. ELECTRONS 
 
 OE 
 
 THE NATUEE AND PROPERTIES 
 OF NEGATIVE ELECTRICITY 
 
 BY 
 
 SIR OLIVER LODGE, F.R.S. 
 
 D.Sc. LOND., HON. D.Sc. OXON. ET VICT., LI/D. ST. ANDREWS, GLASGOW, AND 
 
 VICE-PRESIDENT OF THE INSTITUTION OF ELECTRICAL ENGINKERS 
 
 RUMFORD MEDALLIST OF THE ROYAL SOCIETY 
 EX-PRESIDENT OF THE PHYSICAL SOCIETY OF LONDON 
 
 LATE PROFESSOR OF PHYSICS IN THE UNIVERSITY COLLEGE OF LIVERPOOL 
 
 HONORARY MEMBER OF THE AMERICAN PHILOSOPHICAL SOCIETY OF PHILADELPHIA, OF THE 
 
 BATAVIAN SOCIETY OF ROTTERDAM, AND OF THE ACADEMY OF SCIENCES OF BOLOGNA 
 
 PRINCIPAL OF THE UNIVERSITY OF BIRMINGHAM 
 
 LONDON 
 
 GEORGE BELL AND SONS 
 1906 
 
Q-CW 
 
 L7 
 
 GLASGOW : PRINTED AT THE UNIVERSITY PRESS 
 BY ROBERT MACLEHOSE AND CO. LTD. 
 
TO THE 
 
 CAVENDISH PROFESSORS OF PHYSICS 
 
 IN THE UNIVERSITY OF CAMBRIDGE, AND ESPECIALLY 
 
 TO THE PRESENT HOLDER OF THE CHAIR, THIS SMALL BOOK IS 
 
 DEDICATED WITH PROFOUND ADMIRATION 
 
 BY THE AUTHOR 
 
 1 C>2827 
 
PKEFACE 
 
 IN 1902 I was asked by the President of the 
 Institution of Electrical Engineers to give to that 
 body a discourse on recent progress towards know- 
 ledge of the nature of Electricity, especially con- 
 cerning its discontinuous or atomic structure. This 
 discourse, greatly extended, appeared in Vol. 32 of 
 the Journal of the Institution, and constitutes the 
 nucleus of the present book. 
 
 Many additions have now been made, and some 
 of the difficulties recently promulgated concerning 
 the possibility of an electric theory of matter are 
 touched upon. They are of date too recent to have 
 been mentioned even in my "Komanes Lecture" 
 before the University of Oxford, published under 
 the title Modern Views of Matter by the Clarendon 
 Press. 
 
 The most important addition is a more detailed 
 account of the proof of the purely electrical nature 
 of the mass or inertia of an electron : an investi- 
 gation generally associated on the experimental 
 side with the name of Kaufmann, but of course 
 based on the work of many predecessors and con- 
 temporaries. A proof that the atom of matter is 
 essentially composed of such electrons, and that 
 its mass too is of purely electromagnetic nature, 
 is lacking : the electromagnetic theory of Matter, 
 
viii PREFACE 
 
 unlike the electromagnetic theory of Light, must be 
 regarded for the present as no better than a working 
 hypothesis. It is a hypothesis of stimulating char- 
 acter, and of great probability, but its truth is still 
 an open question that is probably not going to be 
 speedily closed. 
 
 I am indebted to Professor Larmor for information 
 about some recent theoretical work, and for the 
 substance of Appendix M ; I have also to thank Mr. 
 Gwilym Owen, of the University of Liverpool, for 
 assistance in the revision of the proof. 
 
 As "an introduction to an allied subject, the book 
 called Becquerel Rays, by the Hon. K. J. Strutt, 
 is to be recommended ; and the standard treatise 
 of Professor Eutherford on Radioactivity is well 
 known. I have avoided dealing at length with 
 the topics so conveniently to be found in these 
 writings. I have also barely touched on the large 
 subject of ' ionisation ' : it was difficult to do so 
 without overloading the principles with detail, a 
 knowledge of which is nevertheless necessary for 
 investigators. The treatise of Prof. J. J. Thomson, 
 The Discharge of Electricity through Gases, con- 
 tains a mass of information and original work 
 highly valued by physicists. 
 
 The present book is intended throughout for 
 students of general physics, and in places for special- 
 ists, but most of it may be taken as an exposition of 
 a subject of inevitable interest to all educated men. 
 
 OLIVER LODGE. 
 THE UNIVERSITY OF BIRMINGHAM, 
 July, 1906. 
 
CONTENTS 
 
 I. PROPERTIES OF AN ELECTRIC CHARGE, 1 
 
 Charge in Uniform Motion, ----- 3 
 
 Transmission of Energy, - - - - - - 6 
 
 Accelerated Charge, 7 
 
 II. ELECTRIC INERTIA, - - - - - - - 11 
 
 Electrical Inertia or Mass continued, 12 
 
 Effect of Concentration, - - - ,,-.,- - 15 
 
 Summary, 16 
 Historical Remarks, - - - - --17 
 
 III. FORESHADOWING OF THE ATOM OR INDIVISIBLE 
 
 UNIT OF ELECTRICITY, - - ; . ~ . 19 
 
 IV. FORESHADOWING OF THE ELECTRON, - - - 24 
 
 Separate Existence of the Electric Unit suggested 
 
 by Conduction in Gases, 24 
 
 Cathode Bays, --26 
 
 Nature of the Cathode Rays, 30 
 
 V. DETERMINATION OF SPEED AND ELECTROCHEMICAL 
 
 EQUIVALENT OF CATHODE RAYS, - - 41 
 Further Measurements of Cathode Ray Velocity 
 
 and m/e Ratio by Aid of Electrostatic Deflection, 47 
 Measuring Velocity by Combined Electric and 
 
 Magnetic Deflexion Method, - - ''. , - 50 
 
 Effect on Lenard Rays, - - - - - 52 
 Direct Determination of the Speed of Cathode . 
 
 Rays, 54 
 
x CONTENTS 
 
 CHAP. PACK 
 
 VI. DETERMINATION OF ELECTROCHEMICAL EQUIVA- 
 LENT IN THE CASE OF ELECTRIC LEAKAGE 
 
 IN ULTRA-VIOLET LIGHT, - - - . 58 
 
 Positive and Negative Carriers, 66 
 
 VII. lONISATION OF GASES, 70 
 
 Behaviour of Hot Metals in Gases, - - - 71 
 
 Measurements of lonisation Current, 73 
 
 Condensation of Moisture Experiments, 75 
 
 VIII. DETERMINATION OF THE MASS OF AN ELECTRON, 77 
 
 Aitken and Cloud Nuclei, ----- 79 
 
 J. J. Thomson and Electrical Nuclei, 81 
 
 Wilson and Metrical Cloud Condensation, - - 84 
 
 Professor Stokes and Falling Spheres, 86 
 
 J. J. Thomson's Experiment of Counting, 87 
 
 Result, --.- .... 90 
 
 IX. FURTHER DETAILS CONCERNING ELECTRONS AND 
 
 IONS, 91 
 
 Confirmatory Measurements of Charge, 9t 
 
 Thomson's Deductions, 94 
 
 Estimate of Size, - - - - - - - 95 
 
 Penetrability of Matter by Electrons, 97 
 
 Effects of an Encounter, - - 100 
 
 X. THE ELECTRON THEORY OF CONDUCTION AND OF 
 
 EADIATION, .. . - - - - - 105 
 
 Conduction, - -v - * - - - 106 
 
 Radiation, 109 
 
 XL FURTHER DISCUSSION OF THE ELECTRON THEORY 
 OF THE MAGNETISATION OF LIGHT AND 
 DETERMINATION OF THE m/e RATIO IN 
 
 RADIATION, 116 
 
CONTENTS xi 
 
 CHAP. PAGE 
 
 XII. INCREASE OF INERTIA DUE TO VERY RAPID 
 
 MOTION, - .;.-*' ... - - 122 
 
 XIII. JUSTIFICATION FOR ELECTRIC THEORY OF INERTIA, 129 
 
 Proof of the Purely Electrical Nature of the 
 
 Inertia of the /? Particles shot out by Radium, 131 
 
 XIV. MORE ADVANCED DEVELOPMENT OF THE COM- 
 
 BINED ELECTRIC AND MAGNETIC DEFLEXION 
 METHOD FOR MEASURING VELOCITY AND 
 MASS OF THE PARTICLES IN COMPOUND 
 
 RAYS, - ... . . - 136 
 
 Experimental Device used by W. Kaufmann, - 138 
 
 XV. ELECTRIC VIEW OF MATTER, - 146 
 
 XVI. ELECTRIC VIEW OF MATTER (continued), - - 152 
 
 Nature of Cohesion, 152 
 
 On Chemical and Molecular Forces, - - - 153 
 
 Molecular Forces, Cohesion, - - - 155 
 
 XVII. FURTHER CONSIDERATIONS REGARDING THE 
 
 STRUCTURE OF AN ATOM, - - - - 160 
 
 XVIII. SUMMARY OF OTHER CONSEQUENCES OF ELEC- 
 TRON THEORY, - - . * - * - 163 
 Radio-activity, - . - - - - - " 163 
 Solar Corona, Magnetic Storms, and Aurorse, - 168 
 Transformations of Radium, etc., - - - 169 
 Emanations, * - - - ' - ' "> 171 
 Deflexion of Alpha-rays, - * - ; 171 
 Activity of Radium at all Temperatures, - 174 
 
 Spectrum of Radium, 174 
 
 Electric Production, - - - - - -176 
 
 Radio-activity of Ordinary Materials, - - 177 
 Population Analogy, - - ' - - - -180 
 
xii CONTENTS 
 
 CHAP. PAQE 
 
 XIX. RADIATION FROM A KING OF ELECTRONS, AND 
 ITS BEARING ON THE CONSTITUTION OF AN 
 
 ATOM, - - - - 181 
 
 Instability of an Atom, 183 
 
 . Cosmic Analogy, 185 
 
 Another Account of Atomic Instability, - - 185 
 
 Electric Theory of Matter, 186 
 
 XX. DIFFICULTIES CONNECTED WITH THE ELECTRIC 
 
 THEORY OF MATTER, 188 
 
 1. Concerning the Formation of Spectrum Lines, 188 
 
 2. Attempt to determine the Number of Effec- 
 
 tive Corpuscles in an Atom, - - - 192 
 
 XXI. VALIDITY OF OLD VIEWS OF ELECTRICAL 
 
 PHENOMENA, 195 
 
 Number of Ions in Conductors, - - - - 198 
 
 Conclusion, 200 
 
 APPENDICES 
 
 A. CALCULATION OF THE INERTIA OF AN ELECTRIC CHARGE, - 204 
 
 B. THE ELECTRIC FIELD DUE TO A MOVING MAGNET, - - 207 
 
 C. ON ELECTRICITY AND GRAVITATION AND DIMENSIONS, - 209 
 
 D. DIMENSIONS OF SJM RATIO, - -.- - - -211 
 
 E. ELECTRIC SATURATION, ETC., - - - - - 212 
 
 F. SIZE OF ORBIT OF RADIATING ELECTRON, - - - - 213 
 
 G. THE RADIATING POWER OF A REVOLVING ELECTRON, - 214 
 H. FARADAY'S. PROPHETIC NOMENCLATURE, - - - - 217 
 
 J. ON THE /2-RAYS FROM RADIUM, 219 
 
 K. NOTE ON THE BEHAVIOUR OF A CHARGE MOVING NEARLY 
 
 AT THE SPEED OF LIGHT, - - - - - 221 
 
 L. DISTORTION DUE TO HIGH-SPEED MOTION THROUGH THE 
 
 ETHER, - 226 
 
 M. CONSTITUTION OF ELECTRONS, 227 
 
UNIVERSITY 
 
 INTRODUCTION 
 
 IN Maxwell's Electricity published in 1873, section 
 57, the following sentence occurs in connection with 
 the discharge of electricity through gases, especially 
 through rarefied gases : 
 
 " These and many other phenomena of elec- 
 trical discharge are exceedingly important, and, 
 when they are better understood, they will 
 probably throw great light on the nature of 
 electricity as well as on the nature of gases and 
 of the medium pervading space." 
 
 This prediction has been amply justified by the 
 progress of science, and, no doubt, still further 
 possibilities of advance lie in the same direction. 
 The study of conduction through liquids, first, and 
 the study of conduction through gases, next, com- 
 bined with a study of the processes involved in 
 radiation, have resulted in an immense addition to 
 our knowledge of late years, and have opened a new 
 chapter, indeed a new volume, of Physics. 
 
 The net result has been to concentrate attention 
 upon the phenomena of electric charge, and greatly 
 
xiv INTRODUCTION 
 
 to enhance the importance of a study of electro- 
 statics. Not long ago our brilliant and lamented 
 friend, G. F. FitzGerald, used chaffingly to speak 
 of electrostatics as " one of the most beautiful and 
 useless adaptations of nature " ; and it was becoming 
 the custom with teachers, who felt that they must 
 attend exclusively to the practically useful and not 
 waste their students' time on decoration and super- 
 fluities, almost to ignore, or at any rate to scamper 
 through, the domain of electrostatics, and to begin 
 the study of electricity with the phenomena of 
 current, especially with the connection between 
 electricity and magnetism. 
 
 And certainly from the severely practical point 
 of view, as well as from many other aspects, this 
 part of electrical science remains the most impor- 
 tant ; but to him who would not only design 
 dynamos and large-scale machinery, to him who, in 
 addition to the training and aptitude of the 
 engineer, possesses something of the interests, the 
 instinct, and the insight, of a man of science, to 
 such a one the nature and properties of an electric 
 charge, at "rest and in motion, constitute a fascinat- 
 ing study ; for there lies the key to the inner 
 meaning of all the occurrences with which his active 
 life is so intimately concerned there lies the 
 proximate solution of problems which have excited 
 the attention and taxed the ingenuity of philo- 
 sophers and physicists and chemists for more than 
 a century. Indeed it turns out that subjects 
 
INTRODUCTION xv 
 
 broader and more fundamental than those known 
 as ' electric ' are indirectly involved ; and we are 
 now beginning to have some hope of obtaining 
 unexpected answers to riddles such as those con- 
 cerning the fundamental properties of matter which 
 have proposed themselves for solution throughout 
 the history of civilisation. Problems of this kind 
 have aroused interest and attention ever since men 
 began to escape from the struggle for bare exist- 
 ence that most immediately practical of all occupa- 
 tions and felt free to devote themselves, some to 
 art, some to literature, some to the accumulation 
 of superfluous wealth, and some to the gratuitous 
 pursuit of philosophical speculation,, exact experi- 
 ment, and pure theory. To this comparatively 
 leisured group I now address myself. 
 
MEANING OF TERMS AND SYMBOLS AS USED 
 IN THIS BOOK.. 
 
 Electron = the unit electric charge, or atom of negative electricity. 
 e =the amount of this charge, whether positive or nega- 
 tive; about 3xlO~ 10 electrostatic unit. 
 E =an electromotive force, or the strength of an electric 
 
 field. 
 
 H = the strength of a magnetic field. 
 m = mass or inertia, especially the mass of an electron. 
 a = usually, the linear dimension of an electron (about the 
 
 hundred-thousandth of b). 
 
 b =the linear dimension of an atom of matter (the ten- 
 millionth of a millimetre). 
 
 ion = an atom of matter with an unbalanced electric charge, 
 either negative or positive, attached to it : the 
 cause of chemical affinity. 
 K = Faraday's dielectric constant, or the specific inductive 
 
 capacity of free ether. 
 P = the magnetic permeability of free ether. 
 
 [These two are the great ethereal constants, whose 
 value and nature are not yet known. Only their 
 product is known.] 
 v =the velocity of light in vacuo 
 
 = 3 x 10 10 cm. per sec. 
 u = the velocity of a particle. 
 
CHAPTER I. 
 
 PROPERTIES OF AN ELECTRIC CHARGE. 
 
 FIRST I must lay a basis of pure theory : we must 
 consider the properties of the ancient and long known 
 phenomenon called an electrified body. 
 
 Two substances placed in intimate contact and 
 separated are in general united more or less per- 
 manently by lines of force, the region between them 
 being in a state of tension along the lines and of 
 pressure at right angles. These lines have direction 
 and ' sense ' their two ends are not alike : they 
 begin at one body and end at another, they map out 
 a field of electrostatic force, and their terminations on 
 one or other of the bodies constitute what we call 
 an electric charge. Electric charges are of two kinds, 
 positive and negative, the former corresponding to 
 the beginning of the lines, the latter to their ends. 
 To one class of bodies, called insulators, the lines 
 appear rigidly attached : the charges cannot be dis- 
 placed nor transferred elsewhere without violence ; 
 whereas in another class they slip easily along, and 
 are transferred from one such conducting body to 
 another in contact with it, with great ease. 
 
 A tension in the lines tends to bring the ends 
 together as near as possible, while laterally the lines 
 tend to drive each other apart : this image sufficing to 
 
 L.E. 
 
2 PROPERTIES OF AN ELECTRIC CHARGE [CH. I. 
 
 represent all that is observed as electrical attractions 
 and repulsions. 
 
 The field of force mapped by the lines can exist 
 in vacuo perfectly well, but the lines never terminate 
 in vacuo ; the charges are always carried by matter, 
 or by something equivalent thereto. In empty space 
 it is probable that the only way of destroying such a 
 field of force is to allow the two bodies possessing the 
 charges to approach each other, and thus shorten up 
 the lines to nothing ; though, even so, it is not prob- 
 able that the charges are destroyed, but only placed 
 so close together that they have no external effect 
 at any moderate distance. When matter is present, 
 however, it may be able to assist this collapse of the 
 lines in various ways, giving rise to the various 
 phenomena of conduction and of disruptive discharge. 
 
 If one of the two oppositely charged bodies is sent 
 away to a considerable distance, while the other is 
 isolated and regarded alone, the lines of this latter 
 start out in all directions in nearly straight lines, 
 giving rise to the simple notion of a single charged 
 body. There must however be a complementary 
 charge, the other ends of the lines must be some- 
 where ; though they may be so far away as to be 
 spoken of as, for all practical purposes, at infinity. 
 
 Parenthetical remark of general application. 
 People often feel hesitation about the treatment of 
 things as at infinity, as if it introduced a conception 
 of some difficulty ; but they should realise that this 
 mode of expression is always employed as a simplifi- 
 cation, whenever it happens that for present purposes 
 the said things can be ignored. If their existence 
 requires attention, it must be recognised that they 
 are really at some finite distance, and their location 
 must be specified ; but such specification complicates 
 
CH. L] CHARGE IN MOTION 3 
 
 both ideas and equations. Whenever attention to 
 them is unnecessary, or their location immaterial, this 
 specification is avoided by treating them practically 
 as if they were at infinity, that is by ignoring them. 
 Every now and then this policy of ignoration must 
 be suspended, but for a multiplicity of purposes it 
 serves. 
 
 Charge in uniform motion. 
 
 Now consider how far this field of force belongs to 
 the body, and how far it belongs to space, that is to 
 the ether surrounding the body. The body is the 
 nucleus whence the lines radiate, but the lines them- 
 selves, the state of tension and other properties which 
 they represent and map out, do not belong to the 
 body at all ; at each point of space there is a peculiar 
 etherial condition called an electric potential, and this 
 potential represents something "occurring in the ether 
 and in the ether alone, though it is originated and 
 maintained by the body. 
 
 Picture in the mind's eye such a charged body, say 
 a charged sphere, and let it change its position ; how 
 are we to regard the effect of the displacement on its 
 field of force ? Few things in physics are more certain 
 than this, that when a body moves along, the ether 
 in its neighbourhood is not dragged with it, as if it 
 were in the slightest degree viscous.* The ether, in 
 fact, as a whole i.e. when unmodified or in its 
 normal condition is stationary : it is susceptible to 
 strain, but not to motion ; it is the receptacle of 
 potential, not of locomotive kinetic energy. The only 
 generated motion to which it is possibly susceptible is 
 of what is called ' irrotational ' character in other 
 words it behaves as a perfect fluid. It may possess 
 
 * Lodge, Phil. Trans. 1893, p. 727, and especially 1897, p. 149. 
 
4 PROPERTIES OF AN ELECTRIC CHARGE [CH. I. 
 
 other rotational, or vortex-like motion, but, if so, it is 
 indestructible and unproducible by any known means, 
 and has not yet been discovered. 
 
 The effect of the motion of the body, then, is to 
 relieve the strain of the ether at one place and to 
 generate it at another ; the state of strain travels 
 with the body, but through the ether. 
 
 Regarding the matter from the point of view of 
 the ether, we might say that the field of force is 
 constantly being destroyed and regenerated as the 
 body moves. Regarding it from the point of view 
 of the moving body, we should say that it carries its 
 field with it. 
 
 The question now arises and it is far from being 
 an easy question what sort of occurrences go on in 
 the ether when this decay and regeneration of an 
 electrostatic field is occurring, or when a field of force 
 is moving through it ? Can it adapt itself instantly 
 to the new conditions, or does it require time ? This 
 matter has been studied, closely and exhaustively, by 
 Mr. Oliver Heaviside. 
 
 Fix the eye upon a point a mile distant from the 
 body ; does the information about the motion of the 
 body reach that point instantaneously, so that all the 
 lines of force move like absolutely rigid spokes, every 
 part simultaneously ? If so, how is the communi- 
 cation carried on, so that the distant parts of the 
 medium can be thus instantaneously affected ? Or 
 does the disturbance only arrive at the distant point 
 after the lapse of a small but appreciable time ; in 
 other words, has there to be an adjustment to the 
 new conditions an adjustment which reaches the 
 nearest parts first and the further parts later ; and if 
 so, what additional phenomena can be observed 
 during the unsettled period ? 
 
CH.L] CHARGE IN MOTION 5 
 
 The answer is that during the motion of the 
 charged body, and even after the cessation of its 
 motion, until the disturbance has had time to die 
 away and everything to settle down into static con- 
 dition again, the phenomena of magnetism make 
 their appearance : a new set of lines of force quite 
 different from the electrostatic lines (although they, 
 too, exhibit a tension along them and a pressure at 
 right angles) come into temporary being. These do 
 not like the electric ones originate at one place 
 and terminate at another : they are always and 
 necessarily closed curves or rings, and in the present 
 simple case they are circles all centred upon the path 
 of motion of the charged body. At any point of space 
 there are now three directions to consider : (l) there 
 is the original direction of the electrostatic field the 
 original electric line of force ; (2) there is the direction 
 of the motion that is, a direction parallel to the 
 movement of the charged sphere ; and (3) there is the 
 direction at right angles to these two ; this last being 
 the direction of the magnetic lines of force the 
 direction of the magnetic field. 
 
 I spoke of the magnetic field as temporary, but 
 that is on the assumption that the charged body is 
 merely displaced merely shifted from one position to 
 another ; if it is not stopped, but keeps on moving, 
 then the magnetic lines continue as long as the 
 motion lasts. The strength of the magnetic field, 
 at any point with polar coordinates r, 0, is 
 
 TT eu a 
 
 H = r sin 6. 
 
 r 2 
 
 If we are asked whether such a magnetic field is 
 weak or not, I have to reply that that depends 
 entirely on how strong the charge is and how quickly 
 
6 PROPERTIES OF AN ELECTRIC CHARGE [CH. I. 
 
 it is moving. There is, in my opinion, no other 
 kind of magnetic field possible ; and so if ever we 
 come across a magnetic field which we feel entitled 
 to consider " strong," we must conclude that it is 
 associated with the motion of a very considerable 
 charge, at a velocity we may properly style great. 
 But certainly it is true that for any ordinary charged 
 sphere, moving at any ordinary pace, even supposing 
 that it is a cannon-ball shot from the mouth of a 
 gun the concentric circular magnetic field sur- 
 rounding its trajectory is decidedly feeble. Feeble 
 or not, it is there, and to its existence we must trace 
 all the magnetic phenomena of the electric current. 
 
 For just as there is no electrostatic field save that 
 extending from one charged body to another, so 
 there is no electric current except the motion of such 
 a charged body, and no magnetic field except that 
 which surrounds the path of this motion. 
 
 The locomotion of an electric charge is an electric 
 current, and the magnetic field surrounding that 
 current is believed to be the only kind of magnetic 
 field in existence. If any other variety is possible, 
 the burden of proof rests on those who make the 
 positive assertion. 
 
 Transmission of Energy. 
 
 While the charge is stationary everything is steady, 
 and we have an electric field only. 
 
 While the charge is moving at constant speed the 
 current is steady, and we have a steady magnetic 
 field superposed upon a steadily moving electric field; 
 there is likewise a certain conveyance of energy in 
 the direction of the motion. 
 
 This is a special case of the general theorem 
 known as Poynting's : viz. that wherever an electric 
 
CH. i.] ACCELERATED CHARGE 7 
 
 and a magnetic field are superposed there cannot 
 be static equilibrium at that place, energy must flow 
 through the medium ; and the rate of transfer of 
 energy the amount conveyed per second through 
 unit area is equal to 1/4 TT times the vector product of 
 the intensity of the two fields : that is to say, it is 
 measured by the area of the parallelogram bounded 
 by lines representing the two fields in magnitude and 
 direction ; a quantity commonly expressed as 
 
 V(EH), or [EH], or as EH sin 0, 
 
 where is the angle between E and H. 
 
 The direction of propagation of energy is normal 
 to that same area, and its ' sense ' or sign depends 
 upon the sense of the two fields. If both were 
 reversed, the sense of the transmission of energy 
 would continue unchanged : and its amount remains 
 constant so long as the fields are constant, that is 
 so long as the current is steady. Another way of 
 expressing the facts is to say that the space in which 
 two fields are superposed is full of momentum ; and 
 that the moment of momentum ^appropriate to a pole 
 m and a charge e is simply em. 
 
 Accelerated Charge. 
 
 One more statement : 
 
 So far we have dealt with the case of steady rest or 
 steady motion ; but what about the intermediate 
 stages, the stages of starting and stopping ? What is 
 the condition of things after the charge has begun to 
 move but before it has attained a constant speed, and 
 again when the brake is applied and the speed is 
 decreasing, or when the direction of motion is chang- 
 ing? What phenomena are observable during the 
 epoch of acceleration or retardation of speed or 
 
8 PROPERTIES OF AN ELECTRIC CHARGE [CH.L- 
 
 curvature of path ? Something more* than simple 
 electrostatics and simple magnetism is then observed. 
 For whenever a conductor is moved across a 
 magnetic field it is well known that an electromotive 
 force acts in that conductor, of magnitude equal to 
 the rate at which magnetic lines of force are being 
 
 cut ; or in symbols . 
 
 E= dN/dt, 
 
 which is the fundamental ' dynamo ' equation. This 
 is called the phenomenon of magneto-electric in- 
 duction ; it is the induced E.M.F. discovered by 
 Faraday, and it necessarily occurs whenever magne- 
 tism and relative motion are superposed. 
 
 It is quite independent of the conductivity of 
 the conductor however, and would have the same 
 value if the motion took place in an insulator, 
 though of course it could not then produce the 
 same effect as regards conduction-currents. 
 
 The effect of a conductor is to integrate, or add 
 up, the E.M.F.'S generated in each element all along 
 its length, and thus to display the effect in an 
 obvious manner : especially when the conductor is 
 made very long and is compactly coiled (as in an 
 armature). The definition of electromotive force 
 between two points A and B, or round any closed 
 contour, is the line-integral of electric field from A 
 to B, or round the same contour. In the unclosed- 
 path case it is measured by the difference of electric 
 potential between A and B. 
 
 One of the easiest and most ordinary ways of 
 superposing motion and magnetism, is to allow or 
 cause a magnetic field to vary in strength (as in 
 a Ruhmkorff coil) ; for then the lines of force move 
 broadside on, expanding or contracting as the case 
 may be, and thus at once we get the phenomenon 
 
CH. i.] ACCELERATED CHARGE 9 
 
 of induction the generation of an induced E.M.F., 
 of value at any point equal to the rate of change 
 of the lines of magnetic force there. This is what 
 happens whenever an electric charge is accelerated ; 
 for then its magnetic field which, as we have seen, 
 depends upon the velocity necessarily changes in 
 strength, and so an E.M.F. is induced. There being 
 no conductor, this E.M.F. will propel no current, but it 
 will represent an electric force which was not there 
 before, and the new force will be in a new direc- 
 tion ; the direction of an induced electric force is 
 perpendicular to the direction in which the grow- 
 ing magnetic lines are moving, which in the 
 present case is outwards from the charge. Con- 
 sequently the new or induced E.M.F. points in the 
 direction of motion, though in the sense opposed 
 to any change in it ; and the effect of the super- 
 position of this new E.M.F. upon the already existing 
 magnetic field is to cause a certain small transmission . 
 of energy in a radial direction out and away from 
 the accelerated charge. Some energy therefore flashes 
 away with the speed of light ; and although in 
 ordinary cases it may be an exceedingly small amount 
 which is thus radiated into space, yet it is the only 
 mode of generating radiation with which we are 
 acquainted. 
 
 It is from an electric charge during its epochs of 
 acceleration or retardation that we get the pheno- 
 menon called radiation ; it is this and this alone 
 which excites ethereal waves, and gives us the 
 different varieties of light. 
 
 The energy radiated per second has been shown 
 by Larmor to be 
 
10 PROPERTIES OF AN ELECTRIC CHARGE [CH. i. 
 
 where v is the speed of light and u is the acceleration 
 of the charge e. 
 
 After this manner, though of course by means of 
 a very extensive development of these fundamental 
 ideas, are all the phenomena of electricity and mag- 
 netism and optics summarised, and, so to speak, 
 accounted for. 
 
 NOTE. 
 
 Let it be said here, once for all, that in every case one or other 
 of the two etherial constants, p and K, should be exhibited 
 explicitly wherever it rightly occurs. If this be not done the 
 dimensions of most expressions are necessarily wrong; and 
 words have to be added about whether the units intended are 
 c.g.s. or some other system, and likewise whether they are 
 electrostatic or electromagnetic. This latter double system of 
 measurement has served its turn, and still serves it ; but intrinsi- 
 cally it is confusing, and has been only rendered necessary 
 because we do not yet know the values, or even for certain the 
 t nature, of p and K. It is to be hoped that no third system 
 'devised as an attempted escape from confusion, but really an 
 intensification of fog will ever be successfully attempted ; though 
 there are threats in that direction, owing to lack of clear thinking. 
 
 The explicit retention of the constants keeps everything clear 
 and easy. For instance, the expression just above quoted is 
 essentially what it purports to be, an energy divided by a time 
 
 FL 
 
 and is therefore true as it stands in every complete system of 
 units whatever. So also the expression quoted near the be- 
 ginning of the next chapter is essentially what it purports to be, 
 namely, a mass or inertia ; and the same may be said of all other 
 expressions in this book. 
 
 The ordinary convention for numerical specification is, for 
 electromagnetic c.g.s. units, to consider /* = 1, for electrostatic 
 units, to consider K = I \ and this convention must hold until we 
 learn the real facts, by future discovery : for which discovery 
 continual familiarity with the unknown constants undoubtedly 
 serves to pave the way. 
 
CHAPTER II. 
 ELECTEIC INERTIA. 
 
 WHATEVER a charge may be, and whatever the 
 physical constitution of the ether, it must be able 
 to maintain electric lines and magnetic lines 
 separately, and to transmit energy wherever both 
 sets of lines coexist and cross each other. 
 
 An accelerated charge is equivalent to a changing 
 current, for dC/dt may be written d 2 e/dt 2 . When- 
 ever a current changes it is well known that an E.M.F. 
 of self-induction is set up, equal to LdC/dt; and 
 this electrical equation E = L e corresponds to the 
 mechanical equation F = ra x, Newton's second law. 
 
 Considered from the point of view of a current as 
 constituted by a moving charge, this self-induced or 
 reaction E.M.F. corresponds or is analogous to a mass- 
 acceleration. And the electrical acceleration is 
 opposed by the E.M.F., just as the acceleration of 
 matter is opposed by its mechanical inertia. The 
 coefficient of the electric acceleration commonly 
 denoted by L represents therefore an inertia term, 
 and is properly called 'electric inertia.' 
 
 By Lenz's law the effect of induction is always 
 to oppose the cause which is producing it. In the 
 present case the * cause' is the acceleration or retarda- 
 tion of the moving charge ; and so, in each case, this 
 
12 ELECTRIC INERTIA [CH. n. 
 
 is opposed by the reaction of the magnetic lines 
 generated by it. 
 
 Motion is opposed while it is increasing in speed, 
 and it is assisted while it is decreasing in speed 
 an effect precisely analogous to ordinary mechanical 
 inertia ; and therefore force is necessary, and work 
 must be done, either to start or to stop the motion 
 of a charged body. An extra force, that is, by 
 reason of its charge. Whatever ordinary inertia 
 the body may have, considered as a piece of matter, 
 it has a trifle more by reason of its being charged 
 with electricity no matter what the sign of its 
 charge may be. 
 
 The value of this imitation or electrical inertia, 
 for the case of a charged sphere of radius a, was 
 calculated by J. J. Thomson in 1881, and is 
 
 3a 
 
 Electrical Inertia or Mass, continued. 
 
 Since this is very important, I repeat : 
 Just as a changing magnetic field affects an electro- 
 static charge, that is to say generates a feeble field 
 of electric force, into the intensity of which the 
 velocity of light enters squared in the denominator 
 (see Lodge, Phil. Mag., June 1889, p. 472), so it 
 is with a changing electric field, it generates a 
 magnetic field proportional to its velocity of change. 
 And if it is being accelerated, the magnetic field 
 itself varies, and in that case generates an E.M.F. 
 which reacts upon the accelerated moving charge, 
 always in such a way as to oppose its motion 
 by what is called Lenz's law, or simply by the law 
 of conservation of energy : for if it assisted the 
 
CH. II.] ELECTRIC INERTIA 13 
 
 motion, the action and reaction would go on in- 
 tensifying themselves, until any amount of violence 
 was reached. 
 
 The magnetic lines generated by a rising current, 
 that is by a positively accelerated charged body, 
 react back upon the motion which produced them 
 in such a way as to oppose it ; to oppose it 
 actively or elastically, not passively or sluggishly 
 as by friction. The reaction ceases the instant the 
 motion becomes steady : it is not analogous to 
 friction therefore, but to inertia ; it is the coeffi- 
 cient of an acceleration term. 
 
 The magnetic lines generated by a falling current, 
 that is by a negatively accelerated or retarded 
 charged body, react oppositely, and tend to con- 
 tinue the motion : thus here also we have a term 
 corresponding to inertia. And the charged body 
 may be said to have extra momentum, by reason 
 of its charge, while it is moving. The value of 
 the momentum is proportional to the velocity, so 
 long as the velocity is not excessively great ; and 
 accordingly the inertia term is constant, i.e. inde- 
 pendent of speed, under the same restriction. It 
 may therefore be considered to be in existence 
 even when the charge is stationary, and thus it 
 simulates exactly the familiar mechanical inertia 
 of a lump of ordinary matter. 
 
 In Appendix A, is given the simplest form of 
 the quantitative relations here indicated, and the 
 inertia due to an electric charge is there calculated. 
 It is to be understood that whatever inertia a 
 material sphere may possess, considered as matter, 
 it will possess more when it is charged with elec- 
 tricity, and this no matter whether the charge 
 be positive or negative. The amount of extra or 
 
14 ELECTRIC INERTIA [CH. n. 
 
 electrical inertia is proportional to the electrostatic 
 energy of the charge : that is to say, it is pro- 
 portional to the charge and its potential conjointly. 
 Call the charge e, and the radius of the sphere a, 
 the potential will be e/Ka (K being Faraday's 
 dialectric constant) ; and the appropriate inertia is 
 
 where v is the velocity of light. (See Note at end 
 of chap, i.) 
 
 Another way of putting it is to say that if a 
 real mass of this amount were moving with the 
 speed of light, its kinetic energy would be half as 
 great again as the potential energy of the electric 
 charge thus reckoned as mechanically equivalent 
 to it; 
 
 for ~mv 2 = -e . = charge x potential 
 
 4 2 KCI 2 
 
 = potential energy. 
 
 Now any appreciable quantity of matter, even a 
 milligramme, moving with the speed of light, must 
 have a prodigious amount of energy ; for, on the 
 ordinary assumption that mass is quite constant, 
 the energy of one milligramme rushing along with 
 the light-speed would amount to no less than 
 fifteen million foot-tons. Or as Sir William Crookes 
 has expressed it : a gramme, or fifteen grains, of 
 matter, moving with the speed of light, would have 
 energy enough to lift the British Navy to the top 
 of Ben Nevis. 
 
 Consequently the inertia of any ordinary quantity 
 of electric charge must be exceedingly minute. 
 Notwithstanding this, it is quite doubtful whether 
 
CH. ii.] ELECTRIC INERTIA 15 
 
 or not there really exists any other kind of inertia. 
 The question whether there does or not is at 
 present, strictly speaking, an open one. 
 
 Effect of Concentration. 
 
 The only way of conferring upon a given electric 
 charge any appreciable mass, is to make its potential 
 exceedingly high, that is to concentrate it on a 
 very small sphere. 
 
 A coulomb at the potential of a volt has an elec- 
 trostatic energy of half a Joule, that is ^ x 10 r ergs. 
 
 The mass equivalent to this would be 
 
 2 10^ 2 
 
 39xl0 20 = 27 X 10 ~ 13 g ramme= 10 ~ 8 milligramme. 
 
 Kaise the potential to a million volts, and the 
 mass-equivalent to a coulomb at that potential 
 would be the hundredth part of a milligramme ; 
 still barely appreciable therefore. 
 
 The charge on an atom as observed in electrolysis 
 is known to be 10~ 10 electrostatic units.* If this 
 were distributed uniformly on a sphere the nominal 
 size of an atom, viz., one 10~ 8 centimetre in radius, 
 its potential would be one hundredth of an elec- 
 trostatic unit, or . about 3 volts. The energy of 
 such a charge would be 10~ 12 erg, and the inertia 
 of a body which would possess this energy if moving 
 at the speed of light would be 10~ 33 gramme ; which 
 would therefore be its electrical inertia or extra mass. 
 
 But this is incomparably smaller than the mass 
 of a hydrogen atom, which is approximately 10~ 25 
 gramme. Consequently the ionic charge distributed 
 uniformly over an atom would add no appreciable 
 fraction to its apparent mass. 
 
 * More exactly, according to Cambridge measurements, 3*3 x 10 ~ 10 . 
 
16 ELECTRIC INERTIA [CH, n. 
 
 If, however, the atomic charge were concentrated 
 into a sphere of dimension 10~ 13 centimetre, its 
 potential would be 1000 electrostatic units, or 
 300,000 volts; its energy would then be 10~ 7 erg, 
 and its inertia 10 ~ 28 gramme, or about YTHJIT f the 
 mass of a hydrogen atom. 
 
 Summary. 
 
 All this is a preliminary statement of undeniable 
 fact : that is to say of fact which follows from the 
 received and established theory of Electricity, 
 whether such things as electrons have ever been 
 found to exist or not. 
 
 All that we have stated is true of an ordinary 
 charge on any ordinary sphere which can be made 
 to move by mechanical force applied to it. 
 
 It gives us the phenomena 
 
 of electrostatics when at rest, 
 of magnetism when in motion, 
 of radiation when its motion is altered ; 
 and it incidentally, by reason of the known laws of 
 electromagnetic induction, exhibits a kind of imitation 
 inertia, and in that way simulates the possession of 
 the most fundamental property of matter. > 
 
 I will add a few more closely connected assertions, 
 for later application : 
 
 Apply a sufficiently violent E.M.F. to a charged 
 sphere, and the charge may be wrenched off it. 
 
 Insert an obstacle in the path of a violently moving 
 charged sphere, so as to stop it mechanically with 
 sufficient suddenness, and again it is possible for the 
 charge, or something like it, to be jerked off it and 
 passed on. But to do this the speed of the material 
 sphere, as well as the suddenness of stoppage, must be 
 
CH.II.] HISTORICAL REMARKS 17 
 
 excessive. Usually the charge is merely thrown into 
 oscillation, when the sphere is suddenly stopped ; and 
 it then emits a solitary wave or spherical shell of thick- 
 ness equal to the diameter of the sphere : or greater 
 than that diameter by the amount the sphere has 
 moved during its retardation. When the acceleration 
 is moderate, however, the radiation is less energetic 
 and also less intense : less energetic because its power 
 depends on the square of the acceleration, less intense 
 because it is spread over a thicker ethereal shell. 
 Rontgen rays are perceptible only when the speed was^ 
 great and the stoppage so sudden that the wave or 
 pulse- shell is strong and thin (see chap. viii.). The 
 thinner the pulses or wave shells the more penetrating 
 they are. If thin enough they could traverse matter 
 without affecting it or being affected by it. 
 
 Historical Remarks. 
 
 The doctrine of the behaviour of a charged sphere 
 in motion, and the calculation of the value of the 
 quasi inertia of an electric charge, was begun by 
 Professor J. J. Thomson in an epoch-making paper 
 published in the Philosophical Magazine for April, 
 1881 one of the most remarkable physical memoirs 
 of our time. 
 
 The stimulus to this investigation was supplied by 
 those brilliant experiments of Crookes, published in 
 the Philosophical Transactions for 1879, which were 
 preceded by observations of Pliicker and Hittorf, and 
 related to other observations by Goldstein, Spottis- 
 wood and Moulton, and others, about the same period. 
 
 In 1891 Sir William Crookes was President of 
 the Institution of Electrical Engineers, and in his 
 inaugural address he expounded further some of these 
 brilliant experimental investigations, to which Schuster 
 
 L.E. 
 
18 ELECTRIC INERTIA [CH. n. 
 
 and many others had contributed. It is not too much 
 to say that up to the time of Crookes the phenomena 
 of the vacuum tube were shrouded in darkness, not- 
 withstanding much laborious and painstaking work 
 done both in this country and on the Continent in 
 connection with them ; but that since the researches 
 of Crookes in the seventies, the theoretical luminosity 
 of the vacuum tube has steadily increased, until now, 
 as Maxwell predicted, it is shedding light upon the 
 whole domain of electrical science, and even upon the 
 constitution of matter itself. 
 
CHAPTEK III. 
 
 FORESHADOWING OF THE ATOM OR INDIVISIBLE 
 UNIT OF ELECTRICITY. 
 
 So far we have dealt with the fundamental laws of 
 electricity in' general. It is now time to begin to 
 consider the possibly atomic or molecular condition in 
 which it is associated with atoms of matter. 
 
 Quoting again from the great Treatise of Clerk 
 Maxwell, 1st Edition (1873), we find on page 312, 
 in the chapter on electrolysis, the following sentence : 
 
 " Suppose, however, that we leap over this 
 difficulty by simply asserting the fact of the 
 constant value of the molecular charge, and 
 that we call this constant molecular charge, for 
 convenience in description, one molecule of 
 electricity." . . . 
 
 Thus some idea of the conception of the atomic 
 nature of electricity was long ago forced upon men of 
 genius by the facts of electrolysis and a knowledge of 
 Faraday's laws. But Maxwell went on, after a few 
 more paragraphs : 
 
 "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 
 
20 FORESHADOWING OF THE ATOM [CH. in. 
 
 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 theories." 
 
 It is rash to predict what may ultimately happen, 
 but the present state of electrical science seems hostile 
 to this latter prediction of Maxwell. The theory of 
 molecular charges looms bigger to-day, and has taken 
 on a definiteness, largely as the outcome of his 
 own work, that would have pleased and surprised 
 him. 
 
 The unit electric charge, the charge of a monad 
 atom in electrolysis, whatever else it is, is a natural 
 unit of electricity, of which we can have multiples, 
 but of which, so far as we know at present, it is 
 impossible to have fractions. 
 
