium atom in being 
 shot with a known speed through a sheet of gold foil 
 containing a known number of atoms per unit of area of 
 the sheet would suffer a deflection through a given angle. 
 This computation can easily be made in terms of the 
 known kinetic energy and charge of the a-particle, 
 the known number of atoms in the gold foil, and the 
 unknown charge on the nucleus of the gold atom (see 
 Appendix F). Geiger and Marsden 2 then actually 
 counted in Rutherford's laboratory, by means of the 
 scintillations produced on a zinc-sulphide screen, what 
 fraction of, say, a thousand a-particles, which were 
 shot normally into the gold foil, were deflected through 
 a given angle, and from this observed number and 
 Rutherford's theory they obtained the number of free 
 positive charges on the nucleus of the gold atom. 
 
 ' Phil. Mag., XXI (1911), 669-88. 
 
 'Ibid., XXV (1913), 604. 
 
THE STRUCTURE OF THE ATOM 193 
 
 Repeating the experiment and the computations 
 with foils made from a considerable number of other 
 metals, they found that in every case the number of free 
 positive charges on the atoms of different substances was 
 approximately equal to half its atomic weight. This 
 means that the aluminum atom, for example, has a 
 nucleus containing about thirteen free positive charges 
 and that the nucleus of the atom of gold contains in 
 the neighborhood of a hundred. This result Was in 
 excellent agreement with the conclusion reached inde- 
 pendently by Barkla 1 from experiments of a wholly 
 different kind, namely, experiments on the scattering 
 of X-rays. These indicated that the number of scatter- 
 ing centers in an atom that is, its number of free 
 negative electrons was equal to about half the atomic 
 weight. But this number must, of course, equal, the 
 number of free positive electrons in the nucleus. 
 
 v. MOSELEY'S REMARKABLE DISCOVERY 
 
 The foregoing result was only approximate. Indeed, 
 there was internal evidence in Geiger and Marsden's 
 work itself that a half was somewhat too high: The 
 answer has recently been made very definite and very 
 precise through the extraordinary work of a brilliant 
 young Englishman, Moseley, who, at the age of twenty- 
 seven, had accomplished as notable a piece of research 
 in physics as has appeared during the last fifty years. 
 Such a mind has recently fallen a victim to the most 
 ghastly crime in history, the present European war. He 
 was shot and killed instantly in the trenches in the 
 summer of 1915. 
 
 1 Barkla, Phil. Mag., XXI (1911), 648. 
 
194 THE ELECTRON 
 
 Laue in Munich had suggested in 1912 the use of the 
 regular spacing of the molecules of a crystal for the 
 analysis, according to the principle of the grating, of 
 ether waves of very short wave-length, such as X-rays 
 were supposed to be, and the Braggs 1 had not only 
 perfected an X-ray spectrometer which utilized this 
 principle, but had determined accurately the wave- 
 lengths of the X-rays which are characteristic of certain 
 metals. The accuracy with which this can be done is 
 limited simply by the accuracy in the determination of e, 
 so that the whole new field of exact X-ray spectrometry 
 is made available through our exact knowledge of e. 
 Moseley's discovery, 2 made as a result of an elaborate 
 and difficult study of the wave-lengths of the character- 
 istic X-rays which were excited when cathode rays were 
 made to impinge in succession upon anticathodes em- 
 bracing most of the known elements, was that these 
 characteristic wave-lengths of the different elements, or, 
 better, their characteristic frequencies, are related in a 
 very simple but a very significant way. These frequencies 
 were found to constitute the same sort of an arithmetical 
 progression as do the charges which we found to exist on our 
 oil drops. It was the square root of the frequencies rather 
 than the frequencies themselves which showed this beauti- 
 fully simple relationship, but this is an unimportant detail. 
 The significant fact is that, arranged in the order of increas- 
 ing frequency of their characteristic X-ray spectra, all the 
 known elements which have been examined constitute a 
 simple arithmetical series each member of which is obtained 
 from its predecessor by adding always the same quantity. 
 
 1 Bragg, X-Rays and Crystal Structure, 1915. 
 
 * Phil. Mag., XXVI (1912), 1024; XXVII (1914), 703. 
 
.2 
 $ 
 
 CO 
 
THE STRUCTURE OF THE ATOM 195 
 
 The plate opposite this page shows photographs of 
 the X-ray spectra of a number of elements whose atomic 
 numbers that is, the numbers assigned them in Mose- 
 ley's arrangement of the elements on the basis of increas- 
 ing X-ray frequency are given on the left. These 
 photographs were taken by Siegbahn. 1 The distance 
 from the " central image" in this case the black line 
 on the left to a given line of the line spectrum on the 
 right is approximately proportional to the wave-length 
 of the rays producing this line. The photographs show 
 beautifully, first, how the atoms of all the elements 
 produce spectra of just the same type, and, secondly, how 
 the wave-lengths of corresponding lines decrease, or 
 the frequencies increase, with increasing atomic number. 
 The photograph on the left shows this progression for 
 the highest frequency rays which the atoms produce, the 
 so-called K series, while the one on the right shows the 
 same sort of a progression for the next lower frequency 
 rays, namely, those of the so-called L series, which have 
 uniformly from seven to eight times the wave-length 
 of the K series. The plate opposite p. 197 shows some 
 very beautiful photographs taken by De Broglie in Paris 2 
 in October, 1916. The upper one is the X-ray emission 
 spectrum of tungsten. It consists of general radia- 
 tions, corresponding to white light, scattered through- 
 out the whole length of the spectrum as a background 
 and superposed upon this two groups of lines. The 
 two K lines are here close to the central image, for 
 the K wave-lengths are here very short, since tungsten 
 has a high atomic number (74). Farther to the right 
 
 1 Jahrbuch der Radioaktivitat u. Elektronik, XIII (1916), 326. 
 3 Comptes rcndus, CLXV (1916), 87, 352. 
 
196 THE ELECTRON 
 
 is the L series of tungsten lines which will be recognized 
 because of its similarity to the L series in the plate 
 opposite p. 195. Between the K and the L lines are two 
 
 absorption edges marked j^ and j^ . The former 
 
 represents the frequency above which the silver absorbs 
 all the general radiation of tungsten but below which it 
 lets it all through. The latter is the corresponding line 
 for bromine. In a print from a photograph absorption 
 in the plate itself obviously appears as a darkening, 
 transmission as a lightening. Just below is the spectrum 
 obtained by inserting a sheet of molybdenum tn the 
 path of the beam, i.e., before the slit of the spectrometer. 
 Absorption in the molybdenum will obviously appear 
 as a lightening, transmission as a darkening. It will 
 be seen that the molybdenum absorbs all the frequencies 
 in the X-ray emission of tungsten higher than a partic- 
 ular frequency and lets through all frequencies lower 
 than this value. This remarkable characteristic of 
 the absorption of X-rays was discovered by Barkla in 
 I909. 1 The absorption edge at which, with increasing 
 frequency, absorption suddenly begins is very sharply 
 marked. This edge coincides, as will presently be shown, 
 with the highest emission frequency of which molyb- 
 denum is capable. De Broglie has measured accurately 
 these critical absorption frequencies for all the heavy 
 elements up to thorium, thus extending the K series 
 from atomic number N= 60 where he found it, to N= 90, 
 a notable advance. The two absorption edges character- 
 istic of the silver and the bromine in the photographic 
 plate appear in the same place on all the photographs in 
 
 1 Barkla and Sadler, Phil. Mag., XVII (May, 1909), 749, 
 
W TV, Br W W W N74 
 
 Ka* KA Kx Ly , L0 U N5'47 
 
 ry N z 8fl 
 
 FIG. 22. X-RAY ABSORPTION SPECTRA, K SERIES 
 
 FIG. 23 X-RAY ABSORPTION SPECTRA, L SERIES 
 
 FIG. 24. HYDROGEN SPECTRUM FROM A NEBULA 
 
198 
 
 THE ELECTRON 
 
THE STRUCTURE OF THE ATOM 
 
 199 
 
 with the shortest beta line of this L series. The other 
 absorption edge in the L region also coincides in every 
 case with an emission line, though the data are as yet 
 too meager to permit of any general statement as to 
 what this line is. 
 
 TABLE XIV 
 
 COMPARISON OF K A AND K/s 
 
 N 
 
 Element 
 
 K A 
 
 K e 
 
 N 
 
 Element 
 
 K A 
 
 K^ 
 
 2C . . 
 
 Br 
 
 014 
 
 014 
 
 C2 . . 
 
 I 
 
 167 
 
 ( 380) 
 
 27. . 
 
 Rb 
 
 810 
 
 8n 
 
 cc . . 
 
 Cs 
 
 ^8 
 
 340 
 
 2.8 
 
 Sr 
 
 .764 
 
 .767 
 
 56. . 
 
 Ba 
 
 2.2C, 
 
 222) 
 
 4O 
 
 Zr 
 
 681 
 
 ( 60$) 
 
 C7 
 
 La 
 
 7 TO 
 
 2 TQ) 
 
 41 
 
 Nb 
 
 6 AC. 
 
 6c.7 
 
 s8 
 
 Ce 
 
 298 
 
 6^J 
 ( 3O4.) 
 
 42 
 
 Mo 
 
 611 
 
 ( 620) 
 
 78 
 
 Pt 
 
 I C.O 
 
 
 4 6 
 
 Pd 
 
 ^o^ 
 
 ^O^ 
 
 70. . 
 
 Au 
 
 J 47 
 
 
 47 
 
 Ag 
 
 479 
 
 .488 
 
 so. .. 
 
 Hg 
 
 143 
 
 
 48 
 
 Cd 
 
 4.C.8 
 
 ( 4.66) 
 
 81 
 
 Tl 
 
 I 3Q 
 
 
 CQ . 
 
 Sn 
 
 4.10 
 
 ( 4.10) 
 
 82 
 
 Pb 
 
 J 7 C 
 
 
 CT 
 
 Sb 
 
 2QQ 
 
 408 
 
 8* 
 
 Bi 
 
 I 3.O 
 
 
 C2. . 
 
 Te 
 
 381 
 
 ( ^06) 
 
 oo 
 
 Th 
 
 098 about 
 
 
 
 
 
 
 
 
 
 
 COMPARISON OF L A AND L/s 
 
 N 
 
 Element 
 
 L A 
 
 L * 
 
 N 
 
 Element 
 
 LA 
 
 h 
 
 78 . .. 
 
 Pt 
 
 I O67 
 
 I O72 
 
 OO 
 
 Th 
 
 7S6 
 
 7^O 
 
 70 . 
 
 Au 
 
 I O37 
 
 I O3 C. 
 
 02 
 
 u 
 
 7IO 
 
 7O2 
 
 82 
 
 Pb 
 
 04. r 
 
 O4.8 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Since these enormously high X-ray frequencies are 
 presumably due to the vibrations arising from electrons 
 which are in extraordinarily powerful fields of force, such 
 as might be expected to exist in the inner regions of the 
 atom close to the nucleus, Moseley's discovery strongly 
 suggests that the charge on this nucleus is produced in the 
 case of each atom by adding some particular invariable 
 
200 THE ELECTRON 
 
 charge to the nucleus of the atom next below it in 
 Moseley's table. This suggestion gains added weight 
 when it is found that with one or two trifling exceptions, 
 to be considered later, Moseley's series of increasing 
 X-ray frequencies is exactly the series of increasing atomic 
 weights. It also receives powerful support from the 
 following recent discovery. 
 
 Mendeleeff's periodic table shows that the progres- 
 sion of chemical properties among the elements coincides 
 in general with the progression of atomic weights. Now 
 it has recently been pointed out that whenever a radio- 
 active substance loses a doubly charged a-particle it 
 moves two places to the left in the periodic table, while 
 whenever it loses a singly charged /3-particle it moves 
 one place to the right, 1 thus showing that the chemical 
 character of a substance depends upon the number of 
 free positive charges in its nucleus. 
 
 One of the most interesting and striking character- 
 istics of Moseley's table is that all the known elements 
 between sodium (atomic number n, atomic weight 23) 
 and lead (atomic number 82, atomic weight, 207.2) have 
 been fitted into it and there are left but four vacancies 
 within this range. Below sodium there are just 10 
 known elements, and the X-ray spectra of these have 
 not as yet been obtained, but the progression of atomic 
 weights and of chemical properties is here altogether 
 definite and unambiguous. It seems highly probable 
 then from Moseley's work that we have already found 
 all except four of the complete series of different types 
 of atoms from hydrogen to lead, i.e., from i to 82, of 
 which the physical world is built. From 82 to 92 comes 
 
 1 Soddy, The Chemistry of the Radioelements, Part II, 1914. 
 
THE STRUCTURE OF THE ATOM 201 
 
 the group of radioactive elements which are continually 
 transmuting themselves into one another, and above 92 
 (uranium) it is not likely that any elements exist. 
 
