r 
 
 i 
 
 Physical Sciences Library 
 
 University of California 
 
 Riverside 
 
 I
 
 YALE UNIVERSITY 
 MRS. HEPSA ELY SILLIMAN MEMORIAL LECTURES 
 
 ELECTRICITY AND MATTER
 
 ELECTRICITY AND 
 MATTER 
 
 J. J. THOMSON, D.Sc., LL.D., PH.D., F.R.S. 
 
 FELLOW OF TRINITY COLLEGE, CAMBRIDGE; CAVENDISH 
 PROFESSOR OF EXPERIMENTAL PHYSICS, CAMBRIDGE 
 
 WITH DIAGRAMS 
 
 WESTMINSTER 
 
 ARCHIBALD CONSTABLE & CO., LTD. 
 1904
 
 Copyright, 1904, by Charles Scribner's Sons, for Great Britain and the 
 United Slates of America 
 
 Printed by the Trow Directory, Printing and Bookbinding Company 
 New York. U. S. A.
 
 THE SILLIMAN FOUNDATION. 
 
 In the year 1883 a legacy of eighty thousand dollars 
 was left to the President and Fellows of Yale College 
 in the city of New Haven, to be held in trust, as a 
 gift from her children, in memory of their beloved and 
 honored mother Mrs. Hepsa Ely Silliman. 
 
 On this foundation Yale College was requested and 
 directed to establish an annual course of lectures de- 
 signed to illustrate the presence and providence, the 
 wisdom and goodness of God, as manifested in the 
 natural and moral world. These were to be designated 
 as the Mrs. Hepsa Ely Silliman Memorial Lectures. It 
 was the belief of the testator that any orderly presenta- 
 tion of the facts of nature or history contributed to 
 the end of this foundation more effectively than any 
 attempt to emphasize the elements of doctrine or of 
 creed; and he therefore provided that lectures on dog- 
 matic or polemical theology should be excluded from 
 the scope of this foundation, and that the subjects should 
 be selected rather from the domains of natural science 
 and history, giving special prominence to astronomy, 
 chemistry, geology, and anatomy. 
 
 It was further directed that each annual course should 
 be made the basis of a volume to form part of a series 
 constituting a memorial to Mrs. Silliman. The memo- 
 rial fund came into the possession of the Corporation 
 of Yale University in the year 1902; and the present 
 volume constitutes the first of the series of memorial 
 lectures.
 
 PREFACE 
 
 In these Lectures given at Yale University in 
 May, 1903, I have attempted to discuss the bear- 
 ing of the recent advances made in Electrical 
 Science on our views of the Constitution of Matter 
 and the Nature of Electricity; two questions 
 which are probably so intimately connected, that 
 the solution of the one would supply that of the 
 other. A characteristic feature of recent Electri- 
 cal Researches, such as the study and discovery 
 of Cathode and Rontgen Rays and Radio-active 
 Substances, has been the very especial degree in 
 which they have involved the relation between 
 Matter and Electricity. 
 
 In choosing a subject for the Silliman Lectures, 
 it seemed to me that a consideration of the bear- 
 ing of recent work on this relationship might be 
 suitable, especially as such a discussion suggests 
 multitudes of questions which would furnish ad- 
 mirable subjects for further investigation by some 
 of my hearers. 
 
 Cambridge, Aug., 1903. 
 
 J. J. THOMSON.
 
 CONTENTS 
 
 CHAPTER- I 
 
 PAGE 
 
 REPRESENTATION OF THE ELECTRIC FIELD BY LINES 
 OF FORCE 1 
 
 CHAPTER II 
 
 ELECTRICAL AND BOUND MASS 3G 
 
 CHAPTER III 
 
 EFFECTS DUE TO THE ACCELERATION OF FARADAY 
 
 TUBES 53 
 
 CHAPTER IV 
 THE ATOMIC STRUCTURE OF ELECTRICITY ... 71 
 
 CHAPTER V 
 THE CONSTITUTION OF THE ATOM 90 
 
 CHAPTER VI 
 
 RADIO-ACTIVITY AND RADIO-ACTIVE SUBSTANCES . . 140
 
 ELECTRICITY AND MATTER 
 
 CHAPTER I 
 
 REPRESENTATION OF THE ELECTRIC FIELD 
 BY LINES OF FORCE 
 
 MY object in these lectures is to put before you 
 in as simple and untechnical a manner as I can 
 some views as to the nature of electricity, of the 
 processes going on in the electric field, and of the 
 connection between electrical and ordinary matter 
 which have been suggested by the results of recent 
 investigations. 
 
 The progress of electrical science has been 
 greatly promoted by speculations as to the nature 
 of electricity. Indeed, it is hardly possible to 
 overestimate the services rendered by two theories 
 as old almost as the science itself; I mean the 
 theories known as the two- and the one-fluid 
 theories of electricity. 
 
 The two-fluid theory explains the phenomena 
 of electro-statics by supposing that in the universe 
 there are two fluids, uncreatable and indestruc-
 
 2 ELECTRICITY AND MATTER 
 
 tible, whose presence gives rise to electrical effects ; 
 one of these fluids is called positive, the other 
 negative electricity, and electrical phenomena 
 are explained by ascribing to the fluids the fol- 
 lowing properties. The particles of the positive 
 fluid repel each other with forces varying inversely 
 as the square of the distance between them, as do 
 also the particles of the negative fluid; on the 
 other hand, the particles of the positive fluid at- 
 tract those of the negative fluid. The attraction 
 between two charges, m and m, of opposite signs 
 are in one form of the theory supposed to be 
 exactly equal to the repulsion between two 
 charges, m and m of the same sign, placed in 
 the same position as the previous charges. In an- 
 other development of the theory the attraction is 
 supposed to slightly exceed the repulsion, so as to 
 afford a basis for the explanation of gravitation. 
 
 The fluids are supposed to be exceedingly mo- 
 bile and able to pass with great ease through con- 
 ductors. The state of electrification of a body is 
 determined by the difference between the quanti- 
 ties of the two electric fluids contained by it ; if it 
 contains more positive fluid than negative it is 
 positively electrified, if it contains equal quantities 
 it is uncharged. Since the fluids are uncreatable
 
 LINES OF FORCE 3 
 
 and indestructible, the appearance of the positive 
 fluid in one place must be accompanied by the 
 departure of the same quantity from some other 
 place, so that the production of electrification of 
 one sign must always be accompanied by the pro- 
 duction of an equal amount of electrification of 
 the opposite sign. 
 
 On this view, every body is supposed to con- 
 sist of three things : ordinary matter, positive elec- 
 tricity, negative electricity. The two latter are 
 supposed to exert forces on themselves and on 
 each other, but in the earlier form of the theory 
 no action was contemplated between ordinary 
 matter and the electric fluids ; it was not until a 
 comparatively recent date that Helmholtz intro- 
 duced the idea of a specific attraction between 
 ordinary matter and the electric fluids. He did this 
 to explain what is known as contact electricity, 
 i.e.j the electrical separation produced when two 
 metals, say zinc and copper, are put in contact 
 with each other, the zinc becoming positively, the 
 copper negatively electrified. Helmholtz sup- 
 posed that there are forces between ordinary mat- 
 ter and the electric fluids varying for different 
 kinds of matter, the attraction of zinc for positive 
 electricity being greater than that of copper, so
 
 4 ELECTRICITY AND MATTER 
 
 that when these metals are put in contact the 
 zinc robs the copper of some of its positive 
 electricity. 
 
 There is an indefiniteness about the two-fluid 
 theory which may be illustrated by the considera- 
 tion of an unelectrified body. All that the two- 
 fluid theory tells us about such a body is that it 
 contains equal quantities of the two fluids. It gives 
 no information about the amount of either; indeed, 
 it implies that if equal quantities of the two are 
 added to the body, the body will be unaltered, 
 equal quantities of the two fluids exactly neutraliz- 
 ing each other. If we regard these fluids as being 
 anything more substantial than the mathematical 
 symbols + an( i ~~ this leads us into difficulties ; if 
 we regard them as physical fluids, for example, we 
 have to suppose that the mixture of the two fluids 
 in equal proportions is something so devoid of 
 physical properties that its existence has never 
 been detected. 
 
 The other fluid theory the one-fluid theory of 
 Benjamin Franklin is not open to this objection. 
 On this view there is only one electric fluid, the 
 positive ; the part of the other is taken by ordi- 
 nary matter, the particles of which are supposed 
 to repel each other and attract the positive fluid,
 
 LINES OF FORCE 5 
 
 just as the particles of the negative fluid do on 
 the two-fluid theory. Matter when unelectrified 
 is supposed to be associated with just so much of 
 the electric fluid that the attraction of the matter 
 on a portion of the electric fluid outside it is just 
 sufficient to counteract the repulsion exerted on 
 the same fluid by the electric fluid associated with 
 the matter. On this view, if the quantity of mat- 
 ter in a body is known the quantity of electric 
 fluid is at once determined. 
 
 The services which the fluid theories have ren- 
 dered to electricity are independent of the notion 
 of a fluid with any physical properties ; the fluids 
 were mathematical fictions, intended merely to give 
 a local habitation to the attractions and repulsions 
 existing between electrified bodies, and served as 
 the means by which the splendid mathematical 
 development of the theory of forces varying in- 
 versely as the square of the distance which was 
 inspired by the discovery of gravitation could be 
 brought to bear on electrical phenomena. As 
 long as we confine ourself to questions which only 
 involve the law of forces between electrified bodies, 
 and the simultaneous production of equal quantities 
 of -{- and electricity, both theories must give 
 the same results and there can be nothing to
 
 6 ELECTRICITY AND MATTER 
 
 decide between them. The physicists and mathe- 
 maticians who did most to develop the "Fluid 
 Theories " confined themselves to questions of this 
 kind, and refined and idealized the conception of 
 these fluids until any reference to their physical 
 properties was considered almost indelicate. It is 
 not until we investigate phenomena which involve 
 the physical properties of the fluid that we can 
 hope to distinguish between the rival fluid the- 
 ories. Let us take a case which has actually 
 arisen. We have been able to measure the masses 
 associated with given charges of electricity in 
 gases at low pressures, and it has been found that 
 the mass associated with a positive charge is im- 
 mensely greater than that associated with a nega- 
 tive one. This difference is what we should 
 expect on Franklin's one-fluid theory, if that 
 theory were modified by making the electric fluid 
 correspond to negative instead of positive elec- 
 tricity, while we have no reason to anticipate so 
 great a difference on the two-fluid theory. We 
 shall, I am sure, be struck by the similarity be- 
 tween some of the views which we are led to take 
 by the results of the most recent researches with 
 those enunciated by Franklin in the very infancy 
 of the subject.
 
 LINES OF FORCE 7 
 
 Faraday's Line of Force Theory 
 
 The fluid theories, from their very nature, imply 
 the idea of action at a distance. This idea, al- 
 though its convenience for mathematical analysis 
 has made it acceptable to many mathematicians, is 
 one which many of the greatest physicists have 
 felt utterly unable to accept, and have devoted 
 much thought and labor to replacing it by some- 
 thing involving mechanical continuity. Pre-emi- 
 nent among them is Faraday. Faraday was deeply 
 influenced by the axiom, or if you prefer it, dogma 
 that matter cannot act where it is not. Faraday, 
 who possessed, I believe, almost unrivalled mathe- 
 matical insight, had had no training in analysis, 
 so that the convenience of the idea of action at a 
 distance for purposes of calculation had no chance 
 of mitigating the repugnance he felt to the idea of 
 forces acting far away from their base and with 
 no physical connection with their origin. He 
 therefore cast about for some way of picturing to 
 himself the actions in the electric field which 
 would get rid of the idea of action at a distance, 
 and replace it by one which would bring into 
 prominence some continuous connection between 
 the bodies exerting the forces. He was able to
 
 g ELECTRICITY AND MATTER 
 
 do this by the conception of lines of force. As I 
 shall have continually to make use of this method, 
 and as I believe its powers and possibilities have 
 never been adequately realized, I shall devote 
 some time to the discussion and development of 
 this conception of the electric field. 
 
 FIG. i. 
 
 The method was suggested to Faraday by the 
 consideration of the lines of force round a bar 
 magnet. If iron filings are scattered on a smooth 
 surface near a magnet they arrange themselves as 
 in Fig. 1 ; well-marked lines can be traced run-
 
 LINES OF FORCE 9 
 
 ning from one pole of the magnet to the other ; 
 the direction of these lines at any point coincides 
 with the direction of the magnetic force, while the 
 intensity of the force is indicated by the concen- 
 tration of the lines. Starting from any point in 
 the field and travelling always in the direction of 
 the magnetic force, we shall trace out a line which 
 will not stop until we reach the negative pole of 
 the magnet ; if such lines are drawn at all points 
 in the field, the space through which the magnetic 
 field extends will be filled with a system of lines, 
 giving the space a fibrous structure like that pos- 
 sessed by a stack of hay or straw, the grain of the 
 structure being along the lines of force. I have 
 spoken so far only of lines of magnetic force ; the 
 same considerations will apply to the electric field, 
 and we may regard the electric field as full of 
 lines of electric force, which start from positively 
 and end on negatively electrified bodies. Up to 
 this point the process has been entirely geometri- 
 cal, and could have been employed by those who 
 looked at the question from the point of view of 
 action at a distance; to Faraday, however, the 
 lines of force were far more than mathematical 
 abstractions they were physical realities. Fara- 
 day materialized the lines of force and endowed
 
 10 ELECTRICITY AND MATTER 
 
 them with physical properties so as to explain the 
 phenomena of the electric field. Thus he sup- 
 posed that they were in a state of tension, and 
 that they repelled each other. Instead of an in- 
 tangible action at a distance between two electri- 
 fied bodies, Faraday regarded the whole space 
 between the bodies as full of stretched mutually 
 repellent springs. The charges of electricity to 
 which alone an interpretation had been given on 
 the fluid theories of electricity were on this view 
 just the ends of these springs, and an electric 
 charge, instead of being a portion of fluid confined 
 to the electrified body, was an extensive arsenal 
 of springs spreading out in all directions to all 
 parts of the field. 
 
 To make our ideas clear on this point let us 
 consider some simple cases from Faraday's point 
 of view. Let us first take the case of two bodies 
 with equal and opposite charges, whose lines of 
 force are shown in Fig. 2. You notice that the 
 lines of force are most dense along A B, the line 
 joining the bodies, and that there are more lines 
 of force on the side of A nearest to JB than on 
 the opposite side. Consider the effect of the 
 lines of force on A ; the lines are in a state of 
 tension and are pulling away at A] as there
 
 LINES OF FORCE H 
 
 are more pulling at A on the side nearest to 
 than on the opposite side, the pulls on A toward 
 B overpower those pulling A away from J3, so 
 that A will tend to move toward B\ it was in 
 this way that Faraday pictured to himself the 
 attraction between oppositely electrified bodies. 
 Let us now consider the condition of one of the 
 curved lines of force, such as PQ] it is in a state 
 
 FIG. 2. 
 
 of tension and will therefore tend to straighten 
 itself, how is it prevented from doing this and 
 maintained in equilibrium in a curved position? 
 We can see the reason for this if we remember 
 that the lines of force repel each other and that 
 the lines are more concentrated in the region be- 
 tween PQ and AB than on the other side of 
 PQ] thus the repulsion of the lines inside PQ 
 will be greater than the repulsion of those out- 
 side and the line PQ will be bent outwards.
 
 12 
 
 ELECTRICITY AND MATTER 
 
 Let us now pass from the case of two oppositely 
 electrified bodies to that of two similarly elec- 
 trified ones, the lines of force for which are shown 
 in Fig. 3. Let us suppose A and B are positively 
 electrified; since the lines of force start from 
 positively and end on negatively electrified bodies, 
 the lines starting from A and B will travel away 
 to join some body or bodies possessing the 
 
 FIG. 3. 
 
 negative charges corresponding to the positive 
 ones on A and B', let us suppose that these 
 charges are a considerable distance away, so that 
 the lines of force from A would, if B were not 
 present, spread out, in the part of the field under 
 consideration, uniformly in all directions. Consider 
 now the effect of making the system of lines of 
 force attached to A and B approach each other ;
 
 LINES OF FORCE 
 
 13 
 
 since these lines repel each other the lines of force 
 on the side of A nearest B will be pushed to the 
 opposite side of A, so that the lines of force will 
 now be densest on the far side of A ; thus the 
 pulls exerted on A in the rear by the lines of 
 force will be greater than those in the front and 
 the result will be that A will be pulled away 
 from B. We notice that the mechanism produc- 
 ing this repulsion is of exactly the same type as 
 that which produced the attraction in the pre- 
 vious case, and we may if we please regard the 
 repulsion between A and B as due to the attrac- 
 tions on A and B of the 
 complementary negative 
 charges which must exist in 
 other parts of the field. 
 
 The results of the repul- 
 sion of the lines of force 
 are clearly shown in the case 
 represented in Fig. 4, that 
 of two oppositely electrified 
 plates; you will notice that 
 the lines of force between 
 the plates are straight except 
 near the edges of the plates ; this is what we 
 should expect as the downward pressure exerted 
 
 PIG. 4.
 
 14 ELECTRICITY AND MATTER 
 
 by the lines of force above a line in this part of 
 the field will be equal to the upward pressure 
 exerted by those below it. For a line of force 
 near the edge of the plate, however, the pressure 
 of the lines of force below will exceed the press- 
 ure from those above, and the line of force will 
 bulge out until its curvature and tension counter- 
 act the squeeze from inside ; this bulging is very 
 plainly shown in Fig. 4. 
 
 So far our use of the lines of force has been 
 descriptive rather than metrical; it is, however, 
 easy to develop the method so as to make it 
 metrical. We can do this by introducing the 
 idea of tubes of force. If through the boundary 
 of any small closed curve in the electric field we 
 draw the lines of force, these lines will form a 
 tubular surface, and if we follow the lines back to 
 the positively electrified surface from which they 
 start and forward on to the negatively electrified 
 surface on which they end, we can prove that the 
 positive charge enclosed by the tube at its origin 
 is equal to the negative charge enclosed by it at 
 its end. By properly choosing the area of the 
 small curve through which we draw the lines of 
 force, we may arrange that the charge enclosed by 
 the tube is equal to the unit charge. Let us call
 
 LINES OF FORCE 15 
 
 such a tube a Faraday tube then each unit of 
 positive electricity in the field may be regarded 
 as the origin and each unit of negative electricity 
 as the termination of a Faraday tube. We regard 
 these Faraday tubes as having direction, their di- 
 rection being the same as that of the electric force, 
 so that the positive direction is from the positive 
 to the negative end of the tube. If we draw any 
 closed surface then the difference between the 
 number of Faraday tubes which pass out of the 
 surface and those which pass in will be equal to the 
 algebraic sum of the charges inside the surface; this 
 sum is what Maxwell called the electric displace- 
 ment through the surface. What Maxwell called 
 the electric displacement in any direction at a 
 point is the number of Faraday tubes which pass 
 through a unit area through the point drawn at 
 right angles to that direction, the number being 
 reckoned algebraically ; i.e., the lines which pass 
 through in one direction being taken as positive, 
 while those which pass through in the opposite 
 direction are taken as negative, and the number 
 passing through the area is the difference between 
 the number passing through positively and the 
 number passing through negatively. 
 
 For my own part, I have found the conception
 
 16 ELECTRICITY AND MATTER 
 
 of Faraday tubes to lend itself much more readily 
 to the formation of a mental picture of the proc- 
 esses going on in the electric field than that of 
 electric displacement, and have for many years 
 abandoned the latter method. 
 
 Maxwell took up the question of the ten- 
 sions and pressures in the lines of force in 
 the electric field, and carried the problem one 
 step further than Faraday. By calculating the 
 amount of these tensions he showed that the 
 mechanical effects in the electrostatic field could 
 be explained by supposing that each Faraday 
 tube force exerted a tension equal to J?, It being 
 the intensity of the electric force, and that, in 
 addition to this tension, there was in the medium 
 through which the tubes pass a hydrostatic 
 pressure equal to \NIt, N being the density 
 of the Faraday tubes; i.e., the number passing 
 through a unit area drawn at right angles to 
 the electric force. If we consider the effect of 
 these tensions and pressure on a unit volume of 
 the medium in the electric field, we see that 
 they are equivalent to a tension NR along 
 the direction of the electric force and an equal 
 pressure in all directions at right angles to that 
 force.
 
 LINES OF FORCE 
 
 17 
 
 Moving Faraday Tubes 
 
 Hitherto we have supposed the Faraday tubes 
 to be at rest, let us now proceed to the study of 
 the effects produced by the motion of those tubes. 
 Let us begin with the consideration of a very 
 simple case that of two parallel 
 plates, A and J3, charged, one with 
 positive the other with negative 
 electricity, and suppose that after 
 being charged the plates are con- 
 nected by a conducting wire, EF G. 
 This wire will pass through some 
 of the outlying tubes ; these tubes, 
 when in a conductor, contract to 
 molecular dimensions and the repul- 
 sion they previously exerted on 
 neighboring tubes will therefore 
 disappear. Consider the effect of 
 this on a tube PQ between the 
 plates ; PQ was originally in equilibrium under 
 its own tension, and the repulsion exerted by the 
 neighboring tubes. The repulsions due to those 
 cut by E F G have now, however, disappeared so 
 that PQ will no longer be in equilibrium, but will 
 be pushed towards E F G. Thus, more and more 
 tubes will be pushed into E FG, and we shall 
 
 F 
 FIG. 5.
 
 lg ELECTRICITY AND MATTER 
 
 have a movement of the whole set of tubes be- 
 tween the plates toward E F G. Thus, while the 
 discharge of the plates is going on, the tubes be- 
 tween the plates are moving at right angles to 
 themselves. What physical effect accompanies 
 this movement of the tubes ? The result of con- 
 necting the plates by E F G is to produce a cur- 
 rent of electricity flowing from the positively 
 charged plate through E F G- to the negatively 
 charged plate ; this is, as we know, accompanied 
 by a magnetic force between the plates. This 
 magnetic force is at right angles to the plane of 
 the paper and equal to 4?r times the intensity of 
 the current in the plate, or, if cr is the density of 
 the charge of electricity on the plates and v the 
 velocity with which the charge moves, the mag- 
 netic force is equal to kircru. 
 