 I will extract the following sentence from Section 
 32 of my little book called Modern Views of 
 Electricity (1889. See also Brit. Assoc., Aberdeen, 
 1885, p. 763): 
 
 " This quantity, the charge of one monad 
 atom, constitutes the smallest known portion of 
 electricity, and is a real natural unit. Obviously 
 this is a most vital fact. This unit, below which 
 nothing is known, has even been styled an 
 ' atom of electricity,' and perhaps the phrase 
 may have some meaning. . . . This natural 
 unit of electricity is exceedingly small, being 
 about the hundred-thousand-millionth part of 
 the ordinary electrostatic unit,: or less than the 
 hundred- trillionth of a coulomb." 
 
 The atom with its charge is called an " ion." The 
 charge considered alone, without attending to its 
 
CH.IIL] OF ELECTRICITY 21 
 
 atom, was called by Dr. Johnstons Stoney an 
 " electron " or natural electrical unit. 
 
 What we learn with great accuracy from electro- 
 lysis is the ratio of the charge to the mass of 
 substance with which it is associated. It matters 
 nothing how much substance is chosen, whether 100 
 atoms or one, whether an atom or a gramme or a ton, 
 the amount of electricity associated with it in 
 electrolysis, and liberated when the substance is 
 decomposed, increases in the same proportion ; the 
 ratio is constant for each material, and if determined 
 for one is known for all. 
 
 This ratio is the reciprocal of what is technically 
 known as the " electrochemical equivalent " of a sub- 
 stance. In the light of Faraday's laws, if this quantity 
 is measured for one substance it is known for all, 
 because the charge is the same for every kind of 
 atom, up to a simple multiple ; and hence in specify- 
 ing electrochemical equivalents there is nothing 
 to consider but the atomic weight, or combining 
 proportion, of the substance. Thus the electro- 
 chemical equivalent of oxygen is 8 times that of 
 hydrogen, that of zinc is 32|- times, and that of silver 
 108 times that of hydrogen. The substance chosen 
 for a determination of the electrochemical equivalent 
 may be the one which can be most accurately experi- 
 mented on ; and Lord Rayleigh has shown that such a 
 substance is nitrate of silver, and has ascertained that 
 if a current of one ampere is passed from a silver anode 
 to a platinum cathode through a nitrate of silver solu- 
 tion, the cathode gains in weight by 4*025 grammes 
 every hour. Hence the electrochemical equivalent of 
 silver is 
 
 4*025 grammes f 
 
 1 ampere-hour ' 
 
22 FORESHADOWING OF THE ATOM [CH. HL 
 
 the electrochemical equivalent of hydrogen, being 
 Y^-gth of this quantity, is 
 
 4*025 grammes 4*025 
 
 108 ampere-hours = 108 x 360 C ' g ' S * 
 
 = '0001035 c.g.s. = Q gg nn grammes per coulomb. 
 
 Hence the ratio of an atom of electricity to an atom 
 of hydrogen is 9,660 M~^ c.g.s. units, or approximately 
 
 centimetres\ 
 
 { // 
 V 
 
 * grammes/ 
 
 the unknown constant M necessarily making its 
 appearance, because we are comparing quantities of 
 different nature, or at any rate quantities measured 
 in different ways, viz., 'electricity' and 'matter' (see 
 Appendix D). 
 
 The numerical part of this quantity is known 
 with comparative exactitude,* that is to say up to 
 the limits of error of experiment : to proceed 
 further, we must make an estimate of the mass of 
 an atom. That can be done, and has been done, in 
 many ways, and we have been taught both by Dr. 
 Johnston e Stoney and by Loschmidt, originally even 
 by Dr. Thos. Young, but with greatest force and range 
 by Lord Kelvin, that the mass of an atom of water is 
 approximately 10~ 24 of a gramme; wherefore an atom 
 of hydrogen will be approximately 10 ~ 25 gramme; 
 whence the unit of electric charge is 10~ 21 c.g.s. 
 magnetic unit, or 10~ 10 of an electrostatic unit or 
 10- 20 of a coulomb. 
 
 *The decimal places are correctly printed above ; though the fact 
 that 1 coulomb, or 1 ampere-second, is one-tenth of a c.g.s. unit owing 
 to the ohm and volt having been inadvertently defined, one as 10 9 , and 
 the other as 10 8 c.g.s., instead of both the same always stands ready to 
 introduce confusion and error. 
 
CH. in.] OF ELECTRICITY 23 
 
 I have emphasised this matter of the ratio m to e, 
 or e to ra, because it plays a considerable part in 
 what follows. The absolute values are of less 
 consequence to us than the ratio, and are only known 
 approximately, but the ratio is known with fair 
 accuracy ; and the ratio e : m for hydrogen is very 
 nearly 10 4 magnetic units, or more exactly 9,660. 
 
 Thus what we learn from electrolytic conduction, 
 briefly summarised, is that every atom carries a 
 certain definite charge or electric unit, monads 
 carrying one, diads two, triads three, but never a 
 fraction ; that in liquids these charges are definitely 
 associated with the atoms, and can only be torn away 
 from them at the electrodes ; that the current 
 consists of a procession of such charges travelling 
 with the atoms, the atoms carrying the charges, or 
 the charges dragging the atoms, according to the 
 point of view from which we please to regard the 
 process. 
 
CHAPTEE IV. 
 FORESHADOWING OF THE ELECTRON. 
 
 Separate Existence of the Electric Unit suggested 
 by Conduction in Gases. 
 
 WE will now leave liquids and proceed to conduction 
 by ratified gases, that is to say to the phenomena 
 seen in vacuum tubes. If a long glass tube, say a 
 yard long and two inches wide, with an electrode at 
 each end, and full of common air, is connected to an 
 induction coil and attached to an air-pump, the 
 ordinary spark-gap of the coil being, say, two or 
 three inches wide, we find that for some time after 
 working the pump the electric discharge prefers the 
 inch or two of ordinary air to a long journey through 
 the partially rarified air in the tube ; but that at a 
 certain stage of exhaustion, one which any rough 
 air-pump ought to reach, this preference ceases. A 
 flickering light appears in the tube, readily visible in 
 the dark, which very soon takes on the appearance of 
 red streamers like the Aurora Borealis ; and soon the 
 sparks outside in the common air cease, showing that 
 the rarified air is now the better conductor and the 
 preferable alternative path. Let the exhaustion 
 proceed further the axis of the tube becomes 
 illumined with a glow, which is now much brighter, 
 
CH.IV.] VACUUM TUBE 25 
 
 forming a band or thread of light, while the original 
 spark-gap may be shortened down gradually to one- 
 eighth of an inch, or even less, without any spark 
 taking place across it, showing that rarified air is 
 a very good conductor. When the best conducting 
 stage is reached the tube is filled with a glow, called 
 the positive column ; and both ends of the tube are 
 apt to look alike. If we exhaust still further and 
 to exhaust even as far as this something better than 
 an ordinary air-pump is necessary, an oil or mercury 
 pump being the most suitable the column of light 
 is seen to fill the whole tube, to gradually lose its 
 bright red or crimson tint, and to break up into a 
 number of very narrow discs, like pennies seen edge- 
 ways. At the same time the spark-gap must be 
 widened to something more like a quarter or half an 
 inch, to prevent the discharge from taking that path, 
 and a dark space near the cathode now begins to be 
 visible, the cathode itself being covered all over with 
 a glow, while the anode is usually only illuminated 
 at a point or two. The striae, into which the positive 
 column has been broken up, thicken and separate as 
 exhaustion proceeds. The dark space near the 
 cathode also enlarges, driving as it were the positive 
 column before it into the anode, and looking as if it 
 would presently fill the tube ; but before it can do 
 this it is noticed that the glow on the cathode itself 
 is coming off as a kind of shell, leaving another dark 
 space, a narrower and much darker space, inside it. 
 The first dark space has been called Faraday's dark 
 space ; the second is generally known by the name of 
 Crookes'. This second dark space now increases in 
 thickness, pushing the glow before it as the vacuum 
 gets better and better ; but the terminals of the 
 spark-gap must now be pulled still further apart, else 
 
26 FORESHADOWING OF THE ELECTRON [CH. IV. 
 
 the discharge will prefer to take a reasonably long 
 path through the air. Exhausting further still, the 
 glow all disappears and the second dark space fills 
 the whole of the tube ; and now is noticed a new 
 phenomenon, the sides of the glass have begun to 
 glow with a phosphorescent light, the colour of the 
 light depending on the kind of glass used, but 
 generally in practice with a greenish light ; a result 
 evidently of being the boundary of the dark space. 
 If exhaustion proceeds further, the resistance of the 
 tube becomes very high, and the spark may prefer to 
 burst through an equal, and ultimately even a greater, 
 length of ordinary air. This is the condition of the 
 tube so much investigated by Crookes, by Lenard 
 and Rontgen, and by many other observers. It is 
 the phenomena occurring in this dark space which 
 have proved of the most intense interest. 
 
 Cathode Rays. 
 
 So far we have supposed that the cathode is a 
 brass knob or other convenient terminal introduced 
 into the tube ; but if we now proceed to use other 
 shapes, as Plucker did first in 1859, followed by 
 Hittorf (1869), Goldstein (1876),and Crookes (1879) 
 using a flat disc or a saucer-shaped piece of metal, and 
 if we then introduce into the dark space various sub- 
 stances, we shall find that shadows are thrown, and 
 that the dark space is full of properties which are 
 most clearly expressed by saying that it is a region 
 of cathode rays that is to say, of something shot 
 off in straight lines from the cathode. There is 
 evidently something being thus shot off though what- 
 ever it is, it is invisible until it strikes an obstacle 
 something which seems to fly in straight lines and to 
 produce a perceptible effect only when it stopped. 
 
CH. iv.] CATHODE RAYS 27 
 
 Such a * something' might be a bullet from a gun, 
 which is quite invisible when looked at sideways, but 
 may produce a flash of flame when it strikes a target, 
 or may do other damage. So it is with these cathode 
 rays : the region of their flight is the dark space ; the 
 boundaries of that space, where the projectiles strike, 
 are illuminated. A substance with phosphorescent 
 power, such as many minerals, or even glass, phos- 
 phoresces brightly ; and the path of the rays can 
 be traced by smearing a sheet of mica with some 
 phosphorescent powder and placing it edgeways 
 along their path. In this way it can be shown 
 that the rays are like particles travelling definitely 
 in straight lines, not colliding against each other, 
 but each shot like bullets from an immense number 
 of parallel guns. Where they strike the sides of 
 the glass they make it phosphoresce; where they 
 strike residual air in the tube, as they do if the 
 exhaustion is not high enough, they make it phos- 
 phoresce also, and give, in fact, the ordinary glow 
 surrounding the dark space. 
 
 These rays possess a considerable amount of 
 energy, as can be shown by concentrating them, by 
 means of a curved saucer-shaped cathode, and 
 bringing them to a focus. The rays can be brought 
 to a focus in consequence qf the fact that they 
 are projected from the cathode initially normal to 
 its surface, though the focus is further from the 
 cathode than the centre of curvature because of 
 something equivalent to mutual repulsion of the 
 rays. A piece of platinum put at that focus will 
 (if the exhaustion is not too high) show evident 
 signs of being red-hot that is to say, will emit 
 light. If the exhaustion proceeds further, less heat 
 is produced, though a phosphorescent light is 
 
28 FORESHADOWING OF THE ELECTRON [CH. iv. 
 
 now emitted from suitable substances, like alumina 
 and most earths ; and if the exhaustion is pressed 
 further still, the bombarded target emits no visible 
 light but only that higher kind of radiation known 
 as Rontgen or X-rays. It may be doubted, however, 
 whether the target itself emits these rays, whether its 
 function is not rather to stop the projectiles, as 
 suddenly as possible, by the massiveness of its atoms. 
 Thus the best target would be a substance with 
 the heaviest atoms. X-rays are emitted by the 
 suddenly stopped projectiles, in a manner which has 
 been investigated both by Sir G. Stokes and 
 Professor J. J. Thomson, and which is intelligible 
 to anyone who has studied the properties of moving 
 electric charges moving at or near the speed of light : 
 a matter on which Mr. Heaviside has written with 
 great clearness in his volume called Electromagnetic 
 Theory. 
 
 Cathode rays have a remarkable penetrating 
 power; for Hertz found that a thin metal diaphragm, 
 especially if it were of aluminium, was powerless to 
 stop their passage completely ; as could be demon- 
 strated by the phosphorescence and other effects 
 appearing in the further half of the tube beyond the 
 diaphragm. 
 
 The position of the anode in such experiments is of 
 small consequence. There must be one somewhere, 
 and the easiest plan is to make it a cylinder through 
 which the cathode ray bombardment goes. The 
 bombarding particles fly in straight lines and decline 
 to turn a corner, taking no apparent notice of the 
 position of the anode, and exhausting themselves by 
 bombarding the side of the glass opposed to them ; 
 as can be well shown by having the tube bent into 
 a V shape, for instance. 
 
CH. IV.] 
 
 LENARD RAYS 
 
 29 
 
 Lenard extended Hertz's discovery in a remarkable 
 way by skilfully constructing a tube with an outer 
 window of very thin aluminium, so arranged as to be 
 able to stand the atmospheric pressure outside. He 
 then directed the cathode ray bombardment on to this 
 window or aluminium film, and showed that the rays 
 can penetrate it and actually come outside into the 
 ordinary atmosphere, where they are called Lenard 
 rays, in honour of this indefatigable investigator, a 
 friend and disciple of Hertz. (See Fig. 1.) 
 
 FlG. 1. Lenard tube for the production of Lenard rays, which were 
 discovered before Rontgen rays. C is a cathode in high vacuum ; the 
 anode A is a metal cylinder behind it ; the whole is screened in metal, 
 and the cathode rays impinge on a minute hole W covered with ex- 
 ceedingly thin aluminium foil, through which it would seem the rays 
 emerge into the air, radiating in all directions from the aluminium 
 window as Lenard rays L, where they are rapidly diffused and absorbed. 
 
 These Lenard rays make the air phosphoresce and 
 produce the other effects which cathode rays can 
 produce, but they are stopped within a moderate 
 range by the immense obstruction they meet with 
 from a substance of the density of ordinary air. 
 Substances seem to stop them simply in proportion 
 to the quantity of matter which they encounter, 
 without regard to its nature. A thick layer of air 
 would be about as opaque as a layer of water -^^ as 
 thick ; and even if the body put in their way is 
 
30 FORESHADOWING OF THE ELECTRON [CH. iv. 
 
 an opaque solid such as a sheet of metal, provided 
 it is thin enough and not too massive, it will be 
 penetrated by the rays; and phosphorescent effects 
 will be produced on the other side of it. The rays 
 can also affect photographic plates, and indeed do 
 nearly all the things, though on a smaller scale and 
 with much less penetrating power, that the later 
 discovered Rontgen rays can do. 
 
 The Lenard rays are clearly cathode rays emerged 
 from the tube ; and it was the custom, at the date of 
 their discovery, to think of them as flying charged 
 particles of matter ; though the extraordinary dis- 
 tance they could travel through common air, a 
 distance comparable to an inch, was a manifest 
 objection to such a hypothesis, seeing that things as 
 big as atoms of matter cannot travel so much as xeVfy 
 of an inch in ordinary air without many collisions. 
 
 Lenard accordingly adhered to the view, advanced 
 first by Goldstein, that they were not material but 
 ethereal ; and although, in the sense he probably 
 intended, this is not a tenable view for they are 
 not Qthereal waves or anything of the nature of 
 radiation yet, as we shall see, neither are they 
 ordinary material particles, any more than the 
 cathode rays are. But that is just the point which 
 we are now considering, and we will return to them 
 as observed by Crookes in 1879.* 
 
 Nature of the Cathode Rays. 
 
 We have seen that the impact of the cathode rays, 
 speaking in language appropriate to the assumption 
 
 * The biographical history of this subject is set out largely in the 
 contemporary letters that passed between Crookes and Stokes : these 
 have been supplied by Sir William Crookes, and will shortly be 
 published in the Scientific Correspondence of Sir George Stokes. 
 
CH. iv.] BY CATHODE RAYS 31 
 
 that they are charged particles, will result partly in 
 heat, or vibration of the impacted molecules ; partly 
 in light or phosphorescence, due to the quiver of 
 electrically charged atoms (or rather of electrical 
 charges on atoms) as in the ordinary process of 
 radiation ; and partly in X-rays : all of which effects 
 are readily seen at different stages of vacuum in 
 a Crookes' tube. The momentum of the flying 
 particles shot off from the cathode can also be 
 exhibited by putting into their path some form of 
 vane or little windmill, which will then be driven 
 mechanically, as the vanes of a radiometer are 
 driven by the recoil of the molecules of the residual 
 air from the warmer surface, a stress being thus set 
 up between the vanes and their glass enclosure. In 
 the electric vacuum tube experiment, the stress seems 
 to be between the cathode, or gun, and a layer or 
 stratum of the residual gas not very far from it for 
 unless the exhaustion is very high the gradient of 
 potential close to the cathode is very steep, so the 
 propelling force is clearly the force of electrical 
 repulsion, the particles travelling down the grade of 
 potential just as they travel in ordinary electrolysis, 
 and then proceeding for the rest of the journey by 
 their acquired momentum. But whereas in ordinary 
 electrolysis they meet with constant encounters and 
 therefore progress very slowly, in a high vacuum 
 they can fly for several inches in a free path without 
 encountering anything, and therefore without causing 
 any disturbance, thus giving rise to no appearance 
 but that of the dark space. Phenomena occur only 
 where they strike. 
 
 This was the view of the nature of cathode rays taken 
 by the whole world after Crookes' demonstration ; 
 it was supposed that they were flying atoms, and that 
 
 
32 FORESHADOWING OF THE ELECTRON [CH. iv. 
 
 they were flying with ordinary molecular speed, but 
 with a long free path much longer than would have 
 been expected from ordinary gaseous theory. The 
 extraordinary length of free path was somewhat 
 difficult to reconcile with the doctrine that they were 
 flying atoms obedient to the ordinary laws of gases ; 
 'except that, being subject to electrical propulsion all 
 in the same direction, their course was more regular, 
 and their encounters therefore fewer, or less effective 
 in causing deflection, than if they had been moving 
 at random. This same feature of regularity it is 
 which confers momentum upon them ; their motion 
 does not constitute heat, and is not to be considered 
 as corresponding to temperature ; they are moving 
 in orderly succession like an army or like a wind, 
 rather than with the irregular unorganised motion 
 appropriate, and solely appropriate, to the terms 
 " heat " and " temperature," and to the ordinary 
 kinetic theory of gases. Crookes indeed hazarded the 
 surmise by one of those flashes of intuition which 
 are sometimes vouchsafed to a discoverer but are often 
 ridiculed by representatives of orthodox science at the 
 time that he had obtained matter in "a fourth 
 state ; " and even that he had got in his tube some- 
 thing equivalent to what was contemplated in the 
 " corpuscular " theory of light. There is some cor- 
 respondence with fact even in this last mode of 
 statement, when the particles are moving quickly 
 enough, for a nuclear wave- front or ether-pulse is 
 then travelling with them ; but how true the first 
 was that the matter in the dark space was in a 
 fourth state, neither solid nor liquid nor gaseous 
 how true that was we shall presently see. 
 
 Meanwhile let us summarise the evidence for the 
 view that the cathode rays are at any rate charged 
 
CH. iv.j BY CATHODE RAYS 33 
 
 particles of some kind, in extremely rapid motion. 
 That they are in motion must be granted from the 
 fact of their bombardment driving mills, heating 
 platinum, and the like ; and in order to show that 
 they are charged, the most direct plan is to catch 
 them in a hollow vessel connected with an electro- 
 scope, as Perrin did ; but another plan is to show 
 that they have the properties of an electric current. 
 If they are charged while in motion they constitute a 
 current, on Maxwell's theory, and therefore should 
 be able either to deflect a magnet or to be deflected 
 by it; and here comes one of the most simple and 
 
 Electroscope 
 
 FIG. 2. Simplest form of Perrin's apparatus for proving that cathode 
 rays carry a negative charge. The rays from a pass through an earthed 
 screen b into a hollow or Faraday vessel c. 
 
 important experiments in physics at the present 
 time. A definite form of some old experiments 
 foreshadowed by Pliicker (1862), and developed by 
 Hittorf, Goldstein, and many other vacuum tube 
 observers, was arranged by Crookes in 1879, when 
 he made the track of the rays visibly luminous by 
 passing a pencil of them through a slit and letting 
 them graze along the surface of a film of mica covered 
 with phosphorescent powder, and when he then 
 brought near them a common horseshoe magnet. 
 When this is done the track of the rays is at once 
 seen to be curved ; showing that it is not a beam 
 of light we are looking at, but a torrent of charged 
 particles ; since they behave like an electric current 
 and are deflected by a magnet. It is ultimately the 
 very same phenomenon as can be observed with 
 difficulty, owing to its smallness, when a current 
 
 L.E. 
 
34 FORESHADOWING OF THE ELECTRON [CH. iv. 
 
 flows through metals, an effect discovered by E. H. 
 Hall in America, and known as the Hall effect. 
 
 The fact that the particles are thrown off the 
 cathode, being evidently vigorously repelled by it, is 
 sufficient to suggest that they must be negatively 
 charged ; the direction of the curvature caused by a 
 magnetic field enables us to verify at once that the 
 flying particles are negatively charged, and no 
 comparable rush of positive particles in the opposite 
 direction, or in any direction, has been observed. 
 The speed of transmission of the positive current is 
 very great, and it must be conveyed by a multitude 
 of positive particles, but individually their motion 
 is comparatively slow (see however chap. vi.). In 
 that respect evidently the magnetic curvature of 
 cathode rays in gases differs from the magnetic 
 curvature of a current in metals ; viz., that whereas 
 in metals the major action is sometimes upon the 
 negative and sometimes upon the positive stream, 
 according to the nature of the metal the difference, 
 which is all that is observable, being always small, 
 in the cathode stream it is the negative alone -that 
 is acted upon, and so the action is always large. 
 
 It seems, therefore, that for some reason or other 
 the negatively charged bodies in a vacuum tube are 
 much more mobile than the positive, and that the 
 mobility of the negatively charged bodies is extreme. 
 One striking method by which their mobility was 
 displayed consisted in the fundamental observation 
 by Professor Schuster* that all parts of gas in a 
 closed vessel became conducting when an electric 
 discharge had taken place in one corner of it; so 
 that even though the vessel consisted of different 
 compartments, one compartment was made feebly 
 
 * Bakerian lecture 1890, Proc. Roy. Soc., vol. 47, p. 526. 
 
CH. iv.] BY CATHODE RAYS 35 
 
 conducting by a discharge in the other, provided 
 that the two had any kind of gaseous communi- 
 cation ; a fact which looked as if some extremely 
 mobile particles, probably the negatively charged 
 particles of cathode rays, could wander about to 
 a considerable distance in a very short time and 
 take their share in the conveyance of an electric 
 current. The conductivity of gases appeared to be, 
 indeed, entirely due to these loose or dissociated or 
 detached charged particles, or ions, and where they 
 were absent the gas did not conduct at all ; it 
 could be broken down, being a weak dielectric, by a 
 sufficiently strong force, but it would not leak ; 
 whereas, when these loose charged particles were 
 about, it leaked readily, becoming to all intents and 
 purposes an electrolyte amenable to the feeblest 
 electric influence. The production of this electrolytic 
 condition is called " ionisation." The act of breaking 
 down the air by an electric discharge was thus 
 found to render the surrounding air for a time 
 electrolytic. Its electrolytic quality, however, did 
 not last long. The mobility of the particles which 
 enabled them to travel to a considerable distance 
 also enabled them to get rid of themselves by 
 clinging to the sides of the vessel, or perhaps by 
 re-uniting with some opposite charges, which after 
 some time in their rapid journeys they must 
 casually encounter. Prof. Townsend,* however, found 
 that the conducting power lasted unexpectedly long 
 if no dust was present : the dust particles apparently 
 acting as intermediate receivers and storers of 
 charge, promoting interchanges, which did not very 
 
 * J. S. Townsend of Trinity College, Dublin, then working in the 
 Cavendish Laboratory, Cambridge, now Waynflete Professor of Physics 
 in the University of Oxford. 
 
36 FORESHADOWING OF THE ELECTRON [CH. iv. 
 
 readily occur through direct encounters. And the 
 time that thus elapsed before the whole of the 
 conductivity disappeared from dust-free air suggested 
 that the moving particles must be very small, so that 
 intimate collisions were comparatively infrequent. 
 
 The mobility or diffusiveness of the molecules 
 of a gas depends on their mean free path, and 
 that depends on their atomic size ; the smaller 
 they are, the more readily can they escape 
 collision. Hence it is that collisions are so rare in 
 astronomy : the bodies are small compared with the 
 spaces between them. The behaviour of charged par- 
 ticles seemed to indicate that they must in some 
 cases be something smaller than atoms : it seemed 
 hardly likely that material atoms could behave in 
 the way they did. It was recollected that it had 
 occurred to some philosophers, among them Dr. 
 Johnstone Stoney, that electric charges really existed 
 on an atom in concentrated form, not diffused all 
 over its surface but concentrated at one or more 
 points, perhaps acting as satellites to the main 
 bulk of the atom ; so on that view it was j ust 
 possible that these flying particles might be not 
 charged atoms at all, but charges without the atoms, 
 the concentrated charges detached knocked off as 
 it were in the violence of the discharge, and after- 
 wards going about free. Such particles would 
 naturally travel at an immense pace, because they 
 would still be exposed to the full electric force that 
 they had experienced before, and yet would have 
 shaken off the encumbrance of the material atom 
 with which they had been associated. It is true that 
 no such disembodied charges, or electric ghosts, had 
 ever been observed. All the experiments that had 
 been made in electrostatics had been made on charged 
 
CH. iv.] BY CATHODE RAYS 37 
 
 matter, the surface or boundary of the matter acting 
 as the locality for an electric charge ; and no other 
 locality for a charge was known. The facts of 
 electrolysis had suggested or proved that the atoms 
 themselves could carry charges, and hence that if a 
 liquid were electrified, it must be due to some of the 
 atomic charges of one sign, appearing in overbalancing 
 proportion at the surface ; though perhaps still in 
 association with their respective atoms. 
 
 Yet at the same time the occurrences at an 
 electrode, where an ion plainly gave up its charge 
 and escaped without it, indicated the possibility that 
 perhaps the electric charge could exist alone ; at any 
 rate that it could be handed from one atom to 
 another, and thus might conceivably exist alone for 
 an instant. During this momentary isolation some 
 charges might, in the freedom of a rarefied gas 
 discharge, possibly escape, and wander about free. 
 
 To such hypothetical isolated charges, the unit 
 charge or charge of a monad atom, the name 
 "electron" had been given ; and when I speak of an 
 "electron" I mean to signify the, at first purely 
 hypothetical, isolated electric charge. Whereas by 
 the term "ion" I always signify the atom and its j 
 charge together. The ions consist of Faraday's anions 
 and cations. Lord Kelvin prefers the term electrion 
 to electron. 
 
 Now if the flying particles which constitute the 
 cathode rays were electrons rather than ions, if they 
 were detached charges, leaving their atoms behind 
 them (necessarily leaving those atoms positively 
 charged), their extreme mobility and diffusiveness 
 and high speed would be perfectly natural ; and 
 although they would not be ' matter ' in the ordinary 
 sense, yet no difficulty need be felt at their possessing 
 
38 FORESHADOWING OF THE ELECTRON [CH. iv. 
 
 some of the properties of matter, at any rate such 
 properties as appertain to matter by reason of its 
 having inertia ; because, as we have seen, an electric 
 charge itself does possess a certain kind of imitation 
 inertia. Hence these electrons in movement would 
 possess momentum, and might therefore propel wind- 
 mills (though the actual motion of the windmills in 
 Crookes tubes seems more likely due to charge and 
 electric repulsion than to simple momentum) ; they 
 would possess kinetic energy, and therefore might 
 heat a piece of platinum ; and if suddenly stopped by 
 a massive target when travelling at a high speed they 
 might readily give rise to phosphorescent appearances, 
 and even to the sudden pulse of radiation known as 
 X-rays. Indeed the existence of this last property is 
 capable of clear deduction on electrical principles 
 if the matter is further gone into. (See chap, ix.) 
 
 The continued passage of a current through a 
 vacuum tube cannot be explained by a torrent of 
 electrons alone, there must be some mechanism 
 for continually producing them fresh and fresh, 
 near or at the cathode, else they would almost in- 
 stantaneously get exhausted. The most probable 
 view of the matter is that suggested by J. J. Thomson : 
 that the current is conveyed chiefly by positive ions, 
 which are produced in the residual gas by ionisation 
 due to the first discharge of cathode rays. These 
 positive ions then pass along comparatively slowly 
 toward the cathode, creep in towards it, as best they 
 can, in face of the bombardment ; and then at the 
 last experiencing the violent gradient of potential 
 in its immediate neighbourhood rush up against it 
 and by their shock produce a fresh supply of electrons. 
 The glow over the cathode is supposed to mark the 
 region of this ionisation. The negative particles, thus 
 
CH. iv.] BY CATHODE RAYS 39 
 
 set free, then fly off as cathode rays, setting up fresh 
 ionisation, and producing a copious further supply of 
 positive ions ; on the existence of which the possi- 
 bility of the cathode rays themselves depend. The 
 positive and" the negative particles on this view are 
 mutually dependent : each is the cause of each ; and 
 when either fails to be formed in a vacuum tube it is 
 impossible for it to conduct, even when its terminals 
 are highly electrified ; for if the supply of either sign 
 of ion is stopped, that of the other at once fails. 
 This accounts for the action of ' electric valves,' wherein 
 the positive ions are prevented from getting at the 
 cathode in one direction, by reason of a special 
 arrangement for concentrating an electron bombard- 
 ment along the direct route, without any back door 
 or side entrance for the positive ions. The provision 
 of such a back door, even though the route thereto 
 be long, immensely eases the conveyance of current : 
 as was strikingly shown by Hittorf. 
 
 It has been observed that any obstacle introduced 
 into the dark space near the cathode, if it is able to 
 check locally the access of positive ions, will throw a 
 shadow both fore and aft, 1 one towards the cathode, 
 and likewise one down the cathode rays, because 
 the generation of fresh electrons is thereby locally 
 prevented.* At this stage we may conveniently 
 summarise the position thus : 
 
 The magnitudes which need experimental deter- 
 mination in connexion with cathode rays, in order 
 to settle the question and determine their real 
 nature, are the speed, the electric charge, and if 
 possible the mass, bf the flying particles. 
 
 Everything suggests that they are flying with 
 
 * Schuster, Proc. Roy. Soc., xlvii., p. 557, 1890 ; Wehnelt, Wied. Ann. 
 Ixvii., p. 421, 1899. 
 
40 FORESHADOWING OF THE ELECTRON [CH. iv. 
 
 prodigious speed, but it is desirable to make a 
 measurement of that speed. 
 
 The force of propulsion exerted on them indicates 
 that they are highly charged ; and their penetrating 
 power suggests that they are excessively small, so 
 that to them ordinary solids, such as metal sheets, 
 appear porous ; but an experimental method is 
 necessary to determine what may be called their 
 electrochemical equivalent, -that is to say the ratio 
 of their mass or inertia to their electric charge, 
 even if it be not possible to determine the mass 
 and the charge separately. 
 
 In electrolysis the electrochemical equivalent, 
 or the ratio m/e, depends on the nature of the 
 substance; and for hydrogen is of the order 10~ 4 
 in electromagnetic units, as stated in Chapter III. 
 It is a matter of great importance to determine 
 the value of the same ratio for the cathode rays, 
 and to ascertain whether it varies with the substance 
 contained in the vacuum tube, or whether it is the 
 same for all substances being characteristic of 
 a single variety of the flying particle and of nothing 
 else. 
 
CHAPTER V. 
 
 DETERMINATION OF SPEED AND ELECTROCHEMICAL 
 EQUIVALENT OF CATHODE RAYS. 
 
 IF the cathode rays consist of flying electrified 
 particles they will be deflected, or their paths curved, 
 by the proximity of a magnet : and this is a well 
 known and prominent fact concerning them. With 
 some care the amount of deflexion, caused by a 
 magnetic field of known strength, may be measured. 
 
 The curvature of path produced in cathode rays 
 by a transverse magnetic field, or, the amount of 
 spirality produced by a longitudinal magnetic field, 
 constitutes an evident mode of attacking the problem 
 of estimating their velocity. 
 
 If the velocity is constant and the magnetic field 
 uniform, the curve into which the stream is bent 
 round the lines of force will manifestly be a 
 circle ; and its course can be readily traced either 
 directly, after Crookes' manner, by letting it graze 
 a phosphorescent substance, or indirectly by inference 
 from the position of a linear target placed so as to 
 catch the deflected, rays. If the direction of velocity 
 is inclined to the direction of the field, the course of 
 a particle will be compounded of a circular motion 
 round a line of force, and an unchanged rectilinear 
 motion along it : that is to say, it will be a spiral,. 
 
42 DETERMINATION OF SPEED [CH. v. 
 
 more or less elongated, threading itself along the 
 negative field : the direction of twist depending on 
 the sense of the field. 
 
 There is no difficulty in determining the radius 
 of curvature r ; and the theory of normal deflexion 
 is the simplest possible, nothing more than stating 
 that the magnetic force H, acting on the current 
 element eu, is the necessary deflecting or centripetal 
 force, my?/r, required to overcome the mechanical 
 inertia of the particles ; i.e., 
 
 mu 2 
 
 - = jmeun., 
 
 whence u= uKr ; 
 e 
 
 or the ratio e/m is to the velocity of the particles as 
 the curvature of their path is to the intensity of 
 magnetic field which curves it. Prof. Schuster of 
 Manchester was among the first to make measure- 
 ments of this kind. 
 
 The two factors on the right of this equation are 
 directly measurable (/u. being conventionally ignored 
 as usual, or a better mode of expression united 
 with H as induction-density) ; but the two factors 
 on the left are both unknown, hence neither can be 
 determined by this means alone,-an assumption 
 must be made about one or other of them, or else 
 another independent kind of experiment must be 
 made. 
 
 Assume, as many experimenters did, that u is a 
 velocity appropriate to atoms flying in a gas of 
 ordinary temperature, then the value of e/m comes 
 out not so very far discrepant from the usual ionic 
 value, measured in liquid electrolysis, viz., 10 4 c.g.s. 
 Or, conversely, assume the usual ionic or electrolytic 
 
CH. V.] 
 
 OF CATHODE RAYS 
 
 43 
 
 value for this ratio, and the cathode ray velocity 
 comes out something quite appropriate to atoms 
 of matter. 
 
 This, however, is a trap. These accidental coin- 
 cidences may retard progress in a most serious 
 manner, for they satisfy the mind and deter people 
 from investigation. It is almost impossible to be 
 
 FIG. 3. Modified Perrin apparatus adopted by J. J. Thomson for, 
 measuring the charge, and at the same time the magnetic deflexion, and 
 sometimes the thermal energy also, of cathode rays. The rays from the 
 cathode, after passing through a perforated anode and proceeding in a 
 straight line, can be deflected by a magnet a measured amount, so as 
 just to enter a hole in an earthed guard-screen D, and then a hollow 
 cavity provided with an electrode E, whereby the aggregate charge 
 conveyed by them is measured. 
 
 completely on guard against them, and they are 
 usually accepted until a more thorough qualitative 
 acquaintance with the subject leads to an instinctive 
 feeling that something is wrong somewhere. 
 
 So it was in this case : the long free path and the 
 penetrating power of the cathode rays kept insisting 
 that the particles were not really atoms of ordinary 
 matter, a truth which both Lenard and Crookes 
 had instinctively grasped, in spite of much criticism 
 
44 DETERMINATION OF SPEED [CH. v, 
 
 and valid arguments the other way; so in 1897 
 J. J. Thomson made a much more serious attack on 
 the whole position. 
 
 He arranged that the magnet should deflect the 
 rays into an insulated hollow vessel, connected with 
 an electrometer and a known capacity, so that the 
 aggregate charge of the cathode ray particles collected 
 in a given time could be measured by the rise of 
 potential observed (cf. Fig. 3). He also arranged 
 that inside the hollow vessel they should fall upon 
 a thermal junction of known heat capacity, con- 
 nected by very thin wires to a galvanometer (acting 
 therefore as a calorimeter), so as to measure their 
 aggregate energy. 
 
 Thus he could make the following simultaneous 
 determinations : 
 
 m 
 
 u 
 
 In these three equations there are four unknown 
 quantities ; but one pair can be treated as a ratio, 
 and another, N, can be eliminated, and thus we get 
 
 2W 
 
 When these brilliant measurements were actually 
 made in the laboratory, the atomic nature of cathode 
 rays was, if not actually disproved, at all events 
 rendered highly improbable ; for their speed was 
 found to be of the order ten thousand miles per 
 second, or even as high as ^ that of light in a 
 
UNIVERSITY 
 
 <JH. v.] B?8 OP s ^THbDE RAYS 45 
 
 favourable case, being always of the order 10 9 c.g.s., 
 while the electrochemical equivalent was of the order 
 10~ 7 c.g.s., or about T ^Vo that f hydrogen. 
 
 Changing the kind of residual gas in the tube, and 
 changing the electrodes, made no difference to this 
 last value. The cathode rays were evidently inde- 
 pendent of the nature of the matter present : an 
 exceedingly momentous fact. If they were matter at 
 all, they appeared to be matter of some fundamental 
 kind, independent of the distinctions of ordinary 
 chemistry. Their velocity, however, depended on 
 the potential difference between the electrodes, in a 
 way that suggested that they were really projectiles 
 urged by the potential gradient acting along a given 
 length of path. They were propelled by the cathode 
 through an aperture in the anode, and the measure- 
 ment of their speed was made in the tube beyond the 
 anode, where they are travelling by their own 
 momentum. The distance apart of anode and 
 cathode did not, and on .the projectile hypothesis 
 ought not to, affect this speed ; for though the 
 potential gradient is steeper when anode and cathode 
 are put close together, the length of path during 
 which the particles are subject to it is diminished 
 by a compensating amount, -so that the velocity is 
 theoretically independent of the distance between the 
 electrodes, as long as the total difference of potential 
 is maintained ; it is the absolute difference of 
 potential that determines the speed. (This is a 
 familiar result of the conservation of energy, and is 
 illustrated by ordinary falling bodies.) But mani- 
 festly if the electrodes are too close together it may 
 be difficult to secure a high difference of potential 
 between anode and cathode, since they may spark 
 into each other outside the tube; and if there is 
 
46 DETERMINATION OF SPEED [CH. v. 
 
 much residual gas in the tube it will likewise be 
 difficult to maintain a high potential difference ; 
 because that residual gas, under the influence of 
 the cathode rays, will conduct. Consequently the 
 best speeds are obtained at high vacuum ; and if 
 the density of the residual gas inside the tube is 
 constant, the speed will be constant. The nature of 
 the electrodes makes no difference, unless they give 
 off gas or otherwise make it difficult to maintain the 
 required potential difference. 
 
 Although the speed of the particles in cathode 
 rays was thus found excessively great, their energy 
 was only moderate, and their aggregate mass was 
 therefore proved to be excessively minute ; their 
 aggregate electric charge, however, was considerable. 
 They were able to raise an electrical capacity of 
 15 microfarad several volts, sometimes as much 
 as 5 volts, in the course of a second ; and in the 
 same time they might be able to raise a calorimeter, 
 whose heat capacity was about 4 milligrammes of 
 water, by 2 C. Nevertheless their mass was so 
 small that it would have taken one hundred years 
 to collect a weighable amount : and then only 
 about one-thirtieth part of a milligramme. They 
 travelled with a velocity a hundred thousand times 
 greater than the speed of rifle bullets, and re- 
 presented the greatest velocity up to that time 
 observed in matter, if matter they were. And 
 the electrochemical equivalent, instead of coming 
 out in accordance with that observed in liquids, 
 came out some thousand times smaller ; that is to 
 say, the charge associated with each particle of the 
 cathode rays seemed a thousand times greater, in 
 proportion to the mass, than the charge associated 
 with an electrolytic ion, even of hydrogen. 
 
CH. v.] OF CATHODE RAYS 4T 
 
 If the flying particles were really atoms, there was 
 no escape from the certainty that they were 
 extraordinarily highly charged atoms ; but if, as 
 seemed more likely to the instinct of most of those 
 who worked at the subject, the charge on the flying 
 particles was the same as the charge possessed by an 
 atom in electrolysis, then, assuming that the experi- 
 ments were correct and correctly interpreted, there 
 would be no escape from the conclusion that the 
 mass associated with the ionic charge in cathode rays 
 must be a thousand times smaller than the mass of a 
 hydrogen atom ; in which case the cathode projectiles 
 might conceivably be the detached and hitherto 
 hypothetical individual electrons or atoms of elec- 
 tricity themselves. It would be extremely rash, 
 however, to jump to such a far-reaching conclusion 
 on such comparatively scant evidence. The evidence 
 must be confirmed by other departments of Physics 
 or by other determinations based on a different 
 method ; and they must be further scrutinised in 
 the light of other and totally different phenomena. 
 We will first describe a determination made by 
 another method, and then some striking confirmatory 
 measurements applied to phenomena which belong 
 apparently to other departments of Physics. 
 
 Further Measurements of Cathode Ray Velocity 
 
 and m/e Ratio by Aid of Electrostatic 
 
 Deflection. 
 
 Another and perhaps simpler method of deter- 
 mining the two quantities u and m/e was also 
 employed by J. J. Thomson, was indeed the first 
 used by him, though it was not safe to draw a full 
 deduction from it alone viz., by deflecting the 
 same rays both electrostatically and magnetically ; 
 
48 DETERMINATION OF SPEED [CH. v. 
 
 by introducing a pair of supplementary electrodes, one 
 above and one below the course of the rays inside 
 a vacuum tube, and connecting them to the poles 
 of a low-potential battery, a few storage cells for 
 instance, thus obtaining a vertical electrostatic field 
 at right angles to the cathode rays. At the same 
 time a magnetic field, produced by lateral magnet 
 poles or by the lines of force due to an electric 
 current in a circular ring, could be arranged at right 
 angles to both the other directions ; and thus the 
 electrostatic deflection could be compared with, or 
 could be used to neutralise, the magnetic deflection. 
 The electric field, being .fixed in direction and urging 
 the particles along not across the lines of force, 
 will act differently to a magnetic field and will cause 
 the particles to move in a parabola the shape which 
 the earth gives to a horizontal jet of water. 
 
 Fig. 4 shows J. J. Thomson's apparatus for 
 measuring the deflexion of cathode rays caused by 
 an electric field at right angles to them.* The rays 
 starting from the cathode C traverse a couple of 
 earth-connected slits AB and after having passed 
 between the electrified plates D and E, impinge on 
 the glass at P, producing a small but vivid phosphor- 
 escent spot. The position of this spot is read on a 
 scale pasted on the outside of the glass. In ordinary 
 vacua screening prevents any effect from being ob- 
 served, by reason of conducting power in the residual 
 air, developed by ionisation caused by the impact of 
 the flying particles ; consequently Hertz failed to 
 obtain the deflexion which was otherwise to be 
 expected; but by pushing the vacuum to a higher 
 stage J. J. Thomson overcame this difficulty, 
 measured the deflexion PP', and employed this 
 
 * Phil. Mag., vol. 44, p. 293 (1897). 
 
 
CH. V.] 
 
 OF CATHODE RAYS 
 
 49 
 
 method to assist in measuring the velocity and 
 other constants of the cathode ray particles. 
 
 By noting the shift of the luminous spot, the 
 deflexion of the narrow beam which has travelled 
 through a length I of either an electric field of 
 strength E, or a magnetic field of strength H, can 
 be directly measured. 
 