 That hydrogen is indeed the base of the Moseley 
 series is rendered well-nigh certain by the following 
 computation. If we write Moseley's discovery that 
 the square roots of the highest frequencies, n^ n 2 , etc., 
 emitted by different atoms are proportional to the 
 nuclear charges, E I} 2 , etc., in the following form: 
 
 i=|ior^=i. ..(33) 
 
 and substitute for X 2 the observed wave-length of the high- 
 est frequency line emitted by tungsten a wave-length 
 which has been found by Hull to be o.i85Xio~ 8 cm.; 
 and, further, if we substitute for E 2 , 74, the atomic 
 number of tungsten, and for E T , i, we should obtain, by 
 solving for X x , the wave-length of the highest frequency 
 line which can be emitted by the element whose nucleus 
 contains but one single positive electron. The result of 
 this substitution is X x = 101 . 3 up (million ths millimeters). 
 Now the wave-length corresponding to the highest 
 frequency in the ultra-violet series of hydrogen lines 
 recently discovered by Lyman is 91.2/4/4 and there is 
 every reason to believe from the form of the B aimer series 
 of which this is the convergence wave-length that it cor- 
 responds to the highest frequency of which the hydrogen 
 atom is capable. The agreement is only approximate, 
 but it is as close as could be expected in view of the lack 
 of exact equality in the Moseley steps. // is well-nigh 
 certain, then, that this Lyman ultra-violet series of hydrogen 
 
202 THE ELECTRON 
 
 lines is nothing but the K X-ray series of hydrogen. 
 Similarly, it is equally certain that the L X-ray series 
 of hydrogen is the ordinary Balmer series in the visible 
 region, the head of which is at X=365juju. In other 
 words, hydrogen's ordinary radiations are its X-rays 
 and nothing more. 
 
 There is also an M series for hydrogen discovered by 
 Paschen in the ultra-red, which in itself would make it 
 probable that there are series for all the elements of 
 longer wave-length than the L series, and that the 
 complicated optical series observed with metallic arcs 
 are parts of these longer wave-length series. As a 
 matter of fact, an M series has been found for six of the 
 elements of high atomic number. 
 
 Thus the Moseley experiments have gone a long 
 way toward solving the mystery of spectral lines. 
 They reveal to us clearly and certainly the whole series 
 of elements from hydrogen to uranium,. all producing 
 spectra of remarkable similarity, at least so far as the K 
 and L radiations are concerned, but scattered regularly 
 through the whole frequency region, from the ultra- 
 violet, where the K lines for hydrogen are found, all 
 the way up to frequencies (92)* or 8,464 times as high. 
 There can scarcely be a doubt that this whole field will 
 soon be open to exploration. How brilliantly, then, 
 have these recent studies justified the predictions of the 
 spectroscopists that the key to atomic structure lay 
 in the study of spectral lines! 
 
 Moseley's work is, in brief, evidence from a wholly 
 new quarter that all these elements constitute a family, 
 each member of which is related to every other member 
 in a perfectly definite and simple way. It looks as if 
 
THE STRUCTURE OF THE ATOM 203 
 
 the dream of Thales of Miletus had actually come true 
 and that we have not only found a primordial element 
 out of which all substances are made, but that that prim- 
 ordial element is hydrogen itself. It is well known that 
 this result was suggested by Prout just one hundred 
 years ago, arguing as he did from the fact that most of 
 the atomic weights of all the elements are very nearly 
 exact multiples of the weight of hydrogen. Prout's 
 theory failed of general acceptance because the multiple 
 relationships are not found to be exact. These depart- 
 ures from exactness in the case of the atomic weights 
 must, of course, be explained somehow, but if mass is 
 electromagnetic in its origin, it is not impossible to 
 explain them on the basis of the overlapping of the 
 electric fields of the electronic constituents of the atoms. 
 Thus, if a positive and negative charge could be brought 
 into exact coincidence, their fields would entirely disap- 
 pear, and with them their masses also, provided mass is 
 merely a property of an electric field. If, then, when 
 the positive nucleus of the hydrogen atom enters into 
 the nucleus of a heavier atom, it is packed very close to 
 negative electrons, the mass of that nucleus would be 
 somewhat less than the sum of the masses of the hydro- 
 gen atoms which it contains, as it is found in fact to be. 
 This explanation on the basis of close "packing" of the 
 lack of exactness in the multiple relations between the 
 atomic weights of the elements was suggested about 
 1901, as soon as the Kaufmann 1 experiments had given 
 an experimental basis for the electromagnetic theory of 
 the origin of mass. It has been discussed by Lorenz, by 
 
 1 Kaufmann, Gottinger Nachrichten, November 8, 1901. 
 
204 THE ELECTRON 
 
 Rutherford, 1 and later by Harkins. 2 With its aid we 
 can account for the lack of exact coincidence between 
 the progression of atomic weights, and that found in 
 Moseley's table. (See Appendix H.) 
 
 Whether or not hydrogen is the building-stone of all 
 the 92 elements of Moseley's table, we may at least feel 
 fairly sure that the number of free positive electrons in 
 the nucleus of an atom is exactly the number assigned to 
 that atom in Moseley's table. This is, in general, a 
 little less than half the atomic weight, since the highest 
 number in the table is 92, while the atomic weight of the 
 corresponding heaviest known element, uranium, is 
 238.5. It is the positive charge on this nucleus which 
 obviously determines the number of negative electrons 
 which are distributed around the nucleus in the outer 
 regions of the atom, and there is just now an increasing 
 weight of evidence that this number determines the 
 chemical affinity of the atom, and, indeed, all its chem- 
 ical and physical properties except its weight. It is for 
 this reason that we now think there can be no more 
 different kinds of elements between hydrogen and ura- 
 nium than those which correspond to the 92 numbers in 
 Moseley's table. 
 
 How these free positive charges in the nucleus vary- 
 ing from i to 92 are held together we do not know. The 
 experimental evidence at present stops with the fact 
 that a number of free positive electrons equal to the 
 atomic number exist in the nucleus and that a corre- 
 sponding number of free negative electrons are held in 
 
 1 Rutherford, Phil. Mag., XXI (1911), 669. 
 
 2 Harkins, Phil. Mag., XXX (1915), 723. 
 
THE STRUCTURE OF THE ATOM 205 
 
 equilibrium in the outer regions of the atom. We may 
 imagine that there are some negative electrons also 
 inside the nucleus, for they seem to be shot out from it 
 in radioactive changes. Further, to take the case of the 
 lightest of the composite atoms, helium, of atomic num- 
 ber 2, since its nucleus has but two free positive charges, 
 while its atomic weight is 4, we may imagine that its 
 nucleus is actually made up of 4 positive electrons which 
 are held together by 2 negative electrons. In like man- 
 ner, from this point of view, each nucleus would have a 
 number of binding negative electrons equal to its atomic 
 number, and the number of positive electrons bound by 
 them in the nucleus would be twice the atomic number, 
 each negative binding two positives. This would leave, 
 as it should, an equal number of negative electrons to be 
 held in the outer regions of each atom. 
 
 But plausible as this point of view may be, it is as 
 yet speculative. This much, however, is known with 
 certainty, namely, that inside all the atoms there are a 
 definite number of two fundamental entities, namely, 
 positive and negative electrons, which are known not to 
 differ from one another at all in charge, but which do 
 seem to differ both in mass and in volume. The electron 
 then in its two forms is, according to the physicists' 
 present view, the building-stone of the sub-atomic world. 
 Someone has called it the "ultim-atom" of twentieth- 
 century science. 
 
 VI. THE BOHR ATOM 
 
 Thus far nothing has been said as to whether the 
 electrons within the atom are at rest or in motion, or, 
 if they are in motion, as to the character of th motions. 
 
206 THE ELECTRON 
 
 In the hydrogen atom, however, which contains, accord- 
 ing to the foregoing evidence, but one positive and one 
 negative electron, there is no known way of preventing 
 the latter from falling into the positive nucleus unless 
 centrifugal forces are called upon to balance attractions, 
 as they do in the case of the earth and moon. Accord- 
 ingly it seems to be necessary to assume that the negative 
 electron is rotating in an orbit about the positive. But 
 such an orbit would normally be accompanied by a 
 continuous radiation of energy of continuously increasing 
 frequency as the electron, by virtue of its loss of energy, 
 approached closer and closer to the nucleus. Yet 
 experiment reveals no such behavior, for, so far as we 
 know, hydrogen does not radiate at all unless it is 
 ionized, and, when it does radiate, it gives rise, not to a 
 continuous spectrum, as the foregoing picture would 
 demand, but rather to a line spectrum in which the 
 frequencies corresponding to the various lines are 
 related to one another in the very significant way shown 
 in the photograph of Fig. 24 and represented by the 
 so-called B aimer equation, which has the form 
 
 (34) 
 
 In this formula v represents frequency, N a constant, 
 and x , for all the lines in the visible region, has the 
 value 2, while n 2 takes for the successive lines the values 
 3, 4, 5, 6, etc. In the hydrogen series in the infra-red 
 discovered by Paschen 1 t =3 and n 2 takes the successive 
 values 4, 5, 6, etc. It is since the development of the 
 
 1 Paschen, Annalen der Physik, XXVII (1908), 565. 
 
THE STRUCTURE OF THE ATOM 207 
 
 Bohr theory that Lyman 1 discovered his hydrogen 
 series in the ultra-violet in which x = i and n 2 = 2, 3, 4, 
 etc. Since i is the smallest whole number, this series 
 should correspond, as indicated heretofore, to the 
 highest frequencies of which hydrogen is capable, the 
 upper limit toward which these frequencies tend being 
 reached when n l = i and n 2 = oo, that is, when vN. 
 
 Guided by all of these facts except the last, N, Bohr, 
 a young mathematical physicist of Copenhagen, has 
 recently devised 2 an atomic model which has had some 
 very remarkable successes. This model was originally 
 designed to cover only the simplest possible case of one 
 single electron revolving around a positive nucleus. In 
 order to account for the large number of lines which the 
 spectrum of such a system reveals (Fig. 24, taken by 
 Professor Wright of the Lick Observatory, shows all 
 of the Balmer series given by the spectrum of a nebula 
 except the longest wave-length line called H a , which is 
 beyond the left edge of the plate), Bohr's first assump- 
 tion was that the electron may rotate about the nucleus 
 in a whole series of different orbits and that each of these 
 orbits is governed by the w^ll-known Newtonian law, 
 which when mathematically stated takes the form: 
 
 (35) 
 
 in which e is the change of the electron, E that of the 
 nucleus, a the radius of the orbit, n the orbital frequency, 
 and m the mass of the electron. This is merely the 
 
 1 Spectroscopy of the Extreme Ultraviolet, p. 78. 
 *N. Bohr, Phil. Mag., XXVI (1913), i and 476 and 857; XXIX 
 (1915), 332; XXX (1915), 394. 
 
208 THE ELECTRON 
 
 assumption that the electron rotates in a circular orbit 
 which is governed by the laws which are known, from 
 the work on the scattering of the alpha particles, to 
 hold inside as well as outside the atom. The radical 
 element in it is that it permits the negative electron to 
 maintain this orbit without radiating energy even though 
 this appears to conflict with ordinary electromagnetic 
 theory. But, on the other hand, the facts of magnet- 
 ism 1 and of optics, in addition to the successes of 
 the Bohr theory which are to be detailed, appear at 
 present to lend experimental justification to such an 
 assumption. 
 
 Bohr's second assumption is that radiation takes 
 place only when an electron jumps from one to another 
 of these orbits. If A 2 represents the energy of the 
 electron in one orbit and A l that in any other orbit, 
 then it is clear from considerations of energy alone that 
 when the electron passes from the one orbit to the other 
 the amount of energy radiated must be A 2 A^ further, 
 this radiated energy obviously must have some frequency 
 v, and, in view of the experimental work presented in 
 the next chapter, Bohr placed it proportional to p, and 
 wrote: 
 
 to=A,-A t (36) 
 
 h being the so-called Planck constant to be discussed 
 later. It is to be emphasized that this assumption gives 
 no physical picture of the way in which the radiation 
 takes place. It merely states the energy relations 
 which must be satisfied when it occurs. 
 
 1 Einstein and De Haas, Verh. der deutsch. phys. Ges., XVII (1915), 
 152; also Baraett, Phys. Rev., VI (1915), 239. 
 
THE STRUCTURE OF THE ATOM 209 
 
 Bohr's third assumption is that the various possible 
 circular orbits are determined by assigning to each 
 orbit a kinetic energy T such that 
 
 (37) 
 
 in which r is a whole number, n the orbital frequency, 
 and h is again Planck's constant. This value of T is 
 assigned so as to make the series of frequencies agree 
 with that actually observed, namely, that represented 
 by the Balmer series of hydrogen. 
 
 It is to be noticed that, if circular electronic orbits 
 exist at all, no one of these assumptions is arbitrary. 
 Each of them is merely the statement of the existing 
 experimental situation. It is not surprising, therefore, 
 that they predict the sequence of frequencies found in 
 the hydrogen series. They have been purposely made 
 to do so. But they have not been made with any refer- 
 ence whatever to the exact numerical values of these 
 frequencies. 
 
 The evidence for the soundness of the conception 
 of non-radiating electronic orbits is to be looked for, 
 then, first, in the success of the constants involved, and, 
 second, in the physical significance, if any, which 
 attaches to the third assumption. If these constants 
 come out right within the limits of experimental error, 
 then the theory of non-radiating electronic orbits has 
 been given the most crucial imaginable of tests, especially 
 if these constants are accurately determinable. 
 