 Here we have two phenomena which do not 
 take place in the steady electrostatic field, one the 
 movement of the Faraday tubes, the other 
 the existence of a magnetic force; this suggests 
 that there is a connection between the two, and 
 that motion of the Faraday tubes is accompanied 
 by the production of magnetic force. I have fol- 
 lowed up the consequences of this supposition and 
 have shown that, if the connection between the
 
 LINES OF FORCE 19 
 
 magnetic force and the moving tubes is that given 
 below, this view will account for Ampere's laws 
 connecting current and magnetic force, and for 
 Faraday's law of the induction of currents. Max- 
 well's great contribution to electrical theory, that 
 variation in the electric displacement in a dielec- 
 tric produces magnetic force, follows at once from 
 this view. For, since the electric displacement is 
 measured by the density of the Faraday tubes, if 
 the electric displacement at any place changes, 
 Faraday tubes must move up to or away from the 
 place, and motion of Faraday tubes, by hypoth- 
 esis, implies magnetic force. 
 
 The law connecting magnetic force with the 
 motion of the Faraday tubes is as follows : A 
 Faraday tube moving with velocity v at a point 
 P, produces at P a magnetic force whose magni- 
 tude is 4?r v sin 0, the direction of the magnetic 
 force being at right angles to the Faraday tube, 
 and also to its direction of motion ; 6 is the angle 
 between the Faraday tube and the direction in 
 which it is moving. We see that it is only 
 the motion of a tube at right angles to itself 
 which produces magnetic force; no such force 
 is produced by the gliding of a tube along its 
 length.
 
 20 ELECTRICITY AND MATTER 
 
 Motion of a Charged /Sphere 
 
 We shall apply these results to a very simple 
 and important case the steady motion of a 
 charged sphere. If the velocity of the sphere is 
 small compared with that of light then the Fara- 
 day tubes will, as when the sphere is at rest, be 
 uniformly distributed and radial in direction. 
 They will be carried along with the sphere. If 
 e is the charge on the sphere, its centre, the 
 
 p 
 
 density of the Faraday tubes at P is Tjj^r', 
 
 so that if v is the velocity of the sphere, 6 the 
 
 ,p 
 
 FIG. 6. 
 
 angle between OP and the direction of motion of 
 the sphere, then, according to the above rule, the 
 
 magnetic force at P will be - jf , the direc- 
 tion of the force will be at right angles to OP y 
 and at right angles to the direction of motion of 
 the sphere ; the lines of magnetic force will thus
 
 LINES OF FORCE 21 
 
 be circles, having their centres on the path of the 
 centre of the sphere and their planes at right 
 angles to this path. Thus, a moving charge of 
 electricity will be accompanied by a magnetic 
 field. The existence of a magnetic field implies 
 energy; we know that in a unit volume of the 
 field at a place where the magnetic force is H 
 
 there are ^ units of energy, where /u, is the 
 
 magnetic permeability of the medium. In the 
 case of the moving sphere the energy per unit 
 
 D . /xeV sin*0 ,- , . , 
 volume at Jr is ^ n P4 . laking the sum of 
 
 O7T U.L 
 
 this energy for all parts of the field outside the 
 
 IL 0^4)^ 
 
 sphere, we find that it amounts to - , where a 
 
 3a ' 
 
 is the radius of the sphere. If m is the mass of 
 the sphere, the kinetic energy in the sphere is 
 ^ mtP' t in addition to that we have the energy 
 outside the sphere, which as we have seen is 
 
 ^ ; so that the whole kinetic energy of the 
 
 Od 
 
 (2u 2 \ 
 m -{- ~Q~ ~~ I ^ 2 j or the energy is 
 
 the same as if the mass of the sphere were 
 
 2/x $ 
 m -\ *- instead of m. Thus, in consequence of
 
 22 ELECTRICITY AND MATTER 
 
 the electric charge, the mass of the sphere is 
 
 2u e* 
 measured by -~-. This is a very important re- 
 
 od 
 
 suit, since it shows that part of the mass of a 
 charged sphere is due to its charge. I shall later 
 on have to bring before you considerations which 
 show that it is not impossible that the whole mass 
 of a body may arise in the way. 
 
 Before passing on to this point, however, I 
 should like to illustrate the increase which takes 
 place in the mass of the sphere by some analogies 
 drawn from other branches of physics. The first of 
 these is the case of a sphere moving through a 
 frictionless liquid. When the sphere moves it sets 
 the fluid around it moving with a velocity propor- 
 tioned to its own, so that to move the sphere we 
 we have not merely to move the substance of the 
 sphere itself, but also the liquid around it ; the 
 consequence of this is, that the sphere behaves as 
 if its mass were increased by that of a certain vol- 
 ume of the liquid. This volume, as was shown by 
 Green in 1833, is half the volume of the sphere. 
 In the case of a cylinder moving at right angles to 
 its length, its mass is increased by the mass of an 
 equal volume of the liquid. In the case of an 
 elongated body like a cylinder, the amount by
 
 LINES OP FORCE 23 
 
 which the mass is increased depends upon the di- 
 rection in which the body is moving, being much 
 smaller when the body moves point foremost 
 than when moving sideways. The mass of such 
 a body depends on the direction in which it is 
 moving. 
 
 Let us, however, return to the moving electri- 
 fied sphere. We have seen that in consequence of 
 
 its charge its mass is increased by - ; thus, if it 
 
 oa 
 
 is moving with the velocity v, the momentum is 
 
 / 2/i $ \ 
 
 not tnv, but J m -{- ~o ) v. The additional mo- 
 
 2u,<? 2 
 mentum -~ v is not in the sphere, but in the space 
 
 surrounding the sphere. There is in this space 
 ordinary mechanical momentum, whose resultant is 
 
 2/xe 2 
 
 -H v and whose direction is parallel to the di- 
 
 rection of motion of the sphere. It is important 
 to bear in mind that this momentum is not in any 
 way different from ordinary mechanical momen- 
 tum and can be given up to or taken from the 
 momentum of moving bodies. I want to bring 
 the existence of this momentum before you as 
 vividly and forcibly as I can, because the recogni- 
 tion of it makes the behavior of the electric field
 
 24 ELECTRICITY AND MATTER 
 
 entirely analogous to that of a mechanical sys- 
 tem. To take an example, according to Newton's 
 Third Law of Motion, Action and Reaction are 
 equal and opposite, so that the momentum in any 
 direction of any self-contained system is invariable. 
 Now, in the case of many electrical systems there 
 are apparant violations of this principle ; thus, 
 take the case of a charged body at rest struck by 
 an electric pulse, the charged body when exposed 
 to the electric force in the pulse acquires velocity 
 and momentum, so that when the pulse has passed 
 over it, its momentum is not what it was origi- 
 nally. Thus, if we confine our attention to the 
 momentum in the charged body, i.e., if we suppose 
 that momentum is necessarily confined to what we 
 consider ordinary matter, there has been a viola- 
 tion of the Third Law of Motion, for the only 
 momentum recognized on this restricted view 
 has been changed. The phenomenon is, however, 
 brought into accordance with this law if we recog- 
 nize the existence of the momentum in the electric 
 field ; for, on this view, before the pulse reached 
 the charged body there was momentum in the 
 pulse, but none in the body; after the pulse 
 passed over the body there was some momentum 
 in the body and a smaller amount in the pulse,
 
 LINES OF FORCE 25 
 
 the loss of momentum in the pulse being equal to 
 the gain of momentum by the body. 
 
 We now proceed to consider this momentum 
 more in detail. I have in my " Eecent Researches 
 on Electricity and Magnetism" calculated the 
 amount of momentum at any point in the electric 
 field, and have shown that if JV is the number of 
 Faraday tubes passing through a unit area drawn 
 at right angles to their direction, B the magnetic 
 induction, 9 the angle between the induction and 
 the Faraday tubes, then the momentum per unit 
 volume is equal to N B sin 0, the direction of 
 the momentum being at right angles to the mag- 
 netic induction and also to the Faraday tubes. 
 Many of you will notice that the momentum is 
 parallel to what is known as Poynting's vector 
 the vector whose direction gives the direction in 
 which energy is flowing through the field. 
 
 Moment of Momentum Due to an Electrified 
 Point and a Magnetic Pole 
 
 To familiarize ourselves with this distribution 
 of momentum let us consider some simple cases in 
 detail. Let us begin with the simplest, that of an 
 electrified point and a magnetic pole; let A., Fig. 7, 
 be the point, B the pole. Then, since the momen-
 
 26 ELECTRICITY AND MATTER 
 
 turn at any point P is at right angles to A P, the 
 direction of the Faraday tubes and also to P, 
 the magnetic induction, we see that the momentum 
 will be perpendicular to the plane A B P ; thus, 
 if we draw a series of lines such that their direc- 
 tion at any point coincides with the direction of 
 the momentum at that point, these lines will form 
 a series of circles whose planes are perpendicular 
 to the line A. JS, and whose centres 
 lie along that line. This distribution 
 of momentum, as far as direction 
 goes, is that possessed by a top spin- 
 ning around A B. Let us now find 
 what this distribution of momentum 
 throughout the field is equivalent to. 
 It is evident that the resultant 
 momentum in any direction is zero, 
 ?ra ' 7 ' but since the system is spinning 
 round A , the direction of rotation being every- 
 where the same, there will be a finite moment 
 of momentum round A B. Calculating the value 
 of this from the expression for the momentum 
 given above, we obtain the very simple expression 
 em as the value of the moment of momentum 
 about A B, e being the charge on the point and 
 m the strength of the pole. By means of this
 
 LINES OF FORCE 27 
 
 expression we can at once find the moment of 
 momentum of any distribution of electrified points 
 and magnetic poles. 
 
 To return to the system of the point and pole, 
 this conception of the momentum of the system 
 leads directly to the evaluation of the force acting 
 on a moving electric charge or a moving magnetic 
 pole. For suppose that in the time 8 t the electri- 
 fied point were to move from A to Af, the ^ 
 moment of momentum is still em, but \h/ 
 its axis is along A' B instead of A B. A<J 
 The moment of momentum of the field \ 
 has thus changed, but the whole moment \ 
 of momentum of the system comprising \ 
 point, pole, and field must be constant, so \ 
 that the change in the moment of momen- \ 
 turn of the field must be accompanied \ 
 by an equal and opposite change in the \ 
 moment of momentum of the pole and FlG - 8 - 
 point. The momentum gained by the point must 
 be equal and opposite to that gained by the 
 pole, since the whole momentum is zero. If is 
 the angle A B A', the change in the moment of 
 momentum is em sin 6, with an axis at right 
 angles to A B in the plane of the paper. Let 
 8 / be the change in the momentum of A,
 
 28 ELECTRICITY AND MATTER 
 
 S I that of B, then S I and - 8 1 must be 
 equivalent to a couple whose axis is at right 
 angles to A B in the plane of the paper, and 
 whose moment is e m sin 6. Thus 8 /must be at 
 right angles to the plane of the paper and 
 
 e m A A' sin <A 
 
 Where < is the angle B A A'. If v is the 
 velocity of A, A A'=v Stf and we get 
 j_ emvsm<f>$t 
 
 AB* 
 
 This change in the momentum may be sup- 
 posed due to the action of a force F perpen- 
 
 dicular to the plane of the paper, F being the 
 
 * 7 
 rate of increase of the momentum, or * We thus 
 
 , _, ,. . .. . , . 
 
 get J! = ^ p 2 ; or the point is acted on by a 
 
 force equal to e multiplied by the component of 
 the magnetic force at right angles to the direction 
 of motion. The direction of the force acting on 
 the point is at right angles to its velocity and 
 also to the magnetic force. There is an equal 
 and opposite force acting on the magnetic pole. 
 
 The value we have found for F is the ordinary 
 expression for the mechanical force acting on a 
 moving charged particle in a magnetic field; it
 
 LINES OF FOKCE 29 
 
 may be written as ev If sin <f), where ITs is the 
 strength of the magnetic field. The force acting 
 on unit charge is therefore v If Bin <f>. This me- 
 chanical force may be thus regarded as arising 
 from an electric force v H sin <f), and we may 
 express the result by saying that when a charged 
 body is moving in a magnetic field an electric 
 force v If sin </ is produced. This force is the 
 well-known electromotive force of induction due 
 to motion in a magnetic field. 
 
 The forces called into play are due to the 
 relative motion of the pole and point; if these are 
 moving with the same velocity, the line joining 
 them will not alter in direction, the moment of 
 momentum of the system will remain unchanged 
 and there will not be any forces acting either on 
 the pole or the point. 
 
 The distribution of momentum in the system 
 of pole and point is similar in some respects to 
 that in a top spinning about the line A J3. We 
 can illustrate the forces acting on a moving elec- 
 trified body by the behavior of such a top. Thus, 
 let Fig. 9 represent a balanced gyroscope spinning 
 about the axis A H, let the ball at A represent 
 the electrified point, that at the magnetic pole. 
 Suppose the instrument is spinning with A J3
 
 30 ELECTRICITY AND MATTER 
 
 horizontal, then if with a vertical rod I push 
 against A B horizontally, the point A will not 
 merely move horizontally forward in the direction 
 in which it is pushed, but will also move verti- 
 cally upward or downward, just as a charged 
 
 FIG. 9. 
 
 point would do if pushed forward in the same 
 way, and if it were acted upon by a magnetic 
 pole at . 
 
 Maxwell's Vector Potential 
 
 There is a very close connection between the 
 momentum arising from an electrified point and a
 
 LINES OF FORCE 31 
 
 magnetic system, and the Vector Potential of that 
 system, a quantity which plays a very large part 
 in Maxwell's Theory of Electricity. From the ex- 
 pression we have given for the moment of mo- 
 mentum due to a charged point and a magnetic 
 pole, we can at once find that due to a charge e of 
 electricity at a point P, and a little magnet A B ; 
 let the negative pole of this magnet be at A, the 
 positive at 23, and let m be the strength of either 
 pole. A simple calculation shows that in this 
 case the axis of the resultant moment of momen- 
 tum is in the plane P A B at right angles to P O, 
 being the middle point of A B, and that the 
 magnitude of the moment of momentum is equal 
 
 to e. m. A 
 
 makes with P. This moment of momentum is 
 equivalent in direction and magnitude to that due 
 
 to a momentum e. m. A B -z at P directed 
 
 at right angles to the plane P A B, and another 
 momentum equal in magnitude and opposite in 
 
 direction at 0. The vector m A B * at P 
 
 at right angles to the plane P A B is the vector 
 called by Maxwell the Vector Potential at P due 
 to the Magnet.
 
 32 ELECTRICITY AND MATTER 
 
 Calling this Vector Potential I, we see that the 
 momentum due to the charge and the magnet is 
 equivalent to a momentum 07 at P and a momen- 
 tum el&t the magnet. 
 
 We may evidently extend this to any complex 
 system of magnets, so that if / is the Vector Po- 
 tential at P of this system, the momentum in the 
 field is equivalent to a momentum e I at P to- 
 gether with momenta at each of the magnets 
 equal to 
 
 e (Vector Potential at P due to that magnet). 
 If the magnetic field arises entirely from electric 
 currents instead of from permanent magnets, the 
 momentum of a system consisting of an electrified 
 point and the currents will differ in some of its 
 features from the momentum when the magnetic 
 field is due to permanent magnets. In the latter 
 case, as we have seen, there is a moment of mo- 
 mentum, but no resultant momentum. When, 
 however, the magnetic field is entirely due to 
 electric currents, it is easy to show that there is a 
 resultant momentum, but that the moment of mo- 
 mentum about any line passing through the elec- 
 trified particle vanishes. A simple calculation 
 shows that the whole momentum in the field is 
 equivalent to a momentum e I at the electrified
 
 LINES OF FORCE 33 
 
 point / being the Vector Potential at P due to 
 the currents. 
 
 Thus, whether the magnetic field is due to per- 
 manent magnets or to electric currents or partly 
 to one and partly to the other, the momentum 
 when an electrified point is placed in the field at 
 P is equivalent to a momentum e Tat P where / 
 is the Vector Potential at P. If the magnetic 
 field is entirely due to currents this is a complete 
 representation of the momentum in the field ; if 
 the magnetic field is partly due to magnets we 
 have in addition to this momentum at P other 
 momenta at these magnets ; the magnitude of the 
 momentum at any particular magnet is e times 
 the Vector Potential at P due to that magnet. 
 
 The well-known expressions for the electro- 
 motive forces due to Electro-magnetic Induction 
 follow at once from this result. For, from the 
 Third Law of Motion, the momentum of any self- 
 contained system must be constant. Now the 
 momentum consists of (1) the momentum in the 
 field ; (2) the momentum of the electrified point, 
 and (3) the momenta of the magnets or circuits 
 carrying the currents. Since (1) is equivalent to 
 a momentum e 1 at the electrified particle, we see 
 that changes in the momentum of the field must
 
 34 ELECTRICITY AND MATTER 
 
 be accompanied by changes in the momentum of 
 the particle. Let M be the mass of the electrified 
 particle, u, v, w the components parallel to the 
 axes of a?, y, z of its velocity, F, G, If, the com- 
 ponents parallel to these axes of the Vector Po- 
 tential at P, then the momentum of the field is 
 equivalent to momenta e F, e G, eH at P parallel 
 to the axes of x, y, z ; and the momentum of the 
 charged point at P has for components Mu, Mo, 
 Mw. As the momentum remains constant, Mu -f- 
 e F is constant, hence if 8 u and 8 F are simulta- 
 neous changes in u and F, 
 
 = 0; 
 
 m dt 6 dt' 
 
 From this equation we see that the point with the 
 charge behaves as if it were acted upon by a me 
 chanical force parallel to the axis of x and equal to 
 
 - e j~, i.e., by an electric force equal to 
 
 dt - 
 
 In a similar way we see that there are electric 
 
 dG dff 
 
 forces - - t _ _^_, parallel to y and z respec- 
 tively. These are the well-known expressions of 
 the forces due to electro-magnetic induction, and 
 we see that they are a direct consequence of the
 
 LINES OF FORCE 35 
 
 principle that action and reaction are equal and 
 opposite. 
 
 Readers of Faraday's Experimental Researches 
 will remember that he is constantly referring to 
 what he called the " Electrotonic State " ; thus he 
 regarded a wire traversed by an electric current 
 as being in the Electrotonic State when in a 
 magnetic field. No effects due to this state can be 
 detected as long as the field remains constant ; it 
 is when it is changing that it is operative. This 
 Electrotonic State of Faraday is just the momen- 
 tum existing in the field.
 
 CHAPTER II 
 
 ELECTRICAL AND BOUND MASS. 
 
 I WISH in this chapter to consider the connec- 
 tion between the momentum in the electric field 
 and the Faraday tubes, by which, as I showed in 
 the last lecture, we can picture to ourselves the 
 state of such a field. Let us begin by considering 
 the case of the moving charged sphere. The lines 
 of electric force are radial ; those of magnetic force 
 are circles having for a common axis the line of mo- 
 tion of the centre of the sphere ; the momentum 
 at a point P is at right 
 angles to each of these 
 directions and so is at 
 right angles to O P in 
 the plane containing P 
 and the line of motion 
 of the centre of the 
 
 sphere. If the number of Faraday tubes passing 
 through a unit area at P placed at right angles 
 to O P is N, the magnetic induction at P is, 
 if IM is the magnetic permeability of the medium
 
 ELECTRICAL MASS 37 
 
 surrounding the sphere, ^-rr^Nv sin 0, v being 
 the velocity of the sphere and the angle 
 O P makes with the direction of motion of 
 the sphere. By the rule given on page 25 the 
 momentum in unit volume of the medium at P is 
 .2V X kirpNv sin 0, or kirpN^v sin 0, and is 
 in the direction of the component of the veloc- 
 ity of the Faraday tubes at right angles to their 
 length. Now this is exactly the momentum which 
 would be produced if the tubes were to carry 
 with them, when they move at right angles to 
 their length, a mass of the surrounding medium 
 equal to 4?r //, N* per unit volume, the tubes pos- 
 sessing no mass themselves and not carrying any 
 of the medium with them when they glide 
 through it parallel to their own length. We 
 suppose in fact the tubes to behave very much as 
 long and narrow cylinders behave when moving 
 through water ; these if moving endwise, i.e., par- 
 allel to their length, carry very little water along 
 with them, while when they move sideways, i.e., at 
 right angles to their axis, each unit length of the 
 tube carries with it a finite mass of water. When 
 the length of the cylinder is very great compared 
 with its breadth, the mass of water carried by it 
 when moving endwise may be neglected in com-
 
 38 ELECTRICITY AND MATTER 
 
 parison with that carried by it when moving side- 
 ways ; if the tube had no mass beyond that which 
 it possesses in virtue of the water it displaces, it 
 would have mass for sideways but none for end- 
 wise motion. 
 
 We shall call the mass 4?r p N 2 carried by the 
 tubes in unit volume the mass of the bound ether. 
 It is a very suggestive fact that the electrostatic 
 energy E in unit volume is proportional to M the 
 mass of the bound ether in that volume. This can 
 
 easily be proved as follows : E = v , where 
 
 K is the specific inductive capacity of the 
 medium ; while M = 4?r p JV 2 , thus, 
 
 M 
 
 i 
 
 but j= V* where V is the velocity with which 
 light travels through the medium, hence 
 E- 
 
 thus E is equal to the kinetic energy possessed 
 by the bound mass when moving with the veloc- 
 ity of light. 
 
 The mass of the bound ether in unit volume is 
 liriiN* where JV^is the number of Faraday tubes ; 
 thus, the amount of bound mass per unit length of
 
 ELECTRICAL MASS 
 
 each Faraday tube is TT pN. We have seen that 
 this is proportional to the tension in each tube, so 
 that we may regard the Faraday tubes as tightly 
 stretched strings of variable mass and tension ; the 
 tension being, however, always proportional to the 
 mass per unit length of the string. 
 
 Since the mass of ether imprisoned by a Faraday 
 tube is proportional to N the number of Faraday 
 tubes in unit volume, we see that the mass and 
 momentum of a Faraday tube depend not merely 
 upon the configuration and velocity of the tube 
 under consideration, but also upon the number 
 and velocity of the Faraday tubes in its neigh- 
 borhood. We have many analogies to this in the 
 case of dynamical systems ; thus, in the case of a 
 number of cylinders with their axes parallel, mov- 
 ing about in an incompressible liquid, the momen- 
 tum of any cylinder depends upon the positions 
 and velocities of the cylinders in its neighborhood. 
 The following hydro-dynamical system is one by 
 which we may illustrate the fact that the bound 
 mass is proportional to the square of the number 
 of Faraday tubes per unit volume. 
 