 If u is the original velocity of the ray particles, 
 travelling at right angles to one of the deflecting 
 fields, either of them will have a time l/u in which 
 
 FIG. 4. Thomson's apparatus for observing and measuring the 
 electrostatic deflexion of cathode rajs. 
 
 to act ; and in that time an extra velocity w 
 will be caused in the direction of the electric force, or 
 perpendicular to the direction of the magnetic force, 
 such that the rate of change of momentum of each par- 
 ticle will be jj- = Ee in the one case, and = juXieu in 
 
 ijU 
 
 the other ; wherefore the deflexion, if small, will be 
 
 / w e EZ . ,, 
 
 = = s- in the one case, 
 
 u m u 
 
 and O f = - in the other. 
 
 m u 
 
 L.E. 
 
50 DETERMINATION OF SPEED [CH. v 
 
 u = . 
 //xi c; 
 
 Hence 
 
 m 
 
 
 
 This method, when applicable, appears to give fairly 
 accurate results ; and the outcome of the measure- 
 ments is, that when H or C0 2 or Air is in the tube, 
 
 u 2 or 3 x 1 9 centimetres per second, 
 and = from 1*1 to 1*5 x 10~ 7 c.g.s. units. 
 
 e 
 
 The chief difficulty about this mode of experimenting 
 is caused by the fact that the ionisation of residual 
 air in the tube causes it to become a temporary 
 conductor, thereby screening the flying particles from 
 most of the electrical influence. There is no 
 guarantee that they feel the full effect of the electric 
 field which is ostensibly being applied ; indeed it 
 is not easy to let them feel any of the effect. It 
 used to be thought that they were not susceptible 
 to electrostatic action at all, and this was often 
 adduced as an obvious argument against their 
 being electrically charged particles ; but fortunately 
 Thomson soon surmised the cause of this masking 
 of the simple effect to be expected, and succeeded 
 in showing that with high enough vacua, and other 
 
 Erecautions, the screening ionised atmosphere could 
 e removed, and the electrostatic deflexion metrically 
 observed. 
 
 Measuring Velocity by combined Electric and 
 Magnetic Deflexion Method. 
 
 Now that it is possible to apply the electrostatic 
 deflexion method to curve the path of flying charged 
 
CH. v.] OF CATHODE RAYS 51 
 
 particles, the simplicity of combining this with 
 magnetic deflexion, and thereby making a couple 
 of measurements simultaneously, is so great that 
 it has practically replaced the more elaborate plan 
 first described, namely the method by observ- 
 ing the aggregate charge, the aggregate energy, 
 and the magnetic deflexion only, a method which, 
 first as an original determination, and now as a 
 check, has been of high value. 
 
 The simple plan has now been applied to rays of 
 various kinds, and it may be well to give its 
 simplest possible form, before proceeding to a more 
 complicated case. It consists, (1) in observing the 
 radius of curvature r caused by a magnetic field 
 of measured strength H ; (2) in finding the electric 
 field E which, applied at right angles to the magnetic 
 field, just succeeds in neutralising all deflexion ; then 
 a centrifugal force equation 
 
 e u 
 
 applies to experiment No. 1 ; and a balanced force 
 equation ... E 
 
 E 
 or u= 
 
 applies to experiment No. 2. 
 
 This second experiment gives . the velocity, by 
 itself; and the first in combination with it gives the 
 electro-chemical equivalent. 
 
 So the determination of 'velocity for the case of 
 particles 'flying all with one speed is remarkably 
 easy : it comes out, in centimetres per second, as 
 
52 DETERMINATION OF SPEED [CH. v. 
 
 4 
 
 simply the ratio of the strengths of the electric and 
 magnetic fields (both expressed in EM units, that 
 is with M=!) which can produce equal effects 
 upon the flying particles, and which therefore, if 
 applied in opposition, are just able to neutralise 
 each other. 
 
 Note on Dimensions. 
 
 To verify that the " dimensions " of the last given 
 equation are correct, we can remember that an electric 
 
 F TT 
 
 field is of dimension = -= ., _., where F is force, 
 
 e I v (/of ) 
 
 and I is length ; and that a magnetic field is of 
 
 TT T? 
 
 dimension = ^ ., _ x ; so the ratio of an electric 
 
 m TjfjdF) 
 
 to a magnetic field is */(V/K) ; wherefore -th of that 
 
 1 M 
 
 ratio is r/ r = a velocity. 
 
 vV) 
 
 For practical purposes it may be convenient to 
 write the equation as a proportion sum thus : 
 
 the velocity of the particle 
 the velocity of light 
 
 the electric field in electrostatic units 
 the magnetic field in electromagnetic units ' 
 
 it being understood that the fields are adjusted till 
 their effects are equal. 
 
 Effect on Lenard Rays. 
 
 Another mode of demonstration was employed by 
 Professor Lenard, and served to identify his rays with 
 escaped cathode rays. 
 
CH. v.] OF LENARD RAYS 53 
 
 Fig. 5 shows Lenard's apparatus for showing that 
 his rays are accelerated or retarded by passing along 
 the lines in an electric field between two disks ab. 
 Here C is the cathode of a Lenard tube similar to 
 that shown in fig. 1, and the rays enter an 
 aluminium window at A, thence passing on through 
 an earthed tube n leading to one of the charged 
 disks. The disks are perforated to allow the rays to 
 pass through them ; they go on through another tube 
 
 TO EARTH 
 
 FIG. 5. Lenard's apparatus for exhibiting the effect of a longitudinal 
 electric field in affecting the velocity of cathode or Lenard rays. 
 
 m, which, with the disks, is kept at high potential, and 
 thence between the plates de, which represent either 
 an electric or a magnetic field ; after which they 
 encounter a phosphorescent screen S, and depict upon 
 it a luminous spot. The observation consists in 
 observing the change of position of this spot when 
 the sign of the electrification of the plates ab is 
 changed ; for if the longitudinal field alters the 
 velocity, the deflexion caused by the field de will 
 also be modified, and thereby the change in velocity 
 is demonstrated. 
 
54 
 
 DETERMINATION OF SPEED 
 
 [CH. V. 
 
 Direct Determination of the Speed of Cathode 
 
 Rays. 
 
 Figs. 6 and 7 illustrate sufficiently the ingenious 
 device applied by Wiechert, in accordance with a 
 method of Des Coudres, for directly measuring the 
 velocity of cathode rays during the time of their 
 
 J3/ 
 
 FIG. 6. Connexions of the circuits in Wiechert's experiment for 
 measuring directly the speed of cathode rays as they travel down a tube. 
 
 transit down the axis of an exhausted glass tube of 
 moderate length. 
 
 Keferring to either of the figures, the tube has a 
 curved cathode C at one end, whereby the rays are 
 focussed through an aperture in a screen B ; they 
 then travel down the tube to another perforated 
 screen B', whence the central portion of them reaches 
 a phosphorescent screen at S. 
 
 The tube is excited by a kind of Tesla induction 
 
CH. v.] DIRECT PROCESS 55 
 
 coil T, whose terminals lead respectively to the 
 cathode C and to a ring-anode A. 
 
 Ley den jars I and J can be excited by a Ruhm- 
 korff coil, or in any ordinary manner, and they 
 discharge across the spark-gap G. Thereby a sub- 
 sidiary oscillating circuit, of very high frequency, 
 characterised by the condensers H and K, and 
 limited t6 the region above the spark-gap G, is 
 set in action ; and an oscillatory discharge is con- 
 veyed to the symmetrical terminals PQ, whence it 
 can pass round a pair of wire loops in parallel, MN 
 
 S 
 
 FIG. 7. Enlarged portion of fig. 6, showing the vibration of the 
 cathode rays by an alternating circuit and the adjustment of their range 
 of excursion by a fixed magnet. 
 
 and M'N'. The effect of the alternating field, thus 
 generated in the loop MN (fig. 7) is to wave the 
 cathode rays rapidly to and fro, so that only in the 
 middle of their path will they pass through the 
 aperture in the disk B the effect on the distant 
 phosphorescent screen being then quite faint. But 
 if a permanent magnet D is applied to them, the 
 oscillation is deflected, and can be limited to the 
 region between the centre and the circumference of 
 the disk as illustrated by the figure; thereby a 
 greater number of rays get through, and the screen 
 becomes more luminous than when the magnet is not 
 applied, because the aperture will now be at the 
 -extremity of the swing of the oscillating rays. If 
 
56 DETERMINATION OF SPEED [CH. v. 
 
 the magnet is too strong the screen S will become 
 dark, because the oscillating rays will be too much 
 deflected, so it is possible to tell pretty sharply the 
 phase of the oscillating rays in the right-hand portion 
 of the tube by watching the screen S and adjusting 
 the strength of the magnet. 
 
 So much for the right-hand end of the tube. Now 
 proceed to the left-hand end, or rather to the 
 movable portions depicted to the left of figs. 6 and 7. 
 We have there also an oscillating current, M'N', in 
 precisely the same phase of standing oscillation as 
 its other branch MN ; consequently, if the rays take 
 no time to travel down the tube, those which get 
 through the disk B' will be deflected as before ; 
 but if the time taken to travel down the tube 
 corresponds with a quarter of the extremely rapid 
 oscillation-period of the condensers HK, then the 
 rays deflected a maximum amount by the first branch 
 of the circuit will not be deflected at all by the 
 second, and therefore will reach the middle of the 
 screen. 
 
 By either altering the frequency of oscillation, or 
 adjusting the distance apart of the parts represented 
 by BB', it is possible to cause the deflexion on the 
 left-hand side to be either in the same phase, or in 
 opposite phase, with the first half; or to be a zero, of 
 the first, second, or third order. 
 
 In this way, though obviously the experiment is a 
 difficult one, Wiechert was able to make measure- 
 ments of the speed of the cathode rays produced 
 under given circumstances. 
 
 Unfortunately this speed is not a fixed and definite 
 constant, like the velocity of light : it does not indeed 
 depend upon the nature of the gas in the tube, nor 
 on the substance of the electrodes, but it does vary 
 
CH. v.] DIRECT PROCESS 57 
 
 with the density of the residual gas and with the 
 intensity of the electric field. 
 
 In order to prevent the diffusion and spreading out 
 of the rays, on their passage down the tube, a longi- 
 tudinal magnetising helix was applied to it, so as to 
 concentrate the rays along the axis. 
 
 If u is the velocity to be measured, and I the 
 distance they travel to give the first zero, then 
 u knl, where n is the frequency of the electric 
 oscillation in the circuit MN. 
 
 In one experiment I was 39 centimetres, and n 
 was 32 million per second; wherefore u comes out 
 4*5 x 10 9 cm. per sec. 
 
 As soon as the velocity is known, the ratio e/m can 
 be determined by measuring the magnetic deflexion 
 of the rays. The range of uncertainty for this 
 determination, as made by Wiechert, lies between 
 1*55 and 1*01 times 10 r . It can hardly be con- 
 sidered the most accurate method of measurement, 
 but its directness and ingenuity entitle it to atten- 
 tion. 
 
CHAPTER VI. 
 
 DETERMINATION OF ELECTROCHEMICAL EQUIVA- 
 LENT IN THE CASE OF ELECTRIC LEAKAGE 
 IN ULTRA-VIOLET LIGHT. 
 
 THE same ratio of m to e, or a ratio of quite com- 
 parable magnitude, is obtained from phenomena 
 which at first sight appear to be distinct. 
 
 One of these phenomena is the effect of ultra- 
 violet light in discharging negative electricity from 
 a clean metal or other surface ; a phenomenon dis- 
 covered by Hertz, and the investigation of which 
 was continued especially by Righi and by Elster and 
 Geitel. (See one of the appendices to my " Signalling 
 without Wires," published by the Electrician Co.) 
 If ultra-violet light, whether from a spark or from 
 a flame, fall upon a negatively electrified surface, 
 then in general there will be a leak of electricity 
 from that surface : which electricity can be received 
 by any body placed opposite the illuminated one, 
 and can be used to charge an electrometer of 
 known capacity, and so be measured. The writer, 
 assisted by Mr. Benjamin Davies, has made very 
 many experiments in this subject, which, how- 
 ever, have not yet been published. Now Elster 
 and Geitel made the notable discovery that the 
 application of a magnet affected the rate of leak, 
 
CH. VL] DISCHARGE BY LIGHT 59 
 
 according to the direction of its lines of force. This 
 phenomenon suggested a magnetic deflexion of the 
 lines of leak, which were shown by Kighi to be 
 singularly definite trajectories, and indicated that 
 the leakage was due to the bodily propulsion of 
 negatively electrified particles analogous to the 
 cathode rays. A vacuum is not necessary to observe 
 the effect, but in a vacuum the effect is more pro- 
 minent and more accurately measurable. The 
 difference between this case and an ordinary vacuum- 
 tube case, is that there is no great E.M.F. or gradient 
 of potential applied, so there is nothing of the 
 nature of a disruptive discharge ; in fact there is no 
 leak at all until by the stimulus of the presumably 
 synchronous vibrations of ultra-violet light the 
 molecules are thrown into a state of agitation, and 
 the attachment of the negative charge, or of some 
 negatively charged corpuscles, thereby loosened. 
 
 Two things are necessary to get the particles away 
 from the plate ; they must be loosened by the impact 
 of ultra-violet light the direction of polarisation of 
 this light having a very decided influence when 
 the surface is smooth, and the surface on which 
 they exist must likewise be negatively charged, 
 so as to repel them. Neither light alone nor 
 electrification alone will produce any considerable 
 effect ; co-operation is necessary. Light alone is 
 able to cause a slight positive electrification,* by 
 the diffusion away of negative corpuscles a process 
 which is assisted by a blast of air. Whether 
 electrification alone can produce a perceptible effect 
 depends on the temperature of the metal : when 
 that is high, it can as was discovered by Guthrie. 
 
 *This effect was discovered simultaneously by Righi and by 
 Hallwachs. See Phil. Mag., 1888, April, p. 314, and July, p. 78. 
 
60 LEAKAGE IN ULTRA-VIOLET LIGHT [CH. vi. 
 
 J. J. Thomson devised a most ingenious method 
 of carrying out this experiment that of discharge 
 by means of ultra-violet light in a metrical 
 manner, and of deducing from it the electrochemical 
 equivalent of the charged particles, that is to say 
 the amount of matter which each contains com- 
 pared with the electric charge which each carries. 
 
 FIG. 8. J. J. Thomson's apparatus for measuring the magnetic 
 deflexion of the electric charge thrown off clean negative metal by 
 ultra-violet light in a vacuum. The negative electrode is a clean zinc 
 plate AB which can be raised or lowered, the other is wire gauze CD 
 connected to an electroscope. Ultra-violet light enters through the 
 quartz plate EF, and then a magnetic field is applied. 
 
 To this end he employed the usual arrangement 
 of a small negatively charged zinc plate on which 
 ultra-violet light from a distant arc-lamp could 
 shine ; the light passing through a plate of quartz, 
 and also through a parallel piece of wire gauze 
 connected with an electrometer. The distance be- 
 tween the zinc plate and the metallic gauze was 
 variable, and the experiment consisted in observing 
 how much electricity reached the gauze from the 
 
CH. VI.] 
 
 DISCHARGE BY LIGHT 
 
 61 
 
 negatively charged plate, under the influence of 
 light ; first without, and then with, a magnetic 
 field of measured strength applied across the region 
 between them. 
 
 A little calculation of extreme beauty showed him 
 that the paths of the flying particles under magnetic 
 
 Ga.uze 
 
 Zinc 
 
 
 FIG. 9. Diagram showing the theoretical paths of the electrons 
 emitted from clean negatively-charged zinc in ultra-violet light, under the 
 influence of a strong perpendicular magnetic field ; the zinc and gauze 
 being a magnified representation of the AB and CD in fig. 8. The rays 
 would naturally reach the gauze and convey a current to the electrometer, 
 but under the influence of the magnetic field their paths become cycloids 
 and they fail to reach the gauze unless it is brought nearer. The critical 
 distance between the zinc and the gauze when they are just able to 
 reach it is what is measured. 
 
 influence would be cycloids, whose generating circles 
 contained the ratio m/e as well as the ratio E/H 2 ; 
 that is to say their trajectory, if it could be observed, 
 would involve the electrochemical equivalent required, 
 and likewise the ratio of the electric to the magnetic 
 
62 LEAKAGE IN ULTRA-VIOLET LIGHT [CH. vi. 
 
 field applied, as well as the absolute strength of the 
 magnetic field. 
 
 The calculation is so simple that it may be given 
 here : 
 
 Let figure 9 show the zinc and the gauze facing 
 each other, close together, with a gradient of 
 potential (V - V)/d = E between them ; and let a 
 magnetic field of density H (which letter is, in this 
 case, to represent M times the intensity, for brevity 
 of writing) be applied normal to the paper. 
 
 Then the motion of a charged particle detached 
 and propelled from the origin into the region between 
 the plates, provided that the plates are in vacuum 
 so that there is no resisting medium to interfere, 
 will be taking the axis of x as a perpendicular to 
 
 the plate .. ^ TT . 
 
 mx = &e iiey 
 
 my = Hex 
 
 the initial values of x, y, x, and y, being all zero. 
 The solution of these equations, under these initial 
 
 conditions, is /, 7 , x 
 
 x = a(l -cos ot) 
 
 y a(bt sin bt) 
 
 Era , 7 TT e 
 where a = TT9 and b = H . ; 
 He ra 
 
 and from these we see that x is oscillatory in accord- 
 ance with a versine, ranging from to 2a and back ; 
 while y is both oscillatory and progressive, com- 
 pleting its period in a time -=--, and increasing in 
 
 every such period by the amount 2-n-a. In other 
 words, the equations represent a cycloid traced by 
 the rim of a circle of radius a rolling on the zinc 
 plate. 
 
CH. vi.] DISCHARGE BY LIGHT 63 
 
 There is no known way of actually observing this 
 quite invisible and purely theoretical trajectory ; but 
 when it is perceived that in accordance with this 
 theory all the particles moving between the plates 
 will have similar paths so far as they do not come 
 near the edge of either plate, in which case they 
 would not be propelled so far it becomes plain that 
 there should be a critical distance, within which the 
 gauze would receive and intercept all the particles, 
 and beyond which not a single one would be able to 
 reach it. In the figure the gauze is depicted as set 
 just beyond the critical distance, so that it would 
 receive no electricity, even though the ultra-violet 
 light were fully shining ; but so that if either its 
 distance from the zinc were diminished, or the electric 
 field strengthened, or the magnetic field weakened, 
 the gauze would at once come within range and 
 receive a plentiful supply of charge from the hypo- 
 thetical cycloidally-flying particles. And the critical 
 distance at which this would happen a thing easily 
 experimentally observed would be independent of 
 the brightness of the ultra-violet light, and would 
 merely equal the diameter of the generating circle. In 
 other words, the critical distance between the plates, 
 when effective transfer of charge occurred, should be 
 
 2a, or ; a quantity which by this ingenious 
 
 6-Ll 
 
 means is therefore measurable. Wherefore the ratio 
 m/e for this case can be experimentally determined, 
 if E and H are both known. The apparatus 
 employed was shown in Fig. 8. 
 
 The sharpness of actual experimental observation 
 of the critical distance was not found quite so great 
 as this simple theory would indicate, because of 
 disturbing causes ; one of which was the presence of 
 
64 LEAKAGE IN ULTRA-VIOLET LIGHT [CH. vi. 
 
 some residual air, interfering with the perfectly free 
 path of the moving bodies. Nevertheless it was sharp 
 enough for fair determination ; and the result was 
 again, in this case also, that the ratio e/m came out 
 10 7 c.g.s., or more exactly 7xl0 6 ; corresponding 
 closely with the values found by J. J. Thomson, 
 confirmed subsequently by both Lenard and Kauf- 
 mann, for the cathode ray particles. 
 
 Another phenomenon on which measurements were 
 made w r as the discharge of negative electricity from 
 an incandescent carbon filament in an atmosphere of 
 rarified hydrogen. This also is subject to disturb- 
 ance by a magnetic field, as was shown by Elster and 
 Geitel ; and a series of measurements, on lines similar 
 to the preceding, resulted in a value 
 
 - =87x 10 6 c.g.s., 
 m 
 
 a value of the same order of magnitude as before : one 
 thousand times greater than the electrochemical or 
 electrolytic value for hydrogen, and many thousand 
 times greater than for other substances, but always 
 constant and independent of the nature of the sub- 
 stance present. 
 
 Another method for measuring these quantities, in 
 what may seem a more direct manner, was devised 
 by Professor Lenard and is depicted in fig. 10. It 
 will be realised that the remarkable character of 
 these experiments is the fact that nothing is visible : 
 there are no cathode rays to be seen, nor any 
 phosphorescent spot produced ; all that can be 
 observed is either a maximum deflexion of the 
 electrometer, as by Lenard's plan, or a zero deflexion 
 suddenly changed to a finite deflexion, in J. J. 
 Thomson's plan. 
 
GH. VI.] 
 
 DISCHARGE BY LIGHT 
 
 65 
 
 : Lenard's method may be described as follows: *-; 
 Light from the source L, which is a spark between 
 zinc electrodes, passes through a quartz plajbe Q, 
 where it enters the vacuum and falls upon a 
 negatively electrified aluminium plate C. B is a 
 perforated earthed screen through which the particles 
 are shot till they fall upon the plate E, which is 
 connected to an electrometer ; or if deflected by a 
 magnet they will fall upon the plate F. The amount 
 
 FIG. 10. Lenard's apparatus for measuring the electrochemical 
 equivalent of the discharge of negative electricity from a cathode 
 illuminated by ultra-violet light in vacuo. 
 
 IS 
 
 of" charge received by these two terminals 
 separately measured and plotted, with magnetic 
 field as abscissa. The charge received by E tgill 
 decrease, and that received by F will increase; as 
 the magnetic field is increased, until a maximum 
 is received by F ; which will happen when the centre 
 of the plate is the middle of the stream of rays,. 
 A further increase in the magnetic force will cause 
 the charge received to fall off. The field required 
 to give this maximum is measured being determined 
 by metrical examination of the plotted curve. The 
 paths of the particles between B and F must ; be 
 
 L.E. 
 
66 LEAKAGE IN ULTRA-VIOLET LIGHT [CH. VL 
 
 circles, since they are not subjected to any but a 
 deflecting force when they have passed through the 
 screen. When the maximum is received by the plate 
 F, the tangent to the mean circle will be horizontal 
 at the position of the hole B ; and this fact, together 
 with the passing of this circular trajectory through 
 the centre of the plate F, is sufficient to determine it, 
 and so to give its radius of curvature, which will 
 be equal to 
 
 The velocity u is separately estimated by assuming 
 that it is acquired under electrical influence between 
 C and B, the equation being 
 
 the latter factor being the difference of potential 
 between C and B. 
 
 Thus the two quantities u and e/m are determined. 
 
 Positive and Negative Carriers. 
 
 In connexion with the above experiments it is 
 important to notice that the above value of e/m for 
 the negative carriers is only obtained at low pressures. 
 If the pressure is high the ordinary electrolytic value 
 of e/m, or something still smaller, can be obtained; and 
 this suggests that at ordinary pressures the electron 
 becomes loaded up by attaching itself to an atom, or 
 even by collecting round itself a group of atoms. 
 Further evidence of this is afforded by the fact that 
 there is but little difference between the velocities of 
 the positive and negative ions, when urged by an 
 electric field, in a gas at atmospheric pressure. It 
 will be seen, further on, that in the case of the 
 
CH.VI.] POSITIVE CARRIERS 67 
 
 electrons discharged from Radium, their velocity is 
 so great that this loading effect is imperceptible. 
 
 Nothing larger than the ordinary electrolytic value 
 for the e/m ratio is ever given by the positive carriers. 
 These are not so easy to observe, but WIEN* has 
 examined them by detecting and measuring the 
 slight magnetic deflexion exhibited by certain 
 rays behind a perforated cathode in a vacuum tube, 
 which Goldstein discovered and called Kanal-strahlen, 
 and which Wien and Ewers proved were carriers of 
 positive electricity. Wien has shown that they move 
 fairly quickly that is to say about 360 kilometres 
 per second in spite of the fact that in hydrogen their 
 ratio e/m is of the order 10 4 , that is to say the 
 proper value for a hydrogen atom or ion. With 
 other substances the ratio has been found to vary 
 with the substance and approximately to equal the 
 electrolytic value, for these positively charged 
 atoms. J. J. Thomson has likewise made measure- 
 ments on the positive carriers, by means of the 
 discharge from incandescent filaments and other 
 positively charged hot bodies, and has confirmed 
 Wien's results obtaining an electrolytic value for 
 their electrochemical equivalent. 
 
 Thus it is forcibly suggested that whereas the 
 positive carriers of electricity are always ions, con- 
 sisting of a unit + charge associated with an atom, 
 the negative carriers are sometimes dissociated from 
 the main bulk of the atom, as if they were only 
 fractions or fragments or constituents or appendages 
 of an atom. These, detached and flying loose, are 
 able to attain to prodigious speed. For any acceler- 
 ation to which they are subjected is a thousand-fold 
 
 *Wied. Ann. Ixv. p. 440. See also Ewers in Wied. Ann. Ixfx. 
 p. 187. 
 
68 LEAKAGE IN ULTRA-VIOLET LIGHT [CH. vi. 
 
 greater than it is even for an atom of hydrogen, 
 weighed down and burdened as that is with a mass 
 of inert material, and subject only to the very same 
 propulsive force. , i . 
 
 Think of the mobility of a particle which experienced 
 the usual gravitation pull and had only 10 1 00 of the 
 corresponding mass to carry. Such a mobile particle 
 as that would drop under the influence of gravity, not 
 16 feet in the first second, as everything we know 
 does near the surface of the earth, but 16,000 feet, 
 or about three miles ; and would in one second 
 acquire under gravity a velocity of six miles per 
 second ; enough almost to carry it out of the range 
 of the earth's attraction altogether, and more than 
 enough to carry it round the world, if fired horizon- 
 tally with such a speed. 
 
 The acceleration to which particles are subject in a 
 vacuum tube is far greater even than this, because 
 there the forces are so prodigious ; gravitation force 
 on ions is almost infinitesimal compared with common 
 electrical force on their charges. Suppose, for in- 
 stance, that they are in a field such as may easily occur 
 in a vacuum tube, of 3,000 volts per centimetre, one- 
 tenth of what ordinary air will stand, or ten electro- 
 static units. The force urging one of these carriers 
 to move is then 10 x 10~ 10 = 10~ 9 dyne; the mass 
 being moved, if it is a whole atom of hydrogen, e.g. 
 if it were a positive carrier in a hydrogen atmosphere, 
 is only 10~ 24 gramme; and accordingly the acceleration 
 it experiences is 10 15 centimetres per second per second, 
 or a billion times g. Whereas if it were the smallest 
 kind of negative carrier, its acceleration would be a 
 thousand times greater still. 
 
 . The velocity acquired in passing over a distance of 
 five centimetres under this force is obtained by finding 
 
CH. vi.] NEGATIVE CARRIERS 69 
 
 the square root of 2fh ; that is to say, it is 10 8 centi- 
 metres per second for a positive carrier, and 3 x 10 9 
 centimetres per second for a negative carrier ; and 
 these are approximately the orders of magnitude 
 actually observed. 
 
 Thus the hypothesis becomes more and more j ustified 
 that units of positive charge are always associated 
 with atoms, in operations which we can control, 
 and are consequently always complete ions; while 
 the units of negative charge appear in some cases 
 with a separate existence, perhaps carrying with 
 them part of the atom, in which case they might be 
 called corpuscles, having a material nucleus ; perhaps 
 pure disembodied electricity, whatever that may 
 be an electrical charge detached from matter, a 
 mere complexity in the ether, in which case they 
 would correspond with those hypothetical entities 
 familiar in theoretical and mathematical treatment as 
 "electrons." 
 
CHAPTER VII. 
 IONISATION OF GASES. 
 
 IT is constantly necessary to speak of the air or other 
 medium being ' ionised ' by the passage of rays, and 
 by many other processes. The term means that the 
 molecules are split up, or dissociated, into their 
 constituent atoms ; which, being oppositely charged, 
 form anions and cations respectively. It appears to 
 be an effect due to the violent encounter of an ener- 
 getically flying particle with a comparatively stationary 
 molecule : a sudden electric wave or pulse, if thin and 
 forcible enough, may do the same ; the effect in any 
 case is to break the molecule asunder into constituent 
 ions, some positively, some negatively, charged, 
 thereby converting the medium into a true gaseous 
 electrolyte, until the dissociated atoms have had time 
 to recombine a time which may be measured in 
 minutes. It is owing to this effect that X-rays are 
 able so readily to discharge an electroscope or other 
 charged body, whatever the sign of its charge may 
 be ; for it is manifest that any ions in the atmosphere 
 of opposite sign will be attracted to it and will 
 neutralise any charge it may possess. Ionised air 
 can always be detected by its making electroscopes 
 leak, irrespective of any defect of insulation in solid 
 supports. 
 
CH. vii.] HOT METALS 71 
 
 The ionising power of X-rays was observed by 
 Righi soon after their discovery, and almost simul- 
 taneously by other physicists. 
 
 The terrestrial atmosphere out of doors is usually 
 more or less ionised, and in underground air the 
 ionisation is still more marked, probably owing to 
 radio-activity in the soil. Elster and Geitel have 
 
 TO CXECrV3OMCT-/? 
 
 FIG. 11. 
 
 examined this matter thoroughly, and Lenard found 
 that even the splashing of water introduced ions into 
 air, so that the atmosphere at base of a waterfall was 
 usually in some degree ionised. 
 
 Behaviour of Hot Metals in Gases. 
 
 Fig. 11 must stand as representative and typical 
 of a mass of important work on the ionisation and 
 disintegration of material effected by high tempera- 
 ture ; it represents the simple apparatus of Elster 
 
*2 IONISATION OE GASES [CH. vn. 
 
 (ind Geitel by which they examined in great detail 
 a number of incandescent metals in the form of a 
 wire or strip heated by an electric current in different 
 gases. In J. J. Thomson's variety of experiment 
 this current was produced in the secondary of a 
 transformer, so as to be conveniently insulated. The 
 details are long and complicated, and must be referred 
 to in J. J. Thomson's book on The Conduction of 
 Electricity through Gases \ but briefly it may be 
 said that when the gas in the vessel is air, the metal 
 plate A receives a positive charge when the wire is 
 heated to a dull red glow ; as it becomes hotter the 
 charge increases until the wire is at a yellow heat ; 
 if it is made hotter than that, the charge diminishes, 
 and, at the highest temperature, is very small. In 
 hydrogen the plate is found to receive negative elec- 
 tricity when the wire is hot enough, though at a lower 
 temperature it receives positive. To get rid of 
 occluded gases, J. J. Thomson often kept it red hot for 
 a week or more. McClelland, Branly, H. A. Wilson, 
 and others have investigated this phenomenon, which 
 has also been studied in a different form by Preece 
 and Fleming following up a curious observation 
 made by Edison in connexion with incandescent 
 lamps. Kecent measurements by 0. W. Eichardson 
 have done much to reduce it to a definite physical 
 specification. The evidence that an incandescent 
 platinum wire disintegrates, or at any rate gives off 
 material, is the fact discovered by Aitken, that a 
 cloud becomes visible in a luminous beam, if the 
 moist gas surrounding the wire be suddenly cooled. 
 This indeed can occur at a much lower temperature 
 than incandescence. Mr. Owen (Phil. Mag., Sept., 
 1903), found that when a platinum wire was in air 
 there was always a cloud when the temperature of 
 
CH.VIL] CONDUCTION IN AIR 73 
 
 the wire was raised to about 300 C., even after 
 long-continued previous incandescence of the wire ; 
 whereas in pure hydrogen the wire had to be raised 
 to red heat before a cloud formed. 
 
 Measurements of lonisation Current. 
 
 The whole subject of the dissociation or breaking up 
 of molecules which is effected in gases by Rontgen rays, 
 by radium radiation, and by a great number of other 
 influences a process which is known as ionisation, 
 because the broken constituents of the molecule are 
 oppositely charged is too large to be conveniently 
 entered upon here. It has been worked at by a 
 multitude of experimenters, and for an account of 
 their results the work of J. J. Thomson on The 
 Discharge of Electricity through Gases, must be 
 referred to. It may suffice to say that the products 
 of decomposition, though in the first instance no 
 doubt simple ions, seem to be speedily complicated 
 by the aggregation of other molecules round them ; 
 and accordingly the diffusion or progress of these ions 
 is liable to be retarded, and, when measured, is found 
 slower than might otherwise have been expected. 
 On the whole, the negative ions tend to move faster 
 than the positive ones, but the difference is not 
 necessarily greater than can be observed in liquid 
 electrolysis. Eecent work by H. A. Wilson and 
 E. Gold, on conduction in flames, has however shown 
 that the negative carriers in that case are free 
 electrons. 
 
 One of the easiest tilings to measure is the con- 
 ductivity of air in this ionised condition, that is to 
 say, the total current transmitted .by it between two 
 electrodes immersed in it and connected to some 
 sufficiently sensitive current-measuring device a 
 
74 IONISATION OF GASES [CH. vn. 
 
 galvanometer in some cases, or an electrometer 
 arranged so as to show a measured leak in 
 others. 
 
 A saturation value of the current can thus be 
 found, when all the ions present are taking part in 
 the action to the full extent ; the current then 
 reaches a maximum, which cannot be exceeded ; and 
 its amount would furnish an estimate of the number 
 of ions present, if the speed and the charge of each 
 were known. Measurements of the total current Neu, 
 the quantity of electricity conveyed per second, have 
 been made by Lenard 1 and Bighi 2 and Thomson, 3 
 and in various gases by Rutherford, 4 now Professor 
 at Montreal ; by Beattie 6 and de Smolan at Glasgow, 
 by Zeleny 6 of Minnesota, by McClelland 7 on hot 
 gases from flames, by McLennan 8 of Toronto, by 
 Richardson, 9 H. A. Wilson, 10 and Owen 11 on in- 
 candescent filaments. Townsend also has made 
 many experiments on the diffusion speed of ions. 
 
 Professor Zeleny measured the velocity by a safe 
 and direct method of making the particles fly down a 
 tube against a wind, and observing the rate of the 
 current of air which was just able to withstand their 
 progress : these measurements constituting a satis- 
 factory confirmation of Thomson's and Rutherford's 
 more indirectly inferred results. 
 
 1 Wied. Ann., vol. 63, p. 253. 
 z Rend. della R. Accad. dei Linc&i, May, 1896. 
 3 Phil. Mag., November, 1896. 
 *Ibid. t November, 1896, and April, 1897. 
 
 6 Ibid., June, 1897. 6 Ibid., July, 1898. 7 Ibid., July, 1898. 
 
 *Phil. Trans., vol. 195, p. 49, 1899. 
 9 Ibid., vol. 201, 1903. Ibid., vol. 202, 1903. 
 
 11 Phil. Mag., August, 1904. 
 
CH. vii.] BY RONTGEN RAYS T5 
 
 Condensation of Moisture Experiments. 
 
 C. T. R Wilson investigated the amount of expan- 
 sion required by both positive and negative ions to 
 act effectively as nuclei in condensing moisture. The 
 ions were produced by Kontgen rays, and electrolytic 
 terminals were inserted to effect a separation of 
 the ions. He found that with an expansion such 
 that the ratio of the final to the initial volume was 
 1*25, there was a fog in the half of the vessel which 
 contained negative ions, and hardly any condensation 
 in the half containing positive ones, but that when 
 the expansion-ratio was as much as 1*31 there was 
 little or no difference to be seen between the two 
 halves. Thus proving that the negative ions are 
 more efficient, as centres of condensation for water- 
 vapour, than the positive ions. 
 
 It may be doubted whether electrons themselves 
 are able to act as nuclei and condense vapour round 
 them, and it appears unlikely that they can do that 
 without the aid of one or more atoms of matter. 
 On this subject Mr. C. T. K. Wilson has favoured me 
 with the following opinion : 
 
 " I certainly think that in practically all cases the 
 electron has already been loaded to form a negative 
 ion, before the expansion by which the necessary 
 supersaturation is brought about has been effected. 
 In air which contains less moisture than corresponds 
 to a four- fold supersaturation, equilibrium is probably 
 reached when the electron has collected around itself 
 a group of molecules not much larger than the ion 
 in dry air. If however a four-fold supersaturation 
 is exceeded, the conditions become unstable and the 
 cluster of molecules increases to a visible drop. If 
 electrons enter the expansion chamber immediately 
 
76 IONISATION OF GASES [OH vn. 
 
 after an expansion, while the four- fold supersaturation 
 is still exceeded, no doubt they will form nuclei for 
 the condensation of drops without any pause at the 
 ion stage. But in the ultraviolet-light experiments 
 I have no doubt that the electrons, or all but an 
 insignificant proportion of them, had been loaded up 
 and had existed as ions before the expansion was 
 made." 
 
 The next chapter contains an account of what are 
 probably the most important experiments yet made 
 in the Cavendish Laboratory. 
 
 
CHAPTER VIII. 
 DETERMINATION OF THE MASS OF AN ELECTRON. 
 
 So far, all the measurements quoted have resulted in 
 a consensus of certainty respecting our knowledge of 
 e/m. for gaseous conduction and radiation ; and the 
 measurements made on the cathode rays in a Crookes's 
 tube, or near a plate leaking in ultra-violet light, 
 have likewise given us a knowledge of their velocity, 
 and shown that it is about one- thirtieth of the velocity 
 of light : more or less according to circumstances. 
 But so far no direct estimate has been made of either 
 e or m separately. The difficulty of making these 
 measurements is great, because we are dealing with an 
 aggregate of an enormous and unknown number of 
 these bodies. It would not be difficult to make a 
 determination of the aggregate mass of a set of pro- 
 jectiles, say Nra, where N is the number falling on a 
 target in a given time, by means of the heat which 
 the blow generates ; or better, perhaps, by the 
 momentum which they would impart to a moving 
 arm after the fashion of a ballistic pendulum ; 
 provided their velocity u were known, as in this 
 case it is. The aggregate energy ^ Nmu 2 , or the 
 aggregate momentum Nmtt, could thus be found ; but 
 howls m to be separated from N ? 
 
 Again, if the particles are collected in, a hollow 
 
78 DETERMINATION OF THE MASS [CH. vm. 
 
 vessel attached to an electrometer of known capacity, 
 it is not difficult to estimate the total quantity of 
 electricity which enters the vessel in a given time, 
 that is to say, to determine Ne ; but, again, how are 
 we to discriminate e, from N ? 
 
 Another thing that is comparatively easy to deter- 
 mine, especially in such cases as leak from a negative 
 surface under the action of ultra-violet light, or the 
 conductivity of air induced by the influence of Rontgen 
 rays, is the total current transmitted ; viz. the quantity 
 New, the quantity of electricity conveyed per second 
 between electrodes immersed in the air, and main- 
 tained at a sufficiently high difference of potential 
 to cause all the corpuscles or the ions present to 
 take part in conducting the current. 
 
 We may consider the following quantities experi- 
 mentally determined, by researches carried on at 
 the Cavendish laboratory and elsewhere, and so far 
 already described or indicated in the preceding three 
 chapters:- gfm 
 
 u 
 
 Ne 
 Nw 
 
 New 
 
 But still we have not described a method of 
 measuring separately either e ox m: only methods 
 of measuring their ratio. 
 
 If only it were now possible to count the corpuscles 
 or electrons, to determine the number N which are 
 started into existence, or which enter the hollow 
 vessel or which take part in conveying the current in 
 the case of a leak by ultra-violet light, we should no 
 longer have to guess at the actual value of e and of m 
 separately, but should have really determined them. 
 
CH. viii.] OF AN ELECTRON 79 
 
 This brilliant research has actually been carried out 
 by Professor J, J. Thomson, by means of a method 
 partly due to Mr. C. T. K. Wilson, supplementing a 
 fact discovered by Mr. Aitken, and interpreted in the 
 light of hydrodynamic principles laid down long ago 
 by Sir George Stokes. 
 
 I must be excused for waxing somewhat enthusiastic 
 over this matter : it seems to me one of the most 
 brilliant things that has recently been done in experi- 
 mental physics. Indeed I should not need much 
 urging to cancel the " recently " from this sentence ; 
 save that it is never safe for a contemporary to usurp 
 the function of a future historian of science, who can 
 regard matters from a proper perspective. 
 
 The matter is rather long to explain from the 
 beginning, and I must take it in sections. 
 
 Aitken and Cloud Nuclei. 
 
 First of all, Mr. John Aitken,* of Edinburgh, dis- 
 covered in 1880 that cloud or mist globules could 
 not form without solid nuclei, so that in perfectly 
 clear and dust-free air aqueous vapour did not 
 condense, and mist did not form. (See, for instance, 
 my lecture to the British Association at Montreal, in 
 1884, on "Dust" Nature, vol. 31, p. 268.) 
 
 Without solid surfaces, in clear space, vapours 
 could become supersaturated ; but the introduction 
 of a nucleus would immediately start condensation, 
 and according to the number of nuclei, or conden- 
 sation centres, so will be the number of cloud 
 globules formed. 
 
 Every cloud or mist globule is essentially a 
 minute falling raindrop, not floating in the least, but 
 falling through a resisting medium falling slowly 
 
 * Trans. R.S. Edin., vol. 30, pp. 337-368 (1883). 
 
80 DETERMINATION OF THE MASS [CH. vjii. 
 
 because it is of such insignificant weight compared 
 with its surface but falling always relatively to the 
 air. A cloud may readily be carried up by a current 
 of air, but that is only because the air is moving up 
 foster than the drops are trickling down through it. 
 No motion of the air disturbs the relative falling 
 motion : the absolute motion with reference to the 
 earth's surface is the resultant of the two. 
 
 The fact that nuclei are required for mist precipi- 
 tation can be . proved by filtering them out with 
 cotton wool, and finding that as the nuclei get fewer 
 the mist condensation differs in character, becoming 
 ultimately what is called a Scotch mist, such as forms 
 in fairly clean air ; where since the dust particles are 
 comparatively few, the centres of condensation are 
 few also, and accordingly have each to condense a 
 considerable amount of vapour ; so that the drops are 
 not nearly so close together and are bigger ; wherefore 
 they fall quicker, like very fine rain. In perfectly 
 clean elaborately-filtered air the dew point may be far 
 passed without any vapour condensing, and the space 
 will remain quite transparent in spite of its being 
 supersaturated with vapour. 
 
 The reason for this effect of, and necessity for, 
 nuclei, is. thrown into strong relief by Lord Kelvin's 
 theory concerning the effect of curvature on vapour 
 tension,* because the more a liquid surface is curved 
 the more it tends to evaporate, and an infinitely 
 convex surface would immediately flash off into 
 vapour. Consequently an infinitesimal globule of 
 liquid cannot exist; vapour can only, condense on a 
 surface of finite curvature, such as is afforded by a 
 dust particle or other body consisting of a large 
 aggregate of atoms. For it must be remembered 
 
 * See, for instance, Maxwell's Theory of Heat, 1891 edition, p. 290. 
 
 
CH. VIIL] OF AN ELECTRON 81 
 
 that a single grain of lycopodium powder contains 
 about a trillion atoms, and a dust particle big enough 
 to condense vapour need not consist of more than a 
 billion, or perhaps not more than a million, atoms, 
 and need by no means be big enough to be visible 
 even in a microscope. It is, however, material enough 
 to be stopped by a properly packed cotton-wool filter. 
 
 J. J. Thomson and Electrical Nuclei. 
 
 In 1888 it was shown by J. J. Thomson, in his 
 book Applications of Dynamics to Physics and 
 Chemistry, p. 164, that electrification of a body 
 would partially neutralise the effect of curvature, and 
 so assist the condensation of vapour on a convex 
 surface. 
 
 Consider a drop of liquid, or a soap bubble ; the 
 effect of the curvature of the surface is to give a 
 radial component of surface tension inwards, causing 
 an increased pressure internally. The effect of 
 electrification is just the opposite : it causes a direct 
 pressure outwards, which goes by the name of electric 
 tension. 
 