 What are the facts? The constant of the Balmer 
 series in hydrogen, that is, the value of N in equation 
 (34), is known with the great precision attained in all 
 
210 THE ELECTRON 
 
 wave-length determinations and is equal to 3 . 2poX io 15 . 
 From the Bohr theory it is given by the simplest 
 algebra (Appendix G) as 
 
 ............... (38) 
 
 m 
 
 As already indicated, I have recently redetermined 1 e 
 with an estimated accuracy of one part in 1,000 and 
 obtained for it the value 4,774X io~ 10 . As will be shown 
 in the next chapter, I have also determined h photo- 
 electrically 2 with an error, in the case of sodium, of no 
 more than one-half of i per cent, the value for sodium 
 being 6.56Xio~ 27 . The value found by Webster 3 
 by a method recently discovered by Duane and Hunt 4 
 is 6.53Xio~ 27 . Taking the mean of these two results, 
 viz. 6.545 Xio~ 27 , as the most probable value, we get 
 
 with the aid of Bucherer's value of (i . 767 X io 7 ) which 
 
 is probably correct to o.i per cent, #=3. 294X10^, 
 which agrees within a tenth of i per cent with the observed 
 value. This agreement constitutes most extraordinary 
 justification of the theory of non-radiating electronic 
 orbits. It demonstrates that the behavior of the nega- 
 tive electron in the hydrogen atom is at least correctly 
 described by the equation of a circular non-radiating 
 orbit. If this equation can be obtained from some 
 other physical condition than that of an actual orbit, 
 
 1 R. A. Millikan, Proc. Nat. Acad., April, 1917. 
 * R. A. Millikan, Phys. Rev., VII (1916), 362. 
 sPhys. Rev., VII (1916), 599. 
 Ibid., VI (1915), 168. 
 
THE STRUCTURE OF THE ATOM 211 
 
 it is obviously incumbent upon those who so hold to 
 show what that condition is. Until this is done, it is 
 justifiable to suppose that the equation of an orbit 
 means an actual orbit. 
 
 Again, the radii of the stable orbits for hydrogen are 
 easily found from Bohr's assumptions to take the 
 mathematical form (Appendix G) 
 
 ( . 
 (39) 
 
 In other words, since r is a whole number, the radii of 
 these orbits bear the ratios i, 4, 9, 16, 25. If normal 
 hydrogen is assumed to be that in which the electron is 
 in the inmost possible orbit, namely, that for which 
 T=I, 2a, the diameter of the normal hydrogen atom, 
 comes out i.iXio" 8 . The best determination for 
 the diameter of the hydrogen molecule yields 2 . 2X io~ 8 , 
 in extraordinarily close agreement with the prediction 
 from Bohr's theory. Further, the fact that normal 
 hydrogen does not absorb at all the Balmer series lines 
 which it emits is beautifully explained by the foregoing 
 theory, since, according to it, normal hydrogen has no 
 electrons in the orbits corresponding to the lines of the 
 Balmer series. Again, the fact that hydrogen emits Us 
 characteristic radiations only when it is ionized favors 
 the theory that the process of emission is a process of 
 settling down to a normal condition through a series of 
 possible intermediate states, and is therefore in line 
 with the view that a change in orbit is necessary to the 
 act of radiation. Similarly, the fact that in the stars 
 there are 33 lines in the Balmer series, while in the 
 
212 THE ELECTRON 
 
 laboratory we never get more than 12, is easily explicable 
 from the Bohr theory, but no other theory has offered 
 even a suggestion of an explanation. 
 
 Another triumph of the theory is that the third 
 assumption, devised to fit a purely empirical situation, 
 viz., the observed relations between the frequencies 
 of the Balmer series, is found to have a very simple 
 and illuminating physical meaning. It is that all the 
 possible values of the angular momentum of the electron 
 rotating about the positive nucleus are exact multiples 
 of a particular value of this angular momentum. Angu- 
 lar momentum then has in the hydrogen atom the 
 property of atomicity. Such relationships do not in 
 general drop out of empirical formulae. When they do, 
 we usually see in them real interpretations of the 
 formulae not merely coincidences. 
 
 Again, the success of a theory is often tested as much 
 by its adaptability to the explanation of deviations from 
 the behavior predicted by its most elementary form 
 as by the exactness of the fit between calculated and 
 observed results. The theory of electronic orbits has 
 had remarkable successes of this sort. Thus it predicts 
 the Moseley law (33). But this law, discovered after- 
 ward, was found inexact, and it should be inexact when 
 there is more than one electron in the atom, as is the 
 case save for H atoms and for such He atoms as have 
 lost one negative charge, and that because of the way 
 in which the electrons influence one another's fields. 
 It will probably be found to break down completely 
 for very light atoms like those of lithium. The more 
 powerful the nucleus, however, and the closer to it the 
 inner orbit the smaller should this effect be. Now 
 
THE STRUCTURE OF THE ATOM 213 
 
 precisely this result is observed. The Moseley law 
 holds most accurately when tested for hydrogen and 
 the elements of highest atomic number, and much less 
 accurately when tested for hydrogen and aluminum or 
 magnesium. Similarly the ratio between the frequencies 
 of the a and /3 lines of the K series approaches closer 
 to the theoretical value (that for hydrogen) the higher 
 the atomic number of the element. 
 
 Again, it is shown in the photographs opposite p. 195 
 that the various lines in the characteristic X-ray spectra 
 are not single lines as required by the simple theory. 
 Accordingly Sommerfeld 1 extended Bohr equations in 
 the endeavor to account for this structure on the basis 
 of ellipticity in some of the orbits, and Paschen, 2 by 
 measurements on the structure of the complex helium 
 'lines, has obtained such extraordinary checks upon this 
 
 theory that -'- comes out from his measurements to 
 m 
 
 within a tenth of i per cent of the accepted value. 
 
 A further prediction made by the theory and dis- 
 covered as soon as looked for was a relation between the 
 frequencies of the lines of two succeeding series like 
 the K and the L series. This relation is expressed in 
 the equation: 
 
 VRJ3 "Ka =VLa. . (4) 
 
 Thus, according to Bohr, the longest wave-length line 
 of the K series, the a line, is due to jumping from orbit 2 
 (Fig. 26) to orbit i with a change in energy A^A^ 
 the next longest wave-length line, the /3 line is due to 
 
 1 Annalen der Physik, LI (1916), i. 
 
 2 Ibid., October, 1916. 
 
214 
 
 THE ELECTRON 
 
 jumping from 3 to i with a change in energy A^At', 
 while the longest wave-length line of the L series, the 
 a line, is due to jumping from 3 to 2, with a change 
 in energy A 3 A 2 . Hence if the frequency v is in every 
 case proportional to the change in energy, equation (40) 
 follows at once, and, further, it should hold accurately 
 from the energy relations between the orbits whether 
 there be one or many electrons in the atoms. I have been 
 
 able to find no case of its 
 failure, though the data 
 upon which it may be 
 tested are now consider- 
 able. I have also recently 
 pointed out 1 that it is 
 equivalent to the well- 
 known Rydberg-Schuster 
 law, 2 which has been 
 found to hold quite 
 generally among optical 
 series. 
 
 If then the test of truth in a physical theory is large 
 success both in the prediction of new relationships and 
 in correctly and exactly accounting for old ones, the 
 theory of non-radiating orbits, is one of the well- 
 established truths of modern physics. For the present at 
 least it is truth, and no other theory of atomic structure 
 need be considered until it has shown itself able to 
 approach it in fertility. I know of no competitor which 
 is as yet even in sight. 
 
 I Phys. Rev., May, 1917, presented before the American Physical 
 Society, December i, 1916. 
 
 2 Baly's Spectroscopy, p. 488. 
 
 FIG. 26 
 
THE STRUCTURE OF THE ATOM 215 
 
 I am well aware that the facts of organic chemistry 
 seem to demand that the valence electrons be grouped 
 in certain definite equilibrium positions about the 
 periphery of the atom, and that at first sight this demand 
 appears difficult to reconcile with the theory of electronic 
 orbits. As yet, however, there is no necessary clash. 
 Hydrogen and helium present no difficulties, since the 
 former has but one valency, and the latter none. It 
 is to these atoms alone that the unmodified Bohr theory 
 applies, for it treats only the case of a single negative 
 electron rotating about a positive nucleus. That the 
 K radiations of the heavy elements are so accurately 
 predictable from those of hydrogen indicates, indeed, 
 that close to the nucleus of these elements there lie 
 electrons to which the Bohr theory applies fairly accur- 
 ately, but the radiations give us no information about 
 the conditions or behaviors of the external electrons 
 which have to do with the phenomena of valency, and 
 we have investigated but little the radiating properties of 
 the atoms which possess but few electrons. A further 
 study of the behavior with respect to X-rays of the 
 elements from lithium, atomic number 3, to magnesium, 
 atomic number n, may be expected to throw new light 
 on this problem. 
 
 It has been objected, too, that the Bohr theory is 
 not a radiation theory because it gives us no picture 
 of the mechanism of the production of the frequency v. 
 This is true, and therein lies its strength, just as the 
 strength of the first and second laws of thermodynamics 
 lies in the fact that they are true irrespective of a mechan- 
 ism. The Bohr theory is a theory of atomic structure; 
 it is not a theory of radiation, for it merely states what 
 
216 THE ELECTRON 
 
 energy relations must exist when radiation, whatever 
 its mechanism, takes place. It is the first attempt to 
 determine in the light of well-established experimental 
 facts what the electrons inside the atom are doing, and 
 as such a first attempt it must be regarded as, thus far, 
 a success, though it has by no means got beyond the 
 hypothetical stage. Its chief difficulty arises from the 
 apparent contradiction involved in a non-radiating 
 electronic orbit a contradiction which would disappear, 
 however, if the negative electron itself, when inside the 
 atom, were a ring of some sort, capable of expanding to 
 various radii, and capable, only when freed from the 
 atom, of assuming essentially the properties of a point 
 charge, such as we find it endowed with in experiments 
 upon cathode rays, j8-rays, and ionization in gases. 
 That it actually does possess certain properties not in 
 the past always associated with electrical charges will 
 appear in the next chapter. 
 
CHAPTER X 
 THE NATURE OF RADIANT ENERGY 
 
 The problems thus far discussed have all been in the 
 domain of molecular physics, but the discovery and 
 measurement of the electron have also exerted a powerful 
 influence upon recent developments in the domain of 
 ether physics. These developments are of extraordinary 
 interest and suggestiveness, but they lead into regions in 
 which the physicist sees as yet but dimly indeed even 
 more dimly than he thoilght he saw twenty years ago. 
 
 But while the beauty of a problem solved excites the 
 admiration and yields a certain sort of satisfaction, it is 
 after all the unsolved problem, the quest of the unknown, 
 the struggle for the unattained, which is of most universal 
 and most thrilling interest. I make no apologies, there- 
 fore, for introducing in this chapter one of the great 
 unsolved problems of modern physics, nor for leaving it 
 with but the vaguest of suggestions toward a solution. 
 
 I. THE CORPUSCULAR AND THE ETHER THEORIES OF 
 RADIATION 
 
 The newest of the problems of physics is at the same 
 time the oldest. For nothing is earlier in the experiences 
 either of the child or of the race than the sensation of 
 receiving light and heat from the sun. But how does light 
 get to us from the sun and the stars through the empty 
 interstellar spaces ? The Greeks answered this query 
 very simply and very satisfactorily from the standpoint 
 of people who were content with plausible explanations 
 
 217 
 
218 THE ELECTRON 
 
 but had not yet learned perpetually to question nature 
 experimentally as to the validity or invalidity of a 
 conclusion. They said that the sun and all radiators 
 of light and heat must shoot off minute corpuscles whose 
 impact upon the eye or skin produces the sensations 
 of light and warmth. 
 
 This corpuscular theory was the generally accepted 
 one up to 1800 A.D. It was challenged, it is true, about 
 1680 by the Dutch physicist Huygens, who, starting with 
 the observed phenomena of the transmission of water 
 waves over the surface of a pond or of sound waves 
 through the air, argued that light might be some vibra- 
 tory disturbance transmitted by some medium which fills 
 all interstellar space. He postulated the existence of 
 such a medium, which was called the luminiferous or 
 light-bearing ether. 
 
 Partly no doubt because of Newton's espousal of the 
 corpuscular theory, the ether or wave theory gained few 
 adherents until some facts of interference began to appear 
 about 1800 which baffled explanation from the stand- 
 point of the corpuscular theory, but which were easily 
 handled by its rival. During the nineteenth century the 
 evidence became stronger and stronger, until by its close 
 the corpuscular theory had been permanently eliminated 
 for four different reasons: (i) The facts of interference 
 were not only found inexplicable in terms of it, but they 
 were completely predicted by the wave theory. (2) The 
 fact that the speed of propagation of light was experi- 
 mentally found to be greater in air than in water was in 
 accord with the demands of the ether theory, but directly 
 contrary to the demands of the corpuscular theory. 
 (3) Wireless waves had appeared and had been shown 
 
THE NATURE OF RADIANT ENERGY 219 
 
 to be just like light waves save for wave-length, and they 
 had been found to pass over continuously, with increas- 
 ing wave-length, into static electrical fields such as could, 
 not possibly be explained from a corpuscular point of 
 view. (4) The speed of light had been shown to be inde- 
 pendent of the speed of the source as demanded by the 
 ether theory and denied by the corpuscular theory. 
 