 Suppose we have a cylindrical vortex column of 
 strength m placed in a mass of liquid whose ve- 
 locity, if not disturbed by the vortex column, would
 
 40 
 
 ELECTRICITY AND MATTER 
 
 be constant both in magnitude and direction, and 
 at right angles to the axis of the vortex column. 
 The lines of flow in such a case are represented 
 in Fig. 11, where A is the section of the vortex 
 
 FIG. 11. 
 
 column whose axis is supposed to be at right an- 
 gles to the plane of the paper. We see that some 
 of these lines in the neighborhood of the column 
 are closed curves. Since the liquid does not cross 
 the lines of flow, the liquid inside a closed curve 
 will always remain in the neighborhood of the col- 
 umn and will move with it. Thus, the column 
 will imprison a mass of liquid equal to that en- 
 closed by the largest of the closed lines of flow. 
 If m is the strength of the vortex column and a the 
 velocity of the undisturbed flow of the liquid, we 
 can easily show that the mass of liquid imprisoned
 
 ELECTRICAL MASS 41 
 
 by the column is proportional to ^. Thus, if 
 
 d 
 
 we take m as proportional to the number of 
 Faraday tubes in unit area, the system illustrates 
 the connection between the bound mass and the 
 strength of the electric field. 
 
 Effective of Velocity on the Bound Mass 
 
 I will now consider another consequence of the 
 idea that the mass of a charged particle arises from 
 the mass of ether bound by the Faraday tube as- 
 sociated with the charge. These tubes, when they 
 move at right angles to their length, carry with 
 them an appreciable portion of the ether through 
 which they move, while when they move parallel 
 to their length, they glide through the fluid with- 
 out setting it in motion. Let us consider how a 
 long, narrow cylinder, shaped like a Faraday tube, 
 would behave when moving through a liquid. 
 
 Such a body, if free to twist in any direction, 
 will not, as you might expect at first sight, move 
 point foremost, but will, on the contrary, set itself 
 broadside to the direction of motion, setting itself 
 so as to carry with it as much of the fluid through 
 which it is moving as possible. Many illustra- 
 tions of this principle could be given, one very
 
 42 ELECTRICITY AND MATTER 
 
 familiar one is that falling leaves do not fall edge 
 first, but flutter down with their planes more or 
 less horizontal. 
 
 If we apply this principle to the charged sphere, 
 we see that the Faraday tubes attached to the 
 sphere will tend to set themselves at right angles 
 to the direction of motion of the sphere, so that if 
 this principle were the only thing to be considered 
 all the Faraday tubes would be forced up into the 
 equatorial plane, i.e., the plane at right angles to 
 the direction of motion of the sphere, for in this 
 position they would all be moving at right angles 
 to their lengths. We must remember, however, 
 that the Faraday tubes repel each other, so that 
 if they were crowded into the equatorial region 
 the pressure there would be greater than that 
 near the pole. This would tend to thrust the 
 Faraday tubes back into the position in which they 
 are equally distributed all over the sphere. The 
 actual distribution of the Faraday tubes is a com- 
 promise between these extremes. They are not 
 all crowded into the equatorial plane, neither are 
 they equally distributed, for they are more in the 
 equatorial regions than in the others ; the excess of 
 the density of the tubes in these regions increasing 
 with the speed with which the charge is moving.
 
 ELECTRICAL MASS 43 
 
 When a Faraday tube is in the equatorial region 
 it imprisons more of the ether than when it is 
 near the poles, so that the displacement of the 
 Faraday tubes from the pole to the equator will 
 increase the amount of ether imprisoned by the 
 tubes, and therefore the mass of the body. 
 
 It has been shown (see Heaviside, Phil. Mag., 
 April, 1889, "Kecent Kesearches," p. 19) that the 
 effect of the motion of the sphere is to displace 
 each Faraday tube toward the equatorial plane, 
 i.e., the plane through the centre of the sphere at 
 right angles to its direction of motion, in such a 
 way that the projection of the tube on this plane 
 remains the same as for the uniform distribution of 
 tubes, but that the distance of every point in the 
 tube from the equatorial plane is reduced in the 
 proportion of V V^-v* to V, where V is the veloc- 
 ity of light through the medium and v the velocity 
 of the charged body. 
 
 From this result we see that it is only when the 
 velocity of the charged body is comparable with 
 the velocity of light that the change in distribu- 
 tion of the Faraday tubes due to the motion of 
 the body becomes appreciable. 
 
 In " Kecent Kesearches on Electricity and Mag- 
 netism," p. 21, 1 calculated the momentum I, in the
 
 44 ELECTRICITY AND MATTER 
 
 space surrounding a sphere of radius a, having its 
 centre at the moving charged body, and showed that 
 the value of /is given by the following expression : 
 
 where as before v and Fare respectively the ve- 
 locities of the particle and the velocity of light, 
 and is given by the equation 
 
 v 
 sin = -pp. 
 
 The mass of the sphere is increased in conse- 
 quence of the charge by -,and thus we see from 
 
 equation (1) that for velocities of the charged 
 body comparable with that of light the mass of 
 the body will increase with the velocity. It is 
 evident from equation (1) that to detect the influ- 
 ence of velocity on mass we must use exceed- 
 ingly small particles moving with very high ve- 
 locities. Now, particles having masses far smaller 
 than the mass of any known atom or molecule 
 are shot out from radium with velocities ap- 
 proaching in some cases to that of light, and the 
 ratio of the electric charge to the mass for parti-
 
 ELECTRICAL MASS 45 
 
 cles of this kind has lately been made the subject 
 of a very interesting investigation by Kaufmann, 
 with the results shown in the following table ; the 
 first column contains the values of the velocities 
 of the particle expressed in centimetres per sec- 
 ond, the second column the value of the fraction 
 
 where e is the charge and m the mass of the 
 particle : 
 
 v X 10- 10 ^ X 10- T 
 
 2.83 .62 
 
 2.72 .77 
 
 2.59 . .975 
 
 2.48 1.17 
 
 2.36 1.31 
 
 
 
 We see from these values that the value of di- 
 minishes as the velocity increases, indicating, if 
 we suppose the charge to remain constant, that 
 the mass increases with the velocity. Kauf mann's 
 results give us the means of comparing the part of 
 the mass due to the electric charge with the part 
 independent of the electrification; the second 
 part of the mass is independent of the velocity. 
 If then we find that the mass varies appreciably 
 with the velocity, we infer that the part of the
 
 46 ELECTRICITY AND MATTER 
 
 mass due to the charge must be appreciable in 
 comparison with that independent of it. To cal- 
 culate the effect of velocity on the mass of an 
 electrified system we must make some assump- 
 tion as to the nature of the system, for the effect 
 on a charged sphere for example is not quite the 
 same as that on a charged ellipsoid ; but having 
 made the assumption and calculated the theoretical 
 effect of the velocity on the mass, it is easy to de- 
 duce the ratio of the part of the mass independent 
 of the charge to that part which at any velocity de- 
 pends upon the charge. Suppose that the part 
 of the mass due to electrification is at a velocity 
 v equal to m f(v) where/^) is a known function 
 of v, then if Jf w M# are the observed masses at 
 the velocities v and v 1 respectively and M the part 
 of the mass independent of charge, then 
 
 two equations from which M and m can be de- 
 termined. Kaufmann, on the assumption that 
 the charged body behaved like a metal sphere, 
 the distribution of the lines of force of which 
 when moving has been determined by G. F. C. 
 Searle, came to the conclusion that when the parti- 
 cle was moving slowly the " electrical mass " was
 
 ELECTRICAL MASS 
 
 47 
 
 about one-fourth of the whole mass. He was care- 
 ful to point out that this fraction depends upon 
 the assumption we make as to the nature of the 
 moving body, as, for example, whether it is spheri- 
 cal or ellipsoidal, insulating or conducting; and 
 that with other assumptions his experiments might 
 show that the whole mass was electrical, which he 
 evidently regarded as the most probable result. 
 
 In the present state of our knowledge of the 
 constitution of matter, I do not think anything is 
 gained by attributing to the small negatively 
 charged bodies shot out by radium and other 
 bodies the property of metallic conductivity, and 
 I prefer the simpler assumption that the distribu- 
 tion of the lines of force round these particles is 
 the same as that of the lines due to a charged 
 point, provided we confine our attention to the 
 field outside a small sphere of radius a having its 
 centre at the charged point ; on this supposition 
 the part of the mass due to the charge is the value 
 
 of in equation (1) on page 44. I have calcu- 
 lated from this expression the ratio of the masses 
 of the rapidly moving particles given out by ra- 
 dium to the mass of the same particles when at 
 rest, or moving slowly, on the assumption that the
 
 4g ELECTRICITY AND MATTER 
 
 whole of the mass is due to the charge and have com- 
 pared these results with the values of the same 
 ratio as determined by Kaufmann's experiments. 
 These results are given in Table (II), the first col- 
 umn of which contains the values of v, the veloci- 
 ties of the particles ; the second p, the number of 
 times the mass of a particle moving with this ve- 
 locity exceeds the mass of the same particle when 
 at rest, determined by equation (1) ; the third 
 column p 1 , the value of this quantity found by 
 Kaufmann in his experiments. 
 
 TABLE II. 
 
 V -LW 
 
 sec 
 
 P 
 
 P 1 
 
 2.85 
 
 3.1 
 
 3.09 
 
 2.72 
 
 2.42 
 
 2.43 
 
 2.59 
 
 2.0 
 
 2.04 
 
 2.48 
 
 1.66 
 
 1.83 
 
 2.36 
 
 1.5 
 
 1.65 
 
 These results support the view that the whole 
 mass of these electrified particles arises from their 
 charge. 
 
 We have seen that if we regard the Faraday 
 tubes associated with these moving particles as 
 being those due to a moving point charge, and
 
 ELECTRICAL MASS 
 
 49 
 
 confine our attention to the part of the field which 
 is outside a sphere of radius a concentric with the 
 charge, the mass m due to the charge e on the 
 particle is, when the particle is moving slowly, 
 
 given by the equation m = ^ 
 
 In a subsequent lecture I will explain 
 how the values of me and e have been deter- 
 mined ; the result of these determinations is that 
 
 - = 10- T and e = 1.2 X 10' 20 in G. G. 8. elec- 
 
 e 
 
 trostatic units. Substituting these values in the 
 expression for m we find that a is about 5 X 
 10~ 14 cm, a length very small in comparison with 
 the value 10~ 8 c m, which is usually taken as a good 
 approximation to the dimensions of a molecule. 
 
 We have regarded the mass in this case as due 
 to the mass of ether carried along by the Faraday 
 tubes associated with the charge. As these tubes 
 stretch out to an infinite distance, the mass of the 
 particle is as it were diffused through space, and 
 has no definite limit. In consequence, however, of 
 the very small size of the particle and the fact 
 that the mass of ether carried by the tubes (being 
 proportional to the square of the density of the 
 Faraday tubes) varies inversely as the fourth
 
 50 ELECTRICITY AND MATTER 
 
 power of the distance from the particle, we find 
 by a simple calculation that all but the most insig- 
 nificant fraction of mass is confined to a distance 
 from the particle which is very small indeed com- 
 pared with the dimensions ordinarily ascribed to 
 atoms. 
 
 In any system containing electrified bodies a 
 part of the mass of the system will consist of the 
 mass of the ether carried along by the Faraday 
 tubes associated with the electrification. Now 
 one view of the constitution of matter a view, I 
 hope to discuss in a later lecture is that the 
 atoms of the various elements are collections of 
 positive and negative charges held together mainly 
 by their electric attractions, and, moreover, that 
 the negatively electrified particles in the atom 
 (corpuscles I have termed them) are identical 
 with those small negatively electrified particles 
 whose properties we have been discussing. On 
 this view of the constitution of matter, part 
 of the mass of any body would be the mass of 
 the ether dragged along by the Faraday tubes 
 stretching across the atom between the positively 
 and negatively electrified constituents. The view 
 I wish to put before you is that it is not merely a 
 part of the mass of a body which arises in this
 
 ELECTRICAL MASS gj 
 
 way, but that the whole mass of any body is just 
 the mass of ether surrounding the body which is 
 carried along by the Faraday tubes associated 
 with the atoms of the body. In fact, that all mass 
 is mass of the ether, all momentum, momentum of 
 the ether, and all kinetic energy, kinetic energy 
 of the ether. This view, it should be said, requires 
 the density of the ether to be immensely greater 
 than that of any known substance. 
 
 It might be objected that since the mass has to 
 be carried along by the Faraday tubes and since 
 the disposition of these depends upon the relative 
 position of the electrified bodies, the mass of a 
 collection of a number of positively and negatively 
 electrified bodies would be constantly changing 
 with the positions of these bodies, and thus that 
 mass instead of being, as observation and experi- 
 ment have shown, constant to a very high degree 
 of approximation, should vary with changes in 
 the physical or chemical state of the body. 
 
 These objections do not, however, apply to such 
 a case as that contemplated in the preceding theory, 
 where the dimensions of one set of the electrified 
 bodies the negative ones are excessively small 
 in comparison with the distances separating the 
 various members of the system of electrified bodies.
 
 52 ELECTRICITY AND MATTER 
 
 When this is the case the concentration of the 
 lines of force on the small negative bodies the 
 corpuscles is so great that practically the whole 
 of the bound ether is localized around these 
 bodies, the amount depending only on their size 
 and charge. Thus, unless we alter the number or 
 character of the corpuscles, the changes occurring 
 in the mass through any alteration in their rela- 
 tive positions will be quite insignificant in com- 
 parison with the mass of the body.
 
 CHAPTER III 
 
 EFFECTS DUE TO ACCELERATION OF THE 
 FARADAY TUBES 
 
 Hontgen Rays and Light 
 
 WE have considered the behavior of the lines 
 of force when at rest and when moving uniformly, 
 we shall in this chapter consider the phenomena 
 which result when the state of motion of the lines 
 is changing. 
 
 Let us begin with the case of a moving charged 
 point, moving so slowly that the lines of force are 
 uniformly distributed around it, and consider what 
 must happen if we suddenly stop the point. The 
 Faraday tubes associated with the sphere have 
 inertia; they are also in a state of tension, the 
 tension at any point being proportional to the mass 
 per unit length. Any disturbance communicated 
 to one end of the tube will therefore travel along 
 it with a constant and finite velocity ; the tube in 
 fact having very considerable analogy with a 
 stretched string. Suppose we have a tightly 
 stretched vertical string moving uniformly, from
 
 54 
 
 ELECTRICITY AND MATTER 
 
 right to left, and that we suddenly stop one end, 
 A, what will happen to the string ? The end A 
 will come to rest at once, but the forces called 
 into play travel at a finite rate, and each part of 
 the string will in virtue of its inertia continue to 
 move as if nothing had happened to the end A 
 until the disturbance starting from A reaches it. 
 Thus, if V is the velocity with which a disturb- 
 ance travels along the string, then when a time, t, 
 has elapsed after the stoppage of A, the parts of 
 the string at a greater distance than Vt from A 
 will be unaffected by the stoppage, and will have 
 the position and velocity they would have had 
 if the string had continued to move uniformly 
 forward. The shape of the string at successive 
 intervals will be as shown in Fig. 12, the length of 
 
 j 
 
 FIG. 12. 
 
 the horizontal portion increasing as its distance 
 from the fixed end increases.
 
 RONTGEN RAYS AND LIGHT 55 
 
 Let us now return to the case of the mo vino- 
 
 o 
 
 charged particle which we shall suppose suddenly 
 brought to rest, the time occupied by the stoppage 
 being r. To find the configuration of the Faraday 
 tubes after a time t has elapsed since the beginning 
 of the process of bringing the charged particle to 
 rest, describe with the charged particle as centre 
 two spheres, one having the radius Vt, the other 
 the radius V(t T), then, since no disturbance can 
 have reached the Faraday tubes situated outside 
 the outer sphere, these tubes will be in the posi- 
 tion they would have occupied if they had moved 
 forward with the velocity they possessed at the 
 moment the particle was stopped, while inside the 
 inner sphere, since the disturbance has passed 
 over the tubes, they will be in their final positions. 
 Thus, consider a tube which, when the particle 
 was stopped was along the line OPQ (Fig. 13) ; 
 this will be the final position of the tube ; hence at 
 the time t the portion of this tube inside the inner 
 sphere will occupy the position OP, while the 
 portion P' Q f outside the outer sphere will be in the 
 position it would have occupied if the particle had 
 not been reduced to rest, i.e., if ' is the position 
 the particle would have occupied if it had not 
 been stopped, P'$ will be a straight line pass-
 
 gg ELECTRICITY AND MATTER 
 
 ing through a. Thus, to preserve its continuity 
 the tube must bend round in the sheU between the 
 two spheres, and thus be distorted into the shape 
 OPP'Q'. Thus, the tube which before the stop- 
 
 o 
 
 FIG. 13. 
 
 page of the particle was radial, has now in the 
 shell a tangential component, and this tangential 
 component implies a tangential electric force. 
 The stoppage of the particle thus produces a 
 radical change in the electric field due to the par- 
 ticle, and gives rise, as the following calculation 
 will show, to electric and magnetic forces much 
 greater than those existing in the field when the 
 particle was moving steadily. 
 
 If we suppose that the thickness 8 of the shell 
 is so small that the portion of the Faraday tube 
 inside it may be regarded as straight, then if T is
 
 RONTGEN RAYS AND LIGHT 57 
 
 the tangential electric force inside the pulse, R 
 the radial force, we have 
 
 T_ _ P'R _ 00' sin 6 _vtsm0 
 R~ PR S~ ~~8~' W 
 
 Where v is the velocity with which the particle 
 was moving before it was stopped, the angle 
 OP makes with the direction of motion of the 
 particle, t the time which has elapsed since the par- 
 ticle was stopped ; since R = ^ andO P = Vt 
 where Fis the velocity of light, we have, if r = OP, 
 
 T= ^ ^-. (2) 
 
 V TO 
 
 The tangential Faraday tubes moving forward 
 with the velocity y will produce at P a magnetic 
 force H equal to V T, this force will be at right 
 angles to the plane of the paper and in the 
 opposite direction to the magnetic force existing 
 at P before the stoppage of the particle ; since its 
 magnitude is given by the equation, 
 
 Tr evsinff 
 * > 
 
 e v sin . , 
 it exceeds the magnetic force ^ previously 
 
 existing in the proportion of r to 8. Thus, the
 
 gg ELECTRICITY AND MATTER 
 
 pulse produced by the stoppage of the particle is 
 the seat of intense electric and magnetic forces 
 which diminish inversely as the distance from the 
 charged particle, whereas the forces before the 
 particle was stopped diminished inversely as the 
 square of the distance ; this pulse travelling out- 
 ward with the velocity of light constitutes in my 
 opinion the Eontgen rays which are produced 
 when the negatively electrified particles which 
 form the cathode rays are suddenly stopped by 
 striking against a solid obstacle. 
 The energy in the pulse can easily be shown 
 
 to be equal to 
 
 2 eW 
 
 3 8 ' 
 
 this energy is radiated outward into space. 
 The amount of energy thus radiated depends 
 upon 8, the thickness of the pulse, i. e., upon 
 the abruptness with which the particle is 
 stopped; if the particle is stopped instantaneously 
 the whole energy in the field will be absorbed in 
 the pulse and radiated away, if it is stopped grad- 
 ually only a fraction of the energy will be radiated 
 into space, the remainder will appear as heat at 
 the place where the cathode rays were stopped. 
 It is easy to show that the momentum in the
 
 RONTGEN RAYS AND LIGHT 59 
 
 pulse at any instant is equal and opposite to the 
 momentum in the field outside the pulse ; as there 
 is no momentum in the space through which the 
 pulse has passed, the whole momentum in the field 
 after the particle is stopped is zero. 
 
 The preceding investigation only applies to the 
 case when the particle was moving so slowly that 
 the Faraday tubes before the stoppage of the 
 pulse were uniformly distributed; the same 
 principles, however, will give us the effect of 
 stopping a charged particle whenever the dis- 
 tribution of the Faraday tubes in the state of 
 steady motion has been determined. 
 
 Let us take, for example, the case when the 
 particle was initially moving with the velocity of 
 light; the rule stated on page 43 shows that 
 before the stoppage the Faraday tubes were 
 all congregated in the equatorial plane of the 
 moving particle. To find the configuration of 
 the Faraday tubes after a time t we proceed as 
 before by finding the configuration at that time 
 of the tubes, if the particle had not been stopped. 
 The tubes would in that case have been in a plane 
 at a distance Vt in front of the particle. Draw 
 two spheres having their centres at the particle and 
 having radii respectively equal to Vt and V (t T),
 
 gO ELECTRICITY AND MATTER 
 
 where T is the time occupied in stopping the 
 particle; outside the outer sphere the configura- 
 tion of the tubes will be the same as if the par- 
 ticle had not been stopped, i. e., the tubes will be 
 the plane at the distance Vt in front of the par- 
 ticle, and this plane will touch the outer sphere. 
 Inside the inner sphere the Faraday tubes will be 
 uniformly distributed, hence to preserve continuity 
 these tubes must run round in the shell to join the 
 sphere as in Fig. 14. We thus have in this case 
 
 two pulses, one a 
 plane pulse propa- 
 gated in the direc- 
 tion in which the 
 particle was mov- 
 ing before it was 
 stopped, the other a 
 pi' spherical pulse trav- 
 elling outward in all 
 directions. 
 
 The preceding 
 method can be ap- 
 
 PlG. 14. 
 
 plied to the case 
 
 when the charged particle, instead of being 
 stopped, has its velocity altered in any way ; thus, 
 if the velocity v of the particle instead of being
 
 RONTGEN RAYS AND LIGHT 
 
 61 
 
 reduced to zero is merely diminished by A v, we 
 can show, as on page 57, that it will give rise to 
 a pulse in which the magnetic force If is given by 
 the equation 
 
 ^ e&v sin 
 
 H = - 
 
 and the tangential electric force T by 
 m e . A v sin 6 
 
 Now the thickness 8 of the pulse is the space 
 passed over by a wave of light during the time the 
 velocity of the particle is changing, hence if 8 1 
 is the time required to produce the change A v in 
 the velocity 8 = KS t, hence we have 
 
 e &v sin 6 ^ _ e At; sin 
 
 ~- VTt~T~ z T*Wi~r 
 
 but gg is equal to /, where/ is the acceleration 
 of the particle, hence we have 
 
 These equations show that a charged particle 
 whose motion is being accelerated produces a pulse 
 of electric and magnetic forces in which the forces 
 vary inversely as the distance from the particle. 
 