 The way these depend on size is as follows : 
 
 The radial-pressure component of the surface- 
 tension T is 
 
 inwards. 
 
 r 
 
 The electric tension is 
 
 outwards. 
 
 They are differently affected, therefore, by the size 
 of the globule ; hence at some size or other they must 
 balance, and such an electrified convex surface will 
 
 L.E. F 
 
82 DETERMINATION OF THE MASS [CH. vni. 
 
 behave as if it were unelectrified but flat. Accord- 
 ingly vapour which would refuse to condense on an 
 unelectrified convex surface, until far below the dew 
 point, will begin to condense on it, if sufficiently 
 electrified, the instant the dew point is reached. 
 
 The critical size at which the ionic charge enables 
 a sphere of water to act as regards condensation as if 
 it were flat, can be reckoned by equating the pressure 
 to the tension, thus : 
 
 r Sir KT* 
 e 2 10- 21 1 
 
 
 whence r=10~ 8 approximately, or is of atomic 
 magnitude. 
 
 Hence ions may be expected to condense vapour 
 at the ordinary dew-point ; and anything bigger 
 which possesses the same charge can condense it 
 still more easily. 
 
 Accordingly an electric charge assists vapour to 
 condense ; and a sufficient electric charge might 
 cause it to condense on quite a small body as 
 small even as an atom. Hence in the presence of 
 ions, dust particles are not necessary for conden- 
 sation. - Vapour may condense on these electrical 
 nuclei without the need for solids of finite curva- 
 ture. The electrical nuclei cannot be completely 
 filtered out by cotton wool : they will exist or 
 can be produced in dust-free air. No doubt if 
 they are passed through a great amount of metal 
 gauze they may be diminished in number, but 
 they are not easily got rid of except by their 
 own diffusion, which does ultimately enable them 
 to pair off or to migrate to the sides of the vessel. 
 
CH. VIIL] OF AN ELECTRON 83 
 
 They can be got rid of most quickly, however, by intro- 
 ducing an electric field, that is to say by supplying 
 electrodes maintained at a few volts difference of 
 potential. They will then immediately make a 
 procession, as in electrolysis, only with much greater 
 speed, because their motion is much less resisted or 
 interfered with by chance collisions ; so they will 
 soon reach and cling to their respective electrodes, 
 and in that case again no true mist can form. But 
 it must be remembered that any of the numerous 
 causes of ionisation can produce some of them 
 again. 
 
 While ions are present in considerable numbers 
 a thick mist will form whenever the space is 
 saturated with vapour, but it will be a mist 
 of different appearance from the slight rain-like 
 condensation which may be seen forming round the 
 few residual dust particles. The mist globules will 
 usually be of uniform size, and some estimate of that 
 size can be roughly attempted by the diffraction 
 colours which can be seen if a point of light is looked 
 at through the mist : not, however, a very easy plan 
 for making a trustworthy estimate.* 
 
 Electrical nuclei can be produced in various 
 ways by anything, in fact, which dissociates the air 
 or which fills it with ions. Some are produced by 
 the splashing and spray of water ; some are given off 
 from flames, and from red-hot bodies ; they are 
 produced in considerable numbers when Kontgen 
 and when Becquerel rays travel through air ; they 
 can be given off by radio-active substances like 
 uranium; and they are easily emitted by a nega- 
 tively charged metallic surface exposed to ultra-violet 
 light. 
 
 *See C. T. K. Wilson, Phil. Trans., 1897, A, vol. 189, p. 283. 
 
84 DETERMINATION OF THE MASS [CH. vm. 
 
 Wilson and Metrical Cloud Condensation. 
 
 Mr. C. T. K. Wilson,* in his study at the Cavendish 
 Laboratory of cloud formation under the influence 
 of Rontgen rays and other agents, devised a plan 
 for precipitating a definite and known quantity of 
 aqueous vapour in a visible form. This was done by 
 an arrangement for making a sudden or adiabatic 
 expansion of saturated air, and making it to a 
 carefully measured amount. The apparatus employed 
 is shown in Fig. 12. 
 
 One test-tube moving inside another is employed 
 as a piston, and by a certain arrangement the piston 
 was enabled to drop with great suddenness and thus to 
 produce a measured small exhaustion and consequent 
 cooling in the reservoir containing the gas under 
 experiment ; saturated as it is with vapour, and 
 supplied with electric nuclei. The mist at once 
 formed, and the drops began to fall slowly, as 
 usual. Mr. Wilson tried to get an estimate of 
 their size from the colours, but it was difficult and 
 unsatisfactory. If the size had been known, their 
 number would have been known too, because the 
 measured amount of expansion had produced a 
 known fall of temperature below the dew point, 
 and so had condensed a known amount of aqueous 
 vapour, which would be distributed equally among 
 all the equal globules. 
 
 It occurred to J. J. Thomson that a better estimate 
 of size could be made by observing their rate of 
 falling, which is a thing not difficult to observe since 
 they all fall together, being all of the same size. In 
 any mist formed in a bell-jar it is easy to watch it 
 settling down, by watching its fairly definite upper 
 
 *Phil Trans., A, 1897, vol. 189, p. 265. 
 
CH. VIII.] 
 
 OF AN ELECTRON 
 
 85 
 
 To Earth. 
 
 To 
 Eiectrometer. 
 
 FIG. 12. A represents one of the vessels in which the fog is formed 
 whose rate of fall is to be measured by Mr. Wilson's method : it is 
 arranged for the ionisation produced by X-rays. The vessel A, con- 
 taining some water, and covered by an earthed aluminium plate, is 
 in communication with a vessel C through the tube B. Inside C is a thin- 
 walled test-tube P, which serves as a piston or bell-jar (shown rather 
 too stumpy) and with its lip always dipping under water like a gasometer. 
 D is an indiarubber stopper closing the end of tube C : the lower part 
 of the tube C ought to be shown filled with water to such a height that 
 the mouth of the piston is always below the surface. A glass tube con- 
 nects the inside of the test-tube P with a space E. The space E may 
 be put in connection with an exhausted s^ace F through the tube H. 
 The end of the tube H, inside the space E, is ground flat, and is closed 
 by an indiarubber stopper I, which is kept pressed against the tube H 
 by means of a spiral spring. The stopper I is fixed to a rod K ; by 
 pulling the rod down smartly the pressure inside the test-tube is 
 lowered, and the piston P falls rapidly until it strikes against the 
 indiarubber stopper D. The falling of the piston causes the gas in 
 A to expand : the tubes R and S are for the purpose of varying the 
 amount of the expansion. Before an expansion the piston P is raised 
 by admitting air through T, which is then closed. Then, when every- 
 thing is ready, K is pulled, and the cloud forms in A. 
 
86 DETERMINATION OF THE MASS [CH. vm. 
 
 surface, a clear space being left above it which 
 gradually increases in thickness as the cloud falls. 
 The rate of movement of the top of the cloud will 
 give the rate of falling of the individual globules of 
 which it is composed. And this brings us to the 
 next section. 
 
 Prof. Stokes and Falling Spheres. 
 
 Many years ago, in 1849, Sir George G. Stokes* 
 discussed the motion of solids through fluids, and 
 among others of a sphere moving through a viscous 
 fluid urged by its own weight. It is a familiar fact 
 that large bodies fall through air or water or any 
 resisting medium more quickly than small ones of 
 the same shape. Thus coarse sand settles down 
 through water quicker than fine sand, and the finest 
 powder takes a very long time to settle ; in fact 
 this difference of the rate of falling is used as a 
 practical process of separating granular materials into 
 sizes, and is called levigation. 
 
 So it is in air : large raindrops fall violently, small 
 raindrops fall gently, and mist globules hardly fall 
 at all fall so slowly that their motion is difficult 
 to observe, but the same law governs all, so long 
 as the motion is not too violent, or so long as the 
 falling body has no edges such as will cause eddies 
 during the fall. A sphere falling slowly, controlled 
 by viscosity alone without waves or eddies, is the 
 simplest case. It soon reaches what is called a 
 terminal velocity the speed at which the viscous 
 resistance exactly balances its weight. At this 
 speed it is subject to zero resultant force, so it 
 simply obeys the first law of motion and moves at 
 a constant speed, t This constant speed or terminal 
 
 * Camb. Trans. Phil. Soc., ix. 48. t Of. Nature, vol. 31, p. 266. 
 
CH. VIIL] OF AN ELECTRON 87 
 
 velocity was calculated by Sir George Stokes for 
 the case of a falling raindrop of radius r as follows : 
 
 9 viscosity of air' 
 
 where p is the excess density of the sphere over the 
 medium it moves in ; provided there is no finite 
 slip at the surface. The maximum possible effect 
 of surface slip which will occur to some extent 
 when the falling globules are very minute is to 
 make the possible terminal velocity half as great 
 again : in other words to convert the numerical 
 
 2 1 
 
 coefficient - into -. 
 
 This simple formula gives the connexion between 
 the rate of fall of any small rain or fogdrop and its 
 size ; and by observation of this speed, therefore, 
 knowing the viscosity of air, it is possible to calculate 
 the dimensions of the falling drops. 
 
 J. J. Thomsons Experiment of Counting. 
 
 We have now all the materials ready for under- 
 ; standing the experiment to be performed,* so as to 
 count the ions which are produced in air under the 
 influence of Rontgen rays, or which have been produced 
 from a negatively electrified surface illuminated with 
 ultra-violet light. The apparatus for the former is 
 depicted in Fig. 12. The ionising beam of X-rays 
 enters the chamber A from above, through an earthed 
 aluminium lid which keeps it airtight. 
 
 The rate of leak, which must be observed in order 
 to calculate N<m, is determined by connecting the 
 water and the aluminium plate to the terminals of 
 
 * Phil. Mag., December, 1898, and December, 1899. 
 
88 DETERMINATION OF THE MASS [CH. vm. 
 
 an electrometer ; a sufficient difference of potential 
 being maintained between them. 
 
 And now, metrical condensation having been pro- 
 duced by the expansion appliance, and a mist formed, 
 the rate of its fall or gradual subsidence can be 
 observed by looking through the vessel at an illumi- 
 nated surface ; whence by Stokes's theorem the size 
 of each globule is known. The quantity of water 
 which had gone to form globules is known from the 
 measured amount of expansion, by a process the 
 details of which I will not give here ; and so 
 the number of such globules, and therefore the 
 number of their condensation-centres or nuclei or 
 ions, can be determined. 
 
 If c is the observed rate of fall in stagnant air, 
 the linear dimensions of the falling drops will be 
 
 //9//c\ 7/4 '5 x '000 18 
 r = V WJ = Vi 981 
 
 In a given case c was observed to be 0*14 centimetres 
 per second ; hence the volume of each drop was in 
 that case . 
 
 -7rr 3 =l-6xlO- 10 c.c. ; 
 o 
 
 and so, if the aggregate amount of water in all the 
 drops in a given space is reckoned from the measured 
 amount of adiabatic expansion which caused the chill 
 and the precipitation, the drops can be counted. 
 
 Professor Thomson, a few months later, repeated 
 this experiment, the ions being now produced by 
 illuminating a negatively electrified zinc plate with 
 ultra-violet light. The apparatus used is shown in 
 fig. 13. A clean zinc surface in vacuo, faced by a 
 transparent conductor through which the light could 
 shine on it, and by a window of quartz which makes 
 
CH. VIII.] 
 
 OF AN ELECTRON 
 
 89 
 
 the vessel airtight so that it might be exhausted and 
 yet allow the ultra-violet light to pass, was employed, 
 and connected to the expansion apparatus, fig. 12, 
 instead of the vessel A. The current ~Neu was 
 measured just as in the original experiment. 
 
 FIG. 13. J. J. Thomson's auxiliary apparatus for the counting experi- 
 ment. Ultra-violet light passes through the quartz plate CD and 
 through a layer of liquid, which keeps the air saturated, and which 
 constitutes one electrode, to a clean zinc plate K, which constitutes the 
 other, and which is kept negatively electrified. Connexion through 
 the tube L is made with the expansion apparatus shown in fig. 12, this 
 being employed instead of the vessel A in that figure. Then when 
 the sudden measured expansion is caused, a fog is condensed round the 
 negative ions which have sprung into being in consequence of the 
 electrons thrown off by the ultra-violet light; and the rate of settling 
 down of this cloud is then measured. 
 
 A great many precautions must be taken, because 
 there will be some residual cloud found even when 
 electrons or intended nuclei are not present. Positive 
 ions and other stray or undesired nuclei if present 
 can be eliminated by aid of their different behaviour. 
 A differential observation is generally necessary ; 
 
90 DETERMINATION OF THE MASS [CH. vm. 
 
 moreover care must be taken to ensure that all the 
 desired nuclei are utilised, and not only a portion. 
 
 The number of drops found in a certain experiment, 
 by this means, was about 30,000 to the cubic centi- 
 metre ; the total quantity of water which went to 
 form them being about the two-hundredth part of a 
 milligramme. The number of drops is of course 
 equal to the number of nuclei. Wherefore the nuclei 
 are counted. 
 
 Result. 
 
 The result of the execution of this ingenious 
 counting process is that the absolute charge and the 
 absolute mass of an electron are at length directly 
 determined. Hitherto we have determined by many 
 and various ways the ratio e/m and the speed u. We 
 have likewise been able to determine Neu and Ne 
 and Nm^ 2 , as already explained. Now at length we 
 have determined N ; and at once the terms in the 
 ratio e/m are disentangled. 
 
 e comes out, as suspected, in all cases, the regular 
 ionic charge, of the order of magnitude 3 x 10~ 10 
 electrostatic, or 10~ 20 electromagnetic units. Hence, 
 while m comes out for positive carriers and for all ions 
 the appropriate mass of the atoms present, or in 
 some cases greater than this, by reason of the forma- 
 tion of molecular aggregates, for the negative 
 carriers set free by ultra-violet light, and for the other 
 cases where e/m= 10 7 , the masses come out definitely 
 of the order 10~ 27 grammes; or about -7-^0 th part of 
 the smallest and lightest previously known quantity 
 of matter, viz., an atom of hydrogen. 
 
 The existence of masses smaller than atoms is 
 thus experimentally demonstrated, and a discovery 
 clinched of epoch-making importance. 
 
CHAPTER IX. 
 
 FURTHER DETAILS CONCERNING ELECTRONS AND 
 
 IONS. 
 
 Confirmatory Measurements of Charge. 
 
 A CONFIRMATORY measure of the charge e, can be 
 made by first observing the rate of fall of a cloud 
 condensed round the ions acting as nuclei a 
 measurement which gives the weight w of each 
 drop, and, then applying to the cloud a vertical 
 electric field and adjusting its strength until it is just 
 able to check the fall and hang the drops in air like 
 Mahomet's coffin. For under these conditions of 
 course w = Ee, and since everything except e has been 
 measured, e is at once known. This ingenious pro- 
 cess was devised by Mr. H. A. Wilson, and is 
 described by him in the Philosophical Magazine for 
 April, 1903. In practice the above would be slightly 
 modified and a simple differential method employed. 
 The numerical result at which he arrived was that 
 the value of e = 3'I x 10 ~ 10 . The result also had the 
 effect of confirming the applicability of Stokes' law, 
 in the cases where fall had been permitted. 
 
 This seems to be the value obtained for the electric 
 charge associated with every kind of monad ion, both 
 positive and negative, as well as for the separate 
 
92 ELECTRONS AND IONS [CH. ix 
 
 electrons. The same value characterises even the 
 molecular aggregates which are often found in 
 conducting air or other gas. 
 
 Fig. 14 shows H. A. Wilson's apparatus for sus- 
 pending a condensed cloud against gravity by means 
 of a known electric field. The magnet M, attracting 
 its keeper, opens connexion with an injector pump 
 through a valve V, and thereby, through the action 
 of the test tube T, produces a measured amount of 
 expansion in C. T. E. Wilson's manner as exhibited 
 in fig. 12. The expansion could subsequently be 
 measured by the gauge H. 
 
 A cloud is formed in the bell-jar B, and the electric 
 field is applied between the plates attached to the 
 terminals C D, kept electrified by a battery of a great 
 number of cells. The battery, however, was only 
 applied after the cloud had formed, otherwise all the 
 ions would be removed from the vessel by electrolytic 
 action. Rontgen rays were used to produce the ions, 
 but the coil exciting the rays was switched off and 
 stopped, by means of an automatically working switch 
 S, the instant before the valve was pulled by the 
 magnet. 
 
 J. J. Thomson has recently repeated his original 
 experiments, and by combining a determination of 
 New with an independent velocity measurement, he 
 has made what is now regarded as a standard estimate 
 of e, namely, 3'4 x 10~ 10 electrostatic units. 
 
 H. A. Wilson's confirmation of this by a totally 
 different method the Mahomet's coffin method by 
 which he finds 3'1 x 10~ 10 , has already been mentioned. 
 
 The importance of obtaining accuracy in these 
 measurements is that thereby lies our chance of 
 determining ra with accuracy the mass either of 
 an electron, or of an atom of matter. 
 
CH. IX.] 
 
 A CHORD EXPERIMENT 
 
 93 
 
 One of the first direct determinations of the aver- 
 age charge on a gaseous ion was made by Professor 
 
 H 
 
 FIG. 14. 
 
 Townsend (Philosophical Magazine, February, 1898), 
 his method consisting in bubbling newly-prepared 
 gas through water and measuring the charge on each 
 droplet. The deduction must be regarded as rather 
 
94 ELECTRONS AND IONS [CH. ix. 
 
 hypothetical, because it was an assumption that each 
 droplet contained only one ion. Nevertheless, that 
 appears to be the truth, since the charge found on 
 each was 3 x 10~ 10 electrostatic units. 
 
 A further method applied by Professor J. J. Thom- 
 son, and described in the Philosophical Magazine for 
 March, 1903, was used in a determination of the 
 maximum current passing between electrodes in 
 ionised air. 
 
 It may possibly be of assistance to some if we 
 quote here an explanatory remark drafted by Mr. 
 G. Owen : 
 
 Thomson's Deductions. 
 
 " What Professor Thomson succeeded in doing was 
 to measure the charge on the negative ion produced 
 in air by the influence of Rontgen rays. The ques- 
 tion might naturally be asked : What grounds had 
 Professor Thomson for drawing a general conclusion 
 concerning the mass of an electron from a deter- 
 mination of the charge on an ion produced in air by 
 one particular agency? 
 
 " The answer is as follows : The negative ions 
 produced in a gas were known to have the same 
 properties irrespective of the source of their pro- 
 duction f For instance, the negative ions produced 
 by X-rays, radium rays, and ultra-violet light, travel 
 with the same velocity under a given electric force ; 
 and further, behave identically with regard to their 
 power of acting as nuclei of condensation for super- 
 saturated water-vapour. It was therefore justifiable 
 to assume, in the first place, that the charge on an 
 ion produced by X-rays was equal to the charge on 
 an ion produced by the impact of ultra-violet light 
 on a metal surface. (This conclusion Prof. Thomson 
 
 
CH. ix.J SIZE OF ELECTRON 95 
 
 verified later on by direct experiment.) Again, the 
 & 
 
 ratio had been determined for the cathode ray 
 m 
 
 particles, and for the carriers of negative electricity 
 from incandescent filaments and from metal plates 
 illuminated by ultra-violet light at low pressures, 
 and it will be remembered that in all these cases the 
 
 p 
 
 same value of was obtained, thereby justifying 
 
 the surmise that the charge on an electron was the 
 same as that on an ion produced by ultra-violet 
 light, and therefore the same as on a negative ion 
 produced by X-rays." 
 
 Estimate of Size. 
 
 On the hypothesis that the flying or vibrating 
 fragment is a material corpuscle charged with 
 electricity, so that it has a duplex constitution and 
 a compound kind of inertia, part material and part 
 electrical, no further progress can be made. But on 
 the hypothesis that the flying or vibrating particle is 
 an electron a charge of electricity and nothing 
 else a constituent of an atom but with no material 
 nucleus so that the whole of atomic properties 
 might possibly turn out to be due to an aggregate 
 of electrons of opposite sign, of which one or two 
 are comparatively free and detachable on this 
 hypothesis a determination of the mass of a 
 corpuscle carries with it, as a consequence, a de- 
 termination of its size also. 
 
 Because, as has already been pointed out, any 
 required amount of self-induction can be conferred on 
 a wire by making it fine enough, and any required 
 amount of energy can be conferred upon an electric 
 
96 ELECTRONS AND IONS [CH. ix. 
 
 charge by making it concentrated enough. The 
 energy at a given speed of motion will be proportional 
 both to the quantity and the potential, and the latter 
 can be made as great as we please by making the size 
 of the body possessing the charge extremely small. 
 
 It is the intense region of force close to the wire or 
 close to the charged particle which is the effective 
 region ; and so, as stated, a knowledge of the mass or 
 kinetic energy at a given speed suffices, on a purely 
 electric theory of matter, to determine the size of the 
 electron constituents of which it is hypothetically 
 composed. For whether there be any intrinsically 
 material inertia or not, there certainly is an electrical 
 inertia. The cause of it in the electrical case is 
 known : it is due to the reaction of the electric and 
 magnetic fields during acceleration periods, and is 
 denominated self-induction. 
 
 Quite possibly there is no other kind. Quite 
 possibly that which we observe as the inertia of 
 ordinary matter is simply the electric inertia, or self- 
 induction, of an immense number of ionic charges, or 
 electric atoms, or electrons. 
 
 This is by far the most interesting hypothesis, 
 because it enables us to progress, and is definite. 
 The admixture of properties partly explained, viz. 
 the electrical, partly unexplained, viz. the material 
 lands us nowhere ; unless, by some only partially 
 imagined means, we were able to estimate how much 
 of the total appertains to each ingredient. 
 
 The mass of a corpuscle has been measured as 
 something akin to j^Vo f an atom of hydrogen, and 
 its charge asJ'lO" 10 electrostatic unit. Now this 
 amount of electricity will have that amount of inertia 
 if it exists on a sphere of radius 10~ 13 centimetre, 
 but not otherwise. Consequently we may assume 
 
CH. ix.] SIZE OF ELECTRON 97 
 
 the size of the supposed pure electron to be of the 
 order 10~ 13 centimetre in diameter; or 100 * 000 of 
 the linear dimension known as molecular magnitude, 
 viz. 10~ 8 centimetre. 
 
 The calculation of order of magnitude is quite 
 simple, for all ordinary speeds ; because, for them 
 
 
 ,->i a = . pe = 10 7 x 10~ 20 = 10~ 13 centimetre, 
 m 
 
 though it might with some data be estimated as small 
 as 10 ~ 14 .* Minuteness like that easily explains the 
 penetrating power of cathode rays. Especially if the 
 atoms of matter are themselves composed of such 
 minute particles. For the interspaces will be 
 enormous compared with the filled-up space, and a 
 point can penetrate far into such an assemblage 
 without striking anything. 
 
 Penetrability of Matter by Electrons. 
 
 The mean free path of a particle is a question of 
 probability. In a space containing n^ obstacles to the 
 unit volume, a space Ax will contain n = Axn l of 
 them ; and the chances of a collision, while one of 
 them travels a length x, will be approximately their 
 combined areas, as targets, compared with the total 
 area available for both hit or miss that is to say, 
 
 mra 2 1.1 ., o x 
 
 - ; which we may write px or -, 
 A x 
 
 where x is the " mean free path," or average distance 
 travelled by any one particle without a collision with 
 another, and ft the number of encounters while 
 
 *See Lodge in the Electrician for March 12, 1897, vol. 38, page 644, 
 where the size is deduced from the then just discovered Zeeman effect. 
 L.E. G 
 
98 ELECTRONS AND IONS [CH. ix. 
 
 travelling unit distance. But in saying this we are 
 ignoring the forces between the particles, as well as 
 their motion, and are not considering a swing round 
 as a collision. 
 
 Nevertheless, as regards order of magnitude 
 
 Ax 1 d* 
 
 /yi . _ 
 
 mra? n^a" tra 2 ' 
 
 where d? is the cubic space allotted to each particle, 
 while ira z is the actual bulk of each. 
 Therefore approximately 
 
 a; total space occupied 
 
 a ~~ a few times the aggregate volume of the particles* 
 
 a statement roughly analogous to Clausius' or 
 Loschmidt's theorem in the kinetic theory of gases. 
 
 Hence the mean free path can be estimated by 
 considering how much space the substance of all the 
 electrons in an atom occupies, as compared with all 
 the space which the atom occupies itself. In other 
 words, we have to consider what the size 10~ 13 for an 
 electron's diameter means, as compared with the size 
 10" 8 for an atom's diameter. In the solar system the 
 diameter of the earth is 24 ^ 00 th part of the diameter 
 of its orbit round the sun. Consequently if the earth 
 represented an electron, an atom would occupy a 
 sphere with the sun as centre and four times the 
 distance of the earth as radius. 
 
 In other words, if an average atom is composed of 
 electrons, they are about as far apart in that atom in 
 proportion to their size as the planets in the solar 
 system are in proportion to their size. 
 
 In an atom of hydrogen there would have to be 
 roughly 1,000, or say more exactly 700, electrons in 
 order to make up the proper mass. 
 
CH. ix.] SIZE OF ELECTRON 99 
 
 In an atom of sodium, which is twenty-three times 
 as heavy, there must be about 15,000 electrons. 
 
 And in an atom of mercury there must be over 
 100,000 electrons, if atomic mass be wholly due to them. 
 
 Consider then an atom of mercury containing 
 100,000 of these bodies packed in a sphere 10" 8 
 centimetre in diameter. One would think at first 
 they must be crowded ; but there is plenty of room. 
 Each electron is only 10~ 13 centimetre across, and 
 there are only about fifty of them in a row along any 
 diameter of the atom, whereas there might be a 
 hundred thousand in the same length ; hence the 
 empty space inside the atom is enormously greater 
 than the filled spaces. At least a thousand times 
 greater in linear dimension, or a thousand million 
 times greater in bulk. 
 
 The whole volume of the atom is 10~ 24 c.c. ; the 
 aggregate volume of all the electrons composing the 
 atom is 10 5 x 10~ 39 = 10~ 84 c.c. ; consequently the space 
 left empty is 10 10 or ten thousand million times the 
 filled space. 
 
 Even inside an atom of mercury, therefore, the 
 amount of crowding is fairly analogous to that of the 
 planets in the solar system. For though the outer 
 planets are spaced further apart than the inner ones, 
 they are also bigger, to practically a compensating 
 extent. 
 
 Now, going back to what is sometimes called 
 Loschmidt's theorem in the kinetic theory of gases, 
 obtained roughly above 
 
 mean free path 
 ^ diameter of particle 
 
 volume of space available to particles 
 ~ combined volume of all their substance 
 
100 ELECTRONS AND IONS [CH. ix. 
 
 we have reckoned the latter fraction, in the inside 
 of an atom of mercury, as 
 
 =10 
 " 
 
 10 
 
 100,000 x |7r(lO- 13 ) 3 10 5 x 10' 3 
 
 Hence the mean free path of an electron inside 
 an atom of mercury will be comparable to 10 9 times 
 the size of an electron, i.e., it will be 10~ 4 centi- 
 metre ; that is, it may get through, on the average, 
 the substance of some 10,000 mercury atoms in a 
 row, before collision with anything. 
 
 In any other less dense substance it will go 
 further. In ordinary air, on an average free journey, 
 it would escape collision with a hundred million 
 molecules in a room, which would be equivalent to 
 a distance of about four inches. In the case of 
 corpuscles plunging into a dense metal, the actual 
 distance achieved by them is very small, only the 
 thousandth part of a millimetre on the average, and 
 it need by no means necessarily be a straight line; 
 so a target of platinum succeeds in stopping them 
 very near its surface, and enables the X-rays 
 generated by the shock fairly to emerge. Some 
 corpuscles will be stopped more suddenly than this, 
 and some will travel further, but 10~ 4 centimetre, 
 or the thousandth of a millimetre, should be com- 
 parable with the average distance travelled in a 
 solid as dense as platinum. 
 
 Effects of an Encounter. 
 
 This distance, however, gives no notion of the 
 value of the negative acceleration during a collision, 
 because the greater part of that thousandth of a 
 millimetre is free flight; the stoppage occurs only 
 as the last episode of that flight, viz. at the instant 
 
 
CH. ix.] COLLISION 101 
 
 of collision. The colliding masses are 100,000 to 1, 
 so the change of velocity at impact could be esti- 
 mated ; but the impact will really be more of an 
 astronomical or cometary character, and the effect 
 is analogous to the entrapping of comets when they 
 pass near a planet, thereby rendering them per- 
 manent members of the solar system. 
 
 The ordinary behaviour of a foreign comet, which 
 comes and goes, may be called a collision with, and 
 rebound from, the sun; for although there is no real en- 
 counter of main substance, that is what it would appear 
 like if it could be seen from the depths of space ; and 
 the two branches of the comet's hyperbolic orbit would 
 look like straight lines of approach and recession. 
 
 Comets which happen to pass very near a planet, 
 however, are deflected, swirled round, and often 
 virtually caught by that planet, receding only with 
 an insignificant differential velocity which is unable 
 to carry them away from the attraction of the sun : 
 towards which they then drop. If they do not 
 actually drop into it, they will continue to revolve 
 round it in an elliptic orbit, becoming a member of 
 the solar system, and liable ultimately to be degraded 
 into a swarm of meteors. 
 
 This is the sort of process known to occur in 
 astronomy ; and circumstances not unlike that may 
 attend the encounter, or apparent collision, of a 
 furiously-flying comet-like electron with part of 
 the massive system of an atom. 
 
 The stoppage, therefore, will occur well within the 
 limits of atomic magnitude, 10~ 8 centimetre; and so 
 
 u 2 
 the acceleration will be of the order r = 10 26 c.g.s., 
 
 and the force needed thus to stop even a single 
 electron will be the tenth of a dyne. 
 
V 
 102 ELECTRONS AND IONS [CH. ix. 
 
 No wonder that violent radiation -effects are pro- 
 duced. The "power" required to stop an electron, 
 flying with one-thirtieth of the speed of light, inside 
 a molecular thickness, can be estimated thus 
 
 1 u 
 
 energy -f time = - DMT . ^7 
 
 * ' ff *^ 
 
 = 10- 27 (10 9 ) 3 10 8 = 10 8 ergs per second ; 
 or thus 
 
 = 10 again, 
 tt 
 
 which is equivalent to ten watts. (Though the time 
 it lasts is only the 10~ 17 part of a second.) 
 
 But only a small fraction of this goes into 
 radiation. The radiating power can be estimated 
 thus, from Larmor's expression for it, as deduced in 
 Appendix G, 
 
 /xe 2 10~ 40 
 
 -(u) 2 = 10 x 10 62 = 100 ergs per second. 
 
 The rest therefore, it would appear, must take the 
 form of heat. 
 
 It is worth considering what circumstances would 
 give radiation an advantage over heat, and vice versd. 
 Because sometimes conspicuously the target gets 
 heated, and sometimes X-rays are emitted. Let u 
 be the speed and I the distance of stoppage, then 
 
 u z 
 
 so the force required to stop it is 
 
CH. ix.] COLLISION 103 
 
 The " power " of the blow is 
 
 whereas the radiation power is 
 
 2 fu*V_pe*u*. 
 ' \2l) ~~ = 6vP ' 
 
 ,i f radiating power a u 2a 
 
 therefore 6F = T . - = , 
 
 total power I v vt 
 
 where t is the time of stoppage, and v is the velocity 
 of light. 
 
 Hence effective radiating power depends chiefly on 
 very sudden stoppage, and on the speed being 
 near that of light. If the velocity is a tenth that 
 of light, and if an electron can be stopped in some- 
 thing like its own diameter, about 10 per cent, of 
 the energy will go in radiation, and the rest will 
 take other forms, presumably heat. But it would 
 take immense " power " to effect such a stoppage as 
 that : not less than two or three thousand kilowatts 
 for each electron. So probably a stoppage within 
 atomic dimension is all that can be expected, and 
 that could be managed by something like 50 watts. 
 But then an exceedingly small fraction of the whole 
 only about one millionth would in that case take 
 the form of X-rays ; their wave-shell then having a 
 thickness comparable with molecular magnitude : 
 whereas in the previous case it was incomparably 
 thinner, and therefore far more penetrating. Both 
 thicknesses however are very small compared with 
 the wave-lengths of ordinary light. 
 
 As the velocity diminishes, more and more of the 
 energy takes the form of heat ; which agrees with 
 
104 ELECTRONS AND IONS [CH. ix. 
 
 the fact that at moderate vacua the target gets 
 red-hot. 
 
 The ratio of the radiation power to the total power, 
 is as the dimensions of an electron to the distance 
 light would travel during the period of the stoppage : 
 taking the acceleration as uniform. So to get all 
 the energy radiated it is necessary to stop a pellet 
 moving with a tenth the speed of light in something 
 like a tenth of its own diameter. 
 
CHAPTER X. 
 
 THE ELECTRON THEORY OF CONDUCTION 
 AND OF RADIATION. 
 
 MEANWHILE the probability of the existence of elec- 
 trons and the possibility of regarding them as the 
 basis of all electric and of most other material 
 phenomena, had seized hold of the imagination of 
 several mathematical physicists, notably of Professor 
 H. A. Lorentz and of Dr. J. Larmor. The former, 
 who was first in the field (1892 and 1895), was 
 driven in this direction by the problem of the 
 astronomical aberration of light and the optics of 
 moving media treated from the electric standpoint. 
 The latter reached the same goal independently, from 
 the dynamics of the free ether, on the basis of 
 MacCullagh and Kelvin, which required discrete 
 mobile sources of disturbance (electrons) as a basis for 
 development. Both these philosophers endeavoured 
 to trace all electric properties to the behaviour of 
 electrons, usually of course in association with 
 material atoms ; while Larmor's procedure also im- 
 pelled him to make intelligible by conceptual ' models' 
 the dynamical possibility of a structure in the ether 
 which should have the properties of an electron, 
 whether positive or negative, the two being treated 
 as mirror images of each other and so to reduce a 
 
106 CONDUCTION AND RADIATION [CH. x. 
 
 great part of Physics to its simplest terms. This 
 fine attempt, made in 1894, involved definite illus- 
 trative conceptions of the structure of an electron, 
 of its size on the theory that inertia is entirely 
 electric, of the velocities with which electrons revolve 
 in the molecule, and generally of an electronic 
 theory of matter : but in absence of knowledge the 
 mass of an electron was then naturally assumed 
 comparable with that of a hydrogen atom. A great 
 amount of suggestive material is to be found in 
 Dr. Larmor's contributions to the Transactions of the 
 Koyal Society for 1894, 5, 7 ; some of them were 
 summarised in the book called Ether and Matter 
 published by the Cambridge University Press in 
 1900. 
 
 Suffice it here to say that the electron constitutes 
 the basis of the whole treatment, and that there is 
 supposed to be no true electric current except electrons 
 in motion. They may move with the atoms, as in 
 the electrolysis of liquids ; they may fly alone, as in 
 rarefied gases ; or they may be handed on from one 
 fixed atom to the next, as in the process of conduction 
 in solids. 
 
 Conduction. 
 
 The possible modes of conduction or transmission 
 of electricity are in fact three, which I may call 
 respectively the bird-seed method, the bullet method, 
 and the fire-bucket method. 
 
 The bird-seed method is adopted in liquids and 
 usually in gases of ordinary density ; it is exempli- 
 fied in electrolysis ; the bird carries the seed with 
 it, and only drops it when it reaches an electrode. 
 
 The bullet method is the method in rarefied gases, 
 as has been clearly realised by aid of the cathode 
 
CH. x.] CONDUCTION 107 
 
 rays : the space near the cathode represents the length 
 between the breech and the muzzle of the gun, and 
 the rest of the path is analogous to the trajectory 
 of a bullet. When the projectile strikes an atom the 
 shock may cause it to pass another on, and so 
 continue the convection. 
 
 The fire-bucket method must be the method of 
 conduction in solids, where the atoms are not sus- 
 ceptible of locomotion and can only pass electrons 
 on from hand to hand ; oscillating a little in one 
 direction to receive them, and in another direction 
 to deliver them up, and so getting thrown gradually 
 into the state of vibration which we call heat. 
 But it may be observed that this need for motion, 
 in order to pass electrons on, becomes less and less 
 according as the body is less subject to the irregular 
 molecular disturbance we call heat. It may be the 
 expansion and molecular separation, or it may be 
 the irregular jostling and disturbance, that impede 
 easy conduction ; but certainly conduction improves 
 as temperature falls, and transmission becomes quite 
 easy at very low temperatures. The conduction of 
 heterogeneous alloys is a less simple matter, being 
 probably mixed up with back E.M.F. developed at 
 innumerable junctions, otherwise it would be in- 
 structive to examine the effect of low temperature 
 on the conductivity of a metal which did not 
 contract with cold. 
 
 The extra conductivity of hot electrolytes is a 
 totally different phenomenon : it is not true conduc- 
 tion, but convective locomotion of ions, in their 
 case. The same effect of temperature which lessens 
 their viscosity increases their conductivity. 
 
 Insulators are bodies where conduction can only be 
 accomplished with violence. Metals are bodies in 
 
108 CONDUCTION AND RADIATION [CH. x. 
 
 which the transfer of an electron from one atom to 
 another is easy, demanding no force as long as the 
 process is not hurried a process of the nature of a 
 diffusion. The transmission of vibrations along a 
 chain of connected molecules may well occur through 
 a not dissimilar kind of connection ; and hence the 
 conduction of electricity and the conduction of heat, 
 though really different processes, may have many 
 points in common. 
 
 A fair approximation to the phenomena of con- 
 duction in metals has been worked out in detail by 
 Riecke, Drude, Thomson, Lorentz, and many others ; 
 in which the electrons are supposed to remain free 
 for periods so long that their mean energy of motion 
 is a function of the temperature, as in gas-theory. 
 
 Most is known about electrolytic and gaseous 
 conduction. In gaseous conduction the negative 
 electrons, when free, fly fast ; whereas the ions 
 generally, and all the positive charges, travel more 
 slowly by reason of their association with matter. 
 
 In liquid conduction charges of either sign are 
 always associated with atoms, and travel only as 
 ions, at a slow diffusion rate which was calculated 
 by Kohlrausch, has been observed directly by myself,* 
 Mr. Whetham and others, and is well known. 
 
 The rate of transmission in solids can only be 
 inferred, and it would appear from the Hall effect (see 
 Larmor, Phil. Trans., Aug. 1894, p. 815), as if in 
 one class of solids the positive were able to travel 
 fastest, whereas in another class negative travelled 
 fastest : a difference which is familiar in liquids. In 
 acids, for instance, the positive charges travel much 
 the quickest, because they are associated with light 
 
 * Lodge, British Association Report, Birmingham Meeting, 1886, 
 pp. 389-413. 
 
CH. x.] RADIATION 109 
 
 and presumably small hydrogen atoms ; and it is 
 owing to the comparatively easy migration of the 
 light or small hydrogen atom that acids are in 
 general such good conductors. 
 
 The Hall magnetic bend, like Faraday's magnetic 
 rotation, is a differential effect, and would be zero 
 if positive and negative were equally acted upon. In 
 gases it is differential too, but there the negative 
 charges are liable to be so free as compared with 
 the positive, and to be so conspicuous, that the Hall 
 effect in gases, especially in rarefied gases, is very 
 great in comparison with the small residual effects 
 found in liquids and solids. Consequently the 
 effect of a magnet in curving the path of cathode 
 rays in a Crookes tube is readily demonstrated. 
 
 Radiation. 
 
 But it is not only the progressive motion or loco- 
 motion of the electric atomic appendages that we 
 have to consider ; we must assume also that they 
 are susceptible of motion in the atom itself, either 
 vibrating like the bead of a kaleidophone, or re- 
 volving in a minute orbit like an atomic satellite. 
 Indeed it is to the concerted vibrations or revolu- 
 tions of the system of electrons, in, or on, or round, 
 an atom, that its radiating power is due. Matter 
 alone has no perceptible connection with the ether, 
 a fact which is proved in my paper in the Philo- 
 sophical Transactions for 1893 and 1897;* it is 
 electric charge which gives it any connection, and 
 even then it has no viscous connection there is no 
 connection that depends upon odd powers of velocity, 
 so as to be of the nature of friction, t it is purely 
 
 * Lodge, Phil. Trans., vol. 184, pp. 727-804, and vol. 189, pp. 149-166. 
 t See especially Phil. Trans., vol. 189, p. 164. 
 
110 CONDUCTION AND RADIATION [CH. x. 
 
 accelerative connection ; it is only when the charge 
 vibrates, and during its accelerative periods, that it is 
 able to influence the ether at a distance by emission of 
 waves.* These waves consist probably of alternations 
 of shear, with no motion of the ether as a whole, 
 but only a to-and-fro quiver of its equal opposite 
 constituents over some excessively small amplitude : 
 a kind of motion which constitutes what we know as 
 radiation. It is not the atom pulsating as a whole 
 which disturbs the ether, but the pulsations or 
 vibrations, or the startings and stoppings and 
 revolutions, of its electric charge. Acceleration of 
 electric charge is the only known mode of originat- 
 ing ether disturbance. But normal or centripetal 
 acceleration, involving nothing more than change of 
 direction, is just as effective as actual change of 
 speed. If an electric charge is able to describe a 
 small orbit four-hundred-billion times a second, it 
 will emit the lowest kind of visible red light. 
 This number of revolutions is equal to the number 
 of seconds in about fourteen million years, or in 
 the time since some early geologic period. If 
 it revolves faster it will emit light of higher re- 
 frangibility ; and the particular kind of radiation 
 emitted by the atom of any substance, when in a 
 fairly free state, will depend on the orbital period 
 of its electrons, if they could be considered as inde- 
 pendent. But if that were so, every atom would soon 
 radiate itself to destruction. The condition that an 
 atom must fulfil in order to have a chance of survival 
 by retaining its energy, was given by Larmor (Phil. 
 Mag., Dec. 1897) in the form that the vector sum of 
 the accelerations of all its electrons, with due regard 
 to their signs, should be permanently null. This 
 
 * See Chaps. I. and IX., also Appendix G. 
 
CH. x.] MAGNETISED RADIATION 111 
 
 further condition is quite consistent with those 
 imposed by dynamics. 
 
 Every frequency of rotation will correspond to a 
 definite line in the spectrum. But if this be its real 
 cause, radiation must be susceptible to magnetic 
 influence, for a revolving electric charge consti- 
 tutes a circular current ; and if a magnetic field be 
 started into existence with its lines threading that 
 circuit, it must, while it is changing in intensity, cause 
 the speed either to increase or to decrease, and so 
 will either raise or lower the refrangibility. If 
 electrons are revolving in every direction, and if a 
 magnetic field is applied to them, then during the rise 
 of the field the pace of some will be increased and of 
 some decreased ; and this increase or decrease will not 
 stop until the magnetic field is destroyed again. 
 
 Hence it would appear that if a source of radiation 
 is put into a magnetic field, and its lines examined 
 with a spectroscope, they should be affected, either 
 by way of shift or broadening, or in some other way. 
 It happened, however, that when Dr. Larmor theo- 
 retically perceived this, and estimated the order of 
 magnitude of the effect to be expected, he made the 
 assumption natural in 1895 that an electron was 
 comparable in mass with a hydrogen atom. On this 
 assumption, knowing what he did about the massive- 
 ness of an atom, he calculated that the effect would 
 be too small to see ; indeed, Faraday had, with 
 imperfect appliances many years ago, looked for some 
 such effect not then guided by theory, but simply 
 with the object of trying all manner of experiments 
 and had failed to see anything ; Prof. Tait also had 
 been moved by theory in the same direction, but no 
 fresh experimental attempt to examine the question 
 was initiated. Nor was the matter publicly referred 
 
112 CONDUCTION AND RADIATION [CH. x. 
 
 to until, as hinted above, Zeeman of Amsterdam, in 
 1897, with a good grating and a strong electromagnet, 
 skilfully observed a minute effect, consisting in a 
 broadening of the lines emitted by a sodium flame 
 placed between its poles. On seeing a two-line 
 notice of this in Nature in December, 1896, Dr. 
 Larmor wrote to me, saying that this must be the 
 effect which he had thought of, but concluded must 
 be too small to see. On receiving this intimation 
 I immediately, with a little trouble, repeated and 
 verified the experiment,* and exhibited it at the 
 Royal Society soire'e in May that same year. 
 