 By 1900, then, the ether theory had become apparently 
 impregnably intrenched. A couple of years later it met 
 with some opposition of a rather ill-considered sort, as 
 it seems to me, from a group of extreme advocates of the 
 relativity theory, but this theory is now commonly 
 regarded, I think, as having no bearing whatever upon 
 the question of the existence or non-existence of a lumi- 
 niferous ether. For such an ether was called into being 
 solely for the sake of furnishing a carrier for electro- 
 magnetic waves, and it obviously stands or falls with the 
 existence of such waves in vacuo, and this has never been 
 questioned by anyone so far as I am aware. 
 
 II. DIFFICULTIES CONFRONTING THE WAVE THEORY 
 
 Up to 1903, then, the theory which looked upon an 
 electromagnetic wave as a disturbance which originated 
 at some point in the ether at which an electric charge was 
 undergoing a change in speed, and was propagated from 
 that point outward as a spherical wave or pulse, the total 
 energy of the 'disturbance being always spread uniformly 
 over the wave front, had met with no serious question 
 from any source. Indeed, it had been extraordinarily 
 successful, not only in accounting for all the known facts, 
 but in more than one instance in predicting new ones. 
 The first difficulty appeared after the discovery of the 
 
220 THE ELECTRON 
 
 electron and in connection with the relations of the elec- 
 tron to the absorption or emission of such electro- 
 magnetic waves. It was first pointed out in 1903 by 
 Sir J. J. Thomson in his Silliman lectures at Yale. It 
 may be stated thus: 
 
 X-rays unquestionably pass over or pass all but an 
 exceedingly minute fraction, say one in a thousand 
 billion, of the atoms contained in the space traversed 
 without spending any energy upon them or influencing 
 them in any observable way. But here and there they 
 find an atom from which, as is shown in the photographs 
 opposite p. 189, they hurl a negative electron with enor- 
 mous speed. This is the most interesting and most 
 significant characteristic of X-rays, and one which dis- 
 tinguishes them from the a- and /3-rays just as sharply 
 as does the property of non-deviability in a magnetic 
 field; for Figs. 14 and 15 and the plate opposite p. 189 
 show that neither a- nor /3-rays ever eject electrons from 
 the atoms through which they pass, with speeds com- 
 parable with those produced by X-rays, else there would 
 be new zigzag lines branching out from points all along 
 the paths of the a- and /3-particles shown in these photo- 
 graphs. 
 
 But this property of X-rays introduces a serious 
 difficulty into the ether theory. For if the electric 
 intensity in the wave front of the X-ray is sufficient thus 
 to hurl a corpuscle with huge energy from one particular 
 atom, why does it not at least detach corpuscles from 
 all of the atoms over which it passes ? 
 
 Again when ultra-violet light falls on a metal it, too, 
 like X-rays, is found to eject negative electrons. This 
 phenomenon of the emission of corpuscles under the 
 
THE NATURE OF RADIANT ENERGY 221 
 
 influence of light is called the photo-electric effect. 
 Lenard 1 first made the astonishing discovery that the 
 energy of ejection of the corpuscle is altogether independ- 
 ent of the intensity of the light which causes the ejection, 
 no matter whether this intensity is varied by varying 
 the distance of the light or by introducing absorbing 
 screens. I have myself 2 subjected this relation to a very 
 precise test and found it to hold accurately. Further- 
 more, this sort of independence has also been established 
 for the negative electrons emitted by both X- and7-rays. 
 
 Facts of this sort are evidently difficult to account for 
 on any sort of a spreading- wave theory. But it will be 
 seen that they lend themselves to easy interpretation in 
 terms of a corpuscular theory, for if the energy of an 
 escaping electron comes from the absorption of a light- 
 corpuscle, then the energy of emission of the ejected 
 electron ought to be independent of the distance of the 
 source, as it is found to be, and furthermore corpuscular 
 rays would hit but a very minute fraction of the atoms 
 contained in the space traversed by them. This would 
 explain, then, both the independence of the energy of 
 emission upon intensity and the smallness of the number 
 of atoms ionized. 
 
 In view, however, of the four sets of facts mentioned 
 above, Thomson found it altogether impossible to go 
 back to the old and exploded form of corpuscular theory 
 for an explanation of the new facts as to the emission of 
 electrons under the influence of ether waves. He 
 accordingly attempted to reconcile these troublesome 
 new facts with the wave theory by assuming a fibrous 
 
 1 Ann. d. Phys. (4), VIII (1902), 149. 
 2 Phys. Rev., I (1913), 73- 
 
222 THE ELECTRON 
 
 structure in the ether and picturing all electromagnetic 
 energy as traveling along Faraday lines of force con- 
 ceived of as actual strings extending through all space. 
 Although this concept, which we shall call the ether- 
 string theory, is like the corpuscular theory in that the 
 energy, after it leaves the emitting body, remains local- 
 ized in space, and, when absorbed, is absorbed as a whole, 
 yet it is after all essentially an ether theory. For in it 
 the speed of propagation is determined by the properties 
 of the medium and has nothing to do with the nature or 
 condition of the source. Thus the last three of the fatal 
 objections to a corpuscular theory are not here encoun- 
 tered. As to the first one, no one has yet shown that 
 Thomson's suggestion is reconcilable with the facts of 
 interference, though so far as I know neither has its 
 irreconcilability been as yet absolutely demonstrated. 
 
 But interference aside, all is not simple and easy for 
 Thomson's theory. For one encounters serious diffi- 
 culties when he attempts to visualize the universe as an 
 infinite cobweb whose threads never become tangled or 
 broken however swiftly the electrical charges to which 
 they are attached may be flying about. 
 
 in. EINSTEIN'S QUANTUM THEORY or RADIATION 
 
 Yet the boldness and the difficulties of Thomson's 
 "ether-string" theory did not deter Einstein 1 in 1905 
 from making it even more radical. In order to connect 
 it up with some results to which Planck of Berlin had 
 been led in studying the facts of black-body radiation, 
 Einstein assumed that the energy emitted by any radiator 
 not only kept together in bunches or quanta as it traveled 
 . d. Phys. (4), XVII (1905), 132; XX (1906), 199. 
 
THE NATURE. OF RADIANT ENERGY 223 
 
 through space, as Thomson had assumed it to do, but 
 that a given source could emit and absorb radiant energy 
 only in units which are all exactly equal to hv, v being 
 the natural frequency of the emitter and h a constant 
 which is the same for all emitters. 
 
 I shall not attempt to present the basis for such an 
 assumption, for, as a matter of fact, it had almost none 
 at the time. But whatever its basis, it enabled Einstein 
 to predict at once that the energy of emission of cor- 
 puscles under the influence of light would be governed 
 by the equation 
 
 Ve = hv p ............... (41) 
 
 in which hv is the energy absorbed by the electron from 
 the light wave or light quantum, for, according to the 
 assumption it was the whole energy contained in that 
 quantum, p is the work necessary to get the electron 
 out of the metal, and %mv 2 is the energy with which it 
 leaves the surface an energy evidently measured -by the 
 product of its charge e by the potential difference V 
 against which it is just able to drive itself before being 
 brought to rest. 
 
 At the time at which it was made this prediction was 
 as bold as the hypothesis which suggested it, for at that 
 time there were available no experiments whatever for 
 determining anything about how the positive potential 
 V necessary to apply to the illuminated electrode to stop 
 the discharge of negative electrons from it under the 
 influence of monochromatic light varied with the fre- 
 quency v of the light, or whether the quantity h to which 
 Planck had already assigned a numerical value appeared 
 at all in connection with photo-electric discharge. We 
 
224 THE ELECTRON 
 
 are confronted, however, by the astonishing situation 
 that after ten years of work at the Ryerson Laboratory 
 and elsewhere upon the discharge of electrons by light 
 this equation of Einstein's seems to us to predict accu- 
 rately all of the facts which have been observed. 
 
 IV. THE TESTING OF EINSTEIN'S EQUATION 
 
 The method which has been adopted in the Ryerson 
 Laboratory for testing the correctness of Einstein's 
 equation has involved the performance of so many opera- 
 tions upon the highly inflammable alkali metals in a 
 vessel which was freed from the presence of all gases that 
 it is not inappropriate to describe the present experi- 
 mental arrangement as a machine-shop in vacuo. Fig. 27 
 shows a photograph of the apparatus, and Fig. 28 is a 
 drawing of a section which should make the necessary 
 operations intelligible. 
 
 One of the most vital assertions made in Einstein's 
 theory- is that the kinetic energy with which mono- 
 chromatic light ejects electrons from any metal is 
 proportional to the frequency of the light, i.e., if violet 
 light is of half the wave-length of red light, then the 
 violet light should throw out the electron with twice 
 the energy imparted to it by the red light. In order to 
 test whether any such linear relation exists between the 
 energy of the escaping electron and the light which 
 throws it out it was necessary to use as wide a range of 
 frequencies as possible. This made it necessary to use 
 the alkali metals, sodium, potassium, and lithium, for 
 electrons are thrown from the ordinary metals only by 
 ultra-violet light, while the alkali metals respond in this 
 way to any waves shorter than those of the red, that is, 
 
THE NATURE OF RADIANT ENERGY 
 
 225 
 
 they respond throughout practically the whole visible 
 spectrum as well as the ultra-violet spectrum. Cast 
 cylinders of these metals were therefore placed on the 
 wheel W (Fig. 28) and fresh clean surfaces were obtained 
 by cutting shavings from each metal in an excellent 
 vacuum with the aid of the knife K, which was operated 
 
 FIG. 27 
 
 by an electromagnet F outside the tube. After this the 
 freshly cut surface was turned around by another electro- 
 magnet until it was opposite the point O of Fig.. 28 and 
 a beam of monochromatic light from a spectrometer was 
 let in through and allowed to fall on the new surface. 
 The energy of the electrons ejected by it was measured 
 by applying to the surface a positive potential just strong 
 enough to prevent any of the discharged electrons from 
 
226 
 
 THE ELECTRON 
 
 reaching the gauze cylinder opposite (shown in dotted 
 lines) and thus communicating an observable negative 
 
 charge to the quadrant electrometer which was attached 
 to this gauze cylinder. For a complete test of the 
 
THE NATURE OF RADIANT ENERGY 227 
 
 equation it was necessary also to measure the contact- 
 electromotive force between the new surface and a test 
 plate S. This was done by another electromagnetic 
 device shown in Fig. 27, but for further details the original 
 paper may be consulted. 1 Suffice it here to say that 
 Einstein's equation demands a linear relation between 
 the applied positive volts and the frequency of the light, 
 and it also demands that the slope of this line should be 
 
 exactly equal to - . Hence from this slope, since e is 
 
 known, it should be possible to obtain h. How per- 
 fect a linear relation is found may be seen from Fig. 29, 
 which also shows that from the slope of this line h is 
 found to be 6. 26Xio~ 27 , which is as close to the value 
 obtained by Planck from the radiation laws as is to 
 be expected from the accuracy with which the experi- 
 ments in radiation can be made. The most reliable 
 value of h obtained from a consideration of the whole of 
 this work is 
 
 In the original paper will be found other tests of the 
 Einstein equation, but the net result of all this work is to 
 confirm in a very complete way the equation which 
 Einstein first set up on the basis of his semi-corpuscular 
 theory of radiant energy. And if this equation is of 
 general validity it must certainly be regarded as one of 
 the most fundamental and far-reaching of the equations 
 of physics, and one which is destined to play in the future 
 a scarcely less important role than Maxwell's equations 
 have played in the past, for it must govern the trans- 
 1 Phys. Rev., VII (1916), 363, 
 
THE NATURE OF RADIANT ENERGY 229 
 
 formation of all short-wave-length electromagnetic 
 energy into heat energy. 
 
 V. OBJECTIONS TO AN ETHER-STRING THEORY 
 
 In spite of the credentials which have just been pre- 
 sented for Einstein's equation, we are confronted with 
 the extraordinary situation that" the semi-corpuscular 
 theory out of which Einstein got his equation seems to 
 be wholly untenable and has in fact been pretty gener- 
 ally abandoned, though Sir J. J. Thomson 1 and a few 
 others 2 seem still to adhere to some form of ether- 
 string theory, that is, to some form of theory in which 
 the energy remains localized in space instead of spreading 
 over the entire wave front. 
 
 Two very potent objections, however, may be urged 
 against all forms of ether-string theory, of which 
 Einstein's is a particular modification. The first is 
 that no one has ever yet been able to show that 
 such a theory can predict any one of the facts of inter- 
 ference. The second is that there is direct positive evi- 
 dence against the view that the ether possesses a fibrous 
 structure. For if a static electrical field has a fibrous 
 structure, as postulated by any form of ether-string 
 theory, "each unit of positive electricity being the origin 
 and each unit of negative electricity the termination of 
 a Faraday tube," 3 then the force acting on one single 
 electron between the plates of an air condenser cannot 
 possibly vary continuously with the potential difference 
 
 1 Proc. Phys. Soc. of London, XXVII (December 15, 1914), 105. 
 3 Modern Electrical Theory, Cambridge, University Press, 1913, 
 p. 248. 
 
 3 J. J. Thomson, Electricity and Matter, p. 9. 
 
230 THE ELECTRON 
 
 between the plates. Now in the oil-drop experiments 1 
 we actually study the behavior in such an electric field 
 of one single, isolated electron and we find, over the 
 widest limits, exact proportionality between the field 
 strength and the force acting on the electron as measured 
 by the velocity with which the oil drop to which it is 
 attached is dragged through the air. 
 