 Thus, if a charged body were made to vibrate in
 
 Q2 ELECTRICITY AND MATTER 
 
 such a way that its acceleration went through 
 periodic changes, periodic waves of electric and 
 magnetic force would travel out from the charged 
 body. These waves would, on the Electromag- 
 netic Theory of Light, be light waves, provided 
 the periodic changes in the acceleration of the 
 charged body took place with sufficient rapidity. 
 The method we have been investigating, in which 
 we consider the effect produced on the configura- 
 tion of the Faraday tubes by changes in the mo- 
 tion of the body, affords a very simple way of 
 picturing to ourselves the processes going on dur- 
 ing the propagation of a wave of light through 
 the ether. We have regarded these as arising 
 from the propagation of transverse tremors along 
 the tightly stretched Faraday tubes; in fact, we 
 are led to take the same view of the propagation 
 of light as the following extracts from the paper, 
 "Thoughts on Ray Vibrations," show to have 
 been taken by Faraday himself. Faraday says, 
 " The view which I am so bold to put forward 
 considers therefore radiations as a high species of 
 vibration in the lines of force which are known 
 to connect particles and also masses together." 
 
 This view of light as due to the tremors in 
 tightly stretched Faraday tubes raises a question
 
 RONTGEN RAYS AND LIGHT (J3 
 
 which I have not seen noticed. The Faraday 
 tubes stretching through the ether cannot be 
 regarded as entirely filling it. They are rather 
 to be looked upon as discrete threads embedded 
 in a continuous ether, giving to the latter a fibrous 
 structure ; but if this is the case, then on the view 
 we have taken of a wave of light the wave it- 
 self must have a structure, and the front of the 
 wave, instead of being, as it were, uniformly illu- 
 minated, will be represented by a series of bright 
 specks on a dark ground, the bright specks cor- 
 responding to the places where the Faraday tubes 
 cut the wave front. 
 
 Such a view of the constitution of a light wave 
 would explain a phenomenon which has always 
 struck me as being very remarkable and difficult 
 to reconcile with the view that a light wave, or 
 rather in this case a Rontgen ray, does not possess 
 a structure. We have seen that the method of 
 propagation and constitution of a Rontgen ray 
 is the same as in a light wave, so that any 
 general consideration about structure in Ront- 
 gen rays will apply also to light waves. The 
 phenomenon in question is this: Rontgen rays 
 are able to pass very long distances through 
 gases, and as they pass through the gas they
 
 Q ELECTRICITY AND MATTER 
 
 ionize it, splitting up the molecules into posi- 
 tive and negative ions ; the number of molecules 
 so split up is, however, an exceedingly small frac- 
 tion, less than one-billionth, even for strong rays, of 
 the number of molecules in the gas. Now, if the 
 conditions in the front of the wave are uniform, all 
 the molecules of the gas are exposed to the same 
 conditions ; how is it then that so small a propor- 
 tion of them are split up ? It might be argued that 
 those split up are in some special condition that 
 they possess, for example, an amount of kinetic 
 energy so much exceeding the average kinetic 
 energy of the molecules of the gas that, in accord- 
 ance with Maxwell's Law of Distribution of 
 Kinetic energy, their number would be exceedingly 
 small in comparison with the whole number of 
 molecules of the gas ; but if this were the case the 
 same law of distribution shows that the number 
 in this abnormal condition would increase very 
 rapidly with the temperature, so that the ioniza- 
 tion produced by the Rontgen rays ought to in- 
 crease very rapidly as the temperature increases. 
 Recent experiments made by Mr. McClung in the 
 Cavendish Laboratory show that no appreciable 
 increase in the ionization is produced by raising 
 the temperature of a gas from 15C. to 200 C.,
 
 RONTGEN RAYS AND LIGHT 55 
 
 whereas the number of molecules possessing an 
 
 JT O 
 
 abnormal amount of kinetic energy would be 
 enormously increased by this rise in temperature. 
 The difficulty in explaining the small ionization is 
 removed if, instead of supposing the front of the 
 Rontgen ray to be uniform, we suppose that it con- 
 sists of specks of great intensity separated by 
 considerable intervals where the intensity is very 
 small, for in this case all the molecules in the field, 
 and probably even different parts of the same 
 molecule, are not exposed to the same conditions, 
 and the case becomes analogous to a swarm of 
 cathode rays passing through the gas, in which 
 case the number of molecules which get into col- 
 lision with the rays may be a very small fraction 
 of the whole number of molecules. 
 
 To return, however, to the case of the charged 
 particle whose motion is accelerated, we have 
 seen that from the particle electric and magnetic 
 forces start and travel out radially with the ve- 
 locity of light, both the radial and magnetic forces 
 being at right angles to the direction in which 
 they are travelling; but since (see page 25) 
 each unit volume of the electro-magnetic field has 
 an amount of momentum equal to the product of 
 the density of the Faraday tube and the magnetic
 
 QQ ELECTRICITY AND MATTER 
 
 force, the direction of the momentum being at 
 right angles to both these quantities, there will be 
 the wave due to the acceleration of the charged 
 particle, and indeed in any electric or light wave 
 momentum in the direction of propagation of the 
 wave. Thus, if any such wave, for example a 
 wave of light, is absorbed by the substance through 
 which it is passing, the momentum in the wave 
 will be communicated to the absorbing substance, 
 which will, therefore, experience a force tending to 
 push it in the direction the light is travelling. 
 Thus, when light falls normally on a blackened ab- 
 sorbing substance, it will repel that substance. 
 This repulsion resulting from radiation was shown 
 by Maxwell to be a consequence of the Electro- 
 magnetic Theory of Light ; it has lately been de- 
 tected and measured by Lebedew by some most 
 beautiful experiments, which have been confirmed 
 and extended by Nichols and Hull. 
 
 The pressure experienced by the absorbing sub- 
 stance will be proportional to its area, while the 
 weight of the substance is proportional to its vol- 
 ume. Thus, if we halve the linear dimensions we 
 reduce the weight to one-eighth while we only re- 
 duce the pressure of radiation to one-quarter ; thus, 
 by sufficiently reducing the size of the absorbing
 
 RONTGEN RAYS AND LIGHT 67 
 
 body we must arrive at a stage when the forces 
 due to radiation exceed those which, like weight, 
 are proportional to the volume of the substance. 
 On this principle, knowing the intensity of the 
 radiation from the sun, Arrhenius has shown that 
 for an opaque sphere of unit density 10" 5 cm. in 
 diameter the repulsion due to the radiation from 
 the sun would just balance the sun's attraction, 
 while all bodies smaller than this would be re- 
 pelled from the sun, and he has applied this prin- 
 ciple to explain the phenomena connected with 
 the tails of comets. Poynting-has recently shown 
 that if two spheres of unit density about 39 cm. 
 in diameter are at the temperature of 27 C. and 
 protected from all external radiation, the re- 
 pulsion due to the radiation emitted from the 
 spheres will overpower their gravitational at- 
 traction so that the spheres will repel each 
 other. 
 
 Again, when light is refracted and reflected 
 at a transparent surface, the course of the light 
 and therefore the direction of momentum is 
 changed, so that the refracting substance must 
 have momentum communicated to it. It is easy 
 to show that even when the incidence of the light 
 is oblique the momentum communicated to the
 
 gg ELECTRICITY AND MATTER 
 
 substance is normal to the refracting surface. 
 There are many interesting problems connected 
 with the forces experienced by refracting prisms 
 when light is passing through them which will 
 suggest themselves to you if you consider the 
 changes in momentum experienced by the light 
 wave in its course through the prism. Tangential 
 forces due to light have not, so far as I know, 
 been detected experimentally. These, however, 
 must exist in certain cases ; such, for example, as 
 when light incident obliquely is imperfectly re- 
 flected from a metallic surface. 
 
 The waves of electric and magnetic force which 
 radiate from an accelerated charge particle carry 
 energy with them. This energy is radiated into 
 space, so that the particle is constantly losing en- 
 ergy. The rate at which energy is radiating from 
 
 the particle can easily be shown to be where 
 
 e is the charge on the particle,/ its acceleration, 
 and V the velocity of light. If we take into ac- 
 count this loss of energy by the particle when its 
 motion is being accelerated, we find some interest- 
 ing results. Thus, for example, if a particle of 
 mass m and charge e starting from rest is acted 
 upon by a constant electric force, JT, the particle
 
 RONTGEN RAYS AND LIGHT gg 
 
 does not at once attain the acceleration as it 
 
 m 
 
 would if there were no loss of energy by radia- 
 tion; on the contrary, the acceleration of the parti- 
 cle is initially zero, and it is not until after the 
 
 e * 
 lapse of a time comparable with -jj^- that the 
 
 particle acquires even an appreciable fraction of 
 its final acceleration. Thus, the rate at which the 
 
 e* 
 particle loses energy is during the time -y very 
 
 small compared with the ultimate rate. Thus, if 
 the particle were acted on by a wave of electric 
 
 e* 
 force which only took a time comparable with -y 
 
 to pass over the particle, the amount of energy ra- 
 diated by the particle would be a very much smaller 
 fraction of the energy in the wave than it would be 
 if the particle took a time equal to a considerable 
 
 e* 
 multiple of y^ to pass over the particle. This has 
 
 an important application in explaining the greater 
 penetrating power of " hard " Rontgen rays than 
 of " soft " ones. The " hard " rays correspond to 
 thin pulses, the " soft " ones to thick ones ; so that 
 a smaller proportion of the energy in the " hard " 
 rays will be radiated away by the charged particles
 
 70 ELECTRICITY AND MATTER 
 
 over which they pass than in the case of the ''soft" 
 rays. 
 
 By applying the law that the rate at which en- 
 
 ergy is radiating is equal to -y- to the case of 
 
 a charged particle revolving in a circular orbit un- 
 der an attractive force varying inversely as the 
 square of the distance, we find that in this case 
 the rate of radiation is proportional to the eighth 
 power of the velocity, or to the fourth power of 
 the energy. Thus, the rate of loss of energy by 
 radiation increases very much more rapidly than 
 the energy of the moving body.
 
 CHAPTER IV 
 
 THE ATOMIC STRUCTURE OF ELECTRICITY 
 
 HITHERTO we have been dealing chiefly with the 
 properties of the lines of force, with their ten- 
 sion, the mass of ether they carry along with them, 
 and with the propagation of electric disturbances 
 along them ; in this chapter we shall discuss the 
 nature of the charges of electricity which form the 
 beginnings and ends of these lines. We shall show 
 that there are strong reasons for supposing that 
 these changes have what may be called an atomic 
 structure ; any charge being built up of a number 
 of finite individual charges, all equal to each other : 
 just as on the atomic theory of matter a quantity 
 of hydrogen is built up of a number of small par- 
 ticles called atoms, all the atoms being equal to 
 each other. If this view of the structure of elec- 
 tricity is correct, each extremity of a Faraday tube 
 will be the place from which a constant fixed num- 
 ber of tubes start or at which they arrive. 
 
 Let us first consider the evidence given by the 
 laws of the electrolysis of liquids. Faraday
 
 72 ELECTRICITY AND MATTER 
 
 showed that when electricity passes through a 
 liquid electrolyte, the amount of negative electric- 
 ity given up to the positive electrode, and of posi- 
 tive electricity given to the negative electrode, is 
 proportional to the number of atoms coming up 
 to the electrode. Let us first consider monovalent 
 elements, such as hydrogen, chlorine, sodium, and 
 so on ; he showed that when the same number of 
 atoms of these substances deliver up their 
 charges to the electrode, the quantity of electricity 
 communicated is the same whether the carriers 
 are atoms of hydrogen, chlorine, or sodium, in- 
 dicating that each atom of these elements carries 
 the same charge of electricity. Let us now go to 
 the divalent elements. We find again that the ions 
 of all divalent elements carry the same charge, 
 but that a number of ions of the divalent ele- 
 ment carry twice the charge carried by the same 
 number of ions of a univalent element, showing 
 that each ion of a divalent element carries twice 
 as much charge as the univalent ion ; again, a tri- 
 valent ion carries three times the charge of a uni- 
 valent ion, and so on. Thus, in the case of the elec- 
 trolysis of solutions the charges carried by the 
 ions are either the charge on the hydrogen ion or 
 twice that charge, or three times the charge, and
 
 THE ATOMIC STRUCTURE OF ELECTRICITY 73 
 
 so on. The charges we meet with are always an 
 integral multiple of the charge carried by the hy- 
 drogen atom ; we never meet with fractional parts 
 of this charge. This very remarkable fact shows, 
 as Helmholtz said in the Faraday lecture, that 
 " if we accept the hypothesis that the elementary 
 substances are composed of atoms, we cannot avoid 
 the conclusion that electricity, positive as well as 
 negative, is divided into definite elementary por- 
 tions which behave like atoms of electricity." 
 
 When we consider the conduction of electricity 
 through gases, the evidence in favor of the atomic 
 character of electricity is even stronger than it is 
 in the case of conduction through liquids, chiefly 
 because we know more about the passage of elec- 
 tricity through gases than through liquids. 
 
 Let us consider for a moment a few of the prop- 
 erties of gaseous conduction. When a gas has 
 been put into the conducting state say, by expos- 
 ure to Kontgen rays it remains in this state for 
 a sufficiently long time after the rays have ceased 
 to enable us to study its properties. We find that 
 we can filter the conductivity out of the gas by 
 sending the gas through a plug of cotton-wool, or 
 through a water-trap. Thus, the conductivity is 
 due to something mixed with the gas which can
 
 74 ELECTRICITY AND MATTER 
 
 be filtered out of it; again, the conductivity is 
 taken out of the gas when it is sent through a 
 strong electric field. This result shows that the 
 constituent to which the conductivity of the gas is 
 due consists of charged particles, the conductivity 
 arising from the motion of these particles in the 
 electric field. We have at the Cavendish Labora- 
 tory measured the charge of electricity carried by 
 those particles. 
 
 The principle of the method first used is as fol- 
 lows. If at any time there are in the gas n of these 
 particles charged positively and n charged nega- 
 tively, and if each of these carries an electric charge 
 e, we can easily by electrical methods determine n e, 
 the quantity of electricity of our sign present in 
 the gas. One method by which this can be done 
 is to enclose the gas between two parallel metal 
 plates, one of which is insulated. Now suppose we 
 suddenly charge up the other plate positively to a 
 very high potential, this plate will now repel the 
 positive particles in the gas, and these before they 
 have time to combine with the negative particles 
 will be driven against the insulated plate. Thus, 
 all the positive charge in the gas will be driven 
 against the insulated plate, where it can be meas- 
 ured by an electrometer. As this charge is equal
 
 THE ATOMIC STRUCTURE OF ELECTRICITY 75 
 
 to n e we can in this way easily determine n e : if 
 then we can devise a means of measuring n we 
 shall be able to find e. The method by which I 
 determined n was founded on the discovery by 
 C. T. R. Wilson that the charged particles act as 
 nuclei round which small drops of water condense, 
 when the particles are surrounded by damp air 
 cooled below the saturation point. In dust-free 
 air, as Aitken showed, it is very difficult to get a 
 fog when damp air is cooled, since there are no 
 nuclei for the drops to condense around ; if there 
 are charged particles in the dust-free air, however, 
 a fog will be deposited round these by a supersat- 
 uration far less than that required to produce any 
 appreciable effect when no charged particles are 
 present. 
 
 Thus, in sufficiently supersaturated damp air a 
 cloud is deposited on these charged particles, 
 and they are thus rendered visible. This is the 
 first step toward counting them. The drops are, 
 however, far too small and too numerous to be 
 counted directly. We can, however, get their 
 number indirectly as follows : suppose we have a 
 number of these particles in dust-free air in a 
 closed vessel, the air being saturated with water 
 vapor, suppose now that we produce a sudden
 
 76 ELECTRICITY AND MATTER 
 
 expansion of the air in the vessel; this will cool 
 the air, it will be supersaturated with vapor, and 
 drops will be deposited round the charged parti- 
 cles. Now if we know the amount of expansion 
 produced we can calculate the cooling of the gas, 
 and therefore the amount of water deposited. 
 Thus, we know the volume of water in the form of 
 drops, so that if we know the volume of one drop 
 we can deduce the number of drops. To find the 
 size of a drop we make use of an investigation 
 by Sir George Stokes on the rate at which small 
 spheres fall through the air. In consequence of 
 the viscosity of the air small bodies fall exceedingly 
 slowly, and the smaller they are the slower they 
 fall. Stokes showed that if a is the radius of a 
 drop of water, the velocity v with which it falls 
 through the air is given by the equation 
 
 -'& 
 
 when g is the acceleration due to gravity = 981 
 and ji the coefficient of viscosity of air = .00018; 
 thus 
 
 v = 1.21 X 10 6 a 8 ; 
 
 hence if we can determine v we can determine 
 the radius and hence the volume of the drop.
 
 THE ATOMIC STRUCTURE OF ELECTRICITY 77 
 
 But v is evidently the velocity with which the 
 cloud round the charged particle settles down, and 
 can easily be measured by observing the move- 
 ment of the top of the cloud. In this way I 
 found the volume of the drops, and thence n the 
 number of particles. As n e had been determined 
 by electrical measurements, the value of e could 
 be deduced when n was known ; in this way I 
 found that its value is 
 
 3.4 X 10- 10 Electrostatic C. G. S. units. 
 
 Experiments were made with air, hydrogen, 
 and carbonic acid, and it was found that the 
 ions had the same charge in all these gases; a 
 strong argument in favor of the atomic character 
 of electricity. 
 
 We can compare the charge on the gaseous ion 
 with that carried by the hydrogen ion in the elec- 
 trolysis of solutions in the following way: We 
 know that the passage of one electro-magnetic 
 unit of electric charge, or 3 X 10 10 electrostatic 
 units, through acidulated water liberates 1.23 c.c. 
 of hydrogen at the temperature 15C. and pressure 
 of one atmosphere ; if there are N molecules in a 
 c.c. of a gas at this temperature and pressure the 
 number of hydrogen ions in 1.23 c.c. is 2.46 N,
 
 7 g ELECTRICITY AND MATTER 
 
 so that if .#is the charge on the hydrogen ion in 
 the electrolyis of solution, 
 
 2.46 NE=ZX 10 10 , 
 or E= 1.22 X 10 10 ^JV: 
 
 Now, e, the charge on the gas ion is 3.4 X10" 10 , 
 hence if -LV=3.6X10 19 the charge on the gaseous 
 ion will equal the charge on the electrolytic ion. 
 Now, in the kinetic theory of gases methods are 
 investigated for determining this quantity JVJ or 
 Avogadro's Constant, as it is sometimes called ; the 
 values obtained by this theory vary somewhat 
 with the assumptions made as to the nature of 
 the molecule and the nature of the forces which one 
 molecule exerts on another in its near neighbor- 
 hood. The value 3.6X10 19 is, however, in good 
 agreement with some of the best of these deter- 
 minations, and hence we conclude that the charge 
 on the gaseous ion is equal to the charge on the 
 electrolytic ion. 
 
 Dr. H. A. Wilson, of the Cavendish Laboratory, 
 by quite a different method, obtained practically 
 the same value for e as that given above. His 
 method was founded on the discovery by C. T. R 
 Wilson that it requires less supersaturation to 
 deposit clouds from moist air on negative ions
 
 THE ATOMIC STRUCTURE OF ELECTRICITY 79 
 
 than it does on positive. Thus, by suitably 
 choosing the supersaturation, we can get the 
 cloud deposited on the negative ions alone, so 
 that each drop in the cloud is negatively charged ; 
 by observing the rate at which the cloud falls we 
 can, as explained above, determine the weight of 
 each drop. Now, suppose we place above the 
 cloud a positively electrified plate, the plate will 
 attract the cloud, and we can adjust the charge on 
 the plate until the electric attraction just balances 
 the weight of a drop, and the drops, like Mahomet's 
 coffin, hang stationary in the air; if X is the 
 electric force then the electric attraction on the 
 drop is Xe, when e is the charge on the drop. As 
 X e is equal to the weight of the drop which is 
 known, and as we can measure X, e can be at once 
 determined. 
 
 Townsend showed that the charge on the 
 gaseous ion is equal to that on the ion of hydrogen 
 in ordinary electrolysis, by measuring the coeffi- 
 cient of diffusion of the gaseous ions and com- 
 paring it with the velocity acquired by the ion 
 under a given electric force. Let us consider the 
 case of a volume of ionized gas between two 
 horizontal planes, and suppose that as long as we 
 keep in any horizontal layer the number of ions
 
 gO ELECTRICITY AND MATTER 
 
 remains the same, but that the number varies as 
 we pass from one layer to another; let x be the 
 distance of a layer from the lower plane, n 
 the number of ions of one sign in unit volume 
 of this layer, then if D be the coefficient of 
 diffusion of the ions, the number of ions which 
 in one second pass downward through unit area 
 of the layer is 
 
 n dn ' 
 
 so that the average velocity of the particles down- 
 ward is 
 
 n d x 
 
 The force which sets the ions in motion is the 
 variation in the partial pressure due to the ions ; if 
 this pressure is equal top, the force acting on the 
 
 ions in a unit volume is -T-I and the average force 
 
 per ion is - -f. Now we can find the velocity 
 ndx 
 
 which an ion acquires when acted upon by a 
 known force by measuring, as Rutherford and 
 Zeleny have done, the velocities acquired by the 
 ions in an electric field. They showed that this 
 velocity is proportional to the force acting on the 
 ion, so that if A is the velocity when the electric
 
 THE ATOMIC STRUCTURE OF ELECTRICITY gj 
 
 force is Xand when the force acting on the ion is 
 therefore X e, the velocity for unit force will be 
 
 , and the velocity when the force is - ^ will 
 
 n dx 
 
 ^ 
 -<* 
 
 therefore be 
 
 _ 
 
 n dx Xe y 
 
 this velocity we have seen, however, to be equal to 
 
 D dn m 
 
 n dx' 
 hence we have 
 
 Q*=D d *. (1) 
 
 dx Ae dx 
 
 Now if the ions behave like a perfect gas, the 
 pressure p bears a constant ratio to n, the number 
 of ions per unit volume. This ratio is the same 
 for all gases, at the same temperature, so that if 
 jVis Avogadro's constant, i.e., the number of mol- 
 ecules in a cubic centimetre of gas at the atmos- 
 pheric pressure P 
 
 n 
 
 p _ 
 P~ 
 
 and equation (1) gives us 
 PA 
 
 Thus, by knowing D and a we can find the value 
 of Ne. In this way Townsend found that Ne was
 
 g2 ELECTRICITY AND MATTER 
 
 the same in air, hydrogen, oxygen, and carbonic 
 acid, and the mean of his values was Ne = 1.24 
 X 10 10 . We have seen that if ^is the charge on 
 the hydrogen ion 
 
 NE = 1.22 X 10 10 . 
 