 From this simple but important beginning the 
 large subject of the influence of a magnetic field on 
 the radiation from different substances has been 
 laboriously worked at ; not only by the original 
 discoverer, but by Preston in Dublin, Michelson in 
 America, Runge, and others ; and a whole series of 
 important facts have been made out. Every line has 
 been studied separately ; some lines are tripled, some 
 quadrupled, some sextupled, and so on as said above. 
 One mercury line is resolved into nine or perhaps eleven 
 components. The effect is therefore not too small to 
 see, though it needs excessively high power and per- 
 fect appliances to display it ; and so it became evident 
 
 * See Proc. Roy. Soc. t vol. 60, pp. 466, 513, and vol. 61, p. 413, or Nature, 
 vol. 56, p. 237 ; also several articles by Lodge in The Electrician, for 1897, 
 vol. 38. The whole matter is elucidated by Zeeman, aided by Lorentz, 
 on the basis of theory illustrated by a picture or model of an orbitally 
 revolving electron, which, though crude, was adequate as a guide : the 
 small mass of the revolving particle being thereby deduced, and being 
 in general conformity with J. J. Thomson's direct determinations of 
 the mass of an electron some months previously. With higher ex- 
 perimental power greater precision was reached, and an unexpected 
 development appeared in the tripling of each line, a result which was 
 suggested by the model, but could not have been predicted from it 
 alone. Other lines were found to divide into more than three com- 
 ponents, in a very suggestive but still imperfectly understood manner, 
 
CH. x.] ZEEMAN EFFECT 113 
 
 that if radiation were due to moving electrons, their 
 motion could not be handicapped by having very 
 much matter associated and moving with them. It 
 became possible, indeed, by making a measurement 
 of the amount of doubling undergone by the lines in 
 a given field, to ascertain how much matter was 
 associated with the revolving electric charge in any 
 given case ; in other words, to make a determination 
 of the electrochemical equivalent effective in radi- 
 ation i.e., of the ratio m/e. Indeed, Professor 
 Zeeman, with considerable skill, had made a rough 
 determination of this kind at a very early stage, when 
 he only saw the effect as a slight broadening of the 
 sodium lines ; and had come to the conclusion that the 
 electrochemical equivalent was quite different from 
 that appropriate to electrolysis, being some thousand 
 times smaller. He found, in fact, that the ratio e/m 
 had in this case also the notable value already 
 suspected in connection with cathode rays, viz., the 
 value 10 7 c.g.s. 
 
 More recent measurements have confirmed this 
 estimate, and shown that the ratio of charge to 
 matter in the Zeeman case is practically identical 
 with the ratio of charge to matter in the cathode ray 
 case ; in other words, that whatever is flying in the 
 cathode rays is vibrating in a source of radiation ; and 
 that if the cathode rays consist of moving electrons, 
 radiation is due to vibrating or revolving electrons. 
 The more the details of the Zeeman effect are 
 studied, the clearer it becomes that the electron 
 theory attributed to it from the first by Zeeman and 
 H. A. Lorentz, as well as by FitzGerald and Larmor 
 in England, is satisfactory, though not as yet 
 fully and completely worked out. 
 
 One of the earliest publications in England, both 
 
 L.E. H 
 
114 CONDUCTION AND RADIATION [CH. x. 
 
 of the fact and of its elementary theory, is that given 
 by the present writer in two articles in the 
 Electrician for February and March, 1897,* which 
 are worth referring to as representing incipient ideas 
 on the subject before the full significance was grasped. 
 The high value of the e/m ratio, viz., ^x 10 7 c.g.s., 
 or fifty million coulombs per gramme, instead of the 
 moderate electrolytic value, is spoken of on page 643 
 as a difficulty ; and a FitzGerald suggestion amounting 
 virtually to the beginnings of an electron theory of the 
 Zeeman effect is hinted at. Likewise an extremely 
 short way of expressing the theory of the motion is 
 given by the writer, in the following form : 
 
 Consider the resolved part of any orbital motion 
 projected on to a plane normal to the applied magnetic 
 field H ; and let the angular velocity be o>, at any 
 point of an orbit where the radius of curvature is 
 r ; then the field will exert a radial component 
 
 which will represent an increment or decrement of 
 
 centripetal force -, / 2 \ 
 
 a (mrur) ; 
 
 whence it follows, to a first approximation of order of 
 magnitude, that TT 
 
 doo= - , 
 
 2m ' 
 
 and the change of frequency caused by the magnet- 
 isation in the transverse components of the radiation 
 will therefore be 
 
 4-Trm' 
 
 The other or longitudinal component of the original 
 orbit will manifestly be unchanged. This is far from 
 
 * See Lodge, Electrician, vol. 38, pp. 568 and 643. 
 
CH. x.] ZEEMAN EFFECT 115 
 
 being a complete and satisfactory theory, unless the 
 projected motion happen to be circular ; but it was a 
 brief and early attempt. 
 
 An instructive and interesting method of demon- 
 strating the Zeeman effect was devised by W. Konig 
 and described in the Jubilee volume of Wiedemann's 
 Annalen, 1897, of which a brief abstract is given in 
 Nature, vol. 57, p. 402. An emission flame con- 
 taining the salt under examination is placed in a 
 strong magnetic field, and viewed through an absorp- 
 tion flame, containing the same salt, by means of a 
 doubly-refracting prism, or other double image instru- 
 ment, so as to get two images of the emission-flame 
 side by side. On exciting the magnet, the emission 
 frequency, of vibrations perpendicular to the lines of 
 force, is put out of tune with the absorption frequency, 
 and accordingly the amount of absorption is much 
 diminished. The result is that one of the images 
 brightens up every time the magnet is excited ; the 
 other image, which corresponds to vibrations along 
 the lines of force, remaining unchanged and constitut- 
 ing a convenient standard of brightness. 
 
CHAPTER XL 
 
 FURTHER DISCUSSION OF THE ELECTRON THEORY 
 OF THE MAGNETISATION OF LIGHT AND DE- 
 TERMINATION OF THE m/e RATIO IN RADIATION. 
 
 AMONG the early contributions that have been made 
 to the theory of moving charges, few are more 
 remarkable than those of Dr. Johnstone Stoney in 
 connection with the process of radiation, long before 
 there had been any experimental verification of the 
 separate existence of these electrons, or of the fact 
 that the emission of light from a substance is due 
 to their motion. Dr. Stoney had treated them in 
 an astronomical manner, in 1891, dealing with an 
 electron moving round an atom as if it were a 
 satellite moving round a planet, and had discussed 
 the various perturbations to which they might be 
 subject, and the effect of those perturbations on the 
 spectrum of the light emitted.* 
 
 One of the simplest kinds of perturbation, fully 
 analysed by Newton for the motion of the moon, 
 is what is called a progression or recession of the 
 apses, being a slow revolution of the orbit in its own 
 plane. Such a motion was shown to be able to 
 
 * " On the Cause of Double Lines and of Equidistant Satellites in 
 the Spectra of Gases." G. Johnstone Stoney, Transactions of the Royal 
 Dublin Society, iv., 1888-92, pp. 563-608. 
 
CH. XL] MAGNETISATION OF LIGHT 117 
 
 originate a doublet in the spectrum ; for of the two com- 
 ponent circular vibrations into which the motion can be 
 analysed, one has been made more rapid and therefore 
 its light raised in refrangibility, the other has been 
 made slower and therefore lowered in refrangibility. 
 
 Another closely allied kind of perturbation, 
 analogous to precession of the equinoxes in the case 
 of the earth, would result in a triplet in the spectrum. 
 This precessional motion occurs in an orbit subject to 
 any oblique pull or deflecting force. Instead of 
 yielding directly to that pull, its effect is to make the 
 axis describe a kind of cone, the kind of motion 
 that one sees in an inclined spinning-top : the pull of 
 gravity on a spinning- top does not make it topple 
 over, but makes it precess. So also with a hoop or 
 bicycle when not vertical : instead of tumbling, it 
 turns round and round in a circuit, as long as its 
 motion continues ; only falling when the motion 
 ceases, or falls below a certain critical value. Hence 
 if the orbit of an electron were subjected to an 
 oblique or deflecting force, the effect would be, not 
 to place it directly in the desired position per- 
 pendicular to a line of force, but to cause it to 
 precess. And this motion might be analysed into 
 three components, the accelerated and retarded 
 circular orbits above-mentioned, which would result 
 in a doubling of the line, and a third component, 
 viz. the one parallel to the axis, which would be 
 unchanged and would therefore represent a spectral 
 line in its old position, the centre of a group of 
 three. All this was clearly perceived in connection 
 with Dr. Zeeman's discovery, with the assistance of 
 his great compatriot the eminent physicist, H. A. 
 Lorentz ; whose theory was in several respects 
 anticipatory of the experimental results. 
 
118 MAGNETISATION OF LIGHT [CH. XL 
 
 It must be observed that the light emitted by the 
 oscillation-components, above spoken of, will be all 
 of one definite kind, due to vibrations in one definite 
 direction, and will therefore be polarised. The kind 
 of polarisation must depend on the aspect from which 
 the light is seen. If seen at right angles to the axis 
 of precession, all three lines should be plane polar- 
 ised the middle line at right angles to the other 
 two. If, however, it be looked at along the axis of 
 precession, then there should be no middle line ; 
 because the axial vibration would then be end- on, in 
 which direction it produces no optical effect ; and the 
 two side lines would be circularly polarised. 
 
 Fig. 15 consists of diagrams illustrative of the 
 changes caused in a spectrum line by application of a 
 powerful magnetic field to the source of radiation. 
 
 / represents a specially simple case. The cad- 
 mium line A, seen by rays travelling along the 
 lines of force, resolves itself into two lines B and C 
 which are circularly polarised in opposite directions. 
 This is due to the acceleration of one circular 
 component of the rectilinear or elliptical vibration 
 and the equal retardation of the other component. 
 
 // represents the same simple line seen by 
 light travelling across the lines of force. In that 
 case the line becomes triple ; and if A had been 
 plane polarised, B and C are polarised in a plane 
 at right angles to that of A'. This is due to a 
 precessional movement of the plane of the orbital 
 motion, the axial vibration continuing unchanged, 
 and the two at right angles being one accelerated 
 and the other retarded. 
 
 /// and III1 represent the effect of a magnetic 
 field, applied to a sodium source, on the con- 
 stituents of the yellow sodium double-line. D x is 
 
CH. XL] MAGNETISATION OF LIGHT 
 
 119 
 
 resolved into a quartet, and D 2 into a sextet, when 
 the light travels across the magnetic field. 
 
 Directly Zeeman had demonstrated the fact that a 
 magnetic field applied to a source of light was able 
 to act as a perceptible perturbing cause, Professor 
 Lorentz was at once able to predict the main part of 
 that which has been here stated, about the tripling 
 of the line seen sideways to the lines of force, and 
 the doubling of the line seen endways, with all the 
 polarisations as just stated ; because the lines of 
 
 n 
 
 tt 
 
 FIG. 15. 
 
 magnetic force constitute the precessional axis. And 
 all these effects were shortly afterwards seen by 
 Zeeman and others, and are characteristic of the 
 simplest circular orbit. 
 
 As already stated, the full meaning of these very 
 exquisite phenomena is still very far from being 
 unravelled. The most general theoretical result is 
 that of Larmor (Phil. Mag., Dec. 1897) that for any 
 atomic system, however complex, if the effectively 
 moving electrons are all negative, while the attraction 
 of the positive on them is centrical, each line will be 
 divided into three, exactly as in the provisional theory 
 of Zeeman and Lorentz. 
 
 
120 MAGNETISATION OF LIGHT [CH. XL 
 
 At first sight one might be inclined to suppose 
 that the orbits would all face round and set 
 themselves normal to the lines of force, like so 
 many circular currents ; but that is to forget the 
 inerbia of the travelling electron. It is manifest that 
 since a revolving electron constitutes a circular 
 current, its tendency will be to set itself with its 
 plane normal to the lines of force ; but since by 
 hypothesis the revolving electron has inertia, the 
 current will not so set itself, but will yield to 
 the deflecting force in an indirect manner, as a top 
 does ; or as the oblate spinning earth does as 
 explained by Newton in the Principia, the axis of 
 rotation having a conical motion round the lines 
 of force: a motion which is called "the precession 
 of the equinoxes" in the case of the earth, and 
 " the Zeeman effect " in the case of a radiating atom. 
 
 This is an account of the chief part of the Zeeman 
 effect, and may be regarded as the most fundamental 
 kind of disturbance caused by a magnetic field on a 
 source of radiation. But there may be other minor 
 disturbances, just as in the case of the earth, whose 
 axis is not only subject to precession, but also to 
 nutation a nodding movement superposed upon the 
 main motion. It is also quite possible for the middle 
 line, or for the two outer lines, or indeed for all three 
 lines, to be doubled ; thus giving rise not to the 
 standard triplet, but to a quartet or a quintet or 
 even a nonet, appearances seen and photographed 
 by Zeeman, Preston and others. The remarkable 
 * echelon ' spectroscope of Michelson has been in- 
 vented just in time for application to phenomena 
 of this kind its special function being the close 
 examination in detail of a minute portion of a 
 spectrum otherwise produced. 
 
CH. XT.] MAGNETISATION OF LIGHT 121 
 
 Even the two constituents of the double sodium 
 line behave differently, when the source is magnet- 
 ised and the light thus examined as illustrated in 
 fig. 15 : one of the sodium lines, D 2 , which had 
 appeared only broadened to Zeeman at first, really 
 becomes a sextet. The other sodium or D x line 
 becomes a quartet ; and a complete study of the 
 behaviour, under magnetism, of all the lines and 
 groups of lines given by different substances must 
 result in a great extension of our knowledge in many 
 directions ; in fact it is hardly too much to say that 
 the discovery of Zeeman, in the light of the theory of 
 Lorentz, has doubled the power of spectrum analysis 
 to throw light upon the processes of radiation and the 
 properties of atoms, and has opened up a new branch 
 of physics a new department, as it were, of atomic 
 astronomy, with atoms and electrons instead of 
 planets and satellites. 
 
 
CHAPTER XII. 
 INCREASE OF INERTIA DUE TO VERY RAPID MOTION. 
 
 THE hypothesis to which we have been led is that 
 the inertia of an electron is wholly of an electrical 
 character, and is explained by the known magnetic 
 effect of an electric charge in motion, and the con- 
 sequent reaction to any change in that motion. 
 
 Usually inertia is treated as constant and quite 
 independent of speed ; but now arises the question 
 whether the distribution of charge on a charged body, 
 together with its lines of force, will remain constant 
 and unaltered while the body is rapidly moving ; 
 because if the distribution of lines of force is altered, 
 then the inertia due to their lateral motion will 
 probably be altered too. This can be made plain 
 after referring back to Chap. II. 
 
 Thus, for instance, imagine that the lines of electric 
 force of a body in motion became more concentrated 
 towards the axis or line of motion ; the effect would 
 be at once to diminish the lateral component of their 
 motion, therefore to diminish the magnetic force which 
 that lateral component causes, and thus to diminish 
 the apparent or electromagnetic inertia of the moving 
 charge. 
 
 On the other hand, if the lines opened out and 
 became concentrated towards the equator, or plane 
 
H. XIL] EFFECT OF RAPID MOTION 123 
 
 normal to the line of movement, then a greater 
 component of their motion would be of a kind 
 suitable to excite a magnetic field ; moreover, both 
 the fields would by this concentration increase in 
 intensity, and the inertia would increase. 
 
 Thus, then, it may be possible that electric inertia 
 may depend in some fashion on speed, a thing 
 unknown in ordinary mechanics. I do not say 
 that such dependence must be untrue in ordinary 
 
 ! mechanics ; on the contrary, I feel reasonably san- 
 guine that it will be found true for matter also, 
 when moving sufficiently fast say over a thousand 
 miles a second, though it is unlikely that it can 
 have a practical influence in any actual known case 
 of rapid movement in astronomy. But however this 
 
 l may be, there is no doubt that theory points to an 
 increase of electro- magnetic inertia at excessively 
 high speeds, and Mr. Heaviside long ago calculated 
 its amount. 
 
 It will be observed that when a charge moves, 
 it generates circular magnetic lines of force. Now 
 these magnetic lines are not stationary, but are them- 
 selves moving at the same rate as the body ; hence 
 they generate fresh electrostatic lines, i.e., cause an 
 
 j electric displacement away from the axis, which dis- 
 placement is superposed upon the original radial 
 displacement (away from or toward the centre) due 
 to the charge. 
 
 At ordinary, at even violent speeds, this second- 
 order electric effect is insignificant, but it is there all 
 the time, and must not be ignored when the speed 
 becomes extravagantly high. It rapidly rises into 
 prominence when the speed approaches the velocity of 
 light, but at any speed much smaller than this such a 
 second-order effect is negligibly small. 
 
124 INCREASE OF INERTIA [CH. XIL 
 
 Its effect will be, as the annexed figure shows, to 
 alter the arrangement of the lines of force, making 
 them move away from the poles and concentrate 
 towards the equator of the charged sphere, when 
 the speed is very great ; ultimately becoming wholly 
 concentrated upon, or parallel to, the equatorial 
 plane, in the limit ; if the speed could attain that of 
 light. And the electric lines of force would then 
 be opened out into a fan or equatorial brush, like 
 the spokes of a wheel which is rushing furiously 
 along an elongated axle, the circumference of the 
 
 FIG. 16. A is the charge, AB its line of motion, and AE its electric force 
 in a certain direction when stationary ; EF is the magnetically induced 
 electric component due to the motion and AF is the resultant electric 
 force which replaces the original force AE. The magnetic force, to the 
 motion of which EF is due, is perpendicular to the paper, and is itself 
 caused by the motion ; hence EF is a quantity of the second order and 
 is small for speeds distinctly less than that of light. 
 
 wheel representing the direction of the magnetic 
 field ; but this very condensation so intensifies the 
 field as to make the inertia ultimately infinite. 
 
 It might be supposed that rearrangement of the 
 lines means that the distribution of the charge itself 
 is altered by the motion, so that all the charge is 
 concentrated upon the equator, whence the lines 
 of force would start normal to the surface as usual. 
 There are many difficulties about such a conception 
 however (see Appendix K), and it is easier to 
 suppose that the charge retains its distribution un- 
 altered, on the surface of the sphere, and that each 
 line of force starts from its original point ; but that 
 
H. xii.] DUE TO RAPID MOTION 125 
 
 it starts no longer in a direction perpendicular to 
 the surface, when it is in rapid motion, but sets 
 out obliquely, with a deflexion towards the equator, 
 so as to give the arrangement above described ; like 
 trunks of trees on a cliff or landslide which preserve 
 their roots in situ and gradually adjust their growth 
 to the vertical direction without being any longer 
 perpendicular to the soil. 
 
 As a matter of fact the question all depends on 
 what hypothesis we make as to the intrinsic struc- 
 ture of the electron. If we liken it to a perfectly 
 conducting body with an electric charge, the charge 
 must be confined to its surface ; and it may be 
 proved, as Heaviside did. that the distribution will 
 remain uniform (cf. Larmor, dEther and Matter, 
 p. 154). Or it might be likened to a solid globe 
 of uniform electrification. It may be something of 
 which we have as yet no conception : but the 
 experiments of Kaufmann probably suffice to prove 
 that, whatever the structure is, it is symmetrical 
 around a centre, after the general manner of a 
 stratified spherical distribution. 
 
 On the other hand these considerations can be 
 avoided by treating the charge merely as a 
 geometrical point from which the lines of force 
 emanate, and ignoring its size or possible conducting 
 power. This is the keynote of I/armor's treatment 
 throughout his book ^Ether and Matter, and also 
 in his earlier papers : in dealing with atomic structure 
 it implies that the electrons in the atom are at 
 distances apart which are great compared with their 
 radii. Cf. the fundamental investigation of Chapter 
 XL to be referred to below. We could hardly tell 
 a priori which treatment would best correspond 
 with fact, but it will turn out (see Chap. XIII.) that 
 
126 INCREASE OF INERTIA [CH. XIL 
 
 this second method of treatment is not only simpler 
 but that it is adequate to existing knowledge, enabling 
 numerical results to be obtained which are singularly 
 concordant with experimentally measured results. 
 
 In any case an indication of the mode of attack 
 can be suggested thus : 
 
 The magnetic force due to motion is proportional 
 to the speed of the motion. The secondary electro- 
 static force due to the motion of this magnetic field 
 is likewise proportional to the same speed.* Hence 
 the disturbance of the original uniform electrostatic 
 field will be of the second order, u 2 /v 2 ; and when- 
 
 *The value of the magnetic force at any point P, with polar 
 coordinates r f 6, due to a charge e flying with speed U, is 
 
 TI _ 
 
 and is in rings round the line of motion u. It is not shown in the 
 diagram because it is perpendicular to the paper, through P. 
 
 Q 
 
 FIG. 17. 
 
 The electric force generated or induced by motion across this 
 magnetic field which is necessarily at right angles to the direction of 
 motion is fiRu ; and in this case is therefore equal to 
 
 This is the secondary or induced E.M.F., to be superposed at every 
 point on the primary or direct electric force of the charge itself along 
 the line eP, namely e/Kr 2 ; and it is in the direction PQ, being perpen- 
 dicular both to the magnetic field and to the motion. So the ratio of 
 the induced to the original E.M.F., at every point in a direction 0, 
 reckoned from the charge and axis of motion, is 
 
 sin 0, which equals sin 0. 
 
 In consequence of this the original direction of the stationary 
 electric field, eP, is displaced or tilted into a position such as eQ. 
 
CH. xu.] DUE TO RAPID MOTION 127 
 
 ever we can afford to neglect quantities of this order,, 
 the field and therefore the inertia of the moving 
 charge will continue practically constant. 
 
 But when its speed of motion begins to approach 
 the velocity of light, say even no more than T Vth 
 of that speed, then a perceptible disturbance is 
 to be expected, and something like a 1 per cent, 
 increase of inertia must occur. 
 
 The complete investigation makes the inertia 
 infinite when the speed reaches that of light (see 
 Appendix K), but there is probably no need to 
 press this to extremes, unless the charge were an 
 absolute point ; clearly, however, the inertia will 
 ! then be very great, and possibly therefore it may 
 always be impossible to make matter, or at least 
 charged matter, move with a speed greater than 
 that of light. There may be ways out of this, 
 j however, just as it is possible for a bullet to move 
 through air with a velocity greater than that of 
 sound. This is managed by the violent adiabatic 
 condensation of the air in front of such a bullet, 
 the effect being to raise the appropriate velocity of 
 sound to the required value ; and by the ridge behind 
 it where discontinuity makes its appearance. It seems 
 unlikely that the ether can adjust itself to excessive 
 speed beyond the speed of light without a change of 
 structure akin to what would be rupture in the case 
 of a material medium. 
 
 It has been shown both by Mr. Heaviside and 
 by Prof. J. J. Thomson that if the speed of motion 
 is ever greater than that of light, the fan or radial 
 plane of lines of force bends backwards and becomes 
 a conical surface, gradually closing up as the speed 
 further increases : in accordance with the analogy of 
 the conical surface of discontinuity aforesaid, which 
 
128 INCREASE OF INERTIA [CH. xn. 
 
 travels with a sufficiently rapid bullet, and is demon- 
 strated in Mr. Boys' bullet photographs. 
 
 No known speed which exists in ordinary matter 
 is sufficient to bring any variation of inertia into 
 prominence. The quickest available carriage is the 
 earth in its journey round the sun, 19 miles a second, 
 or 60 times faster than a cannon ball ; but the 
 earth's velocity is only the 10000 of the speed of 
 light, and consequently any spurious inertia due 
 to its orbital motion is only 1 part in a hundred 
 million ; and even the accuracy of astronomy could 
 not display an effect of that order of magnitude. 
 
 There are a very few stars which move 200 miles 
 a second, but even these have only one-tenth per 
 cent, of the speed of light, and the excess inertia 
 will be only 1 part in a million. The only known 
 place where charges or charged atoms were known, 
 prior to 1903, to move at speeds greater than this, 
 was in a vacuum tube. There the cathode-propelled 
 particles are flying 20,000 miles a second or T ] ^ n 
 the speed of light, and they may have 1 per cent, 
 excess inertia ; or more if they can be persuaded to 
 go still faster. 
 
 But higher speeds are now known, being obtained 
 in the spontaneous emission of electrons and atoms 
 by radio-active materials ; so it becomes of the 
 greatest interest to determine the constants, and 
 especially the inertia, for rays of this kind. 
 
CHAPTER XIII. 
 JUSTIFICATION FOE ELECTRIC THEOEY OF INERTIA, 
 
 BUT first we must ask, what justification is there 
 for the view that each of the isolated corpuscles, on 
 which measurements have been made, is a purely 
 electrical corpuscle or electron without material 
 nucleus, all of whose properties are to be explained 
 in accordance with purely electric and magnetic 
 laws ? Then we may proceed to discuss the further 
 extraordinarily far-reaching hypothesis first tenta- 
 tively put forward by Larmor in 1894, Phil. Trans., 
 vol. 185A, p. 813, with mechanical illustration of a 
 purely ethereal structure for such an electron that 
 the electrons constitute matter, that atoms of matter 
 are composed of electric charges, that the funda- 
 mental inertia-property of matter is identical with 
 self-induction. 
 
 There is the reasonable philosophical objection to 
 postulating two methods of explaining one thing. If 
 inertia can be explained electrically, from the pheno- 
 mena of charges in motion, it seems needless to 
 require another distinct cause for it also. But this 
 is not all that can be said ; it is quite possible that 
 direct experimental proof will be forthcoming before 
 long. One method suggested by Professor J. J. 
 Thomson, for examining the nature of the corpuscles, 
 
 L.E. 
 
130 ELECTRIC THEORY OF INERTIA [CH. xm. 
 
 had reference to the proportion of radiation to thermal 
 energy developed when corpuscles encounter a target 
 which suddenly stops them. In so far as they consist 
 of non- electric matter they would produce only heat 
 by their dead collision, without any direct generation 
 of ethereal waves ; in so far as they consist of elec- 
 tric charges they would disperse a certain amount of 
 radiation energy ; and so the proportion of radiation 
 to heat might afford a criterion.* Hitherto, however, 
 no adequate measurements have been made in this 
 direction. 
 
 But there is another more likely avenue to a con- 
 clusive result. We have seen that when an electric 
 charge moves with a speed approaching that of light, 
 its inertia is theoretically no longer constant, but 
 rapidly increases and becomes infinite when the 
 light- velocity itself is reached ; and rather complicated 
 and different expressions for this high-speed inertia 
 have been calculated by several mathematical physi- 
 cists, on different views of the constitution of the 
 electron. See Appendix K for a discussion of this 
 difficult subject. It is possible that this fact will 
 give us the necessary clue. 
 
 For in certain cases of the production of cathode 
 rays, or at any rate of beta rays, a speed not far 
 short of that of light is reached, and in such cases 
 the effects of the increased inertia can be observed. 
 Such an experimental determination has been quite 
 recently undertaken and executed with great skill 
 by Dr. Kaufmann,t who employed the method indi- 
 cated above (Chap. V.) of comparing simultaneously 
 the electric and the magnetic deflexion of the same 
 set of rays from a speck of radium submitted 
 
 *See J. J. Thomson, Phil. Mag., April, 1899, p. 416. 
 tSee Comptes Rendus for October 13, 1902. 
 
CH. XIIL] VARIATION OF INERTIA 131 
 
 simultaneously to an electric and a magnetic field 
 coincident in direction. As a matter of fact the 
 speck gives off rays of various speeds, which are 
 differently deflected into a thin streak like a 
 comet's tail (see fig. 18) : and it is the faint 
 impression they make on a photographic plate in 
 high vacuum that is measured and gives the data. 
 Thus the velocity and the e/m ratio are both 
 known, and to summarise briefly the result 
 Kaufman n concluded that when the speeds ap- 
 proached perceptibly near the velocity of light, the 
 electrochemical equivalent m/e increased by just 
 the amount required in accordance with pure electric 
 theory the theory which attributes the whole of 
 inertia to electric influence. There appeared to be 
 no quantitative room for any extra inertia, such 
 as that of an inert particle of non-electric matter 
 travelling with each projectile, retaining its inertia 
 constant at all speeds, and so contributing nothing to 
 the rise of inertia perceived when the speed approaches 
 within hail of that of light. 
 
 We will now enter more into detail concerning this 
 important matter. 
 
 Proof of the purely electrical nature of the inertia 
 of the ft particles shot out by Radium. 
 
 There is every reason to believe that the /3 rays 
 emitted by radium are identical with the cathode 
 rays observable in a vacuum tube ; for both consist 
 of a multitude of electrons or corpuscles travelling at 
 excessively high speed ; and if a determination be 
 made of this speed and of the electro-chemical equiva- 
 lent for the case of P rays for instance, by the 
 
132 ELECTRIC THEORY OF INERTIA [CH. xm. 
 
 method of subjecting them both to magnetic and to 
 electrostatic deflexions, which is the easiest way the 
 numbers come out quite similar to the number 
 obtained for cathode rays, viz., for m/e the value 
 10 ~ 7 in E.M. units, and for u something of the order 
 10 9 centimetres per second. 
 
 But radium under favourable conditions is found 
 to shoot out its particles with a speed exceeding even 
 this, and in some cases to approach within hail of 
 the limiting speed, the velocity of light. This is 
 the very important result obtained by the German 
 physicist W. Kaufmann, who has made an admirable 
 series of determinations of speed and of electro- 
 chemical equivalent for this case. The importance 
 of obtaining these excessively high speeds should be 
 obvious, for thereby we are enabled to test the elec- 
 trical theory of inertia. Theoretically the inertia at 
 high speeds is not constant, but increases according 
 to a complicated but calculated law ; we cannot 
 suppose that the electric charge varies in any 
 way with motion ; hence the electrochemical equiva- 
 lent m/e is proportional simply to the mass, and 
 ought to be a function of the velocity u, nearly 
 constant for ordinary values, but increasing rapidly 
 as it approaches within hail of the velocity of 
 light. 
 
 To obtain numerical values we may apply the 
 theory developed by Mr. Heaviside and by Prof. J. 
 J. Thomson, with regard to the increase in momentum 
 of a flying electric charge, over and above the natural 
 mu value, with m considered constant, which is the 
 value at all ordinary speeds. 
 
 The formula which the latter used for the purpose 
 of numerical calculation is one of those given in his 
 Recent Researches ; it is quoted in his American 
 
CH. xm.] VARIATION OF INERTIA 133 
 
 Lectures on Electricity and Matter, p. 44, as 
 
 / 11 
 
 mu = electric momentum = 
 
 where sin = ^/-y ; and we may express it in a fairly 
 simple form thus : 
 
 The momentum of a particle of electricity moving 
 at excessive speed is greater than the momentum 
 of the same particle estimated on the hypothesis 
 that its mass is constant, in a numerical ratio given 
 by the following expression ; where the ratio of the 
 speed to that of light, u/v 9 is expressed as the sine 
 of a certain angle : 
 
 4 sm 2 sin 20 
 
 We will call this the ratio <(#). It is the measure 
 of the spurious or extra inertia due to rapid motion ; 
 the ratio of the mass at speed u to the stationary 
 mass. We may also write it, rather more conveniently 
 perhaps for calculation, thus : 
 
 3l ~~ 2GOs20 2 2 ~ COS 2e 
 
 l-cos20~sin20 l-cos20/ 
 
 Now the highest speeds measured by Kaufmann 
 were such as the following : 
 
 2'36, 2'48, 2-59, 272, 2*85 times 10 10 cm. per sec. 
 
 while the speed of light is well known to be 3*0 x 1C 10 
 cm. per sec. ; so the ratios u/v, corresponding to the 
 above observed speeds, are respectively 
 
 787, '817, '863, '907, '95. 
 
 These numbers therefore represent the values of sin #, 
 to be inserted in the above formula for obtaining the 
 
134 ELECTRIC THEORY OF INERTIA [CH. xm. 
 
 theoretical ratio </> (0) ; namely, the ratio which 
 expresses the number of times the mass of an electric 
 charge, at specified high speed, exceeds its mass at 
 low or zero speed. 
 
 The successive values of <(#) come out, according 
 o J. J. Thomson, for the above set of velocities, 
 
 1-5, 1'66, 2*0, 2-42, 3'1, 
 
 and these are what must be compared with direct 
 observation or measurement of the apparent or 
 effective mass in each case. 
 
 Now the corresponding values observed experi- 
 mentally by Kaufmann for these same quantities that 
 is to say the factor by which the moving mass 
 exceeded the same mass when stationary were 
 
 1'65, 1*83, 2-04, 2'43, 3'09, 
 
 showing a very remarkable degree of approximate 
 agreement between experiment and theory, especi- 
 ally at the higher speeds. 
 
 Thus at the highest speed ever yet observed for 
 what may be called a particle of matter, at any rate 
 for an electron namely 2*85 x 10 10 cm. per sec. or 
 six hundred million miles per hour the mass of the 
 particle is three times as great as its usual value ; 
 and naturally its momentum and energy are increased 
 in the same proportion. 
 
 Such a surprising agreement as the above, between 
 theory and observation, removes from my mind all 
 reasonable doubt as to the truth of the hypothesis 
 that the inertia of electrons is electrical inertia. 
 I regard this closeness of agreement as specially 
 surprising, for it was not the first deduction of the 
 experimenter, W. Kaufmann, himself: his deduction 
 rather was that the electrical mass constitutes about 
 one-third or one-fourth of the whole; but then he 
 
CH. XIIL] VARIATION OF INERTIA 135 
 
 used another formula for calculating it (given in 
 Appendix K), which assumes that the charged body 
 behaves like a conducting sphere. But when the 
 correct deductions from the Heaviside expressions 
 above referred to were applied, with the collaboration 
 of M. Abraham, results practically equivalent to the 
 above were obtained. The above agreement is attained 
 by Professor J. J. Thomson, who applied his own 
 theory to the results of Kaufmann, working it out on 
 the assumption that the charge behaves like an actual 
 point. 
 
 If it is to be urged in future that an electron 
 contains a material nucleus in addition to its electric 
 charge, the burden of proof rests with those who 
 maintain that thesis. The hypothesis which now 
 holds the field is the purely electrical one. 
 
 But it must be remembered that this is not the 
 same thing as establishing an electrical theory for 
 all matter. The inertia of an electron is purely 
 electrical, but what about the inertia of an atom ? 
 Who knows that the atom is wholly composed of 
 electrons ? We do not know that as yet. 
 
 Nevertheless we are now in a very central chapter 
 of modern physics, and it is desirable to enter into 
 the matter somewhat more in detail than in the 
 above preliminary sketch. 
 
CHAPTER XIV. 
 
 MORE ADVANCED DEVELOPMENT OF THE COM- 
 BINED ELECTRIC AND MAGNETIC DEFLEXION 
 METHOD FOR MEASURING VELOCITY AND MASS 
 OF THE PARTICLES IN COMPOUND RAYS. 
 
 THE methods given in Chaps. V. and VI. and Chap. 
 IX., for measuring u and e/m, made the determina- 
 tion look very simple, if the precaution is taken of 
 having the apparatus in vacua, so as to eliminate 
 the troublesome conducting power of the air and 
 obtain the electric deflexion undiluted, as J. J. 
 Thomson first found feasible. But then the simple 
 theory, there given, assumed that the quantities to 
 be measured were constant, and that the deflexion 
 to be observed in each case was a single deflexion 
 capable of accurate measurement ; but this is often 
 far from being the case, since the velocities of the 
 particles differ ; and when, as in the case of radium, 
 some of the speeds approximate to that of light, it is 
 impossible that it can be the case, for the inertia itself 
 then changes in a complicated way with the speed 
 and must be treated as variable. It is easy to forget 
 that, because it is an unusual feature in mechanics. 
 So the deflexion cannot be a simple deflexion, the rays 
 must be fanned out as it were into a spectrum (see 
 fig. 18); and, since this spectrum is continuous, 
 
CH. xiv.] RADIUM RAYS 137 
 
 it will possess no features which enable anything 
 like measurement to be made on it, unless some 
 still further ingenious device be employed, such as, 
 for instance, that of Kundt for making experiments 
 on anomalous dispersion. 
 
 The experiments of W. Kaufmann at Gottingen 
 were conducted after this very fashion, and may be 
 summarised thus: an electric and a magnetic field 
 were simultaneously applied, in such a way as not to 
 neutralise each other's effect but to cause deflexions 
 
 FIG. 18. Diagram of the deflexion of high-velocity rays from radium. 
 The radium is in a cavity in a lead block a ; the rays pass through an 
 aperture 6, and are spread out by a magnetic field into a spectrum d : d 2 ; 
 the gamma rays or any uncharged rays produce an impression at c on 
 the photographic plate, cd, placed to receive all the rays. In a uniform 
 field each of the lines abd is a circle. 
 
 at right angles to each other. In that case if the rays 
 from a small point source, after traversing the double 
 field, are received upon a photographic plate at a 
 little distance, it may be expected that the two 
 spectra will be compounded into a single spectrum 
 inclined at some angle corresponding to the relative 
 strength of the two fields. But whether the inclined 
 spectrum thus produced will be a straight line or a 
 curve must depend upon circumstances. All that 
 can be said, without further consideration, is that each 
 point of the spectrum would represent a definite 
 ratio of deflexion, and therefore a definite inertia and 
 
 
138 VARIABLE MASS [CH. xiv. 
 
 velocity, for each of the particles which have produced 
 the impression at that point. And inasmuch as the 
 particles of different speeds will be sorted out to 
 different parts of the spectrum, it may be possible 
 to select those points which correspond to the highest 
 speeds, and indeed to compare the ratio of the two 
 deflexions for various speeds, if by any means the 
 velocity corresponding to each point can be determined. 
 A little calculation is needed to bring out the details 
 of the theory, and that shall be given directly, but 
 first I will give an idea of the kind of apparatus used. 
 
 Experimental Device used by W. Kaufmann. 
 
 A minute quantity of radium salt in a little 
 brass box acts as source, and a pencil of its rays 
 penetrates a small hole, about half a millimetre 
 diameter, in a plate of platinum at a distance of 
 2 centimetres from the source ; on the way, they 
 pass between a pair of parallel and insulated plates 
 of brass which are separated by about 2 millimetres 
 from each other and connected to a high-tension 
 battery of from 2,000 to 5,000 volts. After then 
 travelling another 2 centimetres, they encounter 
 the photographic plate placed to receive them. The 
 apparatus is contained in a thoroughly exhausted 
 vessel, and the whole is placed between the poles of 
 a large electromagnet giving a nearly uniform field, so 
 
 FIG. 19. Kaufmann's apparatus for measuring simultaneously the 
 electric and magnetic deflexions of particles possessing very high velocity. 
 The source of radiation is a minute quantity of radium placed in a box 
 at C. All except the highest-velocity rays are deflected out of action by 
 the magnet NS ; some of the highest-velocity rays pass upwards through 
 the aperture D, being deflected forward by the magnetic field, and side- 
 ways by an electric field, whose lines are coincident with the magnetic 
 lines, between the adjustable plates PiP 2 , which are kept as highly 
 electrified as possible through the electrodes R. These thus doubly- 
 deflected rays then fall upon the photographic plate E, where they are 
 spread out into an oblique sort of very minute spectrum, more or less in 
 accordance with diagram 18 ; on which spectrum micrometric measure- 
 ments are subsequently made. 
 
KAUFMANN'S APPARATUS 
 
 139 
 
 nEWtl H 5tfui7 
 
140 VARIABLE MASS [CH. xiv. 
 
 that the magnetic and electric fields are superposed in 
 the same direction, their lines of force being coincident. 
 
 Under these circumstances the particles will 
 describe the beginning of a spiral, being curved 
 round the magnetic lines and deflected along the 
 electric lines, until they escape from the combined 
 field and travel in their deflected direction to the 
 photographic plate as target. The slow-moving 
 particles, if any, will presumably strike the bounding 
 surfaces and be stopped, only the very rapid ones 
 will reach the plate; which is protected from alpha-rays 
 by aluminium foil, while the undeflected gamma-rays 
 would probably mark the direct line of fire, and thus 
 give the geometrical "origin" of the curve or trace 
 which would be found on the plate after long ex- 
 posure, a curve which we may write yf(^)-> where 
 y signifies the electric deflexion and x the magnetic. 
 
 This method may be called the method of the 
 crossed spectra. 
 
 The theory can then be expressed somewhat as 
 follows : 
 
 Let the measured coordinates of any point in the 
 spectrum, as developed on the photographic plate, be 
 
 y ' x being the magnetic deflexion, 
 and y the electric. 
 
 These deflexions may be taken to represent 
 inversely the radii of curvature r and r f produced 
 in the rays by the respective fields H and E, 
 in accordance with the simple mechanical equations 
 
 mu 2 , mu 2 
 
 TT , -r, 
 
 u.e}u, and 7- = Le, 
 
 T 
 
 if. XT fJLtiU U 
 
 wherefore 
 
 y r E 
 
CH. xiv.] AT HIGH SPEEDS 141 
 
 where ki is a constant depending on the relative 
 effective strengths of the fields applied. 
 
 In so far, therefore, as the particles which reach 
 the plate are all emitted with nearly the same velo- 
 city, the photographic trace will be an approximate 
 straight line, whose slope is a measure of that 
 velocity. 
 
 But to get the electrochemical equivalent we must 
 also write, from the above equations, 
 
 r y ( } 
 
 ~ 2 '' 
 
 e~ u*~ E 
 
 where k is another constant expressive of experi- 
 mental conditions ; so in so far as the masses of the 
 particles are all the same, the photographic trace or 
 spectrum will be a parabola. 
 
 But at the highest speeds mfe is not a constant, 
 but a function of u, such a function as is given on 
 page 133, with u = v sin 0. 
 
 So calling; this function = 0(- 1 = </>( -| we 
 
 m T \vj T \v y) 
 
 arrive at the conclusion that the actual equation to 
 the photographic curve should be 
 
 y \o y 
 
 with k 2 another constant. 
 
 At the highest speeds, when u approaches v the 
 velocity of light, u cannot vary much, since it 
 is approaching a limit, and accordingly the curve 
 to be expected will be approximately a straight line ; 
 the only rapid variable will then be the mass, which is 
 getting near to its asymptotic approach to infinity, 
 and therefore varies much more rapidly than u. 
 
 The determination consists therefore in getting as 
 
142 VARIABLE MASS [CH. xiv. 
 
 clear a trace as possible, for purposes of measurement, 
 and then by trial and error choosing a constant k l9 
 such as to make the squares of discrepancies of the 
 ratio here called k 2 , from its mean value, as small as 
 possible. 
 
 If it is possible to find a value for the constant k t 
 which shall bring out the calculated value k 2 constant 
 within the limits of experimental uncertainty, then 
 the form of the theoretical function ^ is to that 
 extent verified ; and inasmuch as that function was 
 calculated on the hypothesis of purely electrical 
 mass, the hypothesis of the purely electrical nature 
 of the inertia of ft rays is thereby similarly verified. 
 
 Kaufmann in one of his papers says the experimental 
 errors in his concluding series only amounted to 1*4 
 per cent. ; which, considering the difficulties to be 
 overcome, is remarkably good. 
 