 When we maintain the field constant and vary the 
 charge on the drop, the granular structure of electricity is 
 proved by the discontinuous changes in the velocity, but 
 when we maintain the charge constant and vary the field 
 the lack of discontinuous change in the velocity disproves 
 the contention of a fibrous structure in the field, unless the 
 assumption be made that there are an enormous number 
 of ether strings ending in one electron. Such an assump- 
 tion takes all the virtue out of an ether-string theory. 
 
 Despite then the apparently complete success of the 
 Einstein equation, the physical theory of which it was 
 designed to be the symbolic expression is found so 
 untenable that Einstein himself, I believe, no longer 
 holds to it, and we are in the position of having built a 
 very perfect structure and then knocked out entirely 
 the underpinning without causing the building to fall. 
 It stands complete and apparently well tested, but with- 
 out any visible means of support. These supports must 
 obviously exist, and the most fascinating problem of 
 modern physics is to find them. Experiment has outrun 
 theory, or, better, guided by erroneous theory, it has 
 discovered relationships which seem to be of the greatest 
 interest and importance, but the reasons for them are as 
 yet not at all understood. 
 
 1 Phys. Rev., II (1913), 109, 
 
THE NATURE OF RADIANT ENERGY 231 
 
 VI. ATTEMPTS TOWARD A SOLUTION 
 
 It is possible, however, to go a certain distance 
 toward a solution and to indicate some conditions which 
 must be satisfied by the solution when it is found. For 
 the energy hv with which the electron is found by experi- 
 ment to escape from the atom must have come either 
 from the energy stored up inside of the atom or else from 
 the light. There is no third possibility. Now the fact 
 that the energy of emission is the same, whether the body 
 from which it is emitted is held within an inch of the 
 source, where the light is very intense, or a mile away, 
 where it is very weak, would seem to indicate that the 
 light simply pulls a trigger in the atom which itself fur- 
 nishes all the energy with which the electron escapes, as 
 was originally suggested by Lenard in 1902,* or else, if 
 the light furnishes the energy, that light itself must 
 consist of bundles of energy which keep together as they 
 travel through space, as suggested in the Thomson- 
 Einstein theory. 
 
 Yet the fact that the energy of emission is directly 
 proportional to the frequency v of the incident light 
 spoils Lenard's form of trigger theory, since, if the atom 
 furnishes the energy, it ought to make no difference what 
 kind of a wave-length pulls the trigger, while it ought to 
 make a difference what kind of a gun, that is, what kind 
 of an atom, is shot off. But both of these expectations 
 are the exact opposite of the observed facts. The energy 
 of the escaping corpuscle must come then, in some way or 
 other, from the incident light. 
 
 When, however, we attempt to compute on the basis 
 of a spreading- wave theory how much energy a corpuscle 
 
 1 Ann. d. Phys. (4), VIII (1902), 149. 
 
232 THE ELECTRON 
 
 can receive from a given source of light, we find it diffi- 
 cult to find anything more than a very minute fraction 
 of the amount which the corpuscle actually acquires. 
 
 Thus, the total luminous energy falling per second 
 from a standard candle on a square centimeter at a dis- 
 tance of 3 m. is i erg. 1 Hence the amount falling per 
 second on a body of the size of an atom, i.e., of cross- 
 section io~ IS cm., is io~ IS ergs, but the energy hv with 
 which a corpuscle is ejected by light of wave-length 500 juju 
 (millionths millimeter) is 4X io~ 12 ergs, or 4,000 times as 
 much. Since not a third of the incident energy is in 
 wave-lengths shorter than 500 juju, a surface of sodium 
 or lithium which is sensitive up to 500 W should require, 
 even if all this energy were in one wave-length, which it 
 is not, at least 12,000 seconds or 4 hours of illumination 
 by a candle 3 m. away before any of its atoms could have 
 received, all told, enough energy to discharge a corpuscle. 
 Yet the corpuscle is observed to shoot out the instant the 
 light is turned on. It is true that Lord Rayleigh has 
 recently shown 2 that an atom may conceivably absorb 
 wave-energy from a region of the order of magnitude of 
 the square of a wave-length of the incident light rather 
 than of the order of its own cross-section. This in no 
 way weakens, however, the cogency of the type of argu- 
 ment just presented, for it is only necessary to apply 
 the same sort of analysis to the case of 7- rays, the wave- 
 length of which is of the order of magnitude of an 
 atomic diameter (io~ 8 cm.) ; and the difficulty is found 
 still more pronounced. Thus Rutherford 3 estimates that 
 
 1 Drude, Lehrbuch der Optik, 1906, p. 472. 
 
 2 Phil. Mag., XXXII (1916), 188. 
 
 3 Radioactive Substances and the Radiations, p. 288. 
 
THE NATURE OF RADIANT ENERGY 233 
 
 the total 7-ray energy radiated per second by one gram 
 of radium cannot possibly be more than 4.7Xio 4 ergs. 
 Hence at a distance of 100 meters, where the 7-rays 
 from a gram of radium would be easily detectable, the 
 total 7- ray energy falling per second on a square milli- 
 meter of surface, the area of which is ten- thousand 
 billion times greater than that either of an atom or of a 
 disk whose radius is a wave-length, would be 4. yX io 4 -r- 
 47rX io IO =4X io~ 7 ergs. This is very close to the energy 
 with which /3-rays are actually observed to be ejected 
 by these 7- rays, the velocity of ejection being about 
 nine- tenths that of light. Although, then, it should take 
 ten thousand billion seconds for the atom to gather in 
 this much energy from the 7-rays, on the basis of classi- 
 cal theory, the /5-ray is observed to be ejected with this 
 energy as soon as the radium is put in place. This 
 shows that if we are going to abandon the Thomson- 
 Einstein hypothesis of localized energy, which is of 
 course competent to satisfy these energy relations, there 
 is no alternative but to assume that at some previous 
 time the corpuscle had absorbed and stored up from 
 light of this or other wave-length enough energy sa that 
 it needed but a minute addition at the time of the 
 experiment to be able to be ejected from the atom with 
 the energy hv. 
 
 Now the corpuscle which is thus ejected by the light 
 cannot possibly be one of the free corpuscles of the metal, 
 for such a corpuscle, when set in motion within a metal, 
 constitutes an electric current, and we know that such 
 a current at once dissipates its energy into heat. In 
 other words, a free corpuscle can have no mechanism 
 for storing up energy and then jerking itself up "by 
 
234 THE ELECTRON 
 
 its boot straps" until it has the huge speed of emission 
 observed. 
 
 The ejected corpuscle must then have come from the 
 inside of the atom, in which case it is necessary to assume, 
 if the Thomson-Einstein theory is rejected, that within 
 the atom there exists some mechanism which will permit 
 a corpuscle continually to absorb and load itself up with 
 energy of a given frequency until a value at least as large 
 as hv is reached. What sort of a mechanism this is we 
 have at present no idea. Further, if the absorption is 
 due to resonance and we have as yet no other way in 
 which to conceive it it is difficult to see how there can 
 be, in the atoms of a solid body, corpuscles having all 
 kinds of natural frequencies so that some are always 
 found to absorb and ultimately be ejected by impressed 
 light of any particular frequency. But apart from these 
 difficulties, the thing itself is impossible if these absorbing 
 corpuscles, when not exposed to radiation, are emitting 
 any energy at all; for if they did so, they would in time 
 lose all their store and we should be able, by keeping 
 bodies in the dark, to put them into a condition in which 
 they should show no emission of corpuscles whatever 
 until after hours or years of illumination with a given 
 wave-length. Since this is contrary to experiment, we 
 are forced, even when we discard the Thomson-Einstein 
 theory of localized energy, to postulate electronic 
 absorbers which, during the process of absorbing, do not 
 radiate at all until the absorbed energy has reached a 
 certain critical value when explosive emission occurs. 
 
 However, then, we may interpret the phenomenon of 
 the emission of corpuscles under the influence of ether 
 waves, whether upon the basis of the Thomson-Einstein 
 
THE NATURE OF RADIANT ENERGY 235 
 
 assumption of bundles of localized energy traveling 
 through the ether, or upon the basis of a peculiar prop- 
 erty of the inside of an atom which, enables it to absorb 
 continuously incident energy and emit only explo- 
 sively, the observed characteristics of the effect seem to 
 furnish proof that the emission of energy by an atom is a 
 discontinuous or explosive process. This was the funda- 
 mental assumption of Planck's so-called quantum theory 
 of radiation. The Thomson-Einstein theory makes both 
 the absorption and the emission sudden or explosive, 
 while the loading theory first suggested by Planck, 
 though from another view-point, makes the absorption 
 continuous and only the emission explosive. 
 
 The h determined above with not more than one- 
 half of i per cent of uncertainty is the explosive con- 
 stant, i.e., it is the unchanging ratio between the energy 
 of emission and the frequency of the incident light. It 
 is a constant the existence of which was first discovered 
 by Planck by an analysis of the facts of black-body 
 radiation, though the physical assumptions underlying 
 Planck's analysis do not seem to be longer tenable. 
 For the American physicists Duane and Hunt 1 and Hull 2 
 have recently shown that the same quantity h appears 
 in connection with the impact of corpuscles against any 
 kind of a target, the observation here being that 
 the highest frequency in the general or white-light 
 X-radiation emitted when corpuscles impinge upon a 
 target is found by dividing the kinetic energy of the 
 impinging corpuscle by h. Since black-body radiation 
 is presumably due to the impact of the free corpuscles 
 within a metal upon the atoms, it is probable that the 
 
 1 Phys. Rev., VI (1915), 166. * Ibid., VII (1916), 157. 
 
236 THE ELECTRON 
 
 appearance of h in black-body radiation and in general 
 X-radiation is due to the same cause, so that, con- 
 trary to Planck's assumption, there need not be, in 
 either of these cases, any coincidence between natural 
 and impressed periods at all. The hv which here appears 
 is not a characteristic of the atom, but merely a property 
 of the ether pulse which is generated by the stopping of 
 a moving electron. Why this ether pulse should be 
 resolvable into a continuous, or white-light spectrum 
 which, however, has the peculiar property of being 
 chopped off sharply at a particular limiting frequency 
 given by hv=PDXe is thus far a complete mystery. 
 All that we can say is that experiment seems to demand 
 a sufficient modification of the ether-pulse theory of 
 white-light and of general X-radiation to take this 
 experimental fact into account. 
 
 On the other hand, the appearance of h in connec- 
 tion with the absorption and emission of monochromatic 
 light (photo-electric effect and Bohr atom) seems to 
 demand some hitherto unknown type of absorbing and 
 emitting mechanism within the atom. This demand is 
 strikingly emphasized by the remarkable absorbing 
 property of matter for X-rays, discovered by Barkla 1 
 and beautifully exhibited in DeBroglie's photographs 
 opposite p. 197. It will be seen from these photographs 
 that the atoms of each particular substance transmit the 
 general X-radiation up to a certain critical frequency and 
 then absorbs all radiations of higher frequency than this 
 critical value. The extraordinary significance of this dis- 
 covery lies in the fact that it indicates that there is a 
 type of absorption which is not due either to resonance or 
 
 *Phil. Mag., XVII (1909), 749. 
 
THE NATURE OF RADIANT ENERGY 237 
 
 to free electrons. But these are the only types of absorp- 
 tion which are recognized in the structure of modern 
 optics. We have as yet no way of conceiving of this 
 new type of absorption in terms of a mechanical model. 
 
 There is one result, however, which seems to be 
 definitely established by all of this experimental work. 
 Whether the radiation is produced by the stopping of a 
 free electron, as in Duane and Hunt's experiments, and 
 presumably also in black-body experiments, or by the 
 absorption and re-emission of energy by bound electrons, 
 as in photo-electric and spectroscopic work, Planck's h 
 seems to be always tied up in some way with the emis- 
 sion and absorption of energy by the electron, h may 
 therefore be considered as one of the properties of the 
 electron. 
 
 The new facts in the field of radiation which have 
 been discovered through the study of the properties of 
 the electron seem, then, to require in any case a very 
 fundamental revision or extension of classical theories 
 of absorption and emission of radiant energy. The 
 Thomson-Einstein theory throws the whole burden of 
 accounting for the new facts upon the unknown nature 
 of the ether and makes radical assumptions about its 
 structure. The loading theory leaves the ether as it 
 was and puts the burden of an explanation upon the 
 unknown conditions and laws which exist inside the 
 atom, and have to do with the nature of the electron. 
 I have already given reasons for discrediting the first type 
 of theory. The second type, though as yet very incom- 
 plete, seems to me to be the only possible one, and it has 
 already met with some notable successes, as in the case 
 of the Bohr atom. Yet the theory is at present woe- 
 
238 THE ELECTRON 
 
 fully incompjete and hazy. About all that we can say 
 now is that we seem to be driven by newly discovered 
 relations in the field of radiation either to the Thomson- 
 Einstein semi-corpuscular theory, or else to a theory 
 which is equally subversive of the established order 
 of things in physics. For either one of these alternatives 
 brings us to a very revolutionary quantum theory of 
 radiation. To be living in a period which faces such a 
 complete reconstruction of our notions as to the way in 
 which ether waves are absorbed and emitted by matter is 
 an inspiring prospect. The atomic and electronic worlds 
 have revealed themselves with beautiful definiteness and 
 wonderful consistency to the eye of the modern physicist, 
 but their relation to the world of ether waves is still to 
 him a profound mystery for which the coming generation 
 has the incomparable opportunity of finding a solution. 
 In conclusion there is given a summary of the most 
 important physical constants the values of which it has 
 become possible to fix, 1 within about the limits indicated, 
 through the isolation and measurement of the electron. 
 