 Thus, these experiments show that e=E,m that 
 the charge on the gaseous ion is equal to the 
 charge carried by the hydrogen ion in the elec- 
 trolysis of solutions. 
 
 The equality of these charges has also been 
 proved in a very simple way by H. A. Wilson, 
 who introduced per second into a volume of air 
 at a very high temperature, a measured quan- 
 tity of the vapor of metallic salts. This vapor 
 got ionized and the mixture of air and vapor ac- 
 quired very considerable conductivity. The cur- 
 rent through the vapor increased at first with the 
 electromotive force used to drive it through the 
 gas, but this increase did not go on indefinitely, 
 for after the current had reached a certain value 
 no further increase in the electromotive force pro- 
 duced any change in the current. The current, as 
 in all cases of conduction through gases, attained 
 a maximum value called the " saturation current," 
 which was not exceeded until the electric field ap- 
 plied to the gas approached the intensity at which
 
 THE ATOMIC STRUCTURE OF ELECTRICITY 53 
 
 sparks began to pass through the gas. Wilson 
 found that the saturation current through the salt 
 vapor was just equal to the current which if it 
 passed through an aqueous solution of the salt 
 would electrolyse in one second the same amount 
 of salt as was fed per second into the hot air. 
 
 It is worth pointing out that this result gives 
 us a method of determining Avogadro's Constant 
 which is independent of any hypothesis as to the 
 shape or size of molecules, or of the way in which 
 they act upon each other. If JVis this constant, e 
 the charge on an ion, then N e = 1.22 X 10 10 and 
 we have seen that e = 3.4 X 10 10 , so that JV= 3.9 
 
 X io 19 . 
 
 Thus, whether we study the conduction of elec- 
 tricity through liquids or through gases, we are 
 led to the conception of a natural unit or atom of 
 electricity of which all charges are integral mul- 
 tiples, just as the mass of a quantity of hydro- 
 gen is an integral multiple of the mass of a 
 hydrogen atom. 
 
 Mass of the Carriers of Electricity 
 
 We must now pass on to consider the nature 
 of the systems which carry the charges, and in 
 order to have the conditions as simple as possible
 
 g4 ELECTRICITY AND MATTER 
 
 let us begin with the case of a gas at a very low 
 pressure, where the motion of the particles is not 
 impeded by collisions with the molecules of the 
 gas. Let us suppose that we have a particle of 
 mass m, carrying a charge e y moving in the plane 
 of the paper, and that it is acted on by a uniform 
 magnetic field at right angles to this plane. We 
 have seen that under these circumstances the par- 
 ticle will be acted upon by a mechanical force 
 equal to He v, where ^Tis the magnetic force and 
 v the velocity of the particle. The direction of 
 this force is in the plane of the paper at right 
 angles to the path of the particle. Since the 
 force is always at right angles to the direction 
 of motion of the particle, the velocity of the par- 
 ticle and therefore the magnitude of the force act- 
 ing upon it will not alter, so that the path of the 
 particle will be that described by a body acted 
 upon by a constant normal force. It is easy to show 
 that this path is a circle whose radius a is given 
 by the equation 
 
 mv , , 
 
 The velocity v of the particle may be deter- 
 mined by the following method : Suppose the par- 
 ticle is moving horizontally in the plane of the
 
 THE ATOMIC STRUCTURE OF ELECTRICITY g5 
 
 paper, through a uniform magnetic field H, at 
 right angles to this plane, the particle will be 
 acted upon by a vertical force equal toffev. Now, 
 if in addition to the magnetic force we apply a 
 vertical electric force X, this will exert a verti- 
 cal mechanical force X e on the moving particle. 
 Let us arrange the direction of JTso that this force 
 is in the opposite direction to that due to the mag- 
 net, and adjust the value of X until the two forces 
 are equal. We can tell when this adjustment has 
 been made, since in this case the motion of the 
 particle under the action of the electric and mag- 
 netic forces will be the same as when both these 
 forces are absent. When the two forces are equal 
 
 we have 
 
 or 
 
 Hence if we have methods of tracing the motion 
 of the particle, we can measure the radius a of the 
 circle into which it is bent by a constant magnetic 
 force, and determine the value of the electric force 
 required to counteract the effect of the magnetic 
 force. Equations (1) and (2) then give us the 
 
 means of finding both v and
 
 gg ELECTRICITY AND MATTER 
 
 Values of for Negatively Electrified Particles 
 m 
 
 in Gases at Low Pressures 
 
 The value of e - has been determined in this 
 
 m 
 
 way for the negatively electrified particles which 
 form the cathode rays which are so conspicuous a 
 part of the electric discharge through a gas at low 
 pressures ; and also for the negatively electrified 
 particles emitted by metals, (1) when exposed to 
 ultra-violet light, (2) when raised to the tempera- 
 ture of incandescence. These experiments have 
 led to the very remarkable result that the value of 
 
 is the same whatever the nature of the gas in 
 m 
 
 which the particle may be found, or whatever the 
 nature of the metal from which it may be sup- 
 posed to have proceeded. In fact, in every case 
 
 p 
 
 in which the value of has been determined for 
 m 
 
 negatively electrified particles moving with veloci- 
 ties considerably less than the velocity of light, it 
 has been found to have the constant value about 
 10 T , the units being the centimetre, gram, and 
 second, and the charge being measured in electro- 
 
 ^ 
 
 magnetic units. As the value of for the hydro-
 
 THE ATOMIC STRUCTURE OF ELECTRICITY 37 
 
 gen ion in the electrolysis of liquids is only 10 4 , 
 and as we have seen the charge on the gaseous 
 ion is equal to that on the hydrogen ion in ordi- 
 nary electrolysis, we see that the mass of a carrier 
 of the negative charge must be only about one- 
 thousandth part of the mass of hydrogen atom ; 
 the mass was for a long time regarded as the small- 
 est mass able to have an independent existence. 
 
 I have proposed the name corpuscle for these 
 units of negative electricity. These corpuscles 
 are the same however the electrification may have 
 arisen or wherever they may be found. Negative 
 electricity, in a gas at a low pressure, has thus a 
 structure analogous to that of a gas, the corpuscles 
 taking the place of the molecules. The " negative 
 electric fluid," to use the old notation, resembles 
 a gaseous fluid with a corpuscular instead of a 
 molecular structure. 
 
 Carriers of Positive Electrification 
 We can apply the same methods to determine 
 the values of for the carriers of positive electri- 
 fication. This has been done by Wien for the 
 positive electrification found in certain parts of 
 the discharge in a vacuum tube, and I have
 
 CQ ELECTRICITY AND MATTER 
 
 oo 
 
 measured for the positive electrification given 
 
 / lYb 
 
 off by a hot wire. The results of these measure- 
 ments form a great contrast to those for the nega- 
 tive electrification, for for the positive charge, 
 
 instead of having, as it has for the negative, the 
 constant high value 10 7 , is found never to have a 
 value greater than 10 4 , the value it would have if 
 the carrier were the atom of hydrogen. In many 
 
 cases the value of is very much less than 10 4 , in- 
 dicating that in these cases the positive charge is 
 carried by atoms having a greater mass than that 
 
 x? 
 
 of the hydrogen atom. The value of varies with 
 
 the nature of the electrodes and with the gas in 
 the discharge tube, just as it would if the carriers 
 of the positive charge were the atoms of the 
 elements which happened to be present when the 
 positive electrification was produced. 
 
 These results lead us to a view of electrification 
 which has a striking resemblance to that of 
 Franklin's "One Fluid Theory of Electricity." 
 Instead of taking, as Franklin did, the electric 
 fluid to be positive electricity we take it to be 
 negative. The "electric fluid" of Franklin cor-
 
 THE ATOMIC STRUCTURE OF ELECTRICITY 39 
 
 responds to an assemblage of corpuscles, negative 
 electrification being a collection of these corpus- 
 cles. The transference of electrification from one 
 place to another is effected by the motion of cor- 
 puscles from the place where is a gain of positive 
 electrification to the place where there is a gain 
 of negative. A positively electrified body is one 
 that has lost some of its corpuscles. We have 
 seen that the mass and charge of the corpuscles 
 have been determined directly by experiment. We 
 in fact know more about the " electric fluid " than 
 we know about such fluids as air or water.
 
 CHAPTER V 
 
 CONSTITUTION OF THE ATOM 
 
 WE have seen that whether we produce the 
 corpuscles by cathode rays, by ultra-violet light, or 
 from incandescent metals, and whatever may be 
 the metals or gases present we always get the same 
 kind of corpuscles. Since corpuscles similar in all 
 respects may be obtained from very different agents 
 and materials, and since the mass of the corpuscles 
 is less than that of any known atom, we see that 
 the corpuscle must be a constituent of the atom of 
 many different substances. That in fact the atoms 
 of these substances have something in common. 
 
 We are thus confronted with the idea that the 
 atoms of the chemical elements are built up of sim- 
 pler systems ; an idea which in various forms has 
 been advanced by more than one chemist. Thus 
 Prout, in 1815, put forward the view that the 
 atoms of all the chemical elements are built up of 
 atoms of hydrogen ; if this were so the combining 
 weights of all the elements would, on the assump-
 
 CONSTITUTION OF THE ATOM 91 
 
 tion that there was no loss of weight when the 
 atoms of hydrogen combined to form the atom of 
 some other element, be integers ; a result not in ac- 
 cordance with observation. To avoid this discrep- 
 ancy Dumas suggested that the primordial atom 
 might not be the hydrogen atom, but a smaller 
 atom having only one-half or one-quarter of the 
 mass of the hydrogen atom. Further support was 
 given to the idea of the complex nature of the 
 atom by the discovery by Newlands and Mende- 
 leeff of what is known as the periodic law, which 
 shows that there is a periodicity in the properties 
 of the elements when they are arranged in the or- 
 der of increasing atomic weights. The simple rela- 
 tions which exist between the combining weights 
 of several of the elements having similar chemical 
 properties, for example, the fact that the combin- 
 ing weight of sodium is the arithmetic mean of 
 those of lithium and potassium, all point to the 
 conclusion that the atoms of the different elements 
 have something in common. Further evidence in 
 the same direction is afforded by the similarity in 
 the structure of the spectra of elements in the same 
 group in the periodic series, a similarity which re- 
 cent work on the existence in spectra of series of 
 lines whose frequencies are connected by definite
 
 92 ELECTRICITY AND MATTER 
 
 numerical relations has done much to emphasize 
 and establish ; indeed spectroscopic evidence alone 
 has led Sir Norman Lockyer for a long time to 
 advocate the view that the elements are really 
 compounds which can be dissociated when the 
 circumstances are suitable. The phenomenon of 
 radio-activity, of which I shall have to speak later, 
 carries the argument still further, for there seems 
 good reasons for believing that radio-activity is 
 due to changes going on within the atoms of the 
 radio-active substances. If this is so then we 
 must face the problem of the constitution of the 
 atom, and see if we can imagine a model which 
 has in it the potentiality of explaining the re- 
 markable properties shown by radio-active sub- 
 stances. It may thus not be superfluous to con- 
 sider the bearing of the existence of corpuscles on 
 the problem of the constitution of the atom; and 
 although the model of the atom to which we are 
 led by these considerations is very crude and im- 
 perfect, it may perhaps be of service by suggesting 
 lines of investigations likely to furnish us with fur- 
 ther information about the constitution of the 
 atom.
 
 CONSTITUTION OF THE ATOM 93 
 
 The Nature of the Unit from which the Atoms 
 are Built Up 
 
 Starting from the hypothesis that the atom 
 is an aggregation of a number of simpler systems, 
 let us consider what is the nature of one of 
 these systems. We have seen that the cor- 
 puscle, whose mass is so much less than that of the 
 atom, is a constituent of the atom, it is natural to 
 regard the corpuscle as a constituent of the primor- 
 dial system. The corpuscle, however, carries a 
 definite charge of negative electricity, and since 
 with any charge of electricity we always associate 
 an equal charge of the opposite kind, we should 
 expect the negative charge on the corpuscle to be 
 associated with an equal charge of positive electri- 
 city. Let us then take as our primordial system an 
 electrical doublet, with a negative corpuscle at one 
 end and an equal positive charge at the other, the 
 two ends being connected by lines of electric force 
 which we suppose to have a material existence. 
 For reasons which will appear later on, we shall 
 suppose that the volume over which the positive 
 electricity is spread is very much larger than the 
 volume of the corpuscle. The lines of force will 
 therefore be very much more condensed near the
 
 94 
 
 ELECTRICITY AND MATTER 
 
 corpuscle than at any other part of the system, and 
 therefore the quantity of ether bound by the lines 
 of force, the mass of which we regard as the mass 
 of the system, will be very much greater near the 
 corpuscle than elsewhere. If, as we have sup- 
 posed, the size of the corpuscle is very small com- 
 pared with the size of the volume occupied by the 
 positive electrification, the mass of the system will 
 practically arise from the mass of bound ether 
 close to the corpuscle ; thus the mass of the sys- 
 tem will be practically independent of the position 
 of its positive end, and will be very approximately 
 the mass of the corpuscles if alone in the field. 
 This mass (see page 21) is for each corpuscle 
 
 equal to , where e is the charge on the corpuscle 
 od 
 
 and a its radius a, as we have seen, being about 
 10- 13 cm. 
 
 Now suppose we had a universe consisting of 
 an immense number of these electrical doublets, 
 which we regard as our primordial system ; if these 
 were at rest their mutual attraction would draw 
 them together, just as the attractions of a lot of 
 little magnets would draw them together if they 
 were free to move, and aggregations of more than 
 one system would be formed.
 
 CONSTITUTION OF THE ATOM 95 
 
 If, however, the individual systems were orig- 
 inally moving with considerable velocities, the rel- 
 ative velocity of two systems, when they came 
 near enough to exercise appreciable attraction on 
 each other, might be sufficient to carry the sys- 
 tems apart in spite of their mutual attraction. In 
 this case the formation of aggregates would be 
 postponed, until the kinetic energy of the units 
 had fallen so low that when they came into 
 collision, the tendency to separate due to their 
 relative motion was not sufficient to prevent them 
 remaining together under their mutual attraction. 
 
 Let us consider for a moment the way in which 
 the kinetic energy of such an assemblage of units 
 would diminish. We have seen (p. 68) that when- 
 ever the velocity of a charged body is changing 
 the body is losing energy, since it generates 
 electrical waves which radiate through space, car- 
 rying energy with them. Thus, whenever the 
 units come into collision, i.e., whenever they 
 come so close together that they sensibly acceler- 
 ate or retard each other's motion, energy will be 
 radiated away, the whole of which will not be 
 absorbed by the surrounding units. There will 
 thus be a steady loss of kinetic energy, and after 
 a time, although it may be a very long time, the
 
 gg ELECTRICITY AND MATTER 
 
 kinetic energy will fall to the value at which aggre- 
 gation of the units into groups of two will begin ; 
 these will later on be followed by the formation 
 of aggregates containing a larger number of units. 
 In considering the question of the further ag- 
 gregation of these complex groups, we must re- 
 member that the possibility of aggregation will 
 depend not merely upon the velocity of the aggre- 
 gate as a whole, i.e., upon the velocity of the 
 centre of gravity, but also upon the relative ve- 
 locities of the corpuscles within the aggregate. 
 
 Let us picture to ourselves the aggregate as, like 
 the ^Epinus atom of Lord Kelvin, consisting of a 
 sphere of uniform positive electrification, and ex- 
 erting therefore a radial electric force proportional 
 at an internal point to the distance from the centre, 
 and that the very much smaller negatively electri- 
 fied corpuscles are moving about 
 inside it. The number of corpus- 
 cles is the number of units which 
 had gone to make up the aggre- 
 gate, and the total negative elec- 
 trification on the corpuscles is 
 
 Fio. 15 
 
 equal to the positive electrifica- 
 tion on the sphere. To fix our ideas let us take 
 the case shown in Fig. 15 of three corpuscles
 
 CONSTITUTION OF THE ATOM 97 
 
 A, B, C, arranged within the sphere at the corners 
 of an equilateral triangle, the centre of the triangle 
 coinciding with the centre of the sphere. First 
 suppose the corpuscles are at rest ; they will be in 
 equilibrium when they are at such a distance 
 from the centre of the sphere that the repulsion 
 between the corpuscles, which will evidently be 
 radial, just balances the radial attraction excited 
 on the corpuscles by the positive electrification of 
 the sphere. A simple calculation shows that this 
 will be the case when the distance of the corpuscle 
 from the centre is equal to .57 times the radius of 
 the sphere. Next suppose that the corpuscles, in- 
 stead of being at rest, are describing circular orbits 
 round the centre of the sphere. Their centrifugal 
 force will carry them farther away from the centre 
 by an amount depending upon the speed with 
 which they are rotating in their orbits. As we 
 increase this speed the distance of the corpuscles 
 from the centre of the sphere will increase until 
 at a certain speed the corpuscles will reach the 
 surface of the sphere ; further increases in speed 
 will cause them first to rotate outside the sphere 
 and finally leave the sphere altogether, when the 
 atom will break up. 
 
 In this way we see that the constitution of the
 
 QO ELECTRICITY AND MATTER 
 
 uo 
 
 aggregate will not be permanent, if the kinetic 
 energy due to the velocity of the corpuscles inside 
 the sphere relative to the centre of the sphere ex- 
 ceeds a certain value. We shall, for the sake of 
 brevity, speak of this kinetic energy of the cor- 
 puscles within the atom as the corpuscular tem- 
 perature of the atom, and we may express the 
 preceding result by saying that the atom will not 
 be stable unless its corpuscular temperature is 
 below a certain value. 
 
 We must be careful to distinguish between cor- 
 puscular temperature, which is the mean kinetic 
 energy of the corpuscles inside the atom, and the 
 molecular temperature, which is the mean kinetic 
 energy due to the motion of the centre of gravity 
 of the atom. These temperatures are probably not 
 in any very close relationship with each other. 
 They would be proportional to each other if the law 
 known as the law of equipartition of energy among 
 the various degrees of freedom of the atom were to 
 apply. This law is, however, inconsistent with the 
 physical properties of gases, and in the proof given 
 of it in the kinetic theory of gases, no estimate is 
 given of the time required to establish the state con- 
 templated by the law ; it may be that this time is so 
 long that gases are never able to get into this state.
 
 CONSTITUTION OF THE ATOM gg 
 
 Let us now take the case of two aggregations, 
 A and B, whose corpuscular temperatures are high, 
 though not so high, of course, as to make A and B 
 unstable when apart, and suppose, in order to give 
 them the best possible chance of combining, that 
 the centres of gravity of A and B when quite 
 close to each other are at rest, will A and B 
 unite to form a more complex aggregate as they 
 would if the corpuscles in them were at rest ? We 
 can easily, I think, see that they will not necessa- 
 rily do so. For as A and B approach each other, 
 under their mutual attractions, the potential en- 
 ergy due to the separation of A and B will dimin- 
 ish and their kinetic energy will increase. This in- 
 crease in the kinetic energy of the corpuscles in A 
 and B will increase the tendency of the corpuscles 
 to leave their atoms, and if the increase in the kin- 
 etic energy is considerable A and B may each lose 
 one or more corpuscles. The departure of a cor- 
 puscle will leave A and B positively charged, 
 and they will tend to separate under the repulsion 
 of these charges. When separated they will have 
 each a positive charge ; but as there are now free 
 corpuscles with negative charges moving about in 
 the region in which A and B are situated, these 
 positive charges will ultimately be neutralized by
 
 100 ELECTRICITY AND MATTER 
 
 corpuscles striking against A and B and remain- 
 ing in combination with them. 
 
 We thus conclude that unless the corpuscular 
 temperature after union is less than a certain limit- 
 ing value, the union cannot be permanent, the 
 complex formed being unstable, and incapable of 
 a permanent existence. Now, the corpuscular 
 temperature of the aggregate formed by A and B 
 will depend upon the corpuscular temperatures of 
 A and B before union, and also upon the diminu- 
 tion in the potential energy of the system occa- 
 sioned by the union of A and B. If the corpuscu- 
 lar temperatures of A and B before union were 
 very high, the corpuscular temperature after union 
 would be high also; if they were above a cer- 
 tain limit, the corpuscular temperature after union 
 would be too high for stability, and the aggre- 
 gate AB would not be formed. Thus, one con- 
 dition for the formation of complex aggregates is 
 that the corpuscular temperature of their constitu- 
 ents before combination should be sufficiently low. 
 
 If the moleculw* temperature of the gas in 
 which A and B are molecules is very high, com- 
 bination may be prevented by the high relative 
 velocity of A and B carrying them apart in spite 
 of their mutual attraction. The point, however,
 
 CONSTITUTION OF THE ATOM JQ1 
 
 which I wish to emphasize is, that we cannot se- 
 cure the union merely by lowering the molecular 
 temperature, i.e., by cooling the gas ; union will 
 be impossible unless the corpuscular temperature, 
 i.e., the kinetic energy due to the motion of the 
 corpuscles inside the atom, is reduced below a cer- 
 tain value. We may prevent union by raising the 
 molecular temperature of a gas, but we cannot en- 
 sure union by lowering it. 
 
 Thus, to take a specific example, the reason, on 
 this view, why the atoms of hydrogen present on 
 the earth do not combine to form some other ele- 
 ment, even at the exceedingly low temperature at 
 which hydrogen becomes liquid, is that even at 
 this temperature the kinetic energy of the corpus- 
 cles inside the atom, i.e., the corpuscular tempera- 
 ture, is too great. It may be useful to repeat here 
 what we stated before, that there is no very inti- 
 mate connection between the corpuscular and mo- 
 lecular temperatures, and that we may reduce the 
 latter almost to the absolute zero without greatly 
 affecting the former. 
 
 We shall now proceed to discuss the bearing of 
 these results on the theory that the different 
 chemical elements have been gradually evolved by 
 the aggregation of primordial units. 
 
 Physical Sciences Libi 
 University of Callforr 
 Riverside
 
 102 ELECTRICITY AND MATTER 
 
 Let us suppose that the first stage has been 
 reached and that we have a number of systems 
 formed by the union of two units. When first 
 these binary systems, as we shall call them, were 
 formed, the corpuscles in the system would have 
 a considerable amount of kinetic energy. This 
 would be so, because when the two units have 
 come together there must be an amount of kinetic 
 energy produced equal to the diminution in the 
 potential energy consequent upon the coalescence of 
 the two units. As these binary systems have or- 
 iginally high corpuscular temperatures they will 
 not be likely to combine with each other or with 
 another unit ; before they can do so the kinetic 
 energy of the corpuscles must get reduced. 
 