 It is also of interest to record that the numerical 
 value obtained for the normal or low speed value 
 
 S) 
 
 of for the ft rays from radium is 1'84 x 10 7 c.g.s. ; 
 
 m Q 
 
 while Dr. Simon's independent determination, by 
 other means, of the same quantity for cathode rays 
 was l*865x!0 7 ; which is likewise a satisfactory 
 agreement. It is needless to emphasise the agreement 
 with J. J. Thomson's much earlier measurement of the 
 same quantity for rays from other sources. 
 
 The formula employed by Dr. Kaufmann, as repre- 
 senting the inertia, was erroneously deduced from 
 results in a paper by Mr. Searle of Cambridge ; and on 
 the strength of that he concluded at first that only a 
 fraction of the mass was electric. But it was pointed 
 out by Dr. Abraham of Gottingen that the inertia thus 
 calculated was only appropriate to direct acceleration, 
 or acceleration in the line of motion ; whereas what 
 
i H. xiv.] AT HIGH SPEEDS 143 
 
 was wanted was the transverse inertia, or the inertia 
 appropriate to a deflecting force at right angles to 
 the line of motion. This is to be obtained from the 
 expression for the tran verse force, derivable from the 
 expression for the energy in the ordinary manner by 
 Lagrange's dynamical equations : at high speeds its 
 value comes out different ; and when the formula 
 supplied for it by Dr. Abraham was subsequently 
 applied by Kaufmann in his calculations, it was found 
 to correspond very nearly with the view that the 
 whole of the inertia is electric. 
 
 This formula, which in fact applies to any solid 
 aggregation of electricity stratified spherically, is 
 that the transverse inertia of a flying particle, m, is 
 to the inertia of the same particle stationary or 
 moving slowly, m , in the following ratio : 
 
 m 
 
 where /3 is the ratio of the velocity of the particle 
 to the velocity of light. 
 
 This formula is not identical with that employed by 
 Thomson, possibly because the latter worked with a 
 different idea of an electron, though it gives numerical 
 results not exceedingly different. Primarily, how- 
 ever, it was employed not so much as an absolute 
 expression, as a form of function to be verified : 
 though it was used absolutely too. Kaufmann was 
 ultimately satisfied by finding out that his observed 
 mass varied if anything more rapidly, not less rapidly, 
 than theory required ; so that if the particles con- 
 tained any outstanding inertia of a non-electrical 
 character, such unexplained inertia must have a 
 negative value, which presumably would be absurd. 
 
 I do not myself find that Abraham's function 
 
144 VARIABLE MASS [CH. xiv. 
 
 agrees with observation, in absolute numerical value, 
 any better than Thomson's formula does ; nor do I 
 obtain even from Thomson's formula exactly the 
 numbers that he quotes in his American lectures ; 
 but to go into the whole matter would be inappro- 
 priate here, nor is it necessary, since the theoretical 
 differences only concern details that could doubtless 
 be removed by a little discussion : it will only become 
 necessary to go into them more fully when the 
 difficulties of the experimental observation are still 
 further overcome, and when even more accurate and 
 trustworthy results are obtained. * 
 
 I have taken the table of Kaufmann's best results, 
 as published in the Physikalische Zeitschrift 4, 
 1902-3, p. 55, and calculated them out by aid of 
 the expression given above on p. 133. 
 
 The results are tabulated below. I quote his given 
 experimental values for x and y, together with the 
 values he gives for /3, or u/v, or what I have called 
 sin 0; and then after reckoning out <(#), which repre- 
 sents the theoretical ratio m/m according to Thomson's 
 theory, I have put a column of y/x 2 ; which should 
 correspond, at least proportionally, to the same 
 quantity as experimentally determined ; and I like- 
 wise quote a column of f^(/#), which represents the 
 same quantity calculated according to Abraham's 
 formula (p. 143). (The numerical agreement of y/x 2 
 with a mean mass ratio, without any constant factor 
 other than unity, must be accidental.) 
 
 *The results of Kaufmann's subsequent work will be discussed in 
 Appendix M. 
 
AT HIGH SPEEDS 
 
 145 
 
 II 
 
 11 
 
 A 
 
 
 
 
 CO <M CM <M 
 
 iOOCOlOOOOOOOOCOI^ 
 I I I I I I I I I + 
 
 ;?S 8 
 
 a OB 
 
 "* Q> 
 ^ d -E 
 O 4) 
 
 '. 
 
 S^'S 
 
 o o o o 
 
 o-2s 
 
 TS rt >H 
 
 OlOOOOiOOiOOO 
 
 lOt^oe^iOt^ocMiOi^- 
 
 I-H i (<M(M(M<MCOOCOCO 
 
 L.E. 
 
CHAPTER XV. 
 ELECTRIC VIEW OF MATTER. 
 
 WHAT has been proved, by the combination of experi- 
 ment and theory now summarised, is that the most 
 important variety of rapidly flying corpuscle the 
 cathode rays in a Crookes tube, the /3 rays emitted 
 by radium and other radio-active substances, the 
 particles thrown off by most clean surfaces when 
 negatively charged and stimulated by ultra-violet light, 
 the carriers of jbhe negative discharge from incandescent 
 bodies, and likewise the revolving or vibrating portion 
 of an atom to which the emission of radiation or 
 ethereal wave-motion is due that these are all of an 
 identical nature and all possess an inertia of purely 
 electromagnetic character ; that is to say that they 
 are all pure electrons without any admixture of 
 ordinary or unexplained matter, that they are 
 simply electrical charges without any material or 
 non- electrical nucleus. 
 
 We thus reach the very important deduction that 
 negative electricity can exist apart from matter in 
 little isolated identical portions, each of exceedingly 
 minute known size, known charge, and known inertia ; 
 and that the laws of mechanics, applied to such 
 particles in given fields of electric and magnetic force, 
 should carry us on towards explaining the fun da- 
 
CH. xv.] CONSTITUTION OF ATOM 
 
 mental phenomena of electric currents, of magnetism, 
 and of the production of light. But in order to explain 
 chemical action, the details of radiation such as 
 groups of spectrum lines and the like, the differences 
 observable between conductors, and the properties of 
 magnetic bodies, it is necessary to treat of matter also ; 
 and to consider whether its inertia too, and therefore 
 its whole nature and properties, can be reduced 
 and simplified and explained as electromagnetic 
 phenomena. 
 
 For observe that though an electron has been 
 shown to possess purely electrical inertia, the same 
 proof has not yet been extended to an atom : the 
 constitution of an atom is so far unknown, and is the 
 subject of hypothesis only. Moreover the only 
 electron observed, so far, has been the negative 
 electron ; the positive has hitherto escaped observa- 
 tion in any isolated form, since it has never been met 
 with apart from a mass comparable with an atom in 
 bulk and weight. It may be that it can have no 
 separate existence apart from the atom of matter, 
 but in that case it will hardly be proper to speak of 
 it as an electron at all ; it may be that an indi- 
 visible positive charge itself constitutes the bulk of 
 an atom of matter ; in any case its nature must be 
 investigated, and many have been the attempts 
 made in that direction, among the best known in 
 recent times being the experiments of Prof. Wien 
 and others on " Canal rays." According to Larmor 
 positive electricity must be the mirror image of 
 negative, and experimental results must be inter- 
 preted to suit that theoretical conclusion. The 
 relations of positive electricity constitute in fact the 
 main outstanding problem of Physics at the present 
 time, and until they can be probed, further progress 
 
148 ELECTRIC VIEW OF MATTER [CH. xv. 
 
 towards understanding the constitution of an atom 
 must remain in a state of suspended animation. 
 
 The only portion of an atom that has been really 
 analysed, and so to speak understood, is that minute 
 but significant fraction of its mass which confers 
 upon it an electric charge, consequent chemical 
 affinity, and radiating power ; and, when we come to 
 ask what all the rest of the atom is composed of, all 
 we can say definitely is that the specific structure 
 must depend on the nature of the chemical element 
 under consideration. But if we consider the simplest 
 known atom, namely that of Hydrogen, we can make 
 various hypotheses somewhat as follows : 
 
 (1) The main bulk of the atom may consist of 
 ordinary matter (whatever unknown entity is hidden 
 by that familiar phrase), associated with sufficient 
 positive electricity (whatever that may be) to 
 neutralise the charge belonging to the electron or 
 electrons which undoubtedly exist in connection with 
 each atom. 
 
 (2) Or the bulk of the atom may consist of a 
 multitude of positive and negative electrons, inter- 
 leaved, as it were, and holding themselves together 
 in a cluster by their mutual attractions, either in a 
 state of intricate orbital motion, or in some static 
 geometrical configuration, kept permanent by appro- 
 priate connexions. 
 
 (3) Or the bulk of the atom may be composed of 
 an indivisible unit of positive electricity, constituting 
 a presumably spherical mass or "jelly," in the midst 
 of which an electrically equivalent number of point 
 electrons are as it were ' sown ' ; these electrons 
 probably distributing themselves in rings, after the 
 fashion of Alfred Mayer's floating magnetic needles, 
 and revolving in regular orbits about the centre of 
 
CH. xv.] CONSTITUTION OF ATOM 149 
 
 the jelly, with a force directed to that centre, and 
 varying as the direct distance from it. 
 
 This hypothesis, in spite of obvious weaknesses con- 
 nected with the nature of the positive unit, has great 
 attractiveness : for it explains the constant period 
 of an orbit ; it can explain the occurrence of visible 
 radiation by perturbations of the orbit during 
 collision ; and it has been shown by J. J. Thomson 
 to be capable of carrying us a long way towards a 
 rational electrical theory of Mendele*efFs series of 
 the chemical elements, together with some of their 
 chemical especially their electro-chemical proper- 
 ties, and some features of their spectra. Moreover 
 it goes further and explains in a fairly natural 
 manner, and without artificiality, the gradual degra- 
 dation of atomic energy by slow uncompensated 
 and unperceived radiation ; the consequent gradual 
 oncoming of instability ; and the occasional cata- 
 clysmic transmutation of one element into another, 
 or rather into others, with explosive violence, as 
 observed in the facts of radio-activity. It gives in 
 fact a rational though preliminary view of the 
 hypothetical evolution of all matter, which many 
 known circumstances now tend to support; and it 
 accounts in a kinetic fashion for the immense store 
 of intra-atomic energy. Nevertheless it is very far 
 from being an established theory, and another view 
 that can be taken of the rest of the atom is : 
 
 (4) That it consists of a kind of interlocked 
 admixture of positive and negative electricity, 
 indivisible and inseparable into units, and incapable 
 of being appreciably sheared by applied forces, but 
 incorporated together as a continuous mass ; in the 
 midst of which one or more isolated and indi- 
 vidualised electrons may move about and carry on 
 
150 ELECTRIC VIEW OF MATTER [CH. xv. 
 
 that display of external activity which confers upon 
 the atom its observed properties. 
 
 (5) A fifth view of the atom would regard it as a 
 central ' sun,' of extremely concentrated positive 
 electricity at the centre, with a multitude of electrons 
 revolving in astronomical orbits, like asteroids, within 
 its range of attraction. But this would give a law of 
 inverse square for the force, and consequently periodic 
 times dependent on distance, which appears not to 
 correspond with anything satisfactorily observed. 
 
 All these views however are painfully indefinite, 
 except the third one, which regards positive electricity 
 as an indivisible unit of perfectly unresisting uniform 
 material (though ' material ' is not the right word), of 
 spherical form the size of an atom, in the midst 
 of which a definite geometrical arrangement of 
 electrons are revolving with known frequency in 
 specified groups or rings. The amount of outstanding 
 vagueness in this view is obvious ; and is necessary, so 
 long as we know little or nothing about the intrinsic 
 nature of what we experience as positive electricity ; 
 but at the same time all the rest of this hypothesis is 
 definite enough, and enables mechanical laws and 
 calculations to be applied with considerable fulness to 
 the elucidation of the phenomena that would be 
 displayed by such a ' model ' or hypothetical com- 
 bination. And if the so-calculated phenomena are 
 found to correspond with fact, it assuredly lends 
 some strength to the hypothetical basis on which the 
 calculation is founded; although it is certain to have 
 to be modified somewhat in the light of growing 
 experience as discovery proceeds. 
 
 Whatever it may be worth, this is the only theory 
 of the nature of the atom which has been to any great 
 extent elaborated; and, extremely imperfect though it 
 
CH. xv.] CONSTITUTION OF ATOM 151 
 
 is at present, it is worthy of some attention from its 
 own intrinsic interest. It will be found developed by 
 Professor J. J. Thomson in the Philosophical Maga- 
 zine for Dec. 1903 and March 1904; and a general 
 idea of its main features can be gathered from his 
 American " Silliman Lectures," published in 1904 by 
 Constable as a book called Electricity and Matter. 
 
 Were it less hypothetical a further account of it 
 would be given here, but an extremely recent paper 
 by the same great Physicist has tended to reduce the 
 whole subject to a state of exaggerated uncertainty; 
 since he gives reasons, which appear to be sound 
 ones, in the Philosophical Magazine for June 1906, 
 for assuming that only one active electron is contained 
 in a hydrogen atom, and that all other elements contain 
 a number of electrons comparable to their atomic 
 weight, reckoned on the basis that H = 1 (see 
 Appendix L). This is an extraordinary and un- 
 suspected result, and at first sight appears very 
 unlikely, since the ordinary chemical assumption of 
 a unit atomic weight for Hydrogen has always been 
 known to be a pure convention, made for convenience 
 alone, and not likely to correspond with anything in 
 nature. I do not suppose that anyone imagined 
 that it would, even provisionally, be found to have 
 a physical and rational basis. The subject is further 
 referred to in Chapters XVII. and XIX. below. 
 
 In that state of uncertainty the matter must be 
 left for the present ; but we may go on to indicate 
 roughly how some of the known properties of matter 
 could be expected or explained, on a view of the 
 electrical constitution of matter which supposes it 
 composed of a large number of positive and nega- 
 tive electric charges, irrespective of the particular 
 mode of their aggregation and distribution. 
 
CHAPTER XVI. 
 ELECTKIC VIEW OF MATTER (CONTINUED). 
 
 Nature of Cohesion. 
 
 WE shall now try to trace some of the consequences 
 of the view that all atoms of matter are built up of 
 the same fundamental units, and are composed 
 of aggregates of a definite number of variously 
 grouped negative and positive charges, which for 
 present purposes we may call electrons, even though 
 some are positive arranged in kinetic patterns and 
 keeping apart by reason of the vigour of their own 
 orbital motions. 
 
 At first it is not easy to do more than imagine 
 the electrons to be statically grouped into regular 
 patterns. It is easy to conceive this on the hypo- 
 thesis No. 3 of last chapter ; for though in free space 
 they would be unstable or disperse, their possible 
 groupings are easily calculated in a positive men- 
 struum ; for instance they might be arranged in 
 triangular or square or hexagonal order ; with 
 other allied three-dimensional possibilities familiar 
 to students of crystallography. See, for instance, 
 William Barlow, Brit. Assoc. Report, 1896, p. 731; 
 also Lord Kelvin, Phil. Mag., March 1902, and 
 elsewhere. 
 
CH. XVL] MOLECULAR FORCES 153 
 
 On Chemical and Molecular Forces. 
 
 The force of chemical affinity has long been known 
 to be electrical. This opinion was propounded by 
 Berzelius, and was also held previously by Davy 
 and afterwards by Faraday. Ordinary electrical 
 attraction between charged bodies may be called 
 molar chemical action ; only there is no combination 
 in ordinary cases, because the opposing charges 
 spark into one another, and so the attraction ceases 
 when a certain proximity is reached. This dis- 
 charge and cessation of attraction does not seem to 
 occur among atoms ; the difference of potential 
 between them is too low to permit of mutual 
 exchange or neutralisation of charge, so the combi- 
 nation is permanent.* 
 
 Keal chemical attraction occurs between two atoms 
 each of which contains an unbalanced electron one 
 extra, or it may be more than one extra, electron of 
 given sign. Such an atom thus has a centre of force 
 whereby it can attach itself to other atoms and enter 
 into pairing or chemical combination with them. It 
 is probable that a negative charge is an excess, and a 
 positive charge a defect ; and that when pairing 
 occurs the excess charge of one fills up the deficiency 
 of the other, and composes a complete and neutral 
 molecule. 
 
 Union of this kind, however, never seems quite as 
 strong and permanent as the union of the electrons in 
 the atom itself: the molecule easily separates at the 
 same place again, under the influence of decomposing 
 influences, and does not seem able to split up in 
 other ways into new substances ; except in organic 
 chemistry, where various modes of splitting up a 
 
 *See Lodge, Brit. Assoc. Report, 1885, pp. 744, 5. 
 
154 ELECTRIC VIEW OF MATTER [CH. xvi. 
 
 complex molecule can be brought about, and are 
 practically utilised for the generation of new com- 
 
 CH 3 . CH 3 = C 2 H 5 . H. 
 
 It is probable that the same sort of thing is possible 
 with simple bodies, but that the so-called "elements" 
 constitute a peculiarly stable group, the ingredients of 
 which so far have only partially been re-associated 
 into isomeric or allotropic forms, and have not yet 
 been detached from each other. 
 
 When chemical combination occurs between two 
 oppositely charged atoms, there is no electric dis- 
 charge between them : the two atoms retain each its 
 own charge, and cling together for that reason. 
 When they are separated, each is an ion and possesses 
 its appropriate charge. 
 
 It is possible to charge an assemblage of neutral 
 molecules with an excess or with a defect of one or 
 more electrons, by processes of ordinary electrification, 
 such as friction ; but the attachment of these super- 
 numerary electrons is loose and they can be shaken 
 away by the agitation of ultra-violet light and in 
 many other ways. Even splashing of water into 
 spray shakes some loose, and can thus perturb an 
 electroscope, although the liquid was not charged 
 beforehand ; * a fact which adds to the probability 
 that the water unit is a molecular aggregate. And 
 in the case of massive atoms, of high atomic weight, 
 they occasionally appear automatically to reach a 
 condition of instability, and rearrange themselves 
 in such a way as to throw off one or more electrons 
 spontaneously, which then fly off tangentially with 
 whatever orbital velocity they may have had, giving 
 
 *Lenard on electrification near waterfalls. See also Chap. VII., . 
 above, on ionisation. 
 
CH. XVL] COHESION 155 
 
 rise to part of phenomena recently discovered under 
 the name of radio-activity. But instead of suppos- 
 ing that their violence of ejection is due to velocity 
 previously possessed by them, it is possible to suppose 
 that they are driven away by intrinsic static force, 
 so that their previous energy was potential ; and 
 this is the form of hypothesis favoured by Lord 
 Kelvin. See Phil. Mag. for March 1902. 
 
 Molecular Forces, Cohesion. 
 
 But there is another kind of adhesion or cohesion of 
 molecules, not chemical but what is called molecular. 
 This occurs between atoms not possessing ionic or 
 extra charges, but each quite neutral, consisting of 
 paired-off groups of electrons. At any moderate 
 distance the force of attraction between paired elec- 
 trons will be next to nothing, but at very minute 
 distances it may be very great ; ultimately becoming 
 almost indistinguishable from chemical combination, 
 except that the cling will be a weak cling at a 
 multitude of points instead of an intense cling at 
 only one. 
 
 Consider the outer surface of an atom consisting 
 of a regular group of interleaved electrons of alter- 
 nately opposite sign. Its equipotential surfaces will 
 be dimpled or corrugated or pimply sheets, which at 
 a little distance away will be almost plain ; but the 
 dimples will increase rapidly in depth and become 
 like the cover of a mattrass, when something less 
 than molecular distance something approaching the 
 internal electron distances apart is reached. 
 
 Two such atoms will therefore tend to settle down 
 with their equipotential surfaces adjusted into uni- 
 formity, the pimples of the one fitting into the hollows 
 of the other ; and this is the state of things suggested 
 
156 ELECTRIC VIEW OF MATTER [CH. xvi. 
 
 by the facts of cohesion. For a diagram representing 
 the state of things intended, see fig. 20. 
 
 To investigate the actual law of force would be 
 difficult, and too many assumptions would have to be 
 made for the geometrical arrangement of the electrons 
 in the adjacent atoms ; it could only be approximate, 
 because we should probably, at least in the first 
 instance, have to assume a static distribution. 
 Nevertheless the attempt might be instructive, and 
 might in a developed form be suitable for an Adams 
 Prize Essay. 
 
 o o o 0*0*0*0 
 
 0*0*0*0 o o o 
 
 * 0*0*0* 0*0*0*0 
 
 0*0*0*0 o o o 
 
 0*0*0* 0*0*0*0 
 
 A B 
 
 FIG. 20. Ordinary Cohesion between two Neutral Atoms A and B : 
 each atom supposed to consist of interleaved electrons of opposite sign 
 depicted in any convenient way which attract each other by residual 
 or spare affinity. This is due to a few of the lines of force which stretch 
 across the interspace, and hold the pair of atoms together. The maxi- 
 mum distortional shear permissible depends on the ratio of the electronic 
 to the atomic distance. 
 
 It is quite plain, however, that the result would be 
 a force rapidly increasing and becoming great at 
 small distances, and practically nil at any perceptible 
 distance. 
 
 A theory of cohesion cannot really be given until 
 the structure of an atom is better known, but in 
 all probability it will proceed on lines not wholly 
 unlike the above. 
 
 Molecular forces on this view are electrical, just as 
 much electrical as are chemical forces ; but they occur 
 between chemically saturated molecules, and are due 
 to the interaction or distant influence of paired 
 
CH. xvi.] U COHERER 157 
 
 electrons on each other across molecular distances. 
 It may be said to be a result of "residual affinity."* 
 
 Ions cannot thus combine ; because if they were 
 oppositely charged their combination would be 
 chemical, and if they were similarly charged they 
 would strongly repel each other. But if ions arrive 
 at a metallic electrode, or are provided with other 
 means of passing on their free charges, they cease 
 to be ions ; and then the diselectrified atoms can and 
 do combine molecularly with each other. 
 
 It is of course possible for an ion to have more 
 than one free electron, forming a dyad or a triad 
 radical ; and the way in which a neutral group can 
 receive, and by rapid re-adjustment pass on, an^ extra 
 foreign electron, reminding one of the re-adjustment 
 of the films in a lather when one compartment bursts, 
 is doubtless instructive. 
 
 The effect of electric polarisation on such a 
 neutral group of electrons is noteworthy. The effect 
 of a charged body in the neighbourhood is at once to 
 disturb the equilibrium, and to perturb the grouping 
 throughout the atom, more or less : it will cause the 
 negative electrons to protrude slightly on one side 
 and the positive on the other (see fig. 21 where two 
 different but very complete kinds of polarisation are 
 shown). 
 
 If two molecules were beyond each other's molecular 
 range, and if the neighbouring surfaces could by any 
 means as by the supply of electricity from without 
 be oppositely electrified, the forces of cohesion 
 would be intensified momentarily, by something akin 
 to chemical affinity, and cohesion would set in over 
 ultra-molecular distances. This appears to be what 
 goes on in a " coherer." The opposite charges 
 
 * See Lodge in Nature, 1904, vol. 70, p. 176. 
 
158 ELECTRIC VIEW OF MATTER [CH. xvi. 
 
 cannot be maintained electrostatically between two 
 neighbouring metallic surfaces, but they can be 
 momentarily imparted, by a sudden jerk or disruptive 
 discharge or received electric impulse ; and these are 
 the things which are effective in promoting cohesion. 
 In the two diagrams ; fig. 20 represents a couple 
 of atoms with interleaved electrons of opposite sign 
 
 c 
 
 o 
 
 0000 
 
 FIG. 21. Two Polarised Atoms, illustrating electrically intensified 
 cohesion. 
 
 in square order, the atoms being within range of 
 one another and so cohering by molecular or non- 
 chemical forces. They have adjusted themselves into 
 a cohering position ; but a vertical shear through half 
 the distance apart of the electrons would disintegrate 
 them. An angle represented by half the electron- 
 distance divided by the molecular distance, is therefore 
 a measure of the maximum distortion a substance can 
 undergo. 
 
CH. XVL] COHESION 159 
 
 Fig. 21 shows a couple of atoms both electrically 
 polarised, as by a positively charged rod held above 
 both. To vary the illustration, the constituents of C 
 are shown polarised into hexagonal order an effect 
 such as might also be caused by lateral pressure 
 in some cases ; while the constituents of D are 
 depicted in diagonal square order which has the 
 effect of violent electric polarisation. In any case 
 polarised atoms such as C and D are clinging by 
 forces much stronger than the force of ordinary 
 cohesion at that distance. They represent adjacent 
 atoms of a momentarily polarised coherer. 
 
 It is not to be supposed that the electrons in a 
 polarised atom need really ever be disturbed as 
 much as is shown in the diagram, nor any more 
 than an almost imperceptible amount, in order to 
 produce this chemical cohesion effect. For that is 
 what polarisation accomplishes : it converts ordinary 
 molecular force, or cohesion, into incipient but real 
 chemical affinity ; both kinds of forces being on the 
 above hypothesis electrically explicable. 
 
CHAPTER XVII. 
 
 FURTHER CONSIDERATIONS REGARDING THE 
 STRUCTURE OF AN ATOM. 
 
 THE hypothesis that has been already referred to, 
 No. 3 in Chap. XV., that an atom consists of a 
 globular mass of positive electricity with minute 
 negative electrons embedded in it either at rest, or 
 vibrating about a position of equilibrium, or revolving 
 in regular annular orbits, is obviously not free from 
 difficulties ; though its success in explaining many 
 observed facts seems to justify an attempt to mini- 
 mise those difficulties, and to render hopeful an 
 effort ultimately to overcome them. 
 
 One objection that can easily be raised is to ask 
 how a mass of positive electricity can hold together 
 against the mutual repulsion of its parts. This diffi- 
 culty is felt more in the case of positive electricity 
 than in the case of negative, because by hypothesis 
 the positive charge has some perceptible bulk, namely 
 the size of an atom, whereas the negative charge or 
 electron is exceedingly small. But however small an 
 electron is, it must be supposed to have parts, and 
 there is just as much reason for supposing the parts 
 of a negative unit to be mutually repulsive as there 
 is in supposing the parts of the positive unit to be 
 mutually repulsive. Hence the question is equally 
 
CH. XVIL] STRUCTURE OF ATOM 161 
 
 valid, how do the parts of an electron hold together ? 
 But nobody seems to ask this question ; and I see no 
 reason. why it should be asked, because there is no 
 evidence that the parts of an electron are mutually 
 repulsive there is no real evidence as yet that it 
 has parts at all. What we know is that different 
 electrons repel each other, and are attracted by 
 positive charges, but we do not know that the parts 
 of one electron repel each other ; in fact we know 
 nothing about the parts of an electron. The lines 
 of force, or field of force, representing the activity 
 of an electron, may be entirely outside itself, and 
 need not penetrate into its interior at all : it may 
 be for all electrical purposes an indivisible unit. 
 
 But then, supposing all this admitted for a negative 
 charge, why should it not be extended to cover a 
 positive charge also ? Why should the parts of a 
 positive unit be mutually repulsive ? It is no answer 
 to say that the unit is bigger, unless the electron is 
 thought of as a geometrical point ; the argument 
 about parts is just as valid in the one case as in 
 the other, and no more so. What we require is some 
 conception as to the nature of the positive charge, 
 and that I confess is wanting ; though " an 
 entanglement of finite size" seems to Larmor quite 
 possible and natural ; and anyhow an argument 
 against its existence based upon the assumed repul- 
 siveness of its parts does not seem to be an argument 
 of any weight. 
 
 Another suggestion can be made : and that is that 
 the main bulk of the atom, in which electrons are 
 embedded, consists not of positive electricity alone 
 but of a close admixture or combination of positive 
 and negative electricities inseparable and as it were 
 rigidly connected behaving to outside forces like the 
 
 L.E. 
 
162 THE STRUCTURE OF AN ATOM [CH. xvn. 
 
 oxygen and hydrogen interlocked together in a gallon 
 of water ; in which water a few extra atoms of oxygen 
 might easily be dissolved, in a relatively free condi- 
 tion that is to say, not forming part of the fixed 
 constituent- oxygen just as a few outstanding elec- 
 trons may exist in the general mass of an atom. 
 
 This is the hypothesis numbered 4 in that list of 
 alternative schemes which was exhibited in Chap. 
 XV.; and the latest results of Thomson, there also 
 mentioned, tend towards supporting it. 
 
 If any lines of force are then postulated between 
 the constituent positive and negative fluids inside an 
 atom they would be entirely of an internal character, 
 and only those belonging to some free unbalanced 
 charges would emerge and produce ionic activities : 
 the internal lines of force would be wholly occupied 
 in holding the atom together, and would have no 
 influence on neighbouring atoms not even molecular 
 or residual influence. The main bulk of atom in 
 that case would be like a finely interleaved condenser, 
 incapable of discharge or of decomposition, except 
 by actual disintegration such as might occasionally 
 accompany or cause radio-activity. 
 
CHAPTER XVIII. 
 
 SUMMARY OF OTHER CONSEQUENCES OF ELECTRON 
 
 THEORY. 
 
 Radio-activity. 
 
 IF many atoms of a substance have electrons attached 
 to them, and if these are performing orbital revolutions; 
 it is natural to ask how then can it be that substances 
 are not constantly emitting waves and radiating away 
 their energy. For we have seen in Chap. X. 
 that electric charges in revolution or vibration 
 constitute radiators, and must emit more or less 
 radiation ; thereby dissipating their kinetic energy 
 and gradually either coming to rest or effecting 
 some other change. Fortunately, owing to the 
 brilliant researches of Becquerel, Curie, and others, 
 certain substances have been found in which the 
 radiation intensity reaches a very perceptible mag- 
 nitude ; and it appears that this radiation may 
 be of several kinds 
 
 1st, of waves or pulses analogous to Rontgen 
 radiation : called 7 rays ; 
 
 2nd, of rays analogous to cathode rays consist- 
 ing of electrons bodily shot off: called ft 
 rays; 
 
 3rd, of positively charged ions or atoms, or 
 
164 SUMMARY OF ELECTRON THEORY [CH. xvm. 
 
 semi-atoms, consisting of something like 
 helium apparently, likewise shot off with 
 great energy : called a rays ; 
 4th, as a consequence of all this radiation, 
 detached portions of the residue of the 
 substance drift away, not charged with 
 electricity, but emanating something after 
 the fashion of an odour. This gaseous 
 emanation is found itself to possess a 
 very high intrinsic radiating power, and 
 to be capable of attaching itself to, or 
 causing a deposit on, other materials in 
 the neighbourhood, so that they too acquire 
 temporary radiating power : a deposit at 
 one time spoken of as induced or excited 
 activity.* 
 
 The substances which possess any noteworthy 
 amount of this radiating power are substances with 
 very high atomic weight ; and their emitting power 
 would appear to be probably due to an internal 
 commotion or convulsion, of sufficient violence to 
 detach and expel, every now and then, some particle 
 or fragment ; and also, by the shock of the expulsion, 
 to generate some feeble but exceedingly penetrating 
 Eontgen rays. 
 
 witn quantitative determinations concerning it. Also in mil. 
 Mag., July and November, 1902. Other references are M. and 
 Mme. Curie, Comptes Rendus, November, 1899 ; Hon. R. J. Strutt, 
 Phil. Trans., A 1901, vol. 196, p. 525; Sir W. Crookes, Proc. Roy. 
 Soc., vol. 66, p. 409 (1900), vol. 69, p. 413 (1902), also "Electrical 
 Evaporation," 1891, Proc. Roy. Soc., vol. 50, p. 88; and many other 
 workers. References to them are now conveniently collected in 
 Professor Rutherford's excellent treatise. 
 
 Madame Curie's original Thesis on Radio-activity for her Doctorate, 
 of date 1903, is a masterly production. 
 
CH. XVIIL] ATOMIC RADIATION 165 
 
 It is easy to grant that, whenever there are actual 
 collisions of sufficient suddenness, some radiation must 
 be emitted ; but we cannot help asking, why does 
 not the quiet orbital revolution of electrons round 
 atoms, in a substance not in a high state of 
 thermal disturbance and not possessing specially 
 massive atoms, why does not this also give rise to 
 a perceptible amount of true radiation and loss of 
 energy ? One answer that has been given is as 
 follows : 
 
 The radiators are not isolated or independent, and 
 surface radiation is maintained by layers at greater 
 depth in the substance. Moreover the radiators are 
 so close together that they are in all sorts of phases 
 within the first quarter wave length, a length which 
 embraces a multitude of them; wherefore a multitude 
 is a worse radiator than one, because they interfere 
 and produce but little external or distant effect ; like 
 the two prongs of a fork, or two neighbouring organ 
 pipes, or the front and back of a vibrating wire. See 
 Larmor, Ether and Matter, page 232 ; the proposition 
 by which he considers the question settled is that the 
 vector sum of accelerations equals zero. 
 
 Of course it must not be forgotten that radiation 
 of a low temperature order is as a matter of fact 
 always going on from all substances ; that energy is 
 conserved, and constancy of temperature persists, 
 merely because loss is equal to gain, because absorption 
 compensates radiation, not because radiation ceases ; 
 and that to make an estimate of the amount of 
 radiation, so occurring, it would be necessary to 
 suppose the body in an enclosure at absolute zero : 
 when undoubtedly its kinetic energy would rapidly 
 leak away, and be dissipated. But this refers to 
 questions connected with ordinary radiation, whereas 
 
166 SUMMARY OF ELECTRON THEORY [CH. xvm. 
 
 we are now dealing with the extraordinary variety 
 known as radio-activity. 
 
 If radiation goes on at the expense of the 
 internal energy of an atom, as it must if the atom 
 contains revolving electrons, still more if, as on 
 the electric theory of matter, it is wholly composed 
 of electric charges, it becomes necessary to ask 
 further : Why are not all atoms temporary and 
 unstable ? Why are they not all liable to internal 
 catastrophe and disruption, akin to earthquakes and 
 volcanoes? Why do they not all exhibit the phe- 
 nomena of radio-activity ? 
 
 The whole subject of radio-activity is a large 
 one, upon which I do not propose to enter at any 
 length here. Suffice it to realise that any difficulty 
 of explanation, in connection with it, is not the fact 
 itself, but rather the question why it is not more 
 notorious. 
 
 However, so far as that most striking and interest- 
 ing phenomenon the excessive photographic and 
 electric radio-activity of certain rare substances is 
 concerned, it has been already hinted that the greater 
 part of that does not consist so much in the emission 
 of radiation proper whether in the form of pulses of 
 X-rays or any other form as in the flinging off of 
 particles ; sometimes negatively charged particles or 
 electrons, sometimes positive ions. And these ex- 
 pelled particles, when they strike a photographic plate, 
 appear to generate by the concussion electric waves 
 which affect the silver salt. The faint photographic 
 influence of ordinary substances, observed by Dr. W. 
 H. Russell, seemed to suggest that incipient power of 
 this kind is not limited to bodies with heavy atoms, 
 like Uranium, Radium, Polonium, etc., as described 
 by Becquerel and the Curies, though these substances 
 
H. xvni.] RADIO-ACTIVITY 167 
 
 show it to an extraordinary degree : Dr. Russell, 
 however, appears to have traced his at first interesting 
 effects to the merely chemical action of hydrogen 
 peroxide. He has quite recently shown that leaves 
 of growing plants have a spontaneous photographic 
 power of the same kind. 
 
 The whole subject, together with the allied one of 
 the loss of charge from hot bodies,* first discovered by 
 Dr. Guthrie long ago (see Phil. Mag., [4], xlvi. p. 273), 
 is one that demands special attention and treatment. 
 
 Crookes discovered that the alpha rays, or particles 
 projected by radium, polonium, and other strongly 
 radio-active substances, were able by their concussion 
 with a target of zinc-sulphide to produce luminous 
 flashes, visible under slight magnification : and the 
 evidence on the whole is in favour of the view that 
 many of the impinging atoms may have speed enough 
 to be able to cause a separate flash, by its own 
 individual action on the crystalline compound : a 
 phenomenon popularised in the little pocket-instru- 
 ment called a * spinthariscope.' When we consider 
 the speed with which these particles are ejected, such 
 an idea is not surprising, although it is novel to have 
 to contemplate any perceptible effect produced by a 
 single atom. But taking these projectiles to be 
 atoms of hydrogen or helium, of mass 10~ 24 grammes, 
 flying with say one-tenth the speed of light, the 
 stoppage of one of them within molecular dimension, 
 that is within its own thickness as ordinarily estimated, 
 10~ 8 centimetre, would require, for an exceedingly v 
 minute fraction of time, the expenditure of 80 horse- 
 power. 
 
 * See, for instance, Strutt on leakage from hot bodies, Phil. 
 July, 1902 ; J. J. Thomson, ditto, Phil. Mag., August, 1902 ; further 
 developed by O. W. Richardson, Phil. Trans., vol. 201, p. 516 (1903). 
 
168 SUMMARY OF ELECTRON THEORY [CH. XVIIL 
 
 Solar Corona, Magnetic Storms, and Aurorce. 
 
 Another subject on which it is tempting to enlarge 
 is the explanation of various astronomical and 
 meteorological phenomena by the electron theory. 
 
 The theory of Aurorse has recently been elaborated 
 by Arrhenius ; but the whole doctrine of emanations 
 from the sun, and of repulsion of small particles both 
 by his light and by his probable electrification, is a 
 matter that has been familiar to me for many years, 
 through conversation with FitzGerald and others. 
 See, for instance, Larmor, Phil. Trans., 1894, vol. 
 185, p. 813; Lodge on Sunspots, Magnetic Storms,. 
 Comets' Tails, Atmospheric Electricity, and Auroras, 
 in the Electrician for December 7, 1900, vol. 46, p. 
 250; FitzGerald, Electrician, December 14, 1900, 
 with reference to his review of a Heaviside volume in 
 1893 (Electrician, vol. 31, p. 390). See also Fitz- 
 Gerald's collected "Scientific Writings," at date 1882. 
 
 The earth is in fact a target exposed to cathode 
 rays, or rather to electrons, emitted by a hot body, 
 viz. the sun. The sun is evidently intensely radio- 
 active : and the result of its discharge of electrons 
 into the approximate vacuum of its immediate 
 neighbourhood is not unlikely to be the appearance 
 known as the corona. The gradual accumulation 
 of negative electricity by the earth is a natural 
 consequence of this electron bombardment extending 
 to greater distances across space, where no residual 
 matter exists ; and the fact that the torrent of particles 
 constitutes an electric current of fair strength gives an 
 easy explanation of one class of magnetic storms ; 
 these storms having long been known, by the method 
 of concomitant variations, to be connected with sun- 
 spots and aurorse. The electric nuclei, when they 
 
CH. XVIIL] AURORA 169> 
 
 form ions, would also serve as centres for condensation 
 of atmospheric water vapour at high altitudes, and so? 
 be liable to affect rainfall. Moreover, the fact that 
 water vapour condenses more readily on negative 
 than on positive ions, seems to furnish us with one ./ 
 explanation of atmospheric electricity ; for a fall of 
 rain would bring down with it a negative charge, 
 and would leave the upper regions positively 
 electrified with respect to the earth's surface : and 
 this agrees with the known sign of the normal field 
 of electric force in the atmosphere. 
 
 These early perceptions have been well elaborated 
 of late by Arrhenius ; and his explanation of the 
 auroraby means of the catching and guiding of 
 rapidly moving electrons by the earth's magnetic 
 lines of force, so as to deflect them away from the 
 tropical sunshine, and to guide them in long spirals, 
 along the lines, to the poles, there to reproduce the 
 phenomena of the vacuum-tube in the rarified upper 
 regions of the atmosphere is particularly definite and 
 pleasing. Some of the other astronomical suggestions 
 he has made are likewise of considerable interest. 
 
 Transformations of Radium, etc. 
 
 The following details are given by Rutherford for 
 the spontaneous transformations which radium under- 
 goes, together with the lifetime constant of the 
 various products that is to say the time required 
 for the activity of the product to fall to one-half its 
 value, and also the kind of particles or rays which 
 are thrown off. 
 
 Certain of the changes are rayless changes, and 
 may be considered to result in an allotropic modi- 
 fication, without change of atomic weight ; but 
 whenever an alpha particle is thrown off, the atomic 
 
170 SUMMARY OF ELECTRON THEORY [CH.XVIII. 
 
 weight must change, presumably by an amount 
 appropriate to the loss of an atom of helium. It 
 will be observed that the gamma or Rontgen rays 
 always accompany the emission of a beta particle or 
 electron, and never appear otherwise ; also that it is 
 only in some of the changes that electrons are thrown 
 off. It will be understood that the so-called " emana- 
 tions" are all of the nature of gas, while the other 
 products are like a solid deposit or coating. These 
 active deposits, or " excited activities," can be sub- 
 jected to ordinary chemical tests : some of them are 
 soluble in acids, some in ammonia ; some of them 
 are volatile at a high temperature, some are not 
 readily volatile. The following table contains the 
 principal features of the transformations of the more 
 remarkable radio-active substances ; for more details 
 Rutherford's book must be referred to. The product 
 here called Radium F appears to be the same as that 
 called by other observers Radio-tellurium, or by its 
 original discoverer, Mme. Curie, Polonium : 
 
 The substance 
 
 has a life-constant 
 
 it shoots off 
 
 and changes into 
 
 Uranium 
 Ur. X 
 
 (say) 600 million 
 years 
 22 days 
 
 an a particle or 
 (?) helium atom 
 Py rays 
 
 Ur. X 
 
 Thorium 
 Th. X 
 Emanation 
 Th. A 
 Th. B 
 
 24 x 10 9 years 
 4 days 
 54 sees. 
 11 hours 
 55 mins. 
 
 an a particle 
 a particle 
 a particle 
 no rays 
 a/3y rays 
 
 Th. X 
 Emanation 
 Th. A 
 Th. B 
 
 Actinium 
 Act. X 
 Emanation 
 Act. A 
 Act. B 
 
 10 days 
 
 4 sees. 
 36 mins. 
 2 mins. 
 
 no rays 
 a particle 
 a particle 
 no rays 
 afty rays 
 
 Act. X 
 Emanation 
 Act. A 
 Act. B 
 
H. XVIII.] 
 
 RADIO-ACTIVITY 
 
 171 
 
 The substance 
 
 has a life-constant 
 
 it shoots off 
 
 and changes into 
 
 Radium 
 
 1300 years 
 
 a particle 
 
 Emanation 
 
 Emanation 
 
 4 days 
 
 a particle 
 
 Radium A 
 
 Radium A 
 
 3 mins. 
 
 a particle 
 
 Radium B 
 
 Radium B 
 
 21 mins. 
 
 no rays 
 
 Radium C 
 
 Radium C 
 
 28 mins. 
 
 afiy rays 
 
 Radium D 
 
 Radium D 
 
 40 years 
 
 no rays 
 
 Radium E 
 
 Radium E 
 
 6 days 
 
 fiy rays 
 
 Radium F 
 
 Radium F 
 
 143 days 
 
 a particle 
 
 Possibly Lead 
 
 Emanations. 
 
 The discovery of thorium and radium emanations 
 was made by Rutherford and Dorn respectively in 
 consequence of an observation of Owens on the 
 irregularity of thorium rays in producing ionisation, 
 the fact being that any of these materials are more 
 active when the emanation has been allowed to 
 accumulate than soon after it has been removed. 
 For the emanation, although so infinitesimal in 
 quantity, is considerably more active than the sub- 
 stance itself; and, being a gas, it can readily be 
 drawn away or otherwise expelled from the pores or 
 neighbourhood of the salt. But it accumulates again, 
 being evidently generated in situ, and presently the 
 full activity of the substance is restored. Radium 
 emanation is shown by Rutherford and Soddy to 
 liquefy at a temperature of about 150 degrees below 
 zero; thorium emanation liquefies at about 120 C. 
 They appear to be quite definite, though transitory 
 and very unstable and disintegrating, materials. 
 
 Deflexion of Alpha-rays. 
 