 The electron e= (4.774=*= o.oo5)Xio~ 10 
 
 The Avogadro constant N= (6 . 062 o. 006) X io 2 * 
 
 Number of gas molecules per cc. at 
 
 oC. 76 cm n= (2.705=*= o.oo3)Xio I 9 
 
 Kinetic energy of translation of a 
 
 molecule at oC E = (5.621=1= o.oo6)Xio~ I 4 
 
 Change of translational molecular 
 
 energy per C e= (2.058=*= o.oo2)Xio~ l6 
 
 Mass of an atom of hydrogen in grams m= (1.662=1= o.oo2)Xio~ 24 
 
 Planck's element of action h= (6.547=*= o.oi3)Xio~ 27 
 
 Wien constant of spectral radiation C 2 = i . 43 1 2 =t o . 0030 
 Stefan-Boltzmann constant of total 
 
 radiation <r= (5.72 o.o34)Xio~ 12 
 
 Grating spacing in calcite d= 3.030=1= o.ooiA 
 
 1 SeeProc.Nat.Acad. Sci., Ill (191 7), 236; also Phil. Mag., July, 191 7. 
 
APPENDIX A 
 
 ne FROM MOBILITIES AND DIFFUSION COEFFICIENTS 
 
 If we assume that gaseous ions, which are merely 
 charged molecules or clusters of molecules, act exactly 
 like the uncharged molecules about them, they will 
 tend to diffuse just as other molecules do and will exert 
 a partial gas pressure of exactly 
 the same amount as would an 
 equal number of molecules of any 
 gas. Imagine then the lower part 
 of the vessel of Fig. 30 to be filled 
 with gas through which ions are 
 distributed and imagine that these 
 ions are slowly diffusing upward. 
 Let n f be the ionic concentration, 
 i.e., the number of ions per cubic 
 centimeter at any distance x from 
 the bottom of the vessel. Then 
 the number N of ions which pass 
 per second through i sq. cm. taken perpendicular to x at 
 a distance x from the bottom must be directly propor- 
 tional to the concentration gradient -j- and the factor 
 
 of proportionality in a given gas is by definition the 
 diffusion coefficient D of the ions through this gas, i.e., 
 
 (42) 
 
 FIG. 30 
 
 dx 
 
 But since N is also equal to the product of the average 
 velocity V with which the ions are streaming upward at 
 
 239 
 
240 THE ELECTRON 
 
 x by the number of ions per cubic centimeter at x, i.e., 
 since N =n'V, we have from equation (42) 
 
 * ~' i j 
 n ax 
 
 The force which is acting on these w'-ions to cause this 
 upward motion is the difference in the partial pressure 
 of the ions at the top and bottom of a centimeter cube at 
 
 the point x. It is, therefore, equal to -7- dynes, and the 
 
 ratio between the force acting and the velocity produced 
 
 by it is 
 
 dp 
 
 dx 
 
 n' dx 
 
 Now this ratio must be independent of the particular 
 type of force which is causing the motion. Imagine then 
 the same w'-ions set in motion, not by the process of 
 diffusion, but by an electric field of strength F. The 
 total force acting on the w'-ions would then be Fen' ', 
 and if we take v as the velocity produced, then the 
 ratio between the force acting and the velocity pro- 
 
 Fen' 
 duced will now be -- . By virtue then of the fact 
 
 that this ratio is constant, whatever kind of force it 
 be which is causing the motion, we have 
 
 dp 
 
 dx 
 
 v 
 
 n' dx 
 
APPENDIX A 241 
 
 Now if v denote the velocity in unit field, a quantity 
 which is technically called the " ionic mobility," -r, = v . 
 Again since the partial pressure p is proportional to n', 
 
 i.e., since p Kn f , it 
 equation (43) reduces to 
 
 i.e., since p Kn r , it follows that ^r = ~T- Hence 
 
 en _ i 
 v ~D 
 
 P 
 or 
 
 v =De (44) 
 
 But if we assume that, so far as all pressure relations 
 are concerned, the ions act like uncharged molecules 
 (this was perhaps an uncertain assumption at the time, 
 though it has since been shown to be correct), we have 
 
 = in which n is the number of molecules per cubic 
 
 centimeter in the air and P is the pressure produced by 
 them, i.e., P is atmospheric pressure. We have_J;hen 
 from equation (44) 
 
 v P , , 
 
 we=-- (45) 
 
APPENDIX B 
 
 TOWNSEND'S FIRST ATTEMPT AT A DETER- 
 MINATION OF e 
 
 Fig. 31 shows the arrangement of apparatus used. 
 The oxygen rising from the electrode E is first bubbled 
 through potassium iodide in A to remove ozone, then 
 through water in B to enable the ions to form a cloud. 
 This cloud-laden air then passes through a channel in an 
 electrical insulator a paraffin block P into the tubes 
 
 FIG. 31 
 
 c,d,e, which contain concentrated sulphuric acid. These 
 drying tubes remove all the moisture from the air and 
 also such part of the charge as is held on ions which in 
 the process of bubbling through c, d, e have actually 
 touched the sulphuric acid. The dry air containing the 
 rest of the charge passes out through a channel in the 
 paraffin block P' into the flask D. (If the gas being 
 studied was lighter than air, e.g., hydrogen, D was of 
 course inverted.) The outside of D is covered with tin 
 foil which is connected to one of the three mercury cups 
 held by the paraffin block P" . If the air in D contained 
 
 242 
 
APPENDIX B 243 
 
 at first no charge, then an electrical charge exactly 
 equal to the quantity of electricity which enters the flask 
 D will appear by induction on the tin-foil coating which 
 covers this flask and this quantity q T can be measured by 
 connecting the mercury cup 2 to cup 3 which is connected 
 to the quadrant electrometer Q, and observing the deflec- 
 tion per minute. Precisely similarly the total quantity 
 of .electricity which is left per minute in the drying tubes 
 Cj d, e is exactly equal to the quantity which appears by 
 induction on the outer walls of the hollow metal vessel G, 
 which surrounds the tubes c, d, e. This quantity q a can 
 be measured by connecting mercury cup i to cup 3 and 
 observing the deflection per minute of the quadrant 
 electrometer. The number of cubic centimeters of gas 
 which pass through the apparatus per minute is easily 
 found from the number of amperes of current which are 
 used in the electrolysis apparatus E and the electro- 
 chemical equivalent of the gas. By dividing the quan- 
 tities of electricity appearing per minute in D and G by 
 the number of cubic centimeters of gas generated per 
 minute we obtain the total charge per cubic centimeter 
 carried by the cloud. 
 
 The increase in weight of the drying tubes c, d, e per 
 cubic centimeter of gas passing, minus the weight per 
 cubic centimeter of saturated water vapor, gives the 
 weight of the cloud per cubic centimeter. This completes 
 the measurements involved in (2) and (3), p. 45. 
 
 As to (4), p. 46, the average size of the droplets 
 of water Town send found 'by passing the cloud emerging 
 from B into a flask and observing how long it took for 
 the top of the cloud to settle a measured number of 
 centimeters. The radius of the drops could then be 
 
244 THE ELECTRON 
 
 obtained from a purely theoretical investigation made 
 by Sir George Stokes, 1 according to which the velocity z>j 
 of fall of a spherical droplet through a gas whose co- 
 efficient of viscosity was rj is given by 
 
 v = 2 ga?^ 
 9 1" 
 
 in which a is the density of the droplet. From this 
 Townsend got the average radius a of the droplets and 
 computed their average weight m by the familiar formula 
 
 w=-7ra 3 <r. He was then ready to proceed as in (5), 
 see p. 46. 
 
 1 Lamb, Hydronamics, 1895, p. 533. 
 
APPENDIX C 
 THE BROWNIAN-MOVEMENT EQUATION 
 
 A very simple derivation of this equation of Einstein 
 has been given by Langevin of Paris 1 essentially as 
 follows: From the kinetic theory of gases we have 
 PV=RT=^Nmc 2 in which c 2 is the average of the squares 
 of the velocities of the molecules, N the number of 
 molecules in a gram molecule, and m the mass of each. 
 Hence the mean kinetic energy of agitation E of each 
 
 ~D r n 
 
 molecule is given by E=^mc*=- -j^- . 
 
 Since in observations on Brownian movements we 
 record only motions along one axis, we shall divide the 
 total energy of agitation into three parts, each part 
 corresponding to motion along one of the three axes, 
 
 and, placing the velocity along the #-axis equal to -rr , 
 
 we have 
 
 E 
 
 Every Brownian particle is then moving about, according 
 to Einstein's assumption, with a mean energy of motion 
 
 RT 
 along each axis equal to %-T . This motion is due to 
 
 molecular bombardment, and in' order to write an 
 
 equation for the motion at any instant of a particle 
 
 subjected to such forces we need only to know (i) the 
 
 1 Comptes Rendtis, CXLVI (1908), 530. 
 
 245 
 
246 THE ELECTRON 
 
 value X of the ^-component of all the blows struck by 
 the molecules at that instant, and (2) the resistance 
 offered by the medium to the motion of the particle 
 through it. This last quantity we have set equal to Kv 
 and have found that in the case of the motion of oil 
 
 droplets through a gas K has the value 671-170 
 
 We may then write the equation of motion of the particle 
 at any instant uncler molecular bombardment in the form 
 
 d 2 x 
 
 Since in the Brownian movements we are interested only 
 in the absolute values of displacements without regard 
 to their sign, it is desirable to change the form of this 
 
 equation so as to involve x 2 and -j-J . This can be done 
 
 by multiplying through by x. We thus obtain, after 
 
 d*x . ,d 2 (x 2 ) /dx 
 
 substituting for x its value 2" 
 
 mf(#) Jdx\_ Kd(x>) 
 
 I ~W~ m \dt) '- "7 ~7T +Xx (48) 
 
 Langevin now considers the mean result arising from 
 applying this equation at a given instant to a large 
 number of different particles all just alike. 
 
 Writing then z for -~- in which x 2 denotes the mean 
 
 at 
 
 of all the large number of different values of x 2 , he gets 
 after substituting for W (^7J and remembering that 
 
APPENDIX C 247 
 
 in taking the mean, since the X in the last term is as 
 likely to be positive as negative and hence that Xx = o, 
 
 mdz RT = Kz 
 
 2 dt N ~ ~ 2 * 
 
 Separating the variables this becomes 
 
 dz _K 
 2RT\ m ' 
 
 which yields upon integration between the limits o and 
 2RT 
 
 NK 
 
 +Ce (49) 
 
 For any interval of time r long enough to measure this 
 takes the value of the first term. For when Brownian 
 movements are at all observable, a is io~ 4 cm. or less, 
 and since K is roughly equal to 6-irrja we see that, 
 taking the density of the particle equal to unity, 
 
 IQ 
 
 - S 
 
 K 67T. 00018X10-4 
 Hence when r is taken greater than about io~ s seconds, 
 
 -*r 
 
 e m rapidly approaches zero, so that for any measurable 
 time intervals 
 
 NK 
 or 
 
 dt NK 
 
248 THE ELECTRON 
 
 and, letting Ao? represent the change in x* in the time T 
 
 - 2RT 
 
 ( 
 (50) 
 
 This equation means that if we could observe a large 
 number n of exactly similar particles through a time r, 
 square the displacement which each undergoes along 
 the -axis in that time, and average all these squared 
 
 ~D r r t 
 
 displacements, we should get the quantity "TTFT. But 
 
 we must obviously obtain the same result if we 
 observe the same identical' particle through w-intervals 
 each of length T and average these w-displa cements. The 
 latter procedure is evidently the more reliable, since 
 the former must assume the exact identity of the 
 particles. 
 
APPENDIX D 
 
 THE INERTIA OR MASS OF AN ELECTRICAL CHARGE 
 ON A SPHERE OF RADIUS a 
 
 If Fig. 3 2 represents a magnet of pole area A , whose 
 two poles are d cm. apart, and have a total magnetization 
 M, a density of magnetization cr, and a field strength 
 between them of H, then the work necessary to carry a 
 unit pole from M to M f is Hd, and the work necessary 
 to create the poles M and M 1 ', i.e., to carry 
 M units of magnetism across against a 
 
 H . HMd 
 
 mean field strength is . Hence 
 
 the total energy Ej. of the magnetic field 
 is given by 
 
 = HMd = HA<rd 
 
 but since H = 
 
 H*Ad 
 
 STT 
 
 FIG. 32 
 
 or since Ad is the volume of the field the energy E per 
 unit volume of the magnetic field is given by 
 
 H ' 
 
 (Si) 
 
 Now the strength of the magnetic field at a distance r 
 
 ev 
 
 from a moving charge in the plane of the charge is , 
 
 if e is the charge and v its speed. Also the magnetic field 
 strength at a point distant rd from the charge, 6 being 
 
 249 
 
250 THE ELECTRON 
 
 the angle between r and the direction of motion, is 
 given by 
 
 Hence the total energy of the magnetic field created by 
 the moving charge is 
 
 in which r is an element of volume and the integration 
 is extended over all space. But in terms of v, 6, and <. 
 
 dr=rdO, dr, r sin Od<f> 
 /. Total energy = 
 
 " (%V = ^ 
 8 'J " 87r J. 
 