 We shall proceed immediately to discuss the 
 way in which this reduction is effected, but we 
 shall anticipate the result of the discussion by 
 saying that it leads to the result that the rate of 
 decay in the corpuscular temperature probably 
 varies greatly from one binary system to another. 
 
 Some of the systems will therefore probably 
 have reached a condition in which they are able 
 to combine with each other or with a single unit 
 long before others are able to do so. The systems 
 of the first kind will combine, and thus we shall
 
 CONSTITUTION OF THE ATOM 103 
 
 have systems formed, some of which contain three, 
 others four units, while at the same time there are 
 many of the binary systems left. Thus, the appear- 
 ance of the more complex systems need not be 
 simultaneous with the disappearance of all the sun- 
 pier ones. 
 
 The same principle will apply to the formation 
 of further aggregations by the systems containing 
 three or four units ; some of these will be ready to 
 unite before the others, and we may have systems 
 containing eight units formed before the more per- 
 sistent of those containing four, three, two or even 
 one unit have disappeared. With the further ad- 
 vance of aggregation the number of different sys- 
 tems present at one and the same time will in- 
 crease. 
 
 Thus, if we regard the systems containing differ- 
 ent numbers of units as corresponding to the 
 different chemical elements, then as the universe 
 gets older elements of higher and higher atomic 
 weight may be expected to appear. Their appear- 
 ance, however, will not involve the annihilation of 
 the elements of lower atomic weight. The number 
 of atoms of the latter will, of course, diminish, 
 since the heavier elements are by hypothesis built 
 up of material furnished by the lighter. The whole
 
 1Q4 ELECTRICITY AND MATTER 
 
 of the atoms of the latter would not, however, all 
 be used up at once, and thus we may have a very 
 large number of elements existing at one and the 
 same time. 
 
 If, however, there is a continual fall in the cor- 
 puscular temperature of the atoms through radia- 
 tion, the lighter elements will disappear in time, 
 and unless there is disintegration of the heavier 
 atoms, the atomic weight of the lightest element 
 surviving will continually increase. On this view, 
 since hydrogen is the lightest known element and 
 the atom of hydrogen contains about a thousand 
 corpuscles, all aggregations of less than a thousand 
 units have entered into combination and are no 
 longer free. 
 
 The way the Corpuscles in the Atom Lose or Gain 
 Kinetic 
 
 If the kinetic energy arising from the motion of 
 the corpuscles relatively to the centre of gravity 
 of the atom could by collisions be transformed 
 into kinetic energy due to the motion of the atom 
 as a whole, i.e., into molecular temperature, it 
 would follow from the kinetic theory of gases, 
 
 / 
 
 since the number of corpuscles in the atom is ex- 
 ceedingly large, that the specific heat of a gas at
 
 CONSTITUTION OP THE ATOM 
 
 105 
 
 constant pressure would be very nearly equal to 
 the specific heat at constant volume ; whereas, as 
 a matter of fact, in no gas is there any approach 
 to equality in these specific heats. We conclude, 
 therefore, that it is not by collisions that the 
 kinetic energy of the corpuscles is diminished. 
 
 We have seen, however (page 68), that a mov- 
 ing electrified particle radiates energy whenever 
 its velocity is changing either in magnitude or 
 direction. The corpuscles in the atom will thus 
 emit electric waves, radiating energy and so losing 
 kinetic energy. 
 
 The rate at which energy is lost in this way by 
 the corpuscles varies very greatly with the num- 
 ber of the corpuscles and the way in which they 
 are moving. Thus, if we have a single corpuscle 
 describing a circular orbit of radius a with uni- 
 form velocity v t the loss of energy due to radia- 
 
 tion per second is - ^ where e is the charge on 
 
 the corpuscles and V the velocity of light. If 
 instead of a single corpuscle we had two corpus- 
 cles at opposite ends of a diameter moving round 
 the same orbit with the same velocity as the sin- 
 gle corpuscle, the loss of energy per second from the 
 two would be very much less than from the single
 
 igg ELECTRICITY AND MATTER 
 
 corpuscle, and the smaller the velocity of the cor- 
 puscle the greater would be the diminution in 
 the loss of energy produced by increasing the 
 number of corpuscles. The effect produced by 
 increasing the number of corpuscles is shown in 
 the following table, which gives the rate of radia- 
 tion for each corpuscle for various numbers of 
 corpuscles arranged at equal angular intervals 
 round the circular orbit. 
 
 The table applies to two cases ; in one the veloc- 
 ity of the corpuscles is taken as one-tenth that of 
 light, and in the second as one-hundredth. The 
 radiation from a single corpuscle is in each case 
 taken as unity. 
 
 Number of corpuscles. Radiation from each corpuscle. 
 
 1 1 
 
 2.. 9. 
 
 4 1.7 x 10- 4 
 
 5 5.6 x 10- 5 
 
 6.. 
 
 F 
 
 10 
 
 F 
 100 
 
 
 1 
 
 X 10- 2 
 
 9.6 x 1CT 4 
 
 x l(r 3 
 
 4.6 x 10~ 7 
 
 x 10- 4 
 
 1.7 x 10- 10 
 
 x KT 5 
 
 5.6 x 10~ 13 
 
 x 10- 7 
 
 1.6 x 10~ 17 
 
 Thus, we see that the radiation from each of a 
 group of six corpuscles moving with one-tenth the 
 velocity of light is less than one-five-millionth part 
 of the radiation from a single corpuscle, describ-
 
 CONSTITUTION OF THE ATOM 107 
 
 ing the same orbit with the same velocity, while, 
 when the velocity of the corpuscles is only one- 
 hundredth of that of light, the reduction in the 
 radiation is very much greater. 
 
 If the corpuscles are displaced from the sym- 
 metrical position in which they are situated at 
 equal intervals round a circle whose centre is at 
 rest, the rate of radiation will be very much in- 
 creased. In the case of an atom containing a large 
 number of corpuscles the variation in the rate at 
 which energy is radiated will vary very rapidly 
 with the way the corpuscles are moving about in 
 the atom. Thus, for example, if we had a large 
 number of corpuscles following close on one an- 
 other's heels round a circular orbit the radiation 
 would be exceedingly small ; it would vanish alto- 
 gether if the corpuscles were so close together 
 that they formed a continuous ring of negative 
 electrification. If the same number of particles 
 were moving about irregularly in the atom, then 
 though the kinetic energy possessed by the cor- 
 puscles in the second case might be no greater 
 than in the first, the rate of radiation, i.e., of cor- 
 puscular cooling, would be immensely greater. 
 
 Thus, we see that in the radiation of energy 
 from corpuscles whose velocity is not uniform we
 
 jQg ELECTRICITY AND MATTER 
 
 have a process going on which will gradually cool 
 the corpuscular temperature of the atom, and so, 
 if the view we have been discussing is correct, 
 enable the atom to form further aggregations and 
 thus tend to the formation of new chemical ele- 
 ments. 
 
 This cooling process must be an exceedingly 
 slow one, for although the corpuscular tempera- 
 ture when the atom of a new element is formed 
 is likely to be exceedingly high, and the lowering 
 in that temperature required before the atom can 
 enter again into fresh aggregations very large, 
 yet we have evidence that some of the elements 
 must have existed unchanged for many thousands, 
 nay, millions of years ; we have, indeed, no direct 
 evidence of any change at all in the atom. I 
 think, however, that some of the phenomena of 
 radio-activity to which I shall have to allude later, 
 afford, I will not say a proof of, but a very strong 
 presumption in favor of some such secular changes 
 taking place in the atom. 
 
 We must remember, too, that the corpuscles in 
 any atom are receiving and absorbing radiation 
 from other atoms. This will tend to raise the 
 corpuscular temperature of the atom and thus 
 help to lengthen the time required for that
 
 CONSTITUTION OF THE ATOM 1Q9 
 
 temperature to fall to the point where fresh 
 aggregations of the atom may be formed. 
 
 The fact that the rate of radiation depends so 
 much upon the way the corpuscles are moving 
 about in the atom indicates that the lives of the 
 different atoms of any particular element will not 
 be equal ; some of these atoms will be ready to 
 enter upon fresh changes long before the others. 
 It is important to realize how large are the 
 amounts of energy involved in the formation of a 
 complex atom or in any rearrangement of the con- 
 figuration of the corpuscles inside it. If we have 
 an atom containing n corpuscles each with a 
 charge e measured in electrostatic units, the total 
 quantity of negative electricity in the atom is n e 
 and there is an equal quantity of positive elec- 
 tricity distributed through the sphere of positive 
 electrification; hence, the work required to sep- 
 arate the atom into its constituent units will be 
 
 (\2 
 WUI/CU,*S.LV, ,x uu ne ' , a being the radius of the 
 a 
 
 sphere containing the corpuscles. Thus, as the 
 atom has been formed by the aggregation of these 
 
 units ( ne ' will be of the same order of magni- 
 a 
 
 tude as the kinetic energy imparted to those con-
 
 HQ ELECTRICITY AND MATTER 
 
 stituents during their whole history, from the 
 time they started as separate units, down to the 
 time they became members of the atom under 
 consideration. They will in this period have radi- 
 ated away a large quantity of this energy, but the 
 following calculation will show what an enormous 
 amount of kinetic energy the corpuscles in the 
 atom must possess even if they have only retained 
 an exceedingly small fraction of that communi- 
 
 cated to them. Let us calculate the value of L J 
 
 a 
 
 for all the atoms in a gram of the substance ; let 
 N be the number of these atoms in a gram, then 
 
 N^- '- is the value of the energy acquired by these 
 atoms. If M is the mass of an atom NM= 1, thus : 
 
 cT ~ M 
 but if m is the mass of a corpuscle 
 
 nm = J/, 
 and therefore 
 
 If O *)* _ e_ ne^ f 
 a ma' 
 
 now when e is measured in electrostatic units 
 L- = 3 X 10 17 and e = 3.4 X 10' 10 ;
 
 CONSTITUTION OF THE ATOM m 
 
 and therefore 
 
 N(^= 10.2X10 'x^s (1) 
 a a 
 
 Let us take the case of the hydrogen atom for 
 which n = 1000, and take for a the value usually 
 assumed in the kinetic theory of gases for the 
 radius of the atom, i.e., 10" 8 cm. then 
 
 = 1.02 X 10 19 ergs; 
 
 this amount of energy would be sufficient to lift a 
 million tons through a height considerably ex- 
 ceeding one hundred yards. We see, too, from 
 (1) that this energy is proportional to the num- 
 ber of corpuscles, so that the greater the molecu- 
 lar weight of an element, the greater will be the 
 amount of energy stored up in the atoms in each 
 gram. 
 
 We shall return to the subject of the internal 
 changes in the atom when we discuss some of 
 the phenomena of radio-activity, but before doing 
 so it is desirable to consider more closely the way 
 the corpuscles arrange themselves in the atom. 
 We shall begin with the case where the corpuscles 
 are at rest. The corpuscles are supposed to be in 
 a sphere of uniform positive electrification which 
 produces a radial attractive force on each cor-
 
 112 
 
 ELECTRICITY AND MATTER 
 
 FlQ. 16. 
 
 puscle proportional to its distance from the centre 
 of the sphere, and the problem is to arrange the 
 corpuscles in the sphere so that 
 they are in equilibrium under this 
 attraction and their mutual re- 
 pulsions. If there are only two 
 corpuscles, A JB, we can see at 
 once that they will be in equi- 
 librium if placed so that A IB 
 and the centre of the sphere are in the same 
 straight line and OA = OB = \ the radius of the 
 sphere. 
 
 If there are three corpuscles, A B O, they will 
 be in equilibrium of A B C as an equilateral tri- 
 angle with its centre at and 
 OA= OB = OC = (iy, or .57 
 times the radius of the sphere. 
 
 If there are four corpuscles 
 these will be in equilibrium if 
 placed at the angular points of a 
 regular tetrahedron with its cen- 
 tre at the centre of the sphere. In these cases the 
 corpuscles are all on the surface of a sphere con- 
 centric with the sphere of positive electrification, 
 and we might suppose that whatever the number 
 of corpuscles the position of equilibrium would be 
 
 FIG. 15.
 
 CONSTITUTION OF THE ATOM H3 
 
 one of symmetrical distribution over the surface 
 of a sphere. Such a distribution would indeed 
 technically be one of equilibrium, but a mathe- 
 matical calculation shows that unless the number 
 of corpuscles is quite small, say seven or eight at 
 the most, this arrangement is unstable and so can 
 never persist. When the number of corpuscles is 
 greater than this limiting number, the corpuscles 
 break up into two groups. One group containing 
 the smaller number of corpuscles is on the surface 
 of a small body concentric with the sphere ; the 
 remainder are on the surface of a larger concen- 
 tric body. When the number of corpuscles is 
 still further increased there comes a stage when 
 the equilibrium cannot be stable even with two 
 groups, and the corpuscles now divide themselves 
 into three groups, arranged on the surfaces of con- 
 centric shells; and as we go on increasing the 
 number we pass through stages in which more and 
 more groups are necessary for equilibrium. With 
 any considerable number of corpuscles the prob- 
 lem of finding the distribution when in equilibrium 
 becomes too complex for calculation ; and we have 
 to turn to experiment and see if we can make a 
 model in which the forces producing equilibrium 
 are similar to those we have supposed to be at
 
 jj A ELECTRICITY AND MATTER 
 
 work in the corpuscle. Such a model is afforded 
 by a very simple and beautiful experiment first 
 made, I think, by Professor Mayer. In this experi- 
 ment a number of little magnets are floated in a 
 vessel of water. The magnets are steel needles 
 magnetized to equal strengths and are floated by 
 being thrust through small disks of cork. The 
 magnets are placed so that the positive poles are 
 either all above or all below the surface of the 
 water. These positive poles, like the corpuscles, 
 repel each other with forces varying inversely as 
 the distance between them. The attractive force 
 is provided by a negative pole (if the little mag- 
 nets have their positive poles above the water) sus- 
 pended some distance above the surface of the 
 water. This pole will exert on the positive poles 
 of the little floating magnets an attractive force 
 the component of which, parallel to the surface 
 of the water, will be radial, directed to <9, the 
 projection of the negative pole on the surface of 
 the water, and if the negative pole is some dis- 
 tance above the surface the component of the force 
 to O will be very approximately proportional to 
 the distance from 0. Thus the forces on the poles 
 of the floating magnets will be very similar to those 
 acting on the corpuscle in our hypothetical atom ;
 
 CONSTITUTION OF THE ATOM 
 
 115 
 
 the chief difference being that the corpuscles are 
 free to move about in all directions in space, while 
 the poles of the floating magnets are constrained 
 to move in a plane parallel to the surface of the 
 water. 
 
 The configurations which the floating magnets 
 assume as the number of magnets increases from 
 two up to nineteen is shown in Fig. 17, which 
 was given by Mayer. 
 
 FIG. 17. 
 
 The configuration taken up when the magnets 
 are more numerous can be found from the follow- 
 ing table, which is also due to Mayer. From this 
 table it will be seen that when the number of 
 floating magnets does not exceed five the magnets
 
 116 
 
 ELECTRICITY AND MATTER 
 
 arrange themselves at the corners of a regular 
 polygon, five at the corners of a pentagon, four at 
 the corners of a square and so on. When the 
 number is greater than five this arrangement no 
 longer holds. Thus, six magnets do not arrange 
 themselves at the corners of a hexagon, but divide 
 into two systems, one magnet being at the centre 
 and five outside it at the corners of a regular penta- 
 gon. This arrangement in two groups lasts until 
 there are fifteen magnets, when we have three 
 groups; with twenty-seven magnets we get four 
 groups and so on. 
 
 Arrangement of Magnets (Mayer) 
 
 i. 
 
 2. 
 
 1.5 (2.6 ( 
 1.6 \ 2 . 7 I 
 1 . 7 
 
 3 . 7 
 3 . 8 
 
 I!: 
 
 8 ( 
 
 . I 5 ' 
 
 9 
 
 1.5.9 j-2 . 7 . 10 
 1-6.9 J 2 . 8 . 10 
 
 8 
 3 
 
 . 7 10 
 . 7 . 11 
 
 i:.:: 
 
 12 |5 . 9 
 13 1 5 . 9 
 
 . 12 
 . 13 
 
 1 . 6 . 10 [2 . 7 . 11 
 
 3 
 
 . 8 . 10 
 
 4.9. 
 
 12 
 
 
 1 . 6 . 11 
 
 8 
 
 . 8 . 11 
 
 U.9. 
 
 13 
 
 
 
 8 
 
 . 8 . 12 
 
 
 
 
 
 3 
 
 . 8 . 13 
 
 

 
 CONSTITUTION OF THE ATOM 
 
 1 . 5 
 
 1 . 5 
 1 . 6 
 1 . 6 
 1 . G 
 1 . 6 
 1 . 6 
 1 . 6 
 .1 . 6 
 
 1. 
 
 . 9 . 
 . 9 . 
 . 9 . 
 . 10 . 
 . 10 . 
 . 11 . 
 . 11 . 
 . 11 . 
 . 11 . 
 
 2. 
 12 ( 2 . 7 . 10 
 13 (2 . 7 . 12 
 
 12 
 12 
 13 
 2 
 13 
 14 
 15 
 
 15 
 14 
 
 7 . 12 . 13 f4 . 9 . 13 . 14 
 . 7 . 12 . 14J4.9. 13. 15 
 . 7 . 13 . 14 [4 . 9 . 14 . 15 
 .7 13 . 15 
 
 Where, for example, 3. 7. 12. 13 means that 
 thirty-five magnets arrange themselves so that 
 there is a ring of three magnets inside, then a ring 
 of seven, then one of twelve, and one of thirteen 
 outside. 
 
 I think this table affords many suggestions tow- 
 ard the explanation of some of the properties 
 possessed by atoms. Let us take, for example, the 
 chemical law called the Periodic Law ; according 
 to this law if we arrange the elements in order of 
 increasing atomic weights, then taking an element 
 of low atomic weight, say lithium, we find certain 
 properties associated with it. These properties 
 are not possessed by the elements immediately 
 following it in the series of increasing atomic 
 weight ; but they appear again when we come to 
 sodium, then they disappear again for a time,
 
 Qg ELECTRICITY AND MATTER 
 
 but reappear when we reach potassium, and so 
 on. Let us now consider the arrangements of 
 the floating magnets, and suppose that the number 
 of magnets is proportional to the combining weight 
 of an element. Then, if any property were asso- 
 ciated with the triangular arrangement of magnets, 
 it would be possessed by the elements whose com- 
 bining weight was on this scale three, but would 
 not appear again until we reached the combining 
 weight ten, when it reappears, as for ten magnets 
 we have the triangular arrangement in the middle 
 and a ring of seven magnets outside. When the 
 number of magnets is increased the triangular 
 arrangement disappears for a time, but reappears 
 with twenty magnets, and again with thirty-five, 
 the triangular arrangement appearing and dis- 
 appearing in a way analogous to the behavior of 
 the properties of the elements in the Periodic 
 Law. As an example of a property that might 
 very well be associated with a particular grouping 
 of the corpuscles, let us take the times of vibra- 
 tion of the system, as shown by the position of 
 the lines in the spectrum of the element. First 
 let us take the case of three corpuscles by them- 
 selves in the positively electrified sphere. The 
 three corpuscles have nine degrees of freedom, so
 
 CONSTITUTION OF THE ATOM HQ 
 
 that there are nine possible periods. Some of 
 these periods in this case would be infinitely long, 
 and several of the possible periods would be equal 
 to each other, so that we should not get nine dif- 
 ferent periods. 
 
 Suppose that the lines in the spectrum of the 
 three corpuscles are as represented in Fig. 18 0, 
 
 A B C D 
 
 2 3 I 2 
 
 D t 
 
 FIG. 18. 
 
 where the figures under the lines represent the 
 number of periods which coalesce at that line ; i.e., 
 regarding the periods as given by an equation with 
 nine roots, we suppose that there is only one root 
 giving the period corresponding to the line A, 
 while corresponding to B there are two equal 
 roots, three equal roots corresponding to O, one
 
 120 ELECTRICITY AND MATTER 
 
 root, to <9, and two to E. These periods would 
 have certain numerical relations to each other, in- 
 dependent of the charge on the corpuscle, the size 
 of the sphere in which they are placed, or their 
 distance from the centre of the sphere. Each of 
 these quantities, although it does not affect the 
 ratio of the periods, will have a great effect upon 
 the absolute value of any one of them. Now, 
 suppose that these three corpuscles, instead of 
 being alone in the sphere, form but one out of 
 several groups in it, just as the triangle of mag- 
 nets forms a constituent of the grouping of 3, 10, 
 20, and 35 magnets. Let us consider how the 
 presence of the other groups would affect the 
 periods of vibration of the three corpuscles. The 
 absolute values of the periods would generally be 
 entirely different, but the relationship existing be- 
 tween the various periods would be much more 
 persistent, and although it might be modified it 
 would not be destroyed. Using the phraseology of 
 the Planetary Theory, we may regard the motion 
 of the three corpuscles as " disturbed " by the 
 other groups. 
 
 When the group of three corpuscles was by it- 
 self there were several displacements which gave 
 the same period of vibration ; for example, corre-
 
 CONSTITUTION OF THE ATOM J21 
 
 spending to the line C there were three displace- 
 ments, all giving the same period. When, how. 
 ever, there are other groups present, then these 
 different displacements will no longer be sym- 
 metrical with respect to these groups, so that the 
 three periods will no longer be quite equal. They 
 would, however, be very nearly equal unless the 
 effect of the other groups is very large. Thus, 
 in the spectrum, (7, instead of being a single line, 
 would become a triplet, while B and E would be- 
 come doublets. A D would remain single lines. 
 Thus, the spectrum would now resemble Fig. 
 18 5; the more groups there are surrounding the 
 group of three the more will the motion of the 
 latter be disturbed and the greater the separation 
 of the constituents of the triplets and doublets. 
 The appearance as the number of groups increases 
 is shown in Fig. 18 b, c. Thus, if we regarded 
 the element which contain this particular group- 
 ing of corpuscles as being in the same group in the 
 classification of elements according to the Periodic 
 Law, we should get in the spectra of these ele- 
 ments homologous series of lines, the distances be- 
 tween the components of the doublets and triplets 
 increasing with the atomic weight of the elements. 
 The investigations of Rydberg, Runge and Pas-
 
 122 ELECTRICITY AND MATTER 
 
 chen and Keyser have shown the existence in the 
 spectra of elements of the same group series of 
 lines having properties in many respects analogous 
 to those we have described. 
 