 When alpha-rays are submitted to a strong 
 magnetic field they are deflected, though very 
 
172 SUMMARY OF ELECTRON THEORY [CH. XVIIK 
 
 slightly, in a direction indicating that they are posi- 
 tively charged particles. Rutherford and Becquerel 
 have both observed this fact, and Strutt has confirmed 
 the fact of positive charge. But quite recently* 
 Soddy has surmised that this positive charge might 
 be acquired by ionisation in travelling through the 
 air, and that in a high enough vacuum no deflexion 
 would be observed ; thereby showing that intrinsi- 
 cally they did not possess a charge. He believes 
 himself to have confirmed this by careful though 
 difficult experiment. So important, and in some 
 respects improbable, a conclusion, however, cannot 
 yet be regarded as at all certain. 
 
 Rutherford was the first to observe the fact and 
 the sign of the magnetic deflexion or curvature of 
 alpha rays, and to make an estimate of its amount. 
 He invented the device of sending them through a 
 magnetic field, up a stream of rarified hydrogen, 
 between a set of narrow plates set edgeways ; which 
 latter constituted a grid that would be opaque 
 unless the trajectories of the flying particles were 
 rigorously straight. He thus made the discovery that 
 the rays consisted of positively charged particles, and 
 arrived at a rough estimate of their atomic weight. 
 
 Becquerel measured the magnetic deflexion of 
 alpha rays, at different distances from the source, 
 by letting them graze a photographic plate at a 
 known angle. The actual trace observed was a 
 short slant line with a slight curvature ; reversal of 
 the field slanted the line the other way, thus giving 
 a resultant impression like the conventional two wings 
 of 'a flying bird drawn at a very acute angle. Subse- 
 quent measurement of the distance apart of different 
 positions of the two wings gave the data sought. 
 
 * See Nature, 2nd August, 1906. 
 
CH. xviii.] RADIO-ACTIVITY 173 
 
 Eutherford has examined the deflexion of alpha 
 particles from radium in a careful manner. Previous 
 experiments, such as his own and those of Becquerel 
 and Des Coudres, were made on a thick layer of 
 radium ; but under these circumstances the particles 
 are projected with a considerable range of velocity. 
 To obtain homogeneous radiation it is necessary to 
 use a very thin layer ; and Rutherford employed 
 for this purpose the product Radium C, namely, 
 part of the active deposit which appears on a fine 
 wire exposed for some hours to radium emanation. 
 This is a deposit of utterly imperceptible thickness, 
 undetectable by any means save radio-activity ; and 
 it consists of Radium A, B, and C. The activity of 
 Radium A disappears in about a quarter of an hour ; 
 Radium B emits no rays ; so Radium C alone is left 
 active, and it emits only alpha rays. It is true it 
 dies away in about a couple of hours, but there is 
 time enough for an experiment. The method em- 
 ployed is like this : 
 
 Rays from the wire pass through a narrow slit, and 
 then on to a photographic plate in a vacuum ; a 
 uniform magnetic field is applied in a direction 
 parallel to the slit, so as to curve the rays ; this field 
 is reversed every ten minutes, so that on developing 
 the plate two narrow parallel lines are observed, the 
 distance between which represents twice the de- 
 flexion ; their sharpness shows that the rays were 
 homogeneous. The path corresponding to a magnetic 
 field of 9470 C.G.S. units had a radius of curvature 
 equal to 42 centimetres. 
 
 Electric deflexion was not then applied ; but, 
 estimating the number of particles expelled from the 
 Radium C as 6*2 x 10 10 per second, and the heating 
 effect as 31 calories per hour, Rutherford calculated 
 
 
174 SUMMARY OF ELECTRON THEORY [CH. xvm. 
 
 the emission of energy as '36 million ergs per second. 
 Combining this with the magnetic deflexion, the 
 result is that u = 2'6xlO Q centimetres per second, 
 while e/m = 6,500 electro-magnetic units. 
 
 Des Coudres, using both electric and magnetic 
 deflexion, but employing more complex rays, obtained 
 u=l'65 x 10 9 , and e/m 6,400. 
 
 Activity of Radium at all Temperatures. 
 
 Messrs. Dewar and Curie have shown that at the 
 temperature of liquid hydrogen, 252 degrees below 
 zero centigrade, the heat evolution of radium is the 
 same as at ordinary temperatures. It has also been 
 shown to be equally active in the solid or in the 
 dissolved state, and elevation of temperature makes 
 it no more active. 
 
 The activity of radium, as observed in Crookes' 
 spinthariscope, is just as marked at the temperature 
 of liquid hydrogen as at ordinary temperatures, 
 provided the luminescent screen is not likewise 
 chilled. 
 
 Spectrum of Radium. 
 
 In speaking of the spectrum of radium there is an 
 ambiguity to be guarded against. We may mean 
 the spectrum of radium itself, when it is put in a 
 flame or subjected to the electric spark ; or we may 
 mean the spectrum of the spontaneous glow of 
 radium chloride or bromide, which can be seen in 
 the dark. The latter spectrum is very difficult to 
 observe, because of its extreme faintness, but the 
 experience of Sir William and Lady Huggins has 
 enabled them to examine it, and to show that it 
 is chiefly the spectrum of atmospheric nitrogen ; 
 which is thereby proved to be ionised and violently 
 
CH. XVIIL] SPECTRUM OF RADIUM 
 
 175 
 
 disturbed by the neighbourhood of radium, to the 
 extent of emitting luminous radiation without eleva- 
 tion of temperature. The spontaneous radium -glow 
 is, in fact, probably due to its influence on other 
 substances ; and ordinary glass, exposed to it, darkens 
 and becomes thermo-luminescent, that is to say, it 
 begins to emit light when raised to a temperature 
 of about 500 degrees. 
 
 M. Eugene Ne'culcea gives the following table of 
 the photographic spectrum of the radium spark, as 
 observed by M. Demargay, the wave lengths being 
 given in " tenth-metres." In the visible spectrum, 
 which is not photographed, there is only one notable 
 ray, of wave-length 5665. For other observations^ 
 see Runge, Astrophysical Journal, 1900, p. 1. 
 
 WAVE-LENGTH. 
 
 INTENSITY. 
 
 WAVE-LENGTH. 
 
 INTENSITY. 
 
 
 f 4826-3 
 
 10 
 
 {4600-3 
 
 3 
 
 
 4726-9 
 
 5 
 
 4533-5 
 
 9 
 
 Blue- 
 
 4699-8 
 4692-1 
 
 3 
 
 7 
 
 4436-1 
 (4340-6 
 
 8 
 12 
 
 
 4683-0 
 
 14 
 
 Ultra-violet \ 3814'7 
 
 16 
 
 
 ^4641-9 
 
 4 
 
 (3649-6 
 
 12 
 
 The detection of radium by the spectroscope, 
 through its strongest line, 38147, though it may be 
 a method perhaps a million times more sensitive than 
 ordinary chemical analysis, has been shown to be a 
 million times less sensitive than a method of detec- 
 tion by means of an electroscope, utilising the 
 extraordinary ionising power of its radio-activity. 
 For Rutherford reckons that each a particle expelled x 
 from radium is able to generate some hundred thou- 
 sand ions before it is stopped, or rather before its 
 
176 SUMMARY OF ELECTRON THEORY [CH. xvm. 
 
 immense initial velocity falls below a certain critical 
 speed at which ionisation ceases to be caused. A 
 charged electroscope of proper sensitiveness is able 
 to indicate by its leak the presence of this number of 
 ions, and accordingly is able to signal the presence 
 of only one a particle. But the number of such 
 particles expelled by a milligramme of fully active 
 radium is estimated as a hundred million every 
 second. 
 
 Electric Production. 
 
 The power of radium constantly to develop elec- 
 tricity was first demonstrated by W. Wien, by 
 suspending a tube in a vacuum. Dorn observed that 
 sometimes sparks were obtained on opening a tube 
 containing radium. Strutt contrived an ingenious 
 device for displaying this constant production of 
 electricity by reason of the very different penetrating 
 power of the + a and the /3 particles, so that one 
 set can be trapped while the other set escapes. 
 
 Fig. 22 shows Strutt's apparatus and "perpetual" 
 more accurately, perennial electric generator and 
 source of mechanical energy. A small tube contain- 
 ing radium salt, with its outside made sufficiently 
 conducting, has a pair of gold or aluminium leaves 
 attached, to it, and is insulated in a very high 
 vacuum by a quartz rod ; a metallic strip, lining 
 the vacuum case, being connected to earth. The 
 radium fires off positive and negative particles in 
 equal quantities ; but the negative, being small and 
 penetrating, are many of them able to escape, while 
 the positive accumulate and thus keep on slowly 
 charging the gold leaves with positive electricity till 
 they periodically overflow. The high vacuum is 
 necessary to prevent the internal atmosphere from 
 
CH. XVIII.] 
 
 RADIO-ACTIVITY 
 
 177 
 
 becoming conducting, by ionisation from the shock 
 of the flying particles, and as a consequence pre- 
 venting the gold leaves from becoming charged. 
 
 Radio-activity of Ordinary Materials. 
 
 Even in the absence of radium, a charged electro- 
 scope is usually found to leak rather more than any 
 creeping along the supports can account for; this 
 
 FIG. 22. Strutt's mode of demonstrating constant electric production 
 by radium. 
 
 leakage must be due to ionisation of the atmosphere, 
 and a consequent kind of gaseous electrolysis in the 
 air. The ionisation is partly due to stray radiation 
 from outside, but some of it may be due to the 
 radio-activity of materials with which the interior 
 of the electroscope can be lined. Definite experi- 
 ments of this kind have been made by M'Lennan and 
 Burton of Toronto, and by Strutt, also by A. Wood, 
 Rutherford and Cooke. When cylinders of zinc, 
 tin, or lead were used to line the electroscope, a 
 
 L.E. 
 
 M 
 
 
178 SUMMARY OF ELECTRON THEORY [CH. xvm. 
 
 certain leakage was observed, but this was reduced 
 some thirty per cent, when the whole was plunged 
 into a tank of water so as to screen the interior 
 from outside radiation. 
 
 Kutherford and Cooke surrounded the electroscope 
 with thick screens of various kinds, and once with 
 
 K. 
 
 FIG. 23. Righi form of electroscope or electrometer, of small capacity. 
 The vital parts DECB, with the gold leaf, are shown on a larger scale in 
 fig. 24. They are contained in a metal case, with a movable wire G, by 
 which they may be charged from outside. The instrument is read by a 
 reading microscope R; an ordinary millimetre scale being placed in a 
 conjugate focus and projected by the lens L on to the plane of observa- 
 tion where the gold leaf is. The radio-active substances are presented 
 to the box outside a window of very thin aluminium foil. 
 
 as much as five tons of lead. A moderate amount 
 of screen, however, was found to produce the same 
 effect as a greater amount, showing that the influence 
 of the outside penetrating-radiation could be checked 
 without stopping more than thirty per cent, of the 
 
CH. XVIII.] 
 
 RADIO-ACTIVITY 
 
 179 
 
 leakage ; the remaining seventy per cent, seemed due 
 to internal radio-activity. Materials such as brick 
 seem specially radio-active, and any metals which 
 have been exposed to the outside atmosphere are 
 more radio-active than virgin metal. 
 
 But, in addition to this induced or excited activity, 
 Strutt and others tried a good many materials and 
 found different characteristic effects with each. 
 
 D. 
 
 E. 
 
 FIG. 24. Working part of the above electroscope, magnified four times. 
 The rod AB with the gold leaf C is cemented to a thin rod of melted 
 quartz D by means of a drop of mastic or guttapercha at the bottom of a 
 minute metallic capsule E attached to the rod AB; thereby lessening 
 any tendency of the charge to creep, and keeping the capacity exceedingly 
 small. 
 
 The question of whether radiation is emitted 
 spontaneously by metals of every kind, and not only 
 by those few substances which are conspicuously 
 radio-active, has been still further examined by Mr. 
 Norman E. Campbell of Trinity College, Cambridge 
 (Phil. Mag., Feb. 7, 1906). He adduces very strong 
 experimental proof that such radiating power actually 
 exists, since they all ionize the air in their neigh- 
 bourhood. Moreover, the experiments indicate a 
 
 
180 SUMMARY OF ELECTRON THEORY [CH. xvm. 
 
 characteristic or specific quality in the radio-activity 
 of the different substances : a result tending to nega- 
 tive the idea that it is due to some residual effect 
 of a common impurity, such as an excessively 
 minute trace of radium common to all metals ; 
 the indication is rather in favour of a specific 
 radio-activity belonging to each metal, not due to 
 any impurity. 
 
 It is not yet absolutely proved that this is identical 
 with orthodox radio-activity, of the kind which is 
 accompanied by atomic change or transformation of 
 substance ; but, inasmuch as the rays appear to consist 
 to a great extent of alpha-rays, there is not much 
 doubt but that the complete identity of the process 
 will be established before long. 
 
 Population Analogy. 
 
 Since radio-activity is a sign of, and is accompanied 
 by, disintegration and loss of material, it is manifest 
 that substances of exceedingly high radio-activity 
 must be comparatively scarce. Ordinary permanent 
 materials cannot be violently radio-active, though 
 each gramme of them might lose a few thousands of 
 atoms per second without any probability of our 
 being able to detect the loss by weighing not even 
 by weighings continued through a century. The 
 plentifulness of a substance must depend on its rate 
 of production, its life time, and its rate of decay; just 
 as the population of a circumscribed area is deter- 
 mined by the birth rate, death rate, and average age. 
 
CHAPTER XIX. 
 
 EADIATION FROM A RING OF ELECTRONS, AND ITS 
 BEARING ON THE CONSTITUTION OF AN ATOM. 
 
 ALTHOUGH the radiating power of a single vibrating 
 or revolving electron is considerable, even when the 
 speed is not excessively high, it must be observed 
 that the amount of radiation emitted is greatly 
 diminished when a second symmetrically situated 
 particle is introduced ; because, at a distance, it will 
 be virtually in opposite phase to the first. The 
 diminution is specially marked when the speed is 
 low. In order to assist the radiation, the second 
 electron at the opposite end of a diameter should 
 be of opposite sign to the first. 
 
 Three similar electrons at the corners of an equi- 
 lateral triangle will radiate much less than two ; and 
 so with every addition to a symmetrical system of 
 rotating particles, the radiating power diminishes ; 
 until when they form a continuous ring there is of 
 course no radiation emitted at all, since everything 
 is then continuous. 
 
 Professor J. J. Thomson has calculated the amount 
 by which the radiation is diminished when the 
 number of particles is increased : and shown how 
 greatly it depends on their velocity. If they are 
 travelling with an orbital velocity of one-tenth the 
 

 182 RADIATION FROM ELECTRONS [CH. xix. 
 
 speed of light, two electrons at opposite ends of a 
 diameter radiate about one-tenth as much as either 
 alone ; four electrons at the corners of a square, 
 likewise rotating with one -tenth of the velocity of 
 light in its own plane, will have a radiating power 
 of about one six-thousandth of that of one of them. 
 But if the velocity of the particles is only one- 
 hundredth that of light as must often, perhaps 
 usually, be the case among constituent electrons 
 in an atom, then a pair would radiate only 
 one-thousandth as much as one. For three, the 
 radiating power is diminished to about one two- 
 millionth ; and for six, to something getting on 
 for a trillionth, which practically means no radiat- 
 ing power at all. 
 
 The actual numbers, and the calculation, can be 
 found in the Philosophical Magazine for December 
 1903, p. 681. 
 
 All this depends on the electrons being sym- 
 metrically situated round the centre of rotation ; 
 but if by any cause such as an atomic clash or 
 chemical collision they are displaced from sym- 
 metry, then their centre of gravity will rotate 
 round the original centre, and will act as a single 
 electron, or rather as an electron of multiple mass 
 and constitution. The constituent particles will now 
 not compensate each other at all, so far as this 
 excentric motion is concerned. Accordingly the 
 , y radiation instantly becomes violent, and must be 
 regarded as the source of the visible spectrum: the 
 nature of the lines depending on the structure of 
 the composite body, which, by reason of temporary 
 displacement, now acts as a single radiator of great 
 power. In this way it is possible to conceive of the 
 particular kind of radiation, exhibited in the spectrum, 
 
CH. xix.] INSTABILITY OF ATOM 183 
 
 as being determined by the character of the composite 
 radiator; while the occurrence of the radiation itself is 
 limited to the periods during which the displacement 
 by chemical clash or collision continues effective : a 
 period in each individual case probably very short, 
 but rapidly renewed in the aggregate by the com- 
 bination or collision of other molecules. 
 
 Radiation due to high temperature may be caused 
 in a somewhat similarly accidental and violent fashion, 
 not occurring at all appreciably during the intervals 
 of peace or regular motion. 
 
 Instability of an Atom. 
 
 The principle on which instability of an atom is 
 to be expected, on the electrical theory, at certain 
 critical points in its history, may, according to 
 J. J. Thomson, depend upon the fact that a rotat- 
 ing ring of electrons is only stable so long as their 
 angular velocity exceeds a certain critical value. 
 Three electrons indeed are stable even when stationary, 
 though they become more stable by rotation ; but 
 four corpuscles in one plane, at the corners of a 
 
 square, are not stable unless they are rotating with an 
 
 // N e 2 \ 
 angular velocity greater than /I *325 J^L or '57c 
 
 as it is called in the next chapter. Whenever their 
 speed falls below that value, they adjust themselves 
 at the corners of a tetrahedron or triangular pyra- 
 mid, tumbling over into the new position with a 
 rapid collapse, analogous to the tumbling over of 
 a top when its rate of spin has fallen below a 
 certain critical value. 
 
 With a greater rate of rotation, five corpuscles in 
 one plane may be stable ; but with six in a ring, 
 
184 RADIATION FROM ELECTRONS [CH. xix. 
 
 stability is impossible at any speed, so long as there 
 are only six present ; but if one of the six, or if a 
 seventh, be placed as a centre to the ring, then they 
 become stable again ; and at a proper speed there can 
 now be seven or even eight corpuscles in a ring, but not 
 more, unless more corpuscles be placed in the centre. 
 Suppose, for instance, that three be put in the centre : 
 they will there form a triangle, and round them there 
 may be a ring of as many as ten others. But to get 
 a stable ring of twelve corpuscles, you must have 
 seven inside altogether ; of which six or five can be in 
 another ring, with one or two at the centre of that. 
 By this means a large number of corpuscles, all in 
 rapid rotation, can be arranged in a series of rings ;. 
 but if the speed of any ring falls below a certain 
 critical value it becomes unstable, and then there 
 has to be a readjustment of corpuscles into another 
 pattern, which must give rise to a sudden con- 
 vulsion in the hypothetical structure of the atom. 
 This readjustment involves a decrease of potential 
 energy and consequent increase of kinetic energy, 
 and hence might result in the expulsion of some 
 corpuscles. 
 
 Note that such a convulsion, on this theory, must 
 undoubtedly occur from time to time, though it may 
 be a rare occurrence in the life of any one atom ; 
 because revolving charges of electricity necessarily 
 radiate energy to some extent though usually to a 
 very small extent, and accordingly their speed must 
 gradually be reduced, until sooner or later it arrives at 
 the critical value at which a convulsion must occur. 
 The convulsion is followed by readjustment into 
 another pattern, and consequent transmutation into 
 another element, or at least into an allotropic form 
 of the first element if no fragment is lost ; and the 
 
CH. xix.] INSTABILITY OF ATOM 185 
 
 occurrence is accompanied, and indeed demonstrated, 
 by radio-activity. 
 
 A list of the series of changes actually observed in 
 radio-active substances will be found above in Chap. 
 XVIII., p. 170. 
 
 Cosmic Analogy. 
 
 An analogy may be drawn between the occasional 
 disruption of one of a large group of atoms, and the 
 phenomenon observed from time to time in the sky 
 called a new or temporary star. Both are outbursts 
 of a kind of radio-activity, though they may be 
 excited by different causes ; both are comparatively 
 rare occurrences, when the whole available number 
 of bodies capable of such outburst or collision is 
 contemplated. 
 
 Assuming that in a gramme of average terrestrial 
 material there are a thousand such eruptions every 
 second, that would correspond to about one new 
 star per century among a cosmic assemblage of ten 
 thousand million bodies. 
 
 Another Account of Atomic Instability. 
 
 A different idea of the nature of Instability was 
 suggested by myself. An electron which is rotating 
 outside an atom, being attracted thereto by a force 
 varying as the inverse square of the distance, will,, 
 as it tends to lose energy by radiation, get drawn 
 nearer and nearer to the atom ; and will increase in 
 speed inversely with the square root of the distance. 
 As the speed thus increases, the effective inertia of the 
 particle will increase, and accordingly it will be more 
 and more difficult to retain it in an orbit by the centri- 
 petal force ; since this force, being merely an electrical 
 
186 RADIATION FROM ELECTRONS [CH. xix. 
 
 attraction, is not a function of the speed, or, in so 
 far as it is a function of the speed, it is a function 
 which diminishes as the speed increases. Accordingly 
 there must come a time when the electrical attraction 
 is incompetent to hold in the revolving mass, which 
 then begins to strain itself a little further off, with 
 the velocity now acquired ; but, by so doing, it still 
 further diminishes the force which holds it in, 
 without diminishing the centrifugal force it is itself 
 exerting ; and accordingly there is no longer equi- 
 librium. The equilibrium at the point of greatest 
 proximity is in fact unstable, and so the particle itself 
 flies off tangentially with the speed which it had then 
 acquired, thus beginning a radio-activity of a fresh 
 kind radio-activity discovered by Becquerel the 
 emission of violently flying electrons or Beta-rays. 
 
 The whole constitution of the atom may be upset 
 by losses of this kind, and a rearrangement of its 
 substance appears occasionally to occur, with the 
 flinging away of some portion as a material pro- 
 jectile ; these particles thus thrown off constituting 
 the observed Alpha-rays. Sometimes electrons are 
 thrown off too. 
 
 The sudden ejection of an electron, like the sudden 
 stoppage of one, is well calculated to excite those 
 vibrations in the ether discovered by Kontgen 
 known in the case of spontaneous radio-activity as 
 Gamma-rays. 
 
 Electric Theory of Matter. 
 
 A scheme or model for the construction of atoms 
 of different sorts of elementary substances, by means 
 of groups of electrons revolving in plane orbits round 
 a centre according to the law of direct distance, 
 together with some indication of the known spectral 
 
CH. xix.] INSTABILITY OF ATOM 187 
 
 and chemical properties of such substances, and the 
 deduction of a series or family likeness akin to 
 Mendelejeff's series on this hypothetical constitution, 
 is to be found worked out in a masterly manner 
 by Professor J. J. Thomson in the Philosophical 
 Magazine for March, 1904. 
 
 If at the present time there were other confirmatory 
 evidence of this mode of regarding the atom if it 
 were possible to understand what is meant by positive 
 electricity existing as a permeable sphere with a large 
 number of electrons sown in it it would be proper to 
 give a further account of this remarkable and attractive 
 theory; but inasmuch as the light which has quite 
 recently fallen upon the whole subject is of a flicker- 
 ing and undecided nature, tending somewhat in the 
 direction of confusion and uncertainty rather than con- 
 firmation of this promising but still necessarily vague 
 hypothesis see Chaps. XV. and XVII. and Chap. 
 XX. I think it better to leave its further discussion 
 and development to a future time, and meanwhile 
 await further theoretical and experimental evidence. 
 For it is neither theory alone nor experiment alone 
 which can be of service in this matter : progress 
 must be achieved by a combination of the two, 
 welded together by genius ; and it is just this 
 combination of theory and experiment ingenious 
 experiment combined with advanced mathematical 
 theory to which of late years all the finest advances 
 in physical science have been due. 
 
CHAPTER XX. 
 
 DIFFICULTIES CONNECTED WITH THE ELECTRIC 
 THEORY OF MATTER. 
 
 1. Concerning the formation of Spectrum lines. 
 
 LORD RAYLEIGH has pointed out, in the Phil. Mag. 
 for January, 1906, that if the radiation from atoms is 
 due to shock and recovery, the series of vibrations 
 that would be obtained would show a simple relation 
 between the squares of the frequencies, as is th case 
 with plates and bells and other disturbed elastic 
 vibrators, and not between the simple frequencies 
 themselves ; whereas the spectrum observations of 
 Rydberg, and of Kayser and Runge, show that 
 simple expressions for the first power of the 
 frequency, and constant differences of frequency 
 among a series of lines, are really applicable to 
 the facts. 
 
 Waves of this observed kind would be emitted by 
 electrons which radiate by reason of their unper- 
 1 turbed orbital motion, or other regular concomitant 
 of the constitution of the atom, but would not be 
 the result of oscillatory recovery from disturbance 
 of equilibrium. 
 
 The natural frequencies of an undisturbed rotating 
 ring of corpuscles, for instance, would be functions of 
 
H. xx.] ELECTRIC THEORY OF MATTER 189 
 
 the angular velocity and of the number of corpuscles 
 in the ring, as well as of other constants. 
 
 (Thus, for instance according to the paper men- 
 tioned near the end of last chapter the frequencies 
 of emission possible to two rotating corpuscles- 
 each of mass m and charge e, rotating with angular 
 velocity inside a spherical mass of positive charge 
 Ne and radius b will be the following six values, 
 corresponding to their six degrees of freedom : 
 
 0, w t c, c-w, o + w, ,/(3c 2 + 2 ), 
 where we have written Ne 2 //cmfr 3 as c 2 . 
 
 The frequencies c and o> belong to vibrations 
 perpendicular to the plane of the orbit : the others 
 are in that plane. 
 
 It may be noted that on the hypothesis of uniform 
 distribution of positive electricity of density p 
 throughout the sphere, the meaning of Ne/6 3 is f irp ; 
 and that c 2 is the ratio of this quantity to the electro- 
 chemical equivalent of an electron, in electrostatic 
 measure. The numerical value of c/J'N is approxi- 
 mately 10 16 , so that c corresponds to high ultra-violet 
 radiation. 
 
 For three corpuscles there should be nine degrees 
 of freedom : six in the plane, and three perpendicular 
 thereto. The corresponding frequencies are 
 
 0, 0), C, -C, V^ + o, 2 ), 0) + ^{^(SC 2 -O) 2 )}. 
 
 When there is no rotation, in each of the two cases 
 considered, three of the frequencies become equal, 
 and two vanish.) 
 
 Ordinarily, however, the constitutional radiation is 
 excessively weak, barely perceptible ; and it is known 
 that the radiation which emits light and produces a 
 spectrum is the result of violence and chemical clash 
 that it requires something of the nature of collision 
 
190 ELECTRIC THEORY OF MATTER [CH. xx. 
 
 to bring it out. But then anything in the nature of 
 collision would give a series of vibrations characterised 
 by the square of the frequency. Hence there is a 
 difficulty. 
 
 The difficulty seems to be capable of being over- 
 come by the suggestion already made on page 182 
 that during the chemical collision in question, 
 the perturbation is of the nature of a disturbance 
 of the centre of gravity of a revolving system. 
 Such an eccentricity, or any other destruction of 
 symmetry, would at once develop strong radiating 
 power; but it might nevertheless leave the harmonic 
 constituents, and peculiarities of the radiation, to be 
 governed by the simple frequency law appropriate 
 to the revolving constituents, rather than to the 
 squared frequency law appropriate to their elastic 
 recovery from vibration. In other words, the fact 
 of considerable radiation would be due to the 
 collision, but the land of radiation emitted would be 
 due to the previously existing constitution, upon 
 which the disturbance had now conferred temporary 
 radiating power of considerable magnitude, tem- 
 porary, because the radiation itself must speedily 
 exhaust the energy of the disturbance and soon 
 restore the pristine condition. 
 
 It may seem an open question whether a disturbance 
 of centre of gravity would allow quiet revolution to 
 continue as before, or whether it would not precipitate 
 a catastrophe. Simple mechanical considerations show, 
 however (Phil. Mag., March, 1904, p. 264), that 
 when the law of force is the direct distance, as it is 
 inside the hypothetical sphere of positive electricity, 
 no such calamity is to be expected ; but that, on the 
 contrary, a triangle or other group of corpuscles, no 
 matter how much displaced provided that they are 
 
CH. xx.] ELECTRIC THEORY OF MATTER 191 
 
 not displaced so as to reach the boundary of the 
 enclosing sphere will continue to rotate round their 
 common centre of gravity in the same relative position 
 as before; while this will revolve, on its own account, 
 round the centre of the enclosing sphere. Such a 
 displaced group being virtually a solitary though 
 compound corpuscle will now be endowed with great 
 radiating power. 
 
 On the fairly verified hypothesis that the mass 
 of a corpuscle is wholly electrical, it is of interest 
 to interpret the constant c further ; it has dimensions 
 of a frequency ; for 
 
 Ne 2 
 c 2 = ^, while m = 
 
 So 
 
 2V 
 
 v I! 
 or c = 
 
 Taking b as of atomic and a as of electronic 
 dimensions, this becomes numerically 
 
 y I AlO 
 
 c= *.8 V( N x !0~ 5 ) = lO'VW P er second, 
 
 where, since Ne measures the positive charge, N is 
 practically the total number of corpuscles contained 
 in the atom : not the number contained in any one 
 ring of it. 
 
 A compound satellite will rotate round the centre 
 of force with the same angular velocity as if it were 
 simple, for its mass and charge are increased in the 
 same proportion ; there is no concentration of the 
 charges into a single point, such as would be required 
 to increase the mass beyond the simple multiple. 
 
192 ELECTRIC THEORY OF MATTER [CH. xx. 
 
 A paper by Prof. Jeans, now of Princeton, N.J., in 
 -continuation of the discussion raised by Lord Rayleigh, 
 is to be found in the Philosophical Magazine for 
 April, 1906 ; also another paper in November, 1901. 
 
 2. Attempt to determine the number of effective 
 corpuscles in an Atom. 
 
 It is premature to do more than briefly refer to the 
 remarkable attempt made by Professor J. J. Thomson, 
 in the Philosophical Magazine for June, 1906, to 
 bring forward three lines of argument which tend to 
 show, on experimental grounds, that the number of 
 electrons in an atom is comparable with its atomic 
 weight, reckoning hydrogen as unity. It seems an 
 improbable result ; but the only way to get round it 
 is either to question the validity of the experiments 
 and the theory applied to them, or else to realise that 
 what is being measured is, not the total number of 
 electrons, but the number of free or available or 
 peculiarly constituted electrons. Cf. p. 162. 
 
 One of the arguments may be simplified as follows : 
 
 If the atom is composed of positive and negative 
 electricities, these constituent charges will tend to be 
 separated, against their mutual attraction, when sub- 
 jected to an external electric field such for instance 
 as the field existing in a wave of light ; and since 
 a light- wave is large compared with an atom, there 
 will be time for a certain amount of this separation 
 to be effected by each pulse. Accordingly the wave 
 will be as it were " loaded " by the electric charges, 
 its velocity of propagation will be reduced, and 
 refraction will occur. 
 
 But the amount of loading, that is, the amount of 
 effective shear or alternating separation of the two 
 
UNIVERSITY 
 
 CH. xx.] DIFFICULTIES 193 
 
 electricities, will depend on their masses ; and if the 
 mass of either the positive or the negative electricity 
 were zero or very small, it would be shifted completely, 
 however short the time. Accordingly a short wave 
 would then be retarded just as much as a long one, 
 that is to say, there would be no discrimination of 
 waves, and therefore no dispersion. The amount of 
 dispersion actually experienced will therefore furnish 
 a measure of the relative inertia of the two kinds of 
 electricity in an atom. 
 
 The only substance to which this theory of refraction 
 and dispersion can apply, will be one whose atoms act 
 individually or in isolated manner ; that is to say, they 
 must be gases, the more perfect the better. Now the 
 dispersive power of hydrogen has been measured, and 
 is not zero ; consequently there must be some mass 
 both in the positive and in the negative electricity 
 which hypothetically constitute an atom of hydrogen, 
 and the measured amount of dispersion will enable us 
 roughly to say what the smaller mass may be. The 
 result is, that if M is the aggregate mass of the 
 carriers of positive electricity, and nm the mass of 
 the carriers of negative electricity, n being their 
 number so that the mass of the whole atom is 
 M + mn we get, with the aid of Ketteler's measure- 
 ments for the refractive index of hydrogen for light 
 of different wave-lengths, 
 
 M 1 
 
 =1 approximately. 
 
 n 
 
 This shows that for a hydrogen atom n is approxi- 
 mately 1 (and it has to be a whole number) ; and it 
 also shows that M is not small compared with nm : in 
 fact that it is much bigger, which is an unexpected 
 and puzzling result. 
 
194 ELECTRIC THEORY OF MATTER [CH. xx. 
 
 The other lines of experimental argument seem to 
 be confirmatory. The second one deduces, from the 
 energy of the Kontgen radiation which is scattered by 
 gases, as measured by Barkla of Liverpool, that mole- 
 cules of air each contain approximately 25 or 28 
 corpuscles ; which again corresponds to the molecular 
 weight of the chief ingredient. 
 
 The third argument is based on the absorption of 
 beta rays by metals ; wherefrom it is deduced that 
 the number of corpuscles liable to be encountered in 
 each atom is nearly equal to the conventional atomic 
 weight of the metal on the hydrogen scale. 
 
 This remarkable paper is the most serious blow yet 
 dealt at the electric theory of matter, at least in its 
 simpler and cruder form ; but modes of getting round 
 it are fore- shadowed in Chaps. XV. and XVII. 
 
CHAPTEK XXL 
 
 VALIDITY OF OLD VIEWS OF ELECTRICAL 
 PHENOMENA. 
 
 Now that the doctrine of electricity (at least of 
 negative electricity) as located in small charges or 
 charged bodies is definitely accepted, and now that a 
 current can be treated as the locomotion of actual 
 electricity, it may seem as if some doubt were thrown 
 upon the doctrine, which a little time ago was spoken 
 of as a " modern view," that the energy of an electric 
 current resides in the space round a conductor. 
 There is no inconsistency, however. The whole of the 
 fields of an electron are outside itself; it is in its 
 fields that its energy resides, and it is in the space 
 round it that energy is conveyed when it moves ; for 
 the ether in that space is subject to the co-existence 
 of an electric and a magnetic field. So, also, its 
 inertia resides in space round it, for it is accounted 
 for by the reaction experienced when its magnetic field 
 changes, that is, when its motion, is accelerated. 
 
 In dealing with the inertia of matter it is commonly 
 supposed that the inertia resides in the matter itself : 
 whereas electrical inertia is known to reside in the 
 space round the nucleus. Yet we have been emphasis- 
 ing and supporting the view that material inertia and 
 electrical inertia are essentially one and the same. 
 
196 ELECTRICAL PHENOMENA [CH. xxi. 
 
 Is there no inconsistency here ? 
 The appearance of inconsistency vanishes when we 
 come to calculate and realise how extremely local and 
 concentrated the intense part of the field of an electron 
 is. There is a sense in which it can be said that a 
 moving body, for instance a vortex ring, disturbs the 
 whole atmosphere ; but any perceptible disturbance 
 resides very near the ring. So it is with an electron. 
 The magnetic field falls off inversely as the square of 
 the distance from the moving nucleus ; hence at a 
 distance far less than a micro-millimetre, less even 
 than the size of an atom, it is quite inappreciable. 
 The whole magnetic field on which its inertia depends 
 lies practically very close to the electron itself : it is 
 just its extremely small size that enables this concen- 
 tration to be possible, and even in a closely packed 
 mercury atom there is practically no encroachment of 
 the field of one electron on its neighbour's. They are 
 all independent, each with its own inertia, almost 
 isolated from the others : for if it were not so, the 
 mass of a body in close chemical combination would 
 not continue constant, but would diminish. Whether 
 it does diminish, in the least degree, is a question 
 perhaps worthy of attack.* Minute effects in this 
 direction have been announced, by Heydweiler and by 
 Landolt ; but the results are doubtful. 
 
 The momentum of a moving charge at ordinary 
 speeds is simply inversely as the radius of the sphere 
 which holds it, as stated in Chap. II. , but the 
 localisation of this momentum, which is the point we 
 are now considering, may be realised approximately 
 as follows: 
 
 The momentum depends on the co-existence and 
 product of the electric and magnetic fields. Each 
 
 *Cf. Rayleigh, British Association Belfast, 1902. 
 
CH. xxi.] VALIDITY OF OLD VIEWS 197 
 
 field varies inversely as the square of the distance 
 from the moving charge ; and their vector product is, 
 as regards direction, perpendicular to the radius 
 vector at any point. It is proportional, at ordinary 
 speeds, to the sine of the angle between the radius 
 vector and the direction of motion ; while in magni- 
 tude it falls off as the inverse fourth power of the 
 distance. All this can be realised by common sense 
 with very little trouble. 
 
 So, then, take a moving electron, and consider the 
 distribution of its momentum in the space round 
 it. Between its surface and a space of a hundred 
 times its diameter, 99 per cent, of its momen- 
 tum is contained ; because, to reckon it, we should 
 have to integrate the factor 
 
 But a hundred times the diameter of an electron 
 is only 10~ n centimetre, that is to say, the thousandth 
 part of the diameter of an atom. So, within the 
 boundary of an atom, which is a hundred-thousand 
 times an electron's diameter, there is practically none 
 of its momentum not included. 
 
 And even in one of the comparatively closely 
 packed atoms, e.g. in a platinum or mercury atom, 
 the overlapping of momentum for each constituent is 
 extremely small, since their average space apart / 
 is some thousand times the size of each constituent 
 electron. 
 
 Consequently the assertions that an electric current 
 is a transfer of electrons, and that the energy of a 
 current travels in the space surrounding the moving 
 electricity, are statements not inconsistent with each 
 other. Nor are the statements inconsistent that the 
 
198 ELECTRICAL PHENOMENA [CH. xxi. 
 
 mass of a body resides in its atoms, and that inertia 
 or momentum is a property due to the self-inductive 
 influence of the electromagnetic field surrounding a 
 moving electric nucleus. 
 
 The same sort of thing may be said of the way in 
 which a current is propelled. The pace of progression 
 of electrons through a solid may be considerable, see 
 next section, but it is very far below the pace at which 
 a telegraphic signal travels along a wire. They must 
 be propelled by a lateral action, transmitted through 
 the ether with the speed of light appropriate to the 
 surrounding insulator, by some arrangement which 
 "Modern Views" symbolised in the form of cog- 
 wheels : they cannot be impelled by end thrust. The 
 vf electric current is a more material entity, or has a 
 more nearly material aspect, than was thought 
 probable a little while since ; but all that was taught 
 about its mode of propulsion, and the diffusion of the 
 propelling force from outside to inside, through 
 successive layers, as it were, of the wire all that 
 was taught about the paths by which the energy 
 travels and arrives at point after point of the 
 conductor, there to be dissipated as heat, remains 
 true. 
 
 Number of Ions in Conductors. 
 
 The immense number of electrons that are necessary 
 to make up the mass of a piece of platinum, or of a 
 lump of matter like the earth, can readily be 
 estimated ; so, also, it is easy to imagine . that an 
 enormous number must be travelling in order to give 
 customary strengths of current such as can readily 
 pass through a liquid. 
 
 Through a gas, a limit is soon found to the available 
 number ; and accordingly the conductivity of an 
 
CH. XXL] MODIFICATION OF OLD VIEWS 199 
 
 ionised gas falls off' if we call upon it to carry more 
 than a certain current, called the saturation current. 
 See investigations by Town send and others briefly 
 referred to in Chapter VII. But I am not aware of 
 any experimental indication of such a limit in solids 
 or liquids, at present. 
 
 In solids the pace of travel is unknown, though it 
 has been ingeniously surmised, and is thought to be 
 very great ; considerations of centrifugal force would 
 make the speed of each electron during an atomic 
 encounter equal to e/J(Kmr) or about 10 8 centimetres 
 per second ; views based on Maxwell's theorem about 
 equal distribution of energy among the particles of 
 mixed gases suggest 10 7 for the average speed of 
 electrons at ordinary temperatures in a solid where 
 they are free, that is, a hundred kilometres or sixty 
 miles per second; though since each particle is subject 
 to constant changes of direction, this is by no means 
 the pace of straightforward progression. But in 
 liquids they are attached to atoms, and the pace 
 of progression is known both theoretically and 
 experimentally with considerable accuracy, and is 
 comparable to an inch an hour for customary 
 gradients of potential. 
 
 The total current is neu ; and to give a unit c.g.s. 
 current at so low a speed we can reckon how many 
 ions there must be. For e= L0~ 20 electromagnetic 
 units; so if we take u=W~ z centimetre per second, 
 the number of ions engaged in conveying the 
 c.g.s. unit of 10 amperes is n=10 23 . But, after all, 
 that is nothing very great ; it is only about the 
 number of atoms in a cubic centimetre of liquid. 
 By applying a greater gradient of potential the ions 
 can be made to move faster. By gradually narrowing 
 down the section of a liquid conductor under a given 
 
200 ELECTRICAL PHENOMENA [CH. xxi. 
 
 gradient of potential, it might be possible to get 
 evidence of an approach to a saturation-current- 
 density in liquids. The observed accuracy of Ohm's 
 law* under such conditions, however, is against this 
 experimental possibility. 
 
 Conclusion. 
 
 The subject is very far from exhausted, but I 
 must not attempt to cover more ground. The 
 most exciting part of the whole is the explanation of 
 matter in terms of electricity, the view that electricity 
 is, after all, the fundamental substance, and that what" 
 we have been accustomed to regard as an indivisible 
 atom of matter is built up out of it ; that all atoms- 
 atoms of all sorts of substances are built up of the 
 same thing. In fact the theoretical and proximate 
 achievement of what philosophers have always sought 
 after, viz., a unification of matter is offering itself 
 to physical enquiry. But it must be remembered 
 that although this solution is strongly suggested 
 it is not yet a completed proof. Much more 
 work remains to be done before we are certain that 
 mass is due to electric nuclei. If it is, then 
 we encounter another surprising and suggestive 
 result, namely that the spaces inside an atom are 
 enormous compared with the size of the electrical 
 nuclei themselves which compose it ; so that an atom 
 ,- < can be regarded as a complicated kind of astronomical 
 system, like Saturn's ring, or perhaps more like a 
 
 1 nebula; with no sun, but with a large number of equal 
 bodies possessing inertia and subject to mutual 
 
 ' electric attractive and repulsive forces of great mag- 
 nitude, to replace gravitation. The radiation of a 
 
 * FitzGerald and Trouton, Brit. Assoc. Reports, 1886, 1887, 1888. 
 
CH. XXL] VIEWS OF ATOMS 201 
 
 nebula may be due to shocks and collisions somewhat 
 like the X-radiation from some atoms. 
 
 The disproportion between the size of an atom and 
 the size of an electron is vastly greater than that 
 between the sun and the earth. If an electron is 
 depicted as a speck one-hundredth of an inch in 
 diameter, like one of the full-stops on this page for 
 instance, the space available for the few hundred or 
 thousand of such constituent dots, to disport them- 
 selves inside an atom, is comparable to a hundred-feet 
 cube ; in other words, an atom on the same scale 
 would be represented by a church 160 feet long, 80 
 feet broad, and 40 feet high, in which therefore the 
 dots would be almost lost. And yet on the electric 
 theory of matter they are all of the atom that there 
 is ; they " occupy " its volume in the sense of keeping 
 other things out, as soldiers occupy a country ; they 
 are energetic and forceful though not bulky ; and in 
 their mutual relations they constitute what we call 
 the atom of matter; they give it its inertia; they 
 enable it to cling on to others which come within 
 short range, with the force we call cohesion ; and by 
 excess or defect of one or more constituents they 
 exhibit chemical properties and attach themselves 
 with vigour to others in like or rather opposite case. 
 