 Since kinetic energy =Jw^, the mass-equivalent m of 
 the moving charge is given by setting 
 
 The radius of the spherical charge which would have a 
 mass equal to the observed mass of the negative electron 
 is found by inserting in the last equation = 4. 774X io" xo 
 
APPENDIX D 251 
 
 electrostatic units =i. 59 iXio~ ao electromagnetic units 
 
 a 
 
 and = i. 767X10' electromagnetic, units. This gives 
 
 a=i.9Xio~ 13 cm. 
 
 The expression just obtained for m obviously holds 
 only so long as the magnetic field is symmetrically 
 distributed about the moving charge, as assumed in the 
 integration, that is, so long as v is small compared with 
 the velocity of light. When v exceeds . i the speed of 
 light c, the mass of the charge begins to increase measur- 
 ably and becomes infinite at the speed of light. According 
 to the theory developed by Lorenz, if the mass for slow 
 speeds is called m and the mass at any speed v is called 
 m, then 
 
 m i 
 
 =p (53) 
 
 This was the formula which Bucherer found to hold 
 accurately for the masses of negative electrons whose 
 speeds ranged from . 3 to .8 that of light. 
 
APPENDIX E 
 
 MOLECULAR CROSS-SECTION AND MEAN 
 FREE PATH 
 
 If there is one single molecule at rest in a cubical 
 space i cm. on a side, the chance that another molecule 
 which is shot through the cube will impinge upon the 
 
 ird* 
 one contained is clearly in which d is the mean 
 
 diameter of the two molecules. If there are n contained 
 molecules the chance is multiplied by n, that is, it 
 
 becomes . But on the average the chance of an im- 
 pact in going a centimeter is the number of impacts 
 actually made in traversing this distance. The mean 
 free path / is the distance traversed divided by the num- 
 ber of impacts made in going that distance. Hence 
 
 This would be the correct expression for the mean free 
 path of a molecule which is moving through a group of 
 molecules at rest. If, however, the molecules are all in 
 motion they will sometimes move into a collision which 
 would otherwise be avoided, so that the collisions will be 
 more numerous when the molecules are in motion than 
 when at rest how much more numerous will depend 
 upon the law of distribution of the speeds of the mole- 
 cules. It is through a consideration of the Maxwell 
 
 252 
 
APPENDIX E 253 
 
 distribution law that the factor V 2 is introduced into 
 the denominator (see Jeans, Dynamical Theory of Gases) 
 so that equation (54) becomes 
 
 (55) 
 
APPENDIX F 
 
 NUMBER OF FREE POSITIVE ELECTRONS IN THE 
 
 NUCLEUS OF AN ATOM BY RUTHERFORD'S 
 
 METHOD 
 
 If N represents the number of free positive electrons 
 in the nucleus, e the electronic charge, E the known 
 charge on the a-particle, namely 2e, and |wF a the 
 known kinetic energy of the a-particle, then, since the 
 inertias of the negative electrons are quite negligible in 
 comparison with that of the a-particle, if the latter 
 suffers an appreciable change in direction in passing 
 through an atom it will be due to the action of the 
 nuclear charge. If b represents the closest possible 
 approach of the a-particle to the center of the nucleus, 
 namely, that occurring when the collision is "head on," 
 and the a-particle is thrown straight back upon its 
 course, then the original kinetic energy \mV* must equal 
 the work done against the electric field in approaching 
 to the distance b, i.e., 
 
 NeE . ,, 
 ( S 6) 
 
 Suppose, however, that the collision is not "head on/' 
 but that the original direction of the a-particle is such 
 that, if its direction were maintained, its nearest distance 
 of approach to the nucleus would be p (Fig. 33). The 
 deflection of the a-particle will now be, not 180, as 
 before, but some other angle 0. It follows simply from 
 
 254 
 
APPENDIX F 
 
 255 
 
 the geometrical properties of the hyperbola and the 
 elementary principles of mechanics that 
 
 FIG. 33 
 
 For let PAP' represent the path of the particle and let 
 POA = 6. Also let V = velocity of the particle on entering 
 the atom and v its velocity at A. Then from the con- 
 servation of angular momentum 
 
 pV=SA-v. 
 
 (58) 
 
256 THE ELECTRON 
 
 and from conservation of energy 
 
 NeE 
 SA 
 
 Since the eccentricity e = sec 6, and for any conic the focal 
 distance is the eccentricity times one-half the major 
 axis, i.e., SO = OA c, it follows that 
 
 SA = SO+OA =So(i+H =/> esc 6(1+ cos 0) = p cot - . 
 But from equations (58) and (59) 
 
 A 
 
 (60) 
 
 and since the angle of deviation is TT 26, it follows 
 that 
 
 Now it is evident from the method used in Appen- 
 dix E that if there are n atoms per cubic centimeter 
 of a metal foil of thickness /, and if each atom has a 
 radius R, then the probability M that a particle of size 
 small in comparison with R will pass through one of 
 these atoms in shooting through the foil is given by 
 
 M=irR 2 nt. 
 
APPENDIX F 257 
 
 Similarly the probability m that it will pass within a 
 distance p of the center of an atom is 
 
 If this probability is small in comparison with unity, it 
 represents the fraction p of any given number of particles 
 shooting through the foil which will actually come within 
 a distance p of the nucleus of an atom of the foil. 
 
 The fraction of the total number which will strike 
 within radii p and p-\-dp is given by differentiation as 
 
 dm=2irpnt'dp 
 but from equation (57) 
 
 #1 < 
 
 ^ 2^ ' 2 
 
 .*. dm=--ntb*cot-csc*-d<j>. 
 
 4 22 
 
 Therefore the fraction p which is deflected between the 
 angles fa and fa is given by integration as 
 
 P =-ntb 2 (cot 2 -cot 3 
 4 \ 2 2 
 
 It was this fraction of a given number of a-particles 
 shot into the foil which Geiger and Marsden found by 
 direct count by the scintillation method to be deflected 
 through the angles included between any assigned limits 
 fa and fa. Since n and t are known, b could be at once 
 obtained. It was found to vary with the nature of the 
 
258 THE ELECTRON 
 
 atom, being larger for the heavy atoms than for the 
 lighter ones, and having a value for gold of 3 .4X io~ 12 cm. 
 This is then an upper limit for the size of the nucleus of 
 the gold atom. 
 
 As soon as b has thus been found for any atom, 
 equation (56) can be solved for N, since E, e, and \mV* 
 are all known. It is thus that the number of free positive 
 electrons in the nucleus is found to be roughly half the 
 atomic weight of the atom, and that the size of the 
 nucleus is found to be very minute in comparison with 
 the size of the atom. 
 
APPENDIX G 
 
 BOHR'S THEORETICAL DERIVATION OF THE VALUE 
 OF THE RYDBERG CONSTANT 
 
 The Newtonian equation of a circular orbit of an 
 electron e rotating about a central attracting charge , 
 at a distance a, with a rotational frequency n, is 
 
 = (2irn) 2 ma ................ (62) 
 
 p 
 The kinetic energy of the electron is %m(27rna)*=% . 
 
 The work required to move the electron from its orbit 
 
 /> 77 /> 77 
 
 to a position at rest at infinity is -- %m(27rna) 2 =% . 
 
 If we denote this quantity of energy by J, it is seen at 
 once that 
 
 eE 
 
 and 
 
 (63) 
 
 If we combine this with (37), p. 209, there results at once 
 
 Upon change in orbit the radiated energy must be 
 
200 THE ELECTRON 
 
 and, if we place this equal to hv, there results the Balmer 
 formula (34), p. 206, 
 
 in which 
 
 Since for hydrogen E=e, we have 
 
 and from (60) 
 
APPENDIX H 
 
 THE ELEMENTS, THEIR ATOMIC NUMBERS, ATOMIC 
 WEIGHTS, AND CHEMICAL .POSITIONS 
 
 iH 
 
 1.008 
 
 o 
 
 I 
 
 II 
 
 III 
 
 IV 
 
 V 
 
 VI 
 
 VII 
 
 VIII 
 
 2 He 
 3-90 
 
 3 Li 
 6.94 
 
 4 Be 
 
 Q.I 
 
 SB 
 
 II. 
 
 6C 
 
 12.00 
 
 7 N 
 14.01 
 
 8O 
 
 16.00 
 
 9F 
 
 19.0 
 
 
 10 Ne 
 
 2O. 2 
 
 ii Na 
 23.00 
 
 12 Mg 
 
 24.32 
 
 13 Al 
 27.1 
 
 I4 Si 
 28.3 
 
 15 P 
 
 31-04 
 
 i6S 
 32.06 
 
 17 Cl 
 35.46 
 
 
 18 A 
 39-88 
 
 19 K 
 
 39.10 
 
 20 Ca 
 40.07 
 
 21 SC 
 44.1 
 
 22 Ti 
 4 8.1 
 
 2 3 V 
 51-0 
 
 24 Cr 
 52.0 
 
 25 Mn 
 54 93 
 
 26 Fe 27 Co 28 Ni 
 55.84 58.97 58.68 
 
 
 29 Cu 
 63-57 
 
 30 Zn 
 65-37 
 
 31 Ga 
 
 69.9 
 
 32 Ge 
 72.5 
 
 33 As 
 74 96 
 
 34 Se 
 79 .2 
 
 35 Br 
 79 92 
 
 
 
 
 36 Kr 
 82.92 
 
 37 Rb 
 85-45 
 
 38 Sr 
 87-63 
 
 HI 
 
 40 Zr 
 90.6 
 
 41 Nb 
 93-5 
 
 42 Mo 
 96.0 
 
 43- 
 
 44 Ru 45 Rh 46 Pd 
 101.7 102.9 106.7 
 
 
 
 47 Ag 
 107.88 
 
 48 Cd 
 
 I I 2 . 40 
 
 49 In 
 114.8 
 
 50 Sn 
 118.7 
 
 Si Sb 
 
 1 2O. 2 
 
 52 Te 
 127.5 
 
 53J 
 126.92 
 
 
 
 
 54 X 
 130.2 
 
 55 Cs 
 132.81 
 
 56 Ba 
 137-37 
 
 57 La 58 Ce 59 Pr 60 Nd 61-62 Sm 63 Eu 64 Gd 65 Tb 66 Ds 
 139.0 140.25140.6 144.3 150.4 152 157.3 159 2 162.5 
 
 67 Ho 68 Ev 69 Tu 70 Yb 71 Lu 72 
 163.5 167.7 168.5 173.5 175-0 
 
 73 Ta 
 181.5 
 
 74 W 
 184.0 
 
 75- 
 
 76 Os 77 Ir 78 Pt 
 190.9 193-1 195-2 
 
 
 
 79 Au 
 197.2 
 
 80 Hg 
 200. 6 
 
 8iTl 
 
 204.0 
 
 82 Pb 
 
 207.20 
 
 83 Bi 
 
 208.0 
 
 84 Po 
 
 (210.0) 
 
 85- 
 
 
 
 86 Em 
 (222.0) 
 
 87- 
 
 88 Ra 
 226.0 
 
 89 Ac 
 (227) 
 
 90 Th 
 232.15 
 
 UrX 2 
 (234) 
 
 92 Ur 
 238.2 
 
 
 
 
 
 
 Elements, the atomic numbers of which are not in the order of atomic weights, are in 
 italics. The numbers corresponding to missing elements are in bold-faced type. 
 