 Another point of interest given by Mayer's ex- 
 periments is that there is more than one stable 
 configuration for the same number of magnets; 
 these configurations correspond to different amounts 
 of potential energy, so that the passage from the 
 configuration of greater potential energy to that of 
 less would give kinetic energy to the corpuscle. 
 From the values of the potential energy stored 
 in the atom, of which we gave an estimate on 
 page 111, we infer that a change by even a small 
 fraction in that potential energy would develop 
 an amount of kinetic energy which if converted 
 into heat would greatly transcend the amount of 
 heat developed when the atoms undergo any known 
 chemical combination. 
 
 An inspection of the table shows that there are 
 certain places in it where the nature of the con- 
 figuration changes very rapidly with the number 
 of magnets ; thus, five magnets form one group, 
 while six magnets form two; fourteen magnets 
 form two groups, fifteen three ; twenty - seven 
 magnets form three groups, twenty-eight four,
 
 CONSTITUTION OF THE ATOM 123 
 
 and so on. If we arrange the chemical elements 
 in the order of their atomic weights we find there 
 are certain places where the difference in proper- 
 ties of consecutive elements is exceptionally great ; 
 thus, for example, we have extreme differences in 
 properties between fluorine and sodium. Then 
 there is more or less continuity in the properties 
 until we get to chlorine, which is followed by 
 potassium; the next break occurs at bromine 
 and rubidium and so on. This effect seems 
 analogous to that due to the regrouping of the 
 magnets. 
 
 So far we have supposed the corpuscles to be 
 at rest ; if, however, they are in a state of steady 
 motion and describing circular orbits round the 
 centre of the sphere, the effect of the centrifugal 
 force arising from this motion will be to drive the 
 corpuscles farther away from the centre of the 
 sphere, without, in many cases, destroying the 
 character of the configuration. Thus, for example, 
 if we have three corpuscles in the sphere, they 
 will, in the state of steady motion, as when they 
 are at rest, be situated at the corners of an equi- 
 angular triangle ; this triangle will, however, be 
 rotating round the centre of the sphere, and the 
 distance of the corpuscles from the centre will be
 
 124 ELECTRICITY AND MATTER 
 
 greater than when they are at rest and will in- 
 crease with the velocity of the corpuscles. 
 
 There are, however, many cases in which rota- 
 tion is essential for the stability of the configura- 
 tion. Thus, take the case of four corpuscles. 
 These, if rotating rapidly, are in stable steady 
 motion when at the corners of a square, the plane 
 of the square being at right angles to the axis of 
 rotation ; when, however, the velocity of rotation 
 of the corpuscles falls below a certain value, the 
 arrangement of four corpuscles in one plane be- 
 comes unstable, and the corpuscles tend to place 
 themselves at the corners of a regular tetrahedron, 
 which is the stable arrangement when the cor- 
 puscles are at rest. The system of four corpuscles 
 at the corners of a square may be compared with 
 a spinning top, the top like the corpuscles being 
 unstable unless its velocity of rotation exceeds 
 a certain critical value. Let us suppose that 
 initially the velocity of the corpuscles exceeds 
 this value, but that in some way or another the 
 corpuscles gradually lose their kinetic energy; 
 the square arrangement will persist until the ve- 
 locity of the corpuscles is reduced to the critical 
 value. The arrangement will then become un- 
 stable, and there will be a convulsion in the sys-
 
 CONSTITUTION OF THE ATOM J25 
 
 tern accompanied by a great evolution of kinetic 
 energy. 
 
 Similar considerations will apply to many as- 
 semblages of corpuscles. In such cases the con- 
 figuration when the corpuscles are rotating with 
 great rapidity will (as in the case of the four cor- 
 puscles) be essentially different from the configu- 
 ration of the same number of corpuscles when at 
 rest. Hence there must be some critical velocity 
 of the corpuscles, such that, for velocities greater 
 than the critical one, a configuration is stable, 
 which becomes unstable when the velocity is 
 reduced below the critical value. When the ve- 
 locity sinks below the critical value, instability 
 sets in, and there is a kind of convulsion or ex- 
 plosion, accompanied by a great diminution in the 
 potential energy and a corresponding increase in 
 the kinetic energy of the corpuscles. This increase 
 in the kinetic energy of the corpuscles may be 
 sufficient to detach considerable numbers of them 
 from the original assemblage. 
 
 These considerations have a very direct bearing 
 on the view of the constitution of the atoms which 
 we have taken in this chapter, for they show that 
 with atoms of a special kind, i.e., with special 
 atomic weights, the corpuscular cooling caused by
 
 12 g ELECTRICITY AND MATTER 
 
 the radiation from the moving corpuscles which 
 we have supposed to be slowly going on, might, 
 when it reached a certain stage, produce instabil- 
 ity inside the atom, and produce such an in- 
 crease in the kinetic energy of the corpuscles as 
 to give rise to greatly increased radiation, and it 
 might be detachment of a portion of the atom. 
 It would cause the atom to emit energy ; this 
 energy being derived from the potential energy 
 due to the arrangement of the corpuscles in the 
 atom. We shall see when we consider the phe- 
 nomenon of radio-activity that there is a class of 
 bodies which show phenomena analogous to those 
 just described. 
 
 On the view that the lighter elements are 
 formed first by the aggregation of the unit 
 doublet, the negative element of which is the cor- 
 puscle, and that it is by the combination of the 
 atoms of the lighter elements that the atoms of 
 the heavier elements are produced, we should ex- 
 pect the corpuscles in the heavy atoms to be ar- 
 ranged as it were in bundles, the arrangement of 
 the corpuscles in each bundle being similar to the 
 arrangement in the atom of some lighter element. 
 In the heavier atom these bundles would act as 
 subsidiary units, each bundle corresponding to
 
 CONSTITUTION OF THE ATOM J27 
 
 one of the magnets in the model formed by the 
 floating magnets, while inside the bundle them- 
 selves the corpuscle would be the analogue of 
 the magnet. 
 
 We must now go on to see whether an atom 
 built up in the way we have supposed could pos- 
 sess any of the properties of the real atom. Is 
 there, for example, in this model of an atom any 
 scope for the electro-chemical properties of the 
 real atom ; such properties, for example, as those 
 illustrated by the division of the chemical ele- 
 ments into two classes, electro-positive and electro- 
 negative. Why, for example, if this is the con- 
 stitution of the atom, does an atom of sodium or 
 potassium tend to acquire a positive, the atom of 
 chlorine a negative charge of electricity ? Again, 
 is there anything in the model of the atom to 
 suggest the possession of such a property as that 
 called by the chemists valency ; i.e., the property 
 which enables us to divide the elements into 
 groups, called monads, dyads, triads, such that in 
 a compound formed by any two elements of the 
 first group the molecule of the compound will 
 contain the same number of atoms of each element, 
 while in a compound formed by an element A in 
 the first group with one B in the second, the mole-
 
 12 o ELECTRICITY AND MATTER 
 
 cule of the compound contains twice as many 
 atoms of A as of , and so on ? 
 
 Let us now turn to the properties of the model 
 atom. It contains a very large number of corpus- 
 cles in rapid motion. We have evidence from the 
 phenomena connected with the conduction of 
 electricity through gases that one or more of these 
 corpuscles can be detached from the atom. 
 These may escape owing to their high veloc- 
 ity enabling them to travel beyond the attrac- 
 tion of the atom. They may be detached also by 
 collision of the atom with other rapidly moving 
 atoms or free corpuscles. When once a corpuscle 
 has escaped from an atom the latter will have a pos- 
 itive charge. This will make it more difficult for 
 a second negatively electrified corpuscle to escape, 
 for in consequence of the positive charge on the 
 atom the latter will attract the second corpuscle 
 more strongly than it did the first. Now we can 
 readily conceive that the ease with which a par- 
 ticle will escape from, or be knocked out of, an 
 atom may vary very much in the atoms of the dif- 
 ferent elements. In some atoms the velocities of 
 the corpuscles may be so great that a corpuscle 
 escapes at once from the atom. It may even be 
 that after one has escaped, the attraction of the
 
 CONSTITUTION OF THE ATOM J 2 9 
 
 positive electrification thus left on the atom is 
 not sufficient to restrain a second, or even a third, 
 corpuscle from escaping. Such atoms would ac- 
 quire positive charges of one, two, or three units, 
 according as they lost one, two, or three corpus- 
 cles. On the other hand, there may be atoms in 
 which the velocities of the corpuscles are so small 
 that few, if any, corpuscles escape of their own 
 accord, nay, they may even be able to receive 
 one or even more than one corpuscle before the 
 repulsion exerted by the negative electrification 
 on these foreign corpuscles forces any of the 
 original corpuscles out. Atoms of this kind if 
 placed in a region where corpuscles were present 
 would by aggregation with these corpuscles re. 
 ceive a negative charge. The magnitude of the 
 negative charge would depend upon the firmness 
 with which the atom held its corpuscles. If a 
 negative charge of one corpuscle were not suf- 
 ficient to expel a corpuscle while the negative 
 charge of two corpuscles could do so, the maxi- 
 mum negative charge on the atom would be one 
 unit. If two corpuscles were not sufficient to expel 
 a corpuscle, but three were, the maximum nega- 
 tive charge would be two units, and so on. Thus, 
 the atoms of this class tend to get charged with
 
 !3Q ELECTRICITY AND MATTER 
 
 negative electricity and correspond to the electro- 
 negative chemical elements, while the atoms of the 
 class we first considered, and which readily lose 
 corpuscles, acquire a positive charge and corre- 
 spond to the atoms of the electro-positive elements. 
 We might conceive atoms in which the equilib- 
 rium of the corpuscles was so nicely balanced 
 that though they do not of themselves lose a cor- 
 puscle, and so do not acquire a positive charge, the 
 repulsion exerted by a foreign corpuscle coming 
 on to the atom would be sufficient to drive out a 
 corpuscle. Such an atom would be incapable of 
 receiving a charge either of positive or negative 
 electricity. 
 
 Suppose we have a number of the atoms that 
 readily lose their corpuscles mixed with a num- 
 ber of those that can retain a foreign corpuscle. 
 Let us call an atom of the first class A, one of the 
 second B, and suppose that the A atoms are of 
 the kind that lose one corpuscle while the B atoms 
 are of the kind that can retain one, but not more 
 than one ; then the corpuscles which escape from 
 the A atoms will ultimately find a home on the B 
 atoms, and if there are an equal number of the 
 two kinds of atoms present we shall get ultimate- 
 ly all the A atoms with the unit positive charge,
 
 CONSTITUTION OF THE ATOM 131 
 
 all the B atoms with the unit negative charge. 
 These oppositely electrified atoms will attract each 
 other, and we shall get the compound A B 
 formed. If the A atoms had been of the kind 
 that lost two corpuscles, and the B atoms the 
 same as before, then the A atoms would get the 
 charge of two positive units, the B atoms a charge 
 of one unit of negative electricity. Thus, to form 
 a neutral system two of the B atoms must com- 
 bine with one of the A'a and thus the compound 
 A _Z? 2 would be formed. 
 
 Thus, from this point of view a univalent elec- 
 tro-positive atom is one which, under the circum- 
 stances prevailing when combination is taking 
 place, has to lose one and only one corpuscle be- 
 fore stability is attained ; a univalent electro-neg- 
 ative atom is one which can receive one but not 
 more than one corpuscle without driving off other 
 corpuscles from the atom; a divalent electro- 
 positive atom is one that loses two corpuscles and 
 no more, and so on. The valency of the atom 
 thus depends upon the ease with which corpus- 
 cles can escape from or be received by the atom ; 
 this may be influenced by the circumstances 
 existing when combination is taking place. Thus, 
 it would be easier for a corpuscle, when once it
 
 132 ELECTRICITY AXD MATTER 
 
 had got outside the atom, to escape being pulled 
 back again into it by the attraction of its positive 
 electrification, if the atom were surrounded by good 
 conductors than if it were isolated in space. We 
 can understand, then, why the valency of an atom 
 may in some degree be influenced by the physical 
 conditions under which combination is taking place. 
 On the view that the attraction between the 
 atoms in a chemical compound is electrical in its 
 origin, the ability of an element to enter into 
 chemical combination depends upon its atom hav- 
 ing the power of acquiring a charge of electricity. 
 This, on the preceding view, implies either that the 
 uncharged atom is unstable and has to lose one or 
 more corpuscles before it can get into a steady 
 state, or else that it is so stable that it can retain 
 one or more additional corpuscles without any of 
 the original corpuscles being driven out. If the 
 range of stability is such that the atom, though 
 stable when uncharged, becomes unstable when it 
 receives an additional corpuscle, the atom will not 
 be able to receive a charge either of positive or 
 negative electricity, and will therefore not be able 
 to enter into chemical combination. Such an atom 
 would have the properties of the atoms of such 
 elements as argon or helium.
 
 CONSTITUTION OF THE ATOM 133 
 
 The view that the forces which bind together 
 the atoms in the molecules of chemical compounds 
 are electrical in their origin, was first proposed 
 by Berzelius ; it was also the view of Davy and of 
 Faraday. Helmholtz, too, declared that the 
 mightiest of the chemical forces are electrical in 
 their origin. Chemists in general seem, however, 
 to have made but little use of this idea, having 
 apparently found the conception of "bonds of 
 affinity" more fruitful. This doctrine of bonds 
 is, however, when regarded in one aspect almost 
 identical with the electrical theory. The theory 
 of bonds when represented graphically supposes 
 that from each univalent atom a straight line 
 (the symbol of a bond) proceeds; a divalent 
 atom is at the end of two such lines, a trivalent 
 atom at the end of three, and so on ; and that 
 when the chemical compound is represented by a 
 graphic formula in this way, each atom must be 
 at the end of the proper number of the lines 
 which represent the bonds. Now, on the electrical 
 view of chemical combination, a univalent atom 
 has one unit charge, if we take as our unit of 
 charge the charge on the corpuscle ; the atom is 
 therefore the beginning or end of one unit Fara- 
 day tube: the beginning if the charge on the
 
 134 ELECTRICITY AND MATTER 
 
 atom is positive, the end if the charge is nega- 
 tive. A divalent atom has two units of charge and 
 therefore it is the origin or termination of two 
 unit Faraday tubes. Thus, if we interpret the 
 "bond" of the chemist as indicating a unit Fara- 
 day tube, connecting charged atoms in the mole- 
 cule, the structural formulae of the chemist can 
 be at once translated into the electrical theory. 
 There is, however, one point of difference which 
 deserves a little consideration : the symbol indi- 
 cating a bond on the chemical theory is not re- 
 garded as having direction ; no difference is made 
 on this theory between one end of a bond and 
 the other. On the electrical theory, however, there 
 is a difference between the ends, as one end cor- 
 responds to a positive, the other to a negative 
 charge. An example or two may perhaps be the 
 easiest way of indicating the effect of this consid- 
 eration. Let us take the gas ethane whose structu- 
 ral formula is written 
 
 According to the chemical view there is no differ-
 
 CONSTITUTION OF THE ATOM ^35 
 
 ence between the two carbon atoms in this com- 
 pound ; there would, however, be a difference on 
 the electrical view. For let us suppose that the 
 hydrogen atoms are all negatively electrified; the 
 three Faraday tubes going from the hydrogen atoms 
 to each carbon atom give a positive charge of 
 three units on each carbon atom. But in addition 
 to the Faraday tubes coming from the hydrogen 
 atoms, there is one tube which goes from one car- 
 bon atom to the other. This means an additional 
 positive charge on one carbon atom and a nega- 
 tive charge on the other. Thus, one of the carbon 
 atoms will have a charge of four positive units, 
 while the other will have a charge of three positive 
 and one negative unit, i.e., two positive units ; so 
 that on this view the two carbon atoms are not in 
 the same state. A still greater difference must 
 exist between the atoms when we have what is 
 called double linking, i.e., when the carbon atoms 
 are supposed to be connected by two bonds, as in 
 the compound
 
 136 ELECTRICITY AND MATTER 
 
 Here, if one carbon atom had a charge of four posi- 
 tive units, the other would have a charge of two 
 positive and two negative units. 
 
 We might expect to discover such differences 
 as are indicated by these considerations by the in- 
 vestigation of which are known as additive prop- 
 erties, i.e., properties which can be calculated 
 when the chemical constitution of the molecule 
 is known. Thus, let ABC represent the atoms of 
 three chemical elements, then if p is the value of 
 some physical constant for the molecule of A^ 
 q the value for _Z? 2 , and r for <7 2 , then if this con- 
 stant obeys the additive law, its value for a mole- 
 cule of the substance whose chemical composition 
 is represented by the formula A & B 7 C z is 
 
 We can only expect relations like this to hold when 
 the atoms which occur in the different compounds 
 corresponding to different values of x y z are 
 the same. If the atom A occurs in different states 
 in different compounds we should have to use 
 different values of p for these compounds. 
 
 A well-known instance of the additive prop- 
 erty is the refractive power of different substances 
 for light, and in this case chemists find it neces-
 
 CONSTITUTION OF THE ATOM ^37 
 
 sary to use different values for the refraction due 
 a carbon atom according as the atom is doubly or 
 singly linked. They use, however, the same value 
 for the refraction of the carbon atom when singly 
 linked with another atom as when, as in the com- 
 pound C HI, it is not linked with another carbon 
 atom at all. 
 
 It may be urged that although we can conceive 
 that one atom in a compound should be positively 
 and the other negatively electrified when the 
 atoms are of different kinds, it is not easy to do 
 so when the atoms are of the same kind, as they 
 are in the molecules of the elementary gases 
 HI, 6> 2 , NI and so on. With reference to this 
 point we may remark that the electrical state of 
 an atom, depending as it does on the power of 
 the atom to emit or retain corpuscles, may be very 
 largely influenced by circumstances external to 
 the atom. Thus, for an example, an atom in a gas 
 when surrounded by rapidly moving atoms or 
 corpuscles which keep striking against it may 
 have corpuscles driven out of it by these collisions 
 and thus become positively electrified. On the 
 other hand, we should expect that, ceteris parilus, 
 the atom would be less likely to lose a corpuscle 
 when it is in a gas than when in a solid or a
 
 13g ELECTRICITY AND MATTER 
 
 liquid. For when in a gas after a corpuscle has 
 just left the atom it has nothing beyond its own 
 velocity to rely upon to escape from the attraction 
 of the positively electrified atom, since the other 
 atoms are too far away to exert any forces upon 
 it. When, however, the atom is in a liquid or a 
 solid, the attractions of the other atoms which 
 crowd round this atom may, when once a corpus- 
 cle has left its atom, help it to avoid falling 
 back again into atom. As an instance of this 
 effect we may take the case of mercury in the 
 liquid and gaseous states. In the liquid state 
 mercury is a good conductor of electricity. One 
 way of regarding this electrical conductivity is 
 to suppose that corpuscles leave the atoms of the 
 mercury and wander about through the inter- 
 stices between the atoms. These charged cor- 
 puscles when acted upon by an electric force 
 are set in motion and constitute an electric cur- 
 rent, the conductivity of the liquid mercury in- 
 dicating the presence of a large number of cor- 
 puscles. When, however, mercury is in the gaseous 
 state, its electrical conductivity has been shown by 
 Strutt to be an exceedingly small fraction of the 
 conductivity possessed by the same number of 
 molecules when gaseous. We have thus indications
 
 CONSTITUTION OF THE ATOM ^39 
 
 that the atoms even of an electro-positive sub- 
 stance like mercury may only lose comparatively 
 few corpuscles when in the gaseous state. Sup- 
 pose then that we had a great number of atoms 
 all of one kind in the gaseous state and thus mov- 
 ing about and coming into collision with each 
 other ; the more rapidly moving ones, since they 
 would make the most violent collisions, would be 
 more likely to lose corpuscles than the slower 
 ones. The faster ones would thus by the loss of 
 their corpuscles become positively electrified, 
 while the corpuscles driven off would, if the 
 atoms were not too electro-positive to be able to 
 retain a negative charge even when in the gase- 
 ous state, tend to find a home on the more slowly 
 moving atoms. Thus, some of the atoms would 
 get positively, others negatively electrified, and 
 those with changes of opposite signs would com- 
 bine to form a diatomic molecule. This argu- 
 ment would not apply to very electro-positive 
 gases. These we should not expect to form mole- 
 cules, but since there would be many free cor- 
 puscles in the gas we should expect them to 
 possess considerable electrical conductivity.
 
 CHAPTER VI 
 
 RADIO-ACTIVITY AND EADIO-ACTIVE SUB- 
 STANCES 
 
 IN 1896 Becquerel discovered that uranium 
 and its salts possess the power of giving out rays 
 which, like Rontgen and cathode rays, affect a 
 photographic plate, and make a gas through which 
 they pass a conductor of electricity. In 1898 
 Schmidt discovered that thorium possesses similar 
 properties. This power of emitting rays is called 
 radio-activity, and substances which possess the 
 power are said to be radio-active. 
 
 This property of uranium led to a careful ex- 
 amination of a large number of minerals contain- 
 ing this substance, and M. and Mme. Curie found 
 that some of these, and notably some specimens of 
 pitch-blende, were more radio-active than equal 
 volumes of pure uranium, although only a fraction 
 of these minerals consisted of uranium. This in- 
 dicated that these minerals contained a substance 
 or substances much more radio-active than uran- 
 ium itself, and a systematic attempt was made to
 
 RADIO-ACTIVE SUBSTANCES 141 
 
 isolate these substances. After a long investigation, 
 conducted with marvellous skill and perseverance, 
 M. and Mme. Curie, with the collaboration of MM. 
 Bemont and Debierne, succeeded in establishing 
 the existence of three new radio-active substances 
 in pitch-blende : radium associated with the ba- 
 rium in the mineral, and closely resembling it in 
 its chemical properties ; polonium associated with 
 the bismuth, and actinium with the thorium. They 
 succeeded in isolating the first of these and deter- 
 mined its combining weight, which was found to be 
 225. Its spectrum has been discovered and exam- 
 ined by Demarcay. Neither polonium nor actinium 
 has yet been isolated, nor have their spectra 
 been observed. The activity of polonium has 
 been found to be fugitive, dying away in some 
 months after its preparation. 
 
 These radio-active substances are not confined 
 to rare minerals. I have lately found that many 
 specimens of water from deep wells contain a 
 radio-active gas, and Elster and Geitel have found 
 that a similar gas is contained in the soil. 
 