 That such a hypothetical atom, composed only 
 of sparse dots, can move through the ether without 
 resistance is not surprising. They have links of 
 attachment with each other, but, so long as the 
 speed is steady, they have no links of attachment 
 with the ether ; if they disturb it at all, in 
 steady motion, it is probably only by the simplest 
 irrotational class of disturbance which permits of 
 no detection by any optical means.* Nor do 
 
 See Lodge, Phil Trans. 1893, vol. 184, pp. 750-754; also vol. 189, p. 166. 
 
202 ELECTRICAL PHENOMENA [CH. XXL 
 
 they tend to drag it about. All known lines of 
 mechanical force reach from atom to atom, they never 
 terminate in ether ; except indeed at an advancing 
 wave front. At a wave front is to be found one 
 constituent of a mechanical pressure of radiation whose 
 other constituent acts on the source. This is an 
 interesting but essentially non-statical case, and it 
 leads away from our subject. 
 
 As to the nature of an electron, regarded as an 
 ethereal phenomenon, it is too early to express any 
 opinion. At present it is not clear why a positive 
 charge should cling so tenaciously in a mass, while 
 an outstanding negative electron should readily 
 escape and travel free. Nor is the nature of gravi- 
 tation yet understood. When the electron theory 
 is complete, to. the second order, or some higher even 
 order, of small quantities it is complete now to the 
 second order if electrons may be treated as geo- 
 metrical points, it is hoped that the gravitative 
 property also will fall into line and form part of 
 the theory ; at present it is an empirical fact which 
 we observe without understanding ; as has been 
 our predicament not only since the days of Newton 
 but for centuries before : though we did not, before 
 Newton, know its importance in the cosmic scheme. 
 
 Attention has hitherto been chiefly concentrated 
 on the freely moving active negative ingredient, the 
 more sluggish positive charges are at first of less 
 interest, but the behaviour of electrons cannot be 
 fully and properly understood without a knowledge 
 of the nature and properties of the positive con- 
 stituent too. According to Larmor, positive charge 
 must be the mirror-image of negative charge, in 
 essential constitution. 
 
 The positive electron has not, so far as I know, been 
 
CH. XXL] ELECTRICITY AND MATTER 203 
 
 as yet observed free. Some think it cannot exist in 
 a free state, that it is in fact the rest of the atom of 
 matter from which a negative unit charge has been 
 removed ; or, to put it crudely that " electricity " 
 repels "electricity," and "matter" repels "matter," 
 but that Electricity and Matter in combination form 
 a neutral substance which is the atom of matter as we 
 know it. Such a statement is an extraordinary and 
 striking return to the views expressed by that great 
 genius, Benjamin Franklin. On any hypothesis those 
 views of his are of exceeding interest, and show once 
 more the kind of prophetic insight which we have 
 had occasion to notice in discoverers before (Appendix 
 H and Chap. IV.). Undoubtedly we are at the \ 
 present time nearer to the view of Benjamin 
 Franklin than men have been at any intervening 
 period between his time and ours. 
 
 The view that an atom is composed of an equal 
 number of interleaved or inter-revolving positive and 
 negative electrons that view is not Franklin's ; nor 
 is it as yet anything but a guess. To make it more, 
 work must be done upon the nature and properties of 
 the positive charge ; and the positive electron, if it 
 exists, must be dragged experimentally to light. 
 
 Especially must the inner ethereal meaning both of 
 positive and negative charges be explained : whether 
 on the notion of a right-and-left-handed self-locked 
 intrinsic wrench-strain in a Kelvin gyrostatically- 
 stable ether, elaborated by Larmor,* or on some 
 hitherto un imagined plan. And this will entail a 
 quantity of exploring mathematical work of the 
 highest order. 
 
 *See Ether and Matter, p. 326 ; or Phil. Trans. 1894, pp. 810, 811, 
 and 1897, pp. 209-212. 
 
APPENDIXES. 
 
 APPENDIX A. 
 Calculation of the Inertia of an Electric Charge. 
 
 Let a spherical conductor of radius a, carrying a 
 charge of electricity, move forward with moderate speed 
 u\ meaning by moderate speed anything distinctly less 
 than the speed of light: it constitutes a current element 
 of magnitude eu, and its circuit is closed by displace- 
 ment currents in the surrounding dielectric. For electric 
 lines of force arise in the medium in front, and subside 
 in the medium behind, and so a displacement of electricity 
 takes place from fore to aft, to compensate the motion 
 forward ; and the lines of displacement are identical with 
 the magnetic lines due to a short magnet. A charge 
 may be said to travel carrying its electrostatic lines 
 with it, or it may be said to be constantly generating an 
 electrostatic field in front and destroying one behind. 
 
 When an electric field thus moves, partly laterally, it 
 generates a magnetic field in the present instance in 
 circular lines round the line of motion; for the moving 
 charge is an element of a linear current. The generation 
 of these magnetic lines acts so as to oppose the current 
 which produced them ; though so long as they continue 
 steady they exert no effect on it. When they subside, 
 
APR A.] CALCULATION OF INERTIA 205 
 
 however, they tend to prolong the current which main- 
 tained them. Consequently, if the moving charge (or 
 current) tries to stop, its retardation meets with 
 obstruction; it is constrained to persist by the sub- 
 sidence of the magnetic field which its motion excited 
 and maintains. Its velocity is not resisted, there is 
 nothing equivalent to friction, but its acceleration + or 
 is obstructed, an effect precisely analogous to inertia. If 
 it is at rest it will need force to start it, and if it is in 
 motion its motion will persist, even against force, for a 
 time. 
 
 The charge acts, therefore, as if it had inertia, and we 
 can proceed to calculate its amount. 
 
 While moving it is a current, and will be surrounded 
 by rings of magnetic force, whose intensity, at any point 
 with polar co-ordinates r, 0, referred to the line of motion 
 as axis and the moving charge as origin, will be the 
 quite ordinary expression (with eu for the current-element 
 
 instead of Cds) . * 
 
 TT eu sin 6 
 ti = - = . 
 
 r 2 
 
 The ordinary expression for the electrostatic force at 
 the same point is 
 
 (see note at end of Chapter I. with reference to the inser- 
 tion of K) and if the motion is slow this value will be 
 preserved; but if it is rapid the electric field gets weaker 
 along the axis and stronger equatorially, having been 
 shown by Mr. Heaviside (Philosophical Magazine, April, 
 1889) to be given by the following expression 
 
 where v is the velocity of light. 
 
206 CALCULATION OF INERTIA [APP. A. 
 
 The strength of the magnetic field will be similarly 
 modified in this case ; but the simplest mode of stating that 
 is to express it in terms of E, and to say that always 
 
 H = K^U sin 0. 
 
 The rate of transmission of energy will be the vector 
 product of E and H ; and the whole magnetic energy, that 
 is the whole kinetic energy due to the current, i.e., due 
 to the motion will be obtained by integrating the ordinary 
 expression yuH 2 /87r, all over space outside the charged 
 sphere, viz., from a to oo all round. Its charge is assumed 
 to be superficial, so that no energy is inside. In the general 
 case this expression is a little long, but in the most im- 
 portant case, when the speed of motion u is decidedly less 
 than the speed of light v, it is quite simple, and the 
 working may as well be given: 
 
 Kinetic energy 
 
 f fsi 
 J J J_ 
 
 COS 2 0-1 
 
 Comparing this with mechanical kinetic energy, 
 we see that the charge on the sphere confers upon it 
 additional kinetic energy, as if its mass were increased on 
 account of the charge by the amount 
 
 2/ze 
 m= 
 3a 
 
 This may also be written 
 
 2 
 
 o~2 
 
 3t> 2 
 
 2 /UiK g 2 2 e 2 
 ra = ^ = o~2 e = ^~9 x charge x potential, 
 
 2 2 
 
 Q 
 
 or, -r rai> 2 = the electrostatic energy of the charge : 
 
 supposed a spherical shell of electricity. 
 
 
APR A.] CALCULATION OF INERTIA 207 
 
 In other words, the mass equivalent to the charge is such 
 that if it were a piece of matter with constant inertia 
 travelling at the speed of light, its kinetic energy would 
 be half as great again as the potential energy of the 
 electric charge when standing still. 
 
 APPENDIX B. 
 The Electric Field due to a Moving Magnet. 
 
 If a short bar magnet or uniformly magnetised sphere 
 (its moment M being the intensity of magnetisation x the 
 volume of the sphere) moves along axially that is in the 
 direction of its magnetisation with velocity u, it generates 
 circular lines of electric force all centred upon its axis, 
 much as a moving charge generates circular lines of 
 magnetic force. If there is a conducting path round 
 any such circle, then the motion of a magnet along its 
 axis will generate a current in it; but if there be no 
 conductor, the motion will only result in an electric dis- 
 placement which subsides when the magnet stops. 
 
 The intensity of the magnet's field at any point along 
 its axis is well known to be 2M/r 8 ; at any point on its 
 equatorial plane it is M/r 3 ; and in any intermediate 
 direction it is, as regards magnitude alone 
 
 All this holds for the moving as for the stationary magnet, 
 provided its speed does not approach that of light. 
 The electric force at the same point is 
 
208 CALCULATION OF INERTIA [APP. B. 
 
 The electrostatic energy resulting will be the integral of 
 AcE 2 /87r everywhere outside the moving magnetised sphere 
 of radius a, viz. 
 
 Energy = 5 1 1 1 ( o ) sin 2 cos 2 $ dr.rdO.r sin dd> 
 
 ^ J STrJJJV r 3 / 
 
 _AcM 2/ & 2 _ M 2 /'M'X 2 
 5<z 3 ~~ Spa? \v/ ' 
 
 The displacement acts like an elastic strain set up in 
 the dielectric, storing the above energy statically; and so 
 long as the magnet continues moving steadily the electric 
 displacement exerts no force upon it. But acceleration 
 will be resisted; for if the magnet begins to go faster it 
 sets up more displacement, and the act of setting this up 
 constitutes a transient current, which opposes the motion 
 as long as the acceleration continues, but dies out the 
 instant the motion becomes steady again. 
 
 Conversely if the motion of the magnet began to 
 slacken, the electric strain would begin to subside, and 
 its subsidence would constitute an inverse transient current 
 which would assist the motion, i.e., oppose the slackening. 
 In other words, the variations of the circular electric strain 
 in the surrounding medium confer upon a moving magnet 
 a spurious or apparent momentum, in addition to its real 
 mechanical momentum , and thus the elastic strain itself 
 may be said to represent a spurious or apparent inertia 
 due to magnetisation, in addition to any real mechanical 
 inertia which the body holding the magnetism may itself 
 possess. And the amount of this extra inertia is 
 
 _2*M 2 = 2 M 2 8 
 = 5a 3 5 ,uaV 15 
 
 = 5"^~' 
 
APR B.] DIMENSIONS 209 
 
 where I is the intensity of magnetisation, and H the 
 intensity of the field, inside the substance of a uniformly 
 magnetised sphere of radius a and magnetic moment M. 
 The equivalent mass moving with the velocity of light 
 would therefore have an energy equal to two-fifths of the 
 intrinsic energy of the magnetised sphere. 
 
 APPENDIX C. 
 On Electricity and Gravitation and Dimensions. 
 
 Referring back to an article of mine in the Philosophical 
 Magazine for November, 1882, page 358, we find the 
 fundamental and necessary relation between constants 
 stated thus, where M shall stand for magnetic pole and y 
 for Cavendish's gravitation constant 
 
 F being force and I being length. 
 
 If it is now going to turn out that a mass is composed 
 of electric charges, it might seem as if e and m were 
 quantities of the same nature, and were only numerically 
 connected ; whence it would follow that AC and y were of 
 similar kind. In other words, Faraday's dielectric constant 
 would become closely related to Cavendish's gravitation 
 constant, and weight as well as mass would be traced to 
 electricity ; but such a deduction is unwarranted, there is 
 nothing to prevent essentially different properties of the 
 ether being involved in the two kinds of force gravitative 
 and electric. 
 
 As to the nature of the gravitation constant itself, we 
 have 
 
 _F 2 _ I 3 v 2 _sq. of velocity _ energy/mass 
 ^ ~~ m 2 ~~ mP ~" mjl ~~ linear density ~~ mass/length' 
 L.E. o 
 
210 GRAVITATION [APR a 
 
 It is clear that if gravitation is in any sense of electric 
 origin it must be a second order disturbance, or some 
 higher even order, superposed upon the main electric effect, 
 and be independent of sign. It would, in fact, depend 
 upon e*. For the gravitative force between two electrons 
 at distance r would be 
 
 - _ 
 
 r i-7 T z- 
 
 The electric force between the same two electrons at the 
 same distance is 
 
 &m 
 
 F 2 = 2 - 
 
 KT 2 
 
 Therefore the ratio of the gravitative to the electric force 
 at any distance is constant and equal to 
 
 where F is the electric force between two spherical 
 electrons in contact, and v is the velocity of light. 
 Numerically this ratio of the two forces is 
 
 FI _ /m\ 2 _ 1 / _1_\ 2 _ -, _ 42 
 
 F 2 ~ Kfy \eJ ~9xl0 20 xl-5xl0 7 \10V " 
 
 so the electric force exceeds the gravitative as much as the 
 globe of the earth exceeds in bulk an ultra-microscopic 
 object. 
 
 When there is an agglomeration of electrons of opposite 
 sign, their electric influence at a distance disappears, but 
 their gravitative potential will be proportional to the sum 
 of the squares of the charges. So with 10 21 mixed electrons 
 in each of two bodies, at any distance apart, the gravitative 
 force between them will equal the electric force between 
 two single electrons at the same distance. 
 
 In my 1885 Report to the British Association on Electro- 
 lysis, page 745, the following statement is made : If the 
 
APR c.] DIMENSIONS 211 
 
 opposite electricities were extracted from a milligramme of 
 water and given to two spheres one mile apart, those two 
 spheres would attract each other with a force equal to the 
 weight of 12 tons. 
 
 APPENDIX D. 
 Dimensions of e/m Ratio. 
 
 The reciprocal of the electrochemical equivalent of a 
 substance, e/m, may be expressed as regards dimensions in 
 several ways, one of which exhibits it as a certain large 
 numerical multiple of >v/(:y), the geometric mean between 
 Faraday's dielectric constant and Cavendish's gravitation 
 constant. For hydrogen, this numerical multiple is of 
 the order 10 18 ; for silver 10 16 . 
 
 Another way is obtained by writing 
 
 whence it follows that 
 
 m/u.e 
 
 centimetres\ 
 
 -, / -, -. . //c 
 
 and so em can be expressed in A /( - 
 
 \ V grammes/ 
 
 The artificiality of these dimensions is due to the fact 
 that e and m have been conventionally measured in 
 different ways ; m is measured by ratio of applied external 
 force to acceleration, while e, is measured by repulsive 
 force self-exerted on a similar charge at given distance. 
 
 If we express //, as a density (see "Modern Views of 
 Electricity," Appendix p), the electrochemical equivalent 
 comes out as expressible in grammes per square centimetre, 
 that is to say a surface density. 
 
212 SATURATION [APR D. 
 
 It is noteworthy that while ^/(/c/x) is of the same 
 dimensions as 1/v, ^/(K~/) corresponds to 1/e, where e is 
 an electrochemical equivalent. 
 
 APPENDIX E. 
 Electric Saturation, etc. 
 
 In my Report on Electrolysis to the British Association 
 for 1885 (see the Aberdeen volume, pp. 762, 763), I call 
 attention to the possibility that an atomic theory of 
 electricity would give rise to a maximum charge possible 
 on a given area. The maximum surface-density would 
 be attained when every atom was polarised so that its 
 atomic charge faced outwards; and for a solid or liquid 
 it would be very great. For the charge on each being 
 10 ~ 10 , and the number of atoms per square centimetre 
 being 10 16 , it follows that the maximum surface density 
 possible is (r=10 6 electrostatic units per square centimetre. 
 The corresponding gradient of potential would be 4?ro-= 10 7 , 
 or 3,000 megavolts per centimetre; and the corresponding 
 tension would be 27r<7 2 = 6 x 1() 12 c.g.s. = 40,000 tons to the 
 square inch. Of course no dielectric would stand this 
 pressure, but absolute vacuum might. 
 
 In practice, therefore, it follows that when a surface is 
 charged highly, only an exceedingly small percentage of 
 the molecules are polarised with their charges facing 
 outwards. For instance, common air breaks down when 
 the tension rises to a value 2-7n7 2 = J gramme per square 
 centimetre = 400 c.g.s. ; wherefore the maximum or in 
 ordinary air is 8 electrostatic units per square centimetre ; 
 and this quantity would be afforded by the facing outwards 
 of 10 11 molecules, or one in every hundred thousand of a 
 solid surface, or about a tenth per cent, of those in air. 
 
APR E.] ORBIT OF ELECTRON 213 
 
 It is shown on p. 760 of my 1885 B.A. Report on 
 Electrolysis, that a potential gradient of the order 1 volt 
 over molecular distance is sufficient to overcome atomic 
 attraction and effect decomposition in liquids. Any liquid 
 which is a conductor throws the whole applied stress on 
 to a molecular layer contiguous to an electrode, and accord- 
 ingly something of the order of a volt or two difference 
 of potential between electrodes in such a liquid is required, 
 and is sufficient, for decomposition. 
 
 APPENDIX F. 
 Size of Orbit of Radiating Electron. 
 
 Consider two electrons of opposite sign revolving round 
 each other with luminous frequency n at any distance r\ 
 or better, consider a free negative electron revolving round 
 a comparatively fixed equal positive charge attached to an 
 atom, at distance r. 
 
 The force between them is e 2 //cr 2 , so the acceleration is 
 
 But the acceleration is also expressible as 47rVr. There- 
 fore 
 
 which is " Kepler's third law " for the case, and indicates 
 that the distance at which luminous frequency is attain- 
 able is the atomic distance 10 ~ 8 centimetre; in other 
 words, that the electron is roaming over the surface 
 of the atom. If it got nearer to the centre of force 
 than this, without penetrating any of the attracting sub- 
 stance, it would have to revolve quicker ; and such rapid 
 
214 RADIATING ELECTRON [APP. F. 
 
 oscillations may be excited among the internal paired elec- 
 trons by shocks and collisions, or other perturbation. 
 
 The most important aspect of the above calculation 
 is that it corresponds with the hypothesis that the whole 
 of the mass of an electron is electric, and none of it 
 material or unexplained ; for it shows that a pure electron 
 is able to revolve at distances of the molecular order 
 with luminous frequency.* The square of the wave length 
 emitted is proportional to the cube of the radius vector ; 
 provided the plane of the orbit contains the centre of 
 force, otherwise there may be constrained motion -of 
 smaller amplitude, analogous to that of a conical pendulum. 
 
 APPENDIX G. 
 The Radiating Power of a Steadily Revolving Electron. 
 
 Consider an electron revolving as above (Appendix F) 
 in an orbit of atomic dimensions b with luminous frequency 
 ^ = a>/27r; and calculate its radiating power. 
 
 By considering separately the electric and magnetic 
 forces due to such a particle, at any point of space, and 
 then applying Poynting's theorem as to the convection 
 of energy wherever the two fields coexist, we get, as the 
 rate of transmission of energy past a point whose polar 
 coordinates, referred to centre and axis of orbit, are r, 0, 
 the mean value ^ 1 + cos s e ^ v 
 
 V ' STT r L 
 
 And integrating this all over the sphere of radius r we 
 get, as the total emission of energy per second 
 
 *See Lodge in The Electrician for March 12th, 1897, vol. 38, p. 644. 
 
APP. a] CALCULATION OF RADIATION 215 
 
 which may be written, with a as the radius, m the mass, 
 and u as the acceleration, of the revolving electron 
 
 man 2 
 
 where v is the velocity of light. 
 
 The fundamental expression for the amount of energy 
 emitted per second as waves in the ether, by a moving 
 charge e, was given by Larmor in Phil. Mag., December, 
 1897, page 512, so far as I know for the first time; 
 also in JZiher and Matter, page 227, namely 
 
 This agrees with the above calculation, since it = u 2 /b = bco 2 ; 
 u being acceleration. Now ju.e 2 may be taken as 10 ~ 40 
 gramme-centimetre, according to most recent measure- 
 ments; and in a circular orbit of radius r the acceler- 
 ation is 
 
 therefore the radiating power of a single electron, so 
 moving, is 
 
 9 ..,,2 9 y TO-* 
 
 w Ai= "9xio"> x 1Q46= 2 x 10 ~ 5 ergs per second - 
 
 But the total available energy possessed by the revolving 
 electron of linear dimensions a is only 
 
 namely its kinetic energy (for of course it cannot radiate 
 away or dissipate its electrostatic energy), and this 
 amounts to 
 
 1 0~ 40 
 
 -r, (2-7T x 5 x 10 U x 10- 8 ) 2 = 3 x 10- 13 ergs, 
 
 3xlO- 13 
 
216 RADIATION OF ELECTRON [APR a 
 
 its velocity being 3 x 10 7 centimetres per second, or one- 
 thousandth that of light. So if the electron were isolated 
 from any supply of energy, and if it could maintain the 
 pace, it would at this rate radiate away all its kinetic 
 energy in 10 ~ 8 of a second, that is to say in three or 
 four million revolutions. This may seem a rapid rate of 
 cooling, but it is not surprising for an isolated and 
 luminous atom : it is a Hertzian vibrator or emitter of 
 simple type. The number of revolutions which an 
 electron must make in one second, in order to emit 
 sodium light, is about 8000 times the number of seconds 
 which have passed since the Christian era. 
 
 We may express the ratio of the radiating power of a 
 single electron to its total kinetic energy, by the fraction 
 
 2<z/'iA 2 2a /0 , a ^ n -n- 
 I - ) = (27m) 2 = S7r 2 n ^- = 70 million per second. 
 v \u/ v A 
 
 In any large assemblage of atoms the radiation is not 
 free and unrestrained, nor is it unmaintained, like this ; 
 but it must always be considerable at anything like 
 luminous frequency, and it is proportional to the fourth 
 power of the frequency. At a frequency which emits a 
 wave ten times as long as a luminous wave, the radiating 
 power of a revolving electron is only one ten-thousandth 
 of that above calculated, but even so it is very significant ; 
 so there must be compensation of some kind or a substance 
 could not permanently exist. The criterion that a mole- 
 cule shall not be destroyed by radiation-losses is given in 
 the concluding sentence of Larmor's paper above quoted : 
 Phil. Mag., Dec., 1897. 
 
 The subject of radiation from a symmetrical group of 
 electrons was pursued above in Chapter XIX. 
 
 The radiating power of an electron suddenly stopped by 
 a collision is of course much greater than the above, and is 
 estimated in Chapter IX. To get copious Rontgen rays 
 
APR G.] HISTORICAL REMARK 217 
 
 the stopping distance must be comparable with the elec- 
 trons' own diameter; which accordingly accounts for the 
 extreme thinness and consequent penetrating character of 
 the emitted pulse. 
 
 APPENDIX H. 
 Faraday's Prophetic Nomenclature. 
 
 Students of the life of Faraday will remember that when 
 he discovered the rotation of the plane of polarisation by 
 a magnetic field applied to dense bodies in which light 
 travelled along the lines of force, wresting the secret from 
 nature by strong and pertinacious experimental research 
 that w r ould not be denied, though the time was as yet by 
 no means ripe for comprehension of the fact when it was 
 discovered he labelled his discovery in a fit of enthusiasm, 
 " The Magnetisation . of Light and the Illumination of 
 Magnetic Lines of Force " : a label which puzzled con- 
 temporaries for a long time. 
 
 It is difficult to see what meaning he can have attached 
 to, these phrases ; and for many years afterwards they 
 appeared unsuitable misnomers, indicating a foggy concep- 
 tion of his own discovery. 
 
 It is not likely that his state of mind was really at all 
 clear on the subject, and probably he would at a later stage 
 have been willing to plead guilty to a less than lucid mode 
 of conceiving the phenomenon ; which nevertheless always 
 specially pleased him, though when it was reduced to a 
 mere rotation of the plane of polarisation, it seemed to 
 many mathematicians and physicists to have lost its unique 
 and surprising interest. It must always be remembered, 
 however, that interest was never lost by either Lord Kelvin 
 or Clerk Maxwell, and that it was the chief fact which 
 
218 HISTORICAL REMARK [APR H. 
 
 incited Maxwell, many years later, to begin developing his 
 electro-magnetic theory of light. 
 
 But how do the titles strike us now ? Do they not 
 indicate some extraordinary unconscious insight, such as 
 is frequently experienced by a great discoverer in the 
 enthusiasm of discovery ? Remember that the Hall effect, 
 the Zeeman effect, the Aurora Borealis, and Faraday's 
 rotation are all closely connected with each other by 
 means of the electron theory. 
 
 In the cathode ray tube the flying electrons are deflected 
 by a cross magnetic field; or if they fly along the lines 
 they are twisted into a spiral path round them. In the 
 Aurora Borealis this effect is carried out in the upper 
 region of the air on a gigantic scale, and the earth's 
 magnetic "lines of force are illuminated" by flying elec- 
 trons from the sun entangled and guided by them. In the 
 Hall effect this same influence is felt by the slowly moving 
 crowd of electrons as they are handed on from one atom to 
 the next, causing a curvature of the current path in which 
 either positive or negative may predominate. In the Zeeman 
 effect the same cause operates on the revolving and vibrating 
 electrons, associated with a radiating atom and constituting 
 a source of light ; wherefore we may truly say that the 
 " light is magnetised," for the source of light is magnetised 
 directly, and the effect is impressed on and retained by the 
 light emitted, and is made visible by spectrum analysis. 
 
 The first intimation of that magnetic influence on light 
 which lies at the base of all these at first sight apparently 
 diverse phenomena was detected by Faraday in his slight 
 differential rotation of the plane of polarisation in one 
 direction or the other by a magnet, according as the posi- 
 tive or the negative element in the dense substance was 
 most affected. 
 
 Hence the title which he affixed to his discovery " The 
 
APP. H.] RADIUM 219 
 
 illumination of the lines of magnetic force and the magneti- 
 sation of light " may be regarded as a prophetic flash of 
 genius. 
 
 A not altogether dissimilar flash has already been 
 referred to, when Crookes hinted prematurely that in the 
 cathode rays we had something like corpuscular light, and 
 also like matter in a fourth state, neither solid, liquid, nor 
 gaseous. For, whether quite right or not, he was far 
 more right than the critics of those days who presumed 
 to deride him. 
 
 APPENDIX J. 
 On the /2-rays from Radium. 
 
 Magnetic deflexion of Beta-rays. 
 
 The following diagram illustrates the spreading out 
 into a sort of spectrum of the Beta-rays or electric 
 particles shot out with different velocities from radium. 
 Some are only slightly bent, being very speedy. 
 c did <** 
 
 a represents the source of radiation ; 
 
 b an aperture through which the rays have to pass; 
 
 c the impression which would be produced on the 
 photographic plate with a magnetic field absent, and 
 
 d v d, d z the impress on the same plate due to the 
 deflected rays. 
 
220 RADIUM [APR j. 
 
 In a uniform magnetic field the rays will all be seg- 
 ments of circles, and it is easy to estimate the radius of 
 curvature of the ray corresponding to any point in the 
 spectrum, since only one circle can be drawn through 
 three given fixed points (Euclid, IV. 5 or III. 25), such points 
 for instance as a, 6, and d ; so, these three points being 
 known, the circle of which the ray forms a part is known, 
 and its radius of curvature is therefore determined. 
 
 Electric charge carried by Beta-rays. 
 
 The fact that ordinary cathode-rays are negatively 
 electrified was proved most conclusively by Perrin with 
 an apparatus diagrammatically represented in the figure; 
 where a represents the cathode, 
 
 6 an earthed diaphragm with small aperture, and 
 c a Faraday cavity or hollow vessel, arranged to 
 catch the rays in its interior and convey the 
 charge to an electroscope. 
 
 b\ c ^ 
 I i I """"^e. Electroscope 
 
 It is not so easy to prove that the beta rays emitted 
 by radium are electrified, because the air and everything in 
 the neighbourhood is rendered conducting by their impact, 
 but Professor Curie succeeded in establishing the fact by 
 enclosing a piece of metal completely in solid paraffin, 
 and showing that when exposed to the rays this metal 
 became charged. 
 
 Strutt exhibits the converse effect in a simple and 
 interesting manner by hanging up a radium tube in a 
 vacuum and attaching to it a pair of gold leaves. As 
 the electric rays are shot away by the radium the leaves 
 diverge with an opposite charge; they go on diverging 
 
APR j.] CHARGE IN RAPID MOTION 221 
 
 to the full extent, and collapsing when they touch the 
 boundary, for as long as the radium lasts, which must 
 be many centuries. 
 
 Strutt's apparatus was shown in figure 22, page 177. 
 
 For a good and clear elementary account of the pheno- 
 mena exhibited by radium, especially of all those most 
 important facts which have reference to things other than 
 electrons, such as alpha-rays, the emanations, and the 
 transmutations of matter, the book on The Becquerel Rays 
 and the Properties of Radium, by the Hon. R. J. Strutt, 
 may satisfactorily be referred to, as an introduction to 
 Prof. Rutherford's treatise. 
 
 APPENDIX K. 
 
 Note on the Behaviour of a Charge Moving Nearly at the 
 Speed of Light. 
 
 According to investigations by Larmor in the Phil. 
 Trans., 1897, pp. 228-9, and also according to the investi- 
 gations of Mr. Searle (Phil. Mag., Oct. 1897) a charge 
 does not re-distribute itself on a moving body when its 
 speed becomes great, but the lines of force bend or 
 are deflected towards the equator, without remaining 
 normal to the surface whence they start. Any un- 
 certainty on this head seems to have been due to a 
 natural confusion between the electric force acting on 
 the convected charge and the etherial force which would 
 act on charges at rest, or would cause corresponding ' dis- 
 placement' in force ether; the former must be normal to 
 a perfect conductor, but the latter need not : an assertion 
 in which we may trace some analogy to the fact that in 
 a moving medium rays of light are not perpendicular to 
 their wave fronts. 
 
222 CHARGE IN RAPID MOTION [APR K. 
 
 There is no question but that the lines of force bend 
 back towards the equator, as stated by me in 1902, but I 
 assumed that this deflexion of the lines would entail their 
 moving up nearer to the equator of the sphere, so as to 
 leave the poles bare of charge, in order that the lines 
 might still continue radial. I admit that the lines of force 
 need not continue radial close to the sphere; but, in so 
 far as the sphere changes its shape, there should still be 
 some unimportant redistribution of the charge as the 
 speed increases. Mr. Searle calculates that whereas a 
 sphere at rest acts as if its charge were at a central 
 point, this equivalent point opens out into a uniformly 
 charged line, forming a medial and small portion of its 
 diameter, when the sphere is in motion ; as the velocity 
 increases, the length of this line gradually increases also, 
 until the speed equals that of light, when it fits the sphere 
 exactly. But this leaves out of account a distortional 
 change in the sphere itself, to which I will presently refer. 
 
 The fact is that the behaviour of a charged body moving 
 at enormous speed may be treated exactly in the manner of 
 elementary potential theory for a charged ellipsoid at rest. 
 
 It is doubtful whether the term " inertia " remains useful 
 under these conditions: it is perhaps best to reserve it 
 for the ordinary case when mass is constant ; for, as 
 Mr. Searle points out, three different estimates of inertia 
 can be made: one the ratio of force to acceleration, 
 another the ratio of momentum to velocity, and a third 
 as the ratio of kinetic energy to half the square of 
 velocity. In ordinary matter, as is well known, and for 
 slow electric motions, these three estimates are one and 
 the same; but for violent electric motions they become 
 different; though it should be realised how small the 
 difference is, until the speed of light is very closely ap- 
 proached ; so that in no material case of great velocity or 
 
APR K.] CHARGE IN RAPID MOTION 223 
 
 great acceleration that has ever been practically dealt 
 with as, for instance, the case of a cannon-ball stopped by 
 armour plate is any sort of unusual effect to be expected ; 
 even on the hypothesis that matter is entirely electrically 
 composed. Nevertheless, now that among free corpuscles 
 in a vacuum tube, or among those expelled from radium, 
 it is becoming practically possible to attain these high 
 speeds, and even to begin to base crucial determinations 
 upon them, it becomes necessary to consider the matter 
 more carefully. In a publication at Gottingen in January, 
 1902, Dr. Abraham has thus discriminated what he calls 
 " longitudinal " from what he calls " transverse " inertia ; 
 making inertia depend not only on the speed but on the 
 direction of acceleration; each direction having a different 
 inertia of its own. 
 
 And all these results are still further complicated by a 
 consideration of the effect of acceleration itself, which, 
 whenever it is violent, gives rise to some perceptible 
 radiation, involving dissipation of energy; and this radia- 
 tion loss of energy, though it will be primarily represented 
 in the motion as a resistance or velocity term, may second- 
 arily have an effect on inertia; probably, however, quite 
 a small and subordinate effect in all practical cases, and 
 no effect at all so long as motion occurs with uniform 
 speed in a straight line: for then there is no radiation. 
 But then, of course, under those conditions it is not possible 
 to test or measure the inertia of a body ; it is only when 
 the motion is either curved or changed in some way that 
 inertia becomes prominent, and then there is necessarily 
 some, though usually very small, radiation too. 
 
 When magnetic deflexion of a charged body is being 
 observed at ultra-high speeds it may be asked whether 
 it is possible for the ordinary expression for the force 
 exerted on a current by a moving field to be departed from. 
 
224 CHARGE IN RAPID MOTION [APR K. 
 
 The ordinary expression for deflecting force is euB. at 
 low speeds, for a charge e moving at speed u across a 
 magnetic field of intensity H; but whether this simple 
 expression is departed from at r high speeds must be a 
 question of etherial dynamics: the procedure of Larmor, 
 based on the principle of 'Least Action' (see ^Ether and 
 Matter, p. 97), would give an answer in the negative, 
 which agrees with the assumption of Lorentz. It has 
 been suggested by others that for speeds at which (u/v) 2 
 becomes sensible, we must use the more complex ex- 
 pression for deflecting force : 
 
 rrV 2 U 2 /V, V + U , \ 
 
 eH- (?r-l !) 
 
 u \2u v u / 
 
 This, however, at low speeds reduces not to the usual 
 
 1 
 simple value, but to one-third of that value, viz. ^ Heu ; 
 
 and Professor Schuster in the Philosophical Magazine 
 for January, 1897, calls attention to the variety of 
 numerical estimates of this quantity given by different 
 varieties of the main theory. But it appears to be now 
 considered that there is no real ambiguity and that 
 Larmor's view is correct. 
 
 As has been said above, at high speeds, not only does 
 effective inertia vary with speed, but it has different 
 values for different directions of acceleration relative to 
 the line of motion; the value of what Abraham calls 
 "transverse inertia," which expresses reaction to a trans- 
 verse deflecting force, is quoted by Kaufmann in Comptes 
 Rendus, vol. cxxxv, p. 577, writing it with ra as the 
 equivalent inertia for slow motion, and with /3 as the 
 ratio u/v the ratio of the velocity of the particles to 
 the velocity of light thus 
 
APR K.] CHARGE IN RAPID MOTION 225 
 
 and is the formula appropriate to his experiments. All 
 this is in fact deducible at once by the usual Lagrangian 
 dynamical method from Mr. Heaviside's expression 
 Electrical Papers, vol. ii., p. 514 for kinetic energy; viz. 
 
 an expression equivalent to ~ V? multiplied by the following 
 quantity : 
 
 a 
 
 r being the squared speed ratio u 2 /v 2 . 
 
 In Larmor's original treatment of electrical inertia, Phil. 
 Trans. 185A (Aug. 1894), pp. 806-818, there was no reason 
 whatever for anticipating velocities greater than one-tenth 
 of light, so a simple inertia theory seemed amply sufficient 
 at that time; the mass being a permanent constant 
 associated with the electron and dependent on its 
 structure. 
 
 It is the hope of seeing somewhat into structure that 
 has made the recent experiments on its modification at 
 high speeds so interesting. 
 
 Professor J. J. Thomson's corresponding formula for 
 momentum is quoted above in the text, page 133, and 
 simplified ; and in simplified form it may be re-quoted : 
 
 It amounts to this, that the mass of an electric charge 
 e on a small non-conducting sphere of radius a, moving 
 with a speed u = v sin 0, is 
 
 which we have tabulated on page 145 (see also page 133) 
 in the form 
 
 L.E. 
 
226 DISTORTION [APR K 
 
 and to a certain extent it must be considered experimentally 
 verified by Kaufmann's results. The function 0(0) has 
 the value unity when u = 0, or even when u/v is small. 
 
 APPENDIX L. 
 Distortion due to High-speed Motion through the Ether. 
 
 Mr. Searle, in the Philosophical Magazine, October, 1897, 
 points out that the simplest charged body when in motion 
 is not a sphere, but an oblate spheroid, oblate in the direc- 
 tion of motion, with its axes in the ratio ^(l A 1> 1 > 
 
 and that this produces on all points outside itself exactly 
 the same effect as a point charge at its centre: where- 
 fore such a spheroid in motion at the speed u takes 
 the place of the sphere in electrostatics. He calls this a 
 Heaviside ellipsoid, because Mr. Heaviside first indicated 
 its importance in the theory of moving charges. 
 
 But it is well known that a spheroid of this kind is 
 exactly what a sphere in rapid motion would auto- 
 matically become, on the FitzGerald-Lorentz theory ; viz., 
 that hypothesis which was started in order to account 
 for the negative result in Michelson's experiment, by postu- 
 lating a change of dimensions in solid bodies according to 
 their direction of motion through the ether. This hypo- 
 thesis, shown to be plausible by Lorentz, became a definite 
 theory when Larmor proved (^Jther and Matter, ch. xi.) 
 that on the electric theory of matter that is, assuming 
 that the whole inertia of matter was electric not only 
 was such a change of dimensions reasonably likely, as 
 FitzGerald had perceived, and likely also to be of the 
 right amount to give a compensating effect, and pre- 
 
APP. L.] DUE TO HIGH SPEED 227 
 
 cisely zero resultant, in the Michelson experiment, but 
 that the change was a necessary consequence of dynamical 
 molecular theory. 
 
 The change of dimensions, thus imagined and justified, 
 is gradually coming to be accepted as certainly true; 
 and it is interesting to note that a sphere in motion, 
 by reason of being subject to this amount of distortion, 
 still retains its property of being the simplest geometrical 
 body, so far as the distribution of its electric field is con- 
 cerned. True, it is then no longer a sphere ; but no 
 measuring instrument could possibly show its distortion, 
 because all standards of measurement would share it. It 
 is a remarkable thing that this imperceptible and un- 
 rneasurable uniform distortion of all matter should ever 
 have been discovered : nothing but an ethereal process 
 could have dragged it to light. Nevertheless dragged to 
 light it has been, by the combined testimony of electrical 
 theory and of optical experiment. 
 
 APPENDIX M. 
 Constitution of Electrons. 
 
 In continuation of the subject treated of in appendices 
 K and L we may consult Larmor, Phil. Trans. 190A 
 (April, 1897), pp. 225-8. In ^Ether and Matter (1898), 
 ch. xi., he substituted an improved (dynamical) investiga- 
 tion, applicable to a system of molecules in the most 
 complicated motion, wherein he claims to cover all 
 possible cases, on the single hypothesis that the electrons 
 in an atom are at distances apart compared with which 
 the diameters of their structure are very small, so that 
 they may be treated as points. On that hypothesis 
 
228 CONSTITUTION OF ELECTRONS [APR M. 
 
 uniform convection of a system at any speed however 
 high should show no internal influence, provided the con- 
 stitution of matter is wholly electric, i.e. provided atoms 
 are active only through the aether. The very important 
 (because purely electrical) experiment of Trouton and 
 Noble is a case in confirmation. So is the absence 
 of influence on either of the two phenomena, magnetic 
 rotation and double refraction (Rayleigh and Brace). 
 
 It is true that this way of explaining the absence 
 of any second order aberration-effect was received with 
 scepticism by Poincare' (Paris Congress, 1900), whose criti- 
 cism was that if in future the third order effect also 
 needed annulment some new artificial arrangement could 
 still be added on, to do even that. The result of the 
 argument has now, however, gained the independent 
 support of Lorentz (1904), whose investigation has sug- 
 gested, what in fact is easily verified, that Larmor's 
 work proves to be exact: his restriction to the second 
 order being unnecessary. He was hardly concerned, how- 
 ever, to go further, since the hypothesis of the infinitesimal 
 effective size of the electron already limited the investi- 
 gation, nor does it seem that Lorentz's work really carries 
 the matter further. Larmor's attitude has been all along 
 (Phil. Mag., June, 1904), that this provisional hypothesis 
 holds the eld until some effect of uniform convection 
 presents itself : every new negative result is a steady 
 corroboration of it: but like any other physical repre- 
 sentation it must ultimately reach the limits of its appli- 
 cation. 
 
 Only negative electrons are known in the free state. 
 It remains unsettled whether this is due to some one- 
 sidedness in the experimental means hitherto employed, 
 or whether physical nature is in reality intrinsically un- 
 symmetrical. If the positive electron were a region of 
 
APP. M.] LARMOR'S THEORY 229 
 
 singularity (beknottedness) of dimension large compared 
 with the negative, it would be but a feeble agent in the 
 transformation of energy, and thus could readily escape 
 detection. Cf. Jfther and Matter, 122. But the 
 absolute structure of an electron is probably very unlike 
 the distributions of electric charge on spheres and ellip- 
 soids that have hitherto been taken to represent it. 
 
 The theory of a simple molecule appeared for the first 
 time in Phil. Trans., 13th August, 1894, pp. 806-818; 
 inertia purely electric, on p. 807 ; estimate of size and 
 dimensions, and electrodynamics of orbital motions, on 
 p. 814; Hall effect, etc., on p. 815. There does not 
 appear to be anything in Lorentz's papers, either of 1892 
 or 1895, to correspond to the ideas there introduced. 
 
 With reference to a theory of the Zeeman effect : . the 
 simplest type of illustrative system, amenable to calcu- 
 lation, would be a statical one, in which the electrons 
 would all vibrate round positions of stable equilibrium. 
 But this requires extraneous supporting force, if they are 
 in empty space. A definite subdivision of the periods 
 has been worked out for J. J. Thomson's statical illustra- 
 tion, in which this innate instability of a statical system 
 of negative electrons (Earnshaw's theorem) is obviated 
 by supposing them inside a region of continuous positive 
 electrification, which may be taken to represent the posi- 
 tive electron. If the volume density of this is small, the 
 resulting stability will be but slight, and a small displace- 
 ment will upset the system, and lead to its break-up ; 
 which is unlikely, perhaps unreasonable. 
 
 But here, as before, it is only isotropic configurations, 
 in the same sense as in the hydrokinetics of solids in 
 fluids, namely, those with which an associated quadratic 
 function must be wholly isotropic, including the configura- 
 tions of the regular solids, that split the lines definitely 
 
230 CONSTITUTION OF ELECTRONS [APP. M. 
 
 instead of merely broadening them : other types will only 
 do so when they are all similarly orientated to the in- 
 ducing magnetic field. 
 
 The experiments of Kaufmann held out a hope that 
 we should get to know something definite about intrinsic 
 electron structure. They have proved sufficiently the 
 fundamental fact that a free electron has no independent 
 material sub-stratum : they have made it very probable 
 that it may be provisionally represented as a region of 
 electricity spherically stratified : also that convection of 
 an electron does not affect the volume relations of this 
 distribution (Bucherer); but unfortunately it has not 
 proved possible to push on the precision of the experi- 
 ment so as to get information beyond this. 
 
 We must still be content to treat the electron as a point, 
 or at most as a spherical electric aggregate of some sort 
 whose volume does not undergo shrinkage. But the in- 
 direct evidence afforded by the entire absence of convection 
 effects of many kinds, such as the earth's motion might 
 be supposed to excite, is strongly in favour of the pro- 
 visional theory that the ultimate elements of which 
 atoms are constituted are in their dynamical relations 
 purely aethereal structures of some sort which probably 
 we cannot yet adequately imagine. 
 
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