 1 Hydrogen 
 
 2 Helium 
 
 3 Lithium 
 
 4 Beryllium 
 
 5 Boron 
 
 6 Carbon 
 
 7 Nitrogen 
 
 8 Oxygen 
 
 9 Fluorine 
 
 10 Neon 
 
 11 Sodium 
 
 12 Magnesium 
 
 13 Aluminium 
 
 14 Silicon 
 
 15 Phosphorus 
 
 1 6 Sulphur 
 
 17 Chlorine 
 
 1 8 Argon 
 
 19 Potassium 
 
 20 Calcium 
 
 21 Scandium 
 
 22 Titanium 
 
 23 Vanadium 
 
 24 Chromium 
 
 25 Manganese 
 
 26 Iron 
 
 27 Cobalt 
 
 28 Nickel 
 
 29 Copper 
 
 30 Zinc 
 
 31 Gallium 
 
 32 Germanium 
 
 33 Arsenic 
 
 34 Selenium 
 
 35 Bromine 
 
 36 Krypton 
 
 37 Rubidium 
 
 38 Strontium 
 
 39 Yttrium 
 
 40 Zirconium 
 
 41 Niobium 
 
 42 Molybdenum 
 
 44 Rhuthenium 
 
 45 Rhodium 
 
 46 Paladium 
 
 47 Silver 
 
 48 Cadmium 
 
 49 Indium 
 
 50 Tin 
 
 51 Antimony 
 
 52 Tellurium 
 
 53 Iodine 
 
 54 Xenon 
 
 55 Caesium 
 
 56 Barium 
 
 57 Lanthanum 
 
 58 Cerium 
 
 59 Praseodymium 
 
 60 Neodymium 
 
 61 
 
 62 Samarium 
 
 63 Europium 
 
 64 Gadolinium 
 
 65 Terbium 
 
 66 Dyprosium 
 
 67 Holmium 
 
 68 Erbium 
 
 69 Thulium 
 
 70 Ytterbium 
 
 71 Lutecium 
 
 72 
 
 73 Tantalum 
 
 74 Tungsten 
 
 76 Osmium 
 
 77 Indium 
 
 78 Platinum 
 
 79 Gold 
 
 80 Mercury 
 
 81 Thallium 
 
 82 Lead 
 
 83 Bismuth 
 
 84 Polonium 
 
 85 
 
 86 Emanation 
 
 87 
 
 88 Radium 
 
 89 Actinium 
 
 90 Thorium 
 
 91 Uranium X 
 
 92 Uranium 
 
 261 
 
INDEXES 
 
AUTHOR INDEX 
 
 Aepinus, 12 
 Ampere, 21 
 Aristotle, 9 
 Arnold, 93 f. 
 Avogadro, 29, 180 
 
 Bacon, 8, 9 
 Balmer, 201, 235 
 Barkla, 193, 196 
 Begeman, 55 
 Bodoszewski, 142, 144 
 Bohr, 205, 207 
 Boltwood, 157 
 Boltzman, 79 
 Brown, 142 
 Bucherer, 210 
 
 Caertner, 115 
 Carbonelle, 142 
 Clausius, 8 
 Coulomb, 31 
 Crookes, 24 
 Cunningham, 88, 160, 164 
 
 Dalton, 2 
 
 De Broglie, 145, 159, 195, I9 6, 
 Delsaulx, 142 
 Democritus, 2, 6, 9, 15 
 Derieux, 176 
 DeWatteville, 145, 158 
 Duane, 210, 235 
 Dufay, ii 
 
 Ehrenhaft, 145, 158 f. 
 Einstein, 143, 173, 222 f. 
 Elizabeth, Queen, n 
 Enright, 44 
 Epicurus, 6 
 Eyring, 153 
 
 197 
 
 Faraday, 12, 15, 19, 28, 222 f. 
 
 Fletcher, 127, 148!., 161 
 Franck, 37, 38, 123 f. 
 Franklin, Benjamin, n f. r 
 
 Geiger, 156, 157, 192, 193 
 Gerlach, 133 f. 
 Gilbert, n 
 Gilchrist, 91 
 Gouy, 142 f. 
 
 Hadamard, 87 
 Harkins, 204 
 Harrington, 92, 118 
 Helmholtz, 22, 23, 24 
 Hemsalech, 145, 158 
 Hertz, 17 
 Hull, 204, 235 
 Hunt, 210, 235 
 Huygens, 218 
 
 133 
 Joule, 7 
 
 Karpowicz, 171 
 Kaufmann, 203 
 Konstaninowsky, 163 
 Kelvin, 4, 23 
 
 Ladenburg, 95 
 
 Laue, 194 
 
 Langevin, 35, 132, 144, 245 
 
 Laplace, 44 
 
 Lavoisier, 44 
 
 Lee,J.Y, 176 
 
 Lenard, 221, 231 
 
 Leucippus, 2 
 
 Lodge, Oliver, 17, 44 
 
 Loeb, 36 
 
 265 
 
2 66 
 
 THE ELECTRON 
 
 Lucretius, 2, 6 
 Lunn, 87 
 Lyman, 201, 207 
 
 Marsden, 192, 193 
 Maxwell, 8, 17. 19, 24, 79, 227 
 Mendelee"ff, 200 
 Meyer, 31, 133 f. 
 
 Moseley, 193, 194, 199, 200, 201, 
 202 
 
 Newton, 207, 218 
 Nordlund, 1 78 
 
 Ostwald, 10, 154 
 
 Paschen, 202, 206 
 Perrin, 144 f., 167 
 Pierson, 134 
 
 Planck, 115, 209, 222, 223 
 Plato, 9 
 Prout, 203 
 Przibram, 153, 163 
 Pythagoras, 4 
 
 Ramsay, 101 
 
 Rapp, 91 
 
 Rayleigh, 232 
 
 Regener, 156, 157 
 
 Rowland, 182 
 
 Rutherford, Sir Ernest, 32, 35, 156, 
 
 192, 204, 232 
 Rydberg, 214, 259 
 
 Salles, 132 
 Schidlof, 171 
 
 Schuster, 214 
 Siegbahn, 195 
 Smoluchowski, 145 
 Soddy, 144 
 Sommerfeld, 213 
 Spencer, 101 
 Stokes, 46, 50, 53, 88 
 Stoney, 21, 25, 31 
 Sutherland, 84 
 Svedberg, 147 
 
 Thales, i, 5, 203 
 
 Thirion, 142 
 
 Thomson, Sir J. J., 14, 27, 32, 34, 
 
 40, 41, 47, 56, 68, 140, 183, 220 
 Townsend, 35, 37, 38, 44, 56, 68, 
 
 .123, 242 f. 
 Tyndall, 8 
 
 Varley, 24 
 
 Warburg, 32 
 
 Webster, 210 
 
 Weiss, 150, 163 
 
 Wellish, 36 
 
 Westgren, 154, 178 
 
 Westphal, 37, 38, 123 f. 
 
 Wiechert, 40 
 
 Wien, 44, 115 
 
 Wilson, C. T. R. ; 46, 50, 132 f., 
 
 187, 189 
 
 Wilson, H. A., 50, 52, 54, 68, 158 
 Wright, 207 
 
 Zeleny, 35 
 Zerner, 163 f. 
 
SUBJECT INDEX 
 
 Absorption and emission frequen- 
 cies, 199 
 
 Absorption spectra, 196 
 
 Alpha particle, range of, 187, 
 charge of, 155 f. 
 
 Amperian currents, 21 
 
 Angular momentum, atomicity of, 
 212 
 
 Atom: a loose structure, 191; 
 diameter of, 180; structure of, 
 179; the nucleus, 190 
 
 Atomic numbers, 197 
 
 Avogadro: constant, 29; rule, 180 
 
 Balance: electrical, 101; quartz, 
 
 101 
 
 Balanced-drop method, 55 
 Balmer series, 201, 206 
 Black-body radiation, 235 
 Bohr atom, 205 f. 
 Brownian movements, 10, 161 f.; 
 
 in gases, 143 f.; theory of, 245 f. 
 
 Cavendish Laboratory, 32, 34 
 Characteristic X-ray spectra, 195 
 Charge: on alpha particle, 155 f.; 
 positive and negative defined, 12 
 Corpuscle, 27 
 Corpuscular theory, 218 f. 
 
 Democritus, principles of, 9 
 Diffusion coefficient of gaseous 
 ions, 34 f., 239 
 
 e: final value of, 119; H. A. Wil- 
 son's work on, 52 ; Sir J. J. Thom- 
 son's work on, 47; Townsend's 
 work on, 43, 242 f. 
 
 Einstein's photo-electric equation, 
 223 
 
 Electricity: atomic theory of, 
 21 f.; early views of, 6 f.; Frank- 
 lin's theory of, 14; growth of 
 theories of, n; proof of atomic 
 nature of, 64 f.; two-fluid the- 
 ory, 13 
 
 Electromagnetic theory of mass, 
 182 
 
 Electron: early values of, 31-58; 
 equality of positive and nega- 
 tive, 80; number of, in atom, 
 192; origin of the word, 25 
 
 : Bucherer's value of, 210: value 
 m 
 
 of, in electrolysis, 27, 30; value 
 of, in exhausted tubes, 40 
 
 Ether, 16, 218 f. 
 
 Ether: stress theory, 17; string 
 theory, 222 
 
 Explosive emission of energy, 235 
 
 Faraday constant, 118 
 Faraday's laws, 15, 19, 28 
 
 Gamma rays, 221, 232 
 
 Gaseous conduction, nature of, 31 
 
 Gram molecule, volume of, in 
 
 gases, 30 
 
 Grating, molecular, 194 
 Greek philosophy, 1,9!. 
 
 h, value of, 210, 227 238 
 Hipp chronoscope, 72 
 
 Inertia due to electrical charge, 
 249 
 
 Ion, gaseous and electrolytic, 33 
 
 Ionic charge, 74, 38 
 
 lonization: by alpha rays, 138; 
 by beta rays, 136; by ether 
 waves, 132; gaseous v. electro- 
 lytic, 39 
 
 267 
 
268 
 
 THE ELECTRON 
 
 Kinetic energy of agitation of air Orbits, non-radiating electronic, 
 molecules directly observed, 78 209 
 
 Kinetic theory, 8, 31 
 Lenard's trigger theory, 231 
 
 Mass, electrical theory of, 182 
 Mass of charge on sphere of radius 
 a, 249 
 
 Periodic table, 200, 260 
 Photo-electric effect, 221 f. 
 Positive rays, 140 
 
 Quantum theory, 222 f. 
 
 Radiant energy, nature of, 217 f. 
 
 Mass, variation of, with speed, Radium, conductivity in air due 
 
 185, 251 
 
 Maxwell-Boltzmann Law, 79 
 Maxwell distribution law, 148 
 
 to, 32 
 
 Radius of the negative electron, 
 182, 185 
 
 Mean free path of a negative elec- Radius of the positive electron, 186 
 
 tron, 1 88 
 Mean free path of gas molecule, 
 
 8, 1 80, 252 
 
 Measurement, value of exact, 46 Rydberg-Schuster law, 214 
 Mechanism of change of charge, 
 
 75 
 Mechanism of gaseous ionization, 
 
 1231. 
 
 Mobility of gaseous ions, 34 f. 
 Molecular cross-section, 252 
 
 Resistance to motion independent 
 
 of charge, 84 
 Rydberg constant, 210, 259 
 
 .Stokes's Law, 46,50, 53, 144, 159 f.; 
 
 failure of, 89; limits of validity 
 
 of, 93 
 Sub-electron, 155 f. 
 
 Moseley's law, 201; inexactness of, I2 r f. 
 
 Valency in gaseous ionization, 
 
 213 
 
 Velocity of agitation of mole- 
 cules, 8 
 
 ne: value of, in electrolysis, 30; in 
 
 gases, 34, 239 Wave theory, 218 f. 
 
 Ne, value of, in electrolysis, 27 f. Wien constant c a , 115, 238 
 Nucleus: atom, 190; charge on, 
 
 193 
 
 X-rays, 32 
 
 Number of electrons in nucleus, x ' ra y spectra, 196 
 
 254 f. 
 
 X-ray spectrometer, 194 
 
The University of Chicago 
 Science Series 
 
 EDITORIAL COMMITTEE 
 
 ELIAKIM HASTINGS MOORE, Chairman 
 JOHN MERLE COULTER ROBERT ANDREWS M1LLIKAN 
 
 The Evolution of Sex in Plants. By JOHN MERLE COULTER. X+I4O 
 pages, i2mo, cloth; $1.00, postage extra (weight 14 oz.). 
 
 Individuality in Organisms. By CHARLES MANNING CHILD, x+212 
 pages, small i2mo, cloth; $1.25, postage extra (weight i Ib. 6 oz.). 
 
 The Origin of the Earth. By THOMAS C. CHAMBERLIN. xii+272 pages, 
 small i2mo, cloth; $i .50, postage extra (weight i Ib. 6 oz.). 
 
 Finite Collineation Groups. By HANS F. BucHFELDT. xii+ig6 pages, 
 small i2mo, cloth; $1.50 net. 
 
 A Chemical Sign of Life. By SniRO TASHIRO. ix+i42 pages, small 
 i2mo, cloth; $i .00, postage extra (weight 14 oz.). 
 
 The Biology of Twins. By HORATIO HACKETT NEWMAN, ix-f 186 
 pages, i2mo, cloth; $1.25, postage extra (weight i Ib.). 
 
 Food Poisoning. By EDWIN OAKES JORDAN, viii+ii2 pages, small 
 i2mo, cloth; $1.00, postage extra (weight 12 oz.). 
 
 The Electron: Its Isolation and Measurement, and the Determination of Some 
 of Its Properties. By ROBERT ANDREWS MlLLlKAN. Small I2mo, 
 cloth; $i .50, postage extra. 
 
 VOLUMES PLANNED OR IN PREPARATION 
 The Living Cycads. By CHARLES JOSEPH CHAMBERLAIN. 
 Mechanics of Delayed Germination in Seeds. By W. CROCKER. 
 The Rigidity of the Earth and of Materials. By A. A. MlCHELSON. 
 The Problem of Fertilization. By FRANK R. LlLLlE. 
 
 Linear Integral Equations in General Analysis. By ELIAKIM HASTINGS 
 MOORE. 
 
 THE UNIVERSITY OF CHICAGO PRESS 
 
 CHICAGO - ILLINOIS 
 

 
 /s 
 > 8*. 
 
 /9 
 
 
\ 
 
 ^ -* 
 
 \S t 
 
 *. .<" 
 
 
 
 V 
 
 ^> 
 *'^ 
 
 \ 
 
 V -^pyg; ^ 
 
 V ./ 
 
 *. .^ 
 
 < f 
 
 V \ 
 
 * ^ 
 
 * > 
 
 > 
 
 1 
 
 s\ 
 
 / 
 
 XN 
 
 r - 
 
 * v 
 
 \ 
 
 V 
 
 / 
 
 ^ > 
 
 sx 
 
 i 
 
 ( 
 
U. C. BERKELEY LIBRARIES