 These radio-active substances may be expected 
 to be of the greatest possible assistance in the task 
 of investigating problems dealing with the nature 
 of the atom, and with the changes that go on in
 
 142 ELECTRICITY AND MATTER 
 
 the atom from time to time. For the properties 
 possessed by these substances are so marked as to 
 make the detection of exceedingly minute quanti- 
 ties of them a matter of comparative ease. The 
 quantity of these substances which can be detected 
 is to the corresponding amount of the other ele- 
 ments which have to be detected by the ordinary 
 methods of chemical analysis, in the proportion of 
 a second to thousands of years. Thus, changes 
 which would have to go on for almost geological 
 epochs with the non-radio-active substances, be- 
 fore they became large enough to be detected, 
 could with radio-active substances prove appreci- 
 able effects in the course of a few hours. 
 
 Character of the Radiation 
 
 Rutherford found that the radiation from uran 
 ium, and it has subsequently been found that the 
 same is true for thorium and radium, is made up 
 of three distinct types which he calls the a, /3, and 
 y radiations. 
 
 The a radiation is very easily absorbed, being 
 unable to penetrate more than a few millimetres 
 of air at atmospheric pressure, the /? radiation is 
 much more penetrating, while the y radiation is 
 the most penetrating of all. Investigations of the
 
 RADIO-ACTIVE SUBSTANCES 143 
 
 effects of magnetic and electric forces on these 
 three types of radiation have shown that they are 
 of entirely different characters. Becquerel showed 
 that the /3 rays were deflected by electric and mag- 
 netic forces, the direction of the deflection show- 
 ing that the rays carried a charge of negative elec- 
 tricity. He determined, using the method described 
 
 in Chapter IV, the value of --. the ratio of -the 
 
 m 
 
 charge to the mass of the carriers of the negative 
 electricity ; he found that it was about 10 7 , and that 
 the velocity for some of the rays was more than 
 two-thirds that of light. He thus proved that the 
 /3 rays consisted of corpuscles travelling at prodig- 
 ious speeds. 
 
 The a rays are not nearly so easily deflected as 
 the /3 rays, but Rutherford has recently shown 
 that they can be deflected, and the direction of 
 deflection shows that they carry & positive charge. 
 He finds, and his measurements have been con 
 
 firmed by Des Coudres, that the ratio of 1 is 6 X 
 10 3 , and the velocity of these particles is 2 X 10 9 
 centimetres per second. The value of 1 shows that 
 the carriers of the positive electrification have
 
 J44 ELECTRICITY AND MATTER 
 
 masses comparable with those of ordinary atoms ; 
 
 thus for hydrogen is 10 4 and for helium 2.5 X 
 m 
 
 10 3 . The very high velocity with which these are 
 shot out involves an enormous expenditure of en- 
 ergy, a point to which we shall return later. One 
 of the most interesting things about this result is 
 
 that the value of shows that the atoms shot off 
 m 
 
 are not the atoms of radium, indicating either that 
 radium is a compound containing lighter elements 
 or else that the atom of radium is disintegrating 
 
 into such elements. The value of for the a 
 
 m 
 
 rays obtained by Rutherford and Des Coudres 
 suggests the existence of a gas heavier than hy- 
 drogen but lighter than helium. The y rays, as 
 far as we know, are not deflected either by mag- 
 netic or electric forces. 
 
 There is considerable resemblance between a 
 radio-active substance and a substance emitting 
 secondary radiation under the influence of Ront- 
 gen rays : the secondary radiation is known to 
 contain radiation of the ft and y types ; and as 
 part of the radiation is exceedingly easily absorbed, 
 being unable to penetrate more than a millimetre 
 or so of air at atmospheric pressure, it is possible
 
 RADIO-ACTIVE SUBSTANCES 145 
 
 that closer investigation may show that a rays, i.e., 
 positively electrified particles, are present also. 
 This analogy raises the question as to whether 
 there may not, in the case of the body struck by 
 the Rontgen rays, be a liberation of energy 
 such as we shall see occurs in the case of the 
 radio-active substances, the energy emitted by the 
 radiating substances being greater than the energy 
 in the Rontgen rays falling upon it; this excess of 
 energy being derived from changes taking place 
 in the atoms of the body exposed to the Rontgen 
 rays. This point seems worthy of investigation, 
 for it might lead to a way of doing by external 
 agency what radio-active bodies can do spontane- 
 ously, i.e., liberate the energy locked up in the 
 atom. 
 
 Emanation from Radio-Active Substances 
 Rutherford proved that thorium emits some- 
 thing which is radio-active and which is wafted 
 about by currents of air as if it were a gas; in 
 order to avoid prejudging the question as to the 
 physical state in which the substance given off by 
 radium exists, Rutherford called it the "emana- 
 tion." The emanation can pass through water or 
 the strongest acid and can be raised to tempera-
 
 J46 ELECTRICITY AND MATTER 
 
 tures at which platinum is incandescent without 
 suffering any loss of radio-activity. In this inertness 
 it resembles the gases argon and helium, the latter 
 of which is almost always found associated with 
 thorium. The radio-activity of the thorium emana- 
 tion is very transient, sinking to half its value in 
 about one minute. 
 
 The Curies found that radium also gives off 
 a radio-active emanation which is much more 
 persistent than that given off by thorium, taking 
 about four days to sink to half its activity. 
 
 There seems every reason for thinking that 
 those emanations are radio-active matter in the 
 gaseous form ; they can be wafted from one place 
 to another by currents of air ; like a gas they dif- 
 fuse through a porous plug at a rate which shows 
 that their density is very high. They diffuse 
 gradually through air and other gases. The coeffi- 
 cient of diffusion of the radium emanation through 
 air has been measured by Rutherford and Miss 
 Brooks and they concluded that the density of 
 the emanation was about eighty. The emanation 
 of radium has been liquefied by Rutherford and 
 Soddy ; and I have, by the kindness of Professor 
 Dewar, been able to liquefy the radio-active gas 
 found in water from deep wells, which very
 
 RADIO-ACTIVE SUBSTANCES 147 
 
 closely resembles the emanation and is quite 
 possibly identical with it. In short the emana- 
 tions seem to satisfy every test of the gaseous 
 state that can be applied to them. It is true 
 that they are not capable of detection by any 
 chemical tests of the ordinary type, nor can they 
 be detected by spectrum analysis, but this is only 
 because they are present in very minute quantities 
 quantities far too small to be detected even by 
 spectrum analysis, a method of detection which is 
 exceedingly rough when compared with the elec- 
 trical methods which we are able to employ for 
 radio-active substances. It is not, I think, an ex- 
 aggeration to say that it is possible to detect with 
 certainty by the electrical method a quantity of a 
 radio-active substance less than one-hundred-thou- 
 sandth part of the least quantity which could be 
 detected by spectrum analysis. 
 
 Each portion of a salt of radium or thorium is 
 giving off the emanation, whether that portion be 
 on the inside or the outside of the salt; the 
 emanation coming from the interior of a salt, how- 
 ever, does not escape into the air, but gets entangled 
 in the salt and accumulates. If such a radio- 
 active salt is dissolved in water, there is at first a 
 great evolution of the emanation which has been
 
 }48 ELECTRICITY AND MATTER 
 
 stored up in the solid salt. The emanation can be 
 extracted from the water either by boiling the 
 water or bubbling air through it. The stored up 
 emanation can also be driven off from salts in the 
 solid state by raising them to a very high tern- 
 perature. 
 
 Induced Radio-Activity 
 
 Kutherford discovered that substances exposed 
 to the emanation from thorium become radio-active, 
 and the Curies discovered almost simultaneously 
 that the same property is possessed by the emana- 
 tion from radium. This phenomenon is called in- 
 duced radio-activity. The amount of induced 
 radio-activity does not depend upon the nature of 
 the substance on which it is induced ; thus, paper 
 becomes as radio-active as metal when placed 
 in contact with the emanations of thorium or 
 radium. 
 
 The induced radio-activity is especially de- 
 veloped on substances which are negatively elec- 
 trified. Thus, if the emanation is contained in a 
 closed vessel, in which a negatively electrified wire 
 is placed, the induced radio-activity is concentrated 
 on the negatively electrified wire, and this induced 
 activity can be detected on negatively electrified
 
 RADIO-ACTIVE SUBSTANCES 14 g 
 
 bodies when it is too weak to be detected on un- 
 electrified surfaces. The fact that the nature of 
 the induced radio-activity does not depend on the 
 substance in which it is induced points to its being 
 due to a radio-active substance which is deposited 
 from the emanation on substances with which it 
 comes in contact. 
 
 Further evidence of this is afforded by an ex- 
 periment made by Miss Gates, in which the in- 
 duced radio-activity on a fine wire was, by raising 
 it to incandescence, driven off the wire and de- 
 posited on the surrounding surfaces. The induced 
 radio-activity due to the thorium emanation is 
 very different from that due to the radium emana- 
 tion, for whereas the activity of the thorium ema- 
 nation is so transient that it drops to half its 
 value in one minute, the induced radio-activity 
 due to it takes about eleven hours to fall in the 
 same proportion. The emanation due to radium, 
 which is much more lasting than the thorium 
 emanation, taking about four days instead of one 
 minute to fall to half its value, gives rise to a very 
 much less durable induced radio-activity, one fall, 
 ing to half its value in about forty minutes instead 
 of, as in the case of thorium, eleven hours. The 
 emanation due to actinium is said only to be active
 
 150 ELECTRICITY AND MATTER 
 
 for a few seconds, but the induced radio-activity 
 due to it seems to be nearly as permanent as that 
 due to radium. 
 
 Sqparatimiof the Active Constituent from Thorium 
 Kutherford and Soddy, in a most interesting 
 and important investigation, have shown that the 
 radio-activity of thorium is due to the passage of 
 the thorium into a form which they call TTiX, 
 which they showed could be separated from the 
 rest of the thorium by chemical means. When this 
 separation has been effected the thorium left be- 
 hind is for a time deprived of most of its radio-activ- 
 ity, which is now to be found in the T h X. The 
 radio-activity of the thorium X slowly decays while 
 that of the rest of the thorium increases until it 
 has recovered its original activity. While this has 
 been going on, the radio-activity of the Th Xhas 
 vanished. The time taken for the radio-activity 
 of the T h X to die away to half its original value 
 has been shown by Rutherford and Soddy to be 
 equal to the time taken by the thorium from which 
 the TJiX has been separated to recover half its 
 original activity. All these results support the 
 view that the radio-active part of the thorium, the 
 thorium X, is continually being produced from the
 
 RADIO-ACTIVE SUBSTANCES 151 
 
 thorium itself; so that if the activity of thorium 
 X were permanent, the radio-activity of the tho- 
 rium would continually increase. The radio-activ. 
 ity of the thorium X, however, steadily dies away. 
 This prevents the unlimited increase of the radio- 
 activity of the mixture, which will reach a steady 
 value when the increase in the radio-activity due 
 to the production of fresh T h X is balanced by 
 the decay in the activity of that already produced. 
 The question arises as to what becomes of the 
 Th X and the emanation when they have lost their 
 radio-activity. This dead ThX, as we may call 
 it, is accumulating all the time in the thorium; 
 but inasmuch as it has lost its radio-activity, we 
 have only the ordinary methods of chemical analy- 
 sis to rely upon, and as these are almost infinitely 
 less delicate than the tests we can apply to radio- 
 active substances, it might take almost geological 
 epochs to accumulate enough of the dead ThX 
 to make detection possible by chemical analysis. 
 It seems possible that a careful examination of the 
 minerals in which thorium and radium occur 
 might yield important information. It is remark- 
 able that helium is almost invariably a constitu- 
 ent of these minerals. 
 
 You will have noticed how closely, as pointed
 
 J52 ELECTRICITY AND MATTER 
 
 out by Rutherford and Soddy, the production of 
 radio-activity seems connected with changes tak- 
 ing place in the radio-active substance. Thus, to 
 take the case of thorium, which is the one on 
 which we have the fullest information, we have first 
 the change of thorium into thorium X, then the 
 change of the thorium X into the emanation and 
 the substance forming the a rays. The radio- 
 activity of the emanation is accompanied by a fur- 
 ther transformation, one of the products being the 
 substance which produces induced radio-activity. 
 
 On this view the substance while radio-active 
 is continually being transformed from one state 
 to another. These transformations may be ac- 
 companied by the liberation of sufficient energy 
 to supply that carried off by the rays it emits 
 while radio-active. The very large amount of 
 energy emitted by radio-active substances is strik- 
 ingly shown by some recent experiments of the 
 Curies on the salts of radium. They find that those 
 salts give out so much energy that the absorption 
 of this by the salt itself is sufficent to keep the 
 temperature of the salt permanently above that of 
 the air by a very appreciable amount in one of 
 their experiments as much as 1.5 C. It appears 
 from their measurements that a gram of radium
 
 RADIO-ACTIVE SUBSTANCES 153 
 
 gives out enough energy per hour to raise the 
 temperature of its own weight of water from the 
 freezing to the boiling point. This evolution of 
 energy goes on uninterruptedly and apparently 
 without diminution. If, however, the views we 
 have just explained are true, this energy arises 
 from the transformation of radium into other 
 forms of matter, and its evolution must cease when 
 the stock of radium is exhausted ; unless, indeed, 
 this stock is continually being replenished by the 
 transformation of other chemical elements into 
 radium. 
 
 We may make a rough guess as to the probable 
 duration of a sample of radium by combining the 
 result that a gram of radium gives out 100 
 calories per hour with Rutherford's result that 
 the a rays are particles having masses comparable 
 with the mass of an atom of hydrogen projected 
 with a velocity of about 2 X 10 9 centimetres per 
 second ; for let us suppose that the heat measured 
 by the Curies is due to the bombardment of the 
 radium salt by these particles, and to get a 
 superior limit to the time the radium will last, 
 let us make the assumption that the whole of the 
 mass of radium gets transformed into the a par- 
 ticles (as a matter of fact we know that the emana-
 
 154 ELECTRICITY AND MATTER 
 
 tion is produced as well as the a particles). Let 
 x be the life in hours of a gram of radium ; 
 then since the gram emits per hour 100 calories, 
 or 4.2 X 10 9 ergs, the amount of energy emitted by 
 the radium during its life is a?X 4.2 X 10 9 ergs. 
 If jVis the number of a particles emitted in this 
 time, m the mass of one of them in grams, v 
 the velocity, then the energy in the a particles is 
 1 Nmv\ but this is to be equal to a? X 4.2 X 10 9 
 ergs, hence % Nm v* = x X 4.2 X 10 9 J but if the 
 gram of radium is converted into the a particles, 
 Nm = 1, and by Kutherford's experiments v = 2 
 
 4 X 10 18 10 9 
 X 10 9 , hence we have x = % ^ ^ 1Q9 = ^ 
 
 hours, or about 50,000 years. 
 
 From this estimate we should expect the life 
 of a piece of radium to be of the order of 50,000 
 years. This result shows that we could not 
 expect to detect any measurable changes in the 
 space of a few months. In the course of its life 
 the gram of radium will have given out about 
 5 X 10 10 calories, a result which shows that if this 
 energy is derived from transformations in the 
 state of the radium, the energy developed in these 
 transformations must be on a very much greater 
 scale than that developed in any known chemical
 
 RADIO-ACTIVE SUBSTANCES 155 
 
 reactions. On the view we have taken the differ- 
 ence between the case of radium and that of or- 
 dinary chemical reactions is that in the latter the 
 changes are molecular, while in the case of ra- 
 dium the changes are atomic, being of the nature 
 of a decomposition of the elements. The example 
 given on page (111) shows how large an amount 
 of energy may be stored up in the atom if we re- 
 gard it as built up of a number of corpuscles. 
 
 We may, I think, get some light on the processes 
 going on in radium by considering the behavior 
 of a model atom of the kind described on page 
 124, and which may be typified by the case of 
 the corpuscles which when rotating with a high 
 velocity are stable when arranged in a certain 
 way, which arrangement becomes unstable when 
 the energy sinks below a certain value and is 
 succeeded by another configuration. A top spin- 
 ning about a vertical axis is another model of the 
 same type. This is stable when in a vertical 
 position if the kinetic energy due to its rotation 
 exceeds a certain value. If this energy were 
 gradually to decrease, then, when it reached the 
 critical value, the top w T ould become unstable and 
 would fall down, and in so doing would give a 
 considerable amount of kinetic energy.
 
 15 g ELECTRICITY AND MATTER 
 
 Let us follow, then, the behavior of an atom of 
 this type, i.e., one which is stable in one configura- 
 tion of steady motion when the kinetic energy of 
 the corpuscles exceeds a certain value, but be- 
 comes unstable and passes into a different config- 
 uration when the kinetic energy sinks below that 
 value. Suppose now that the atom starts with an 
 amount of kinetic energy well above the critical 
 value, the kinetic energy will decrease in conse- 
 quence of the radiation from the rapidly moving 
 corpuscles ; but as long as the motion remains 
 steady the rate of decrease will be exceedingly 
 slow, and it may be thousands of years before the 
 energy approaches the critical value. When it gets 
 close to this value, the motion will be very easily 
 disturbed and there will probably be considerable 
 departure from the configuration for steady motion 
 accompanied by a great increase in the rate at 
 which kinetic energy is loss by radiation. The atom 
 now emits a much greater number of rays and the 
 kinetic energy rapidly approaches the critical 
 value ; when it reaches this value the crash comes, 
 the original configuration is broken up, there is a 
 great decrease in the potential energy of the sys- 
 tem accompanied by an equal increase in the 
 kinetic energy of the corpuscles. The increase in
 
 RADIO-ACTIVE SUBSTANCES 157 
 
 the velocity of the corpuscles may cause the dis- 
 ruption of the atom into two or more systems, cor- 
 responding to the emission of the a rays and 
 the emanation. 
 
 If the emanation is an atom of the same type 
 as the original atom, i.e., one whose configuration 
 for steady motion depends on its kinetic energy, 
 the process is repeated for the emanation, but in a 
 very much shorter time, and is repeated again for 
 the various radio-active substances, such as the 
 induced radio-active substance formed out of the 
 emanation. 
 
 We have regarded the energy emitted by 
 radium and other radio-active substances as de- 
 rived from an internal source, i.e., changes in the 
 constitution of the atom ; as changes of this kind 
 have not hitherto been recognized, it is desirable 
 to discuss the question of other possible sources 
 of this energy. One source which at once sug- 
 gests itself is external to the radium. We might 
 suppose that the radium obtained its energy by 
 absorbing some form of radiation which is passing 
 through all bodies on the surface of the earth, 
 but which is not absorbed to any extent by any 
 but those which are radio-active. This radiation 
 must be of a very penetrating character, for radium
 
 15 g ELECTRICITY AND MATTER 
 
 retains its activity when surrounded by thick lead 
 or when placed in a deep cellar. We are familiar 
 with forms of Kontgen rays, and of rays given 
 out by radium itself, which can produce appreci- 
 able effects after passing through several inches of 
 lead, so that the idea of the existence of very pene- 
 trating radiation does not seem so improbable as it 
 would have done a few years ago. It is interest- 
 ing to remember that very penetrating radiation 
 was introduced by Le Sage more than a century 
 ago to explain gravitation. Le Sage supposed 
 that the universe was thronged with exceedingly 
 small particles moving with very high velocities. 
 He called these ultra-mundane corpuscles and as- 
 sumed that they were so penetrating that they 
 could pass through masses as large as the sun or 
 the planets without suffering more than a very 
 slight absorption. They were, however, absorbed 
 to a slight extent and gave up to the bodies 
 through which they passed a small fraction of 
 their momentum. If the direction of the ultra- 
 mundane corpuscles passing through a body were 
 uniformly distributed, the momentum communi- 
 cated by them to the body would not tend to move 
 it in one direction rather than another, so that 
 a body A alone in the universe and exposed to
 
 RADIO-ACTIVE SUBSTANCES ^59 
 
 bombardment by Le Sage's corpuscles would re- 
 main at rest ; if, however, there is a second body 
 in the neighborhood of A, B will shield off 
 from A some of the corpuscles moving in the 
 direction B A ; thus, A will not receive as much 
 momentum in this direction as it did when it was 
 alone in the field, but in the latter case it only re- 
 ceived enough momentum in this direction to keep 
 it in equilibrium ; hence, when B is present, the 
 momentum in the opposite direction will get the 
 upper hand so that A will move in the direction, 
 A B, i.e., will be attracted to B. Maxwell pointed 
 out that this transference of momentum from Le 
 Sage's corpuscles to the body through which they 
 were passing involved the loss of kinetic energy 
 by the corpuscles ; and that if the loss of momen- 
 tum were sufficient to account for gravitation, 
 the kinetic energy lost by the ultra-mundane cor- 
 puscles would be sufficient, if converted into heat, 
 to keep the gravitating body white hot. The 
 fact that all bodies are not white hot was urged 
 by Maxwell as an argument against Le Sage's 
 theory. It is not necessary, however, to suppose 
 that the energy of the corpuscles is transformed 
 into heat ; we might imagine it transformed into a 
 very penetrating radiation which might escape
 
 jgQ ELECTRICITY AND MATTER 
 
 from the gravitating body. A simple calculation 
 will show that the amount of kinetic energy 
 transformed per second in each gram of the 
 gravitating body must be enormously greater than 
 that given out in the same time by one gram of 
 radium. 
 
 We have seen in the first chapter that waves 
 of electric and magnetic force possess momentum 
 in their direction of propagation; we might there- 
 fore replace Le Sage's corpuscles by very pene- 
 trating Rontgen rays. Those, if absorbed, would 
 give up momentum to the bodies through which 
 they pass, and similar consideration to those 
 given by Le Sage would show that two bodies 
 would attract each other inversely as the square 
 of the distance between them. If the absorption 
 of these waves per unit volume depended only 
 upon, and was proportional to, the density, the 
 attraction between the bodies would be directly 
 proportional to the product of their masses. It 
 ought to be mentioned that on this view any 
 changes in gravitation would be propagated with 
 the velocity of light; whereas, astronomers be- 
 lieve they have established that it travels with a 
 very much greater velocity. 
 
 As in the case of Le Sage's corpuscles, the loss
 
 RADIO-ACTIVE SUBSTANCES IQI 
 
 of momentum by the Rontgen rays would be ac- 
 companied by a loss of energy; for each unit of 
 momentum lost v units of energy would be lost, v 
 being the velocity of light. If this energy were 
 transformed into that of rays of the same type as 
 the incident rays, a little reflection will show that 
 he absorption of the rays would not produce 
 gravitational attraction. To get such attraction 
 the transformed rays must be of a more pene- 
 trating type than the original rays. Again, as 
 in the case of Le Sage's corpuscles, the absorp- 
 tion of energy from these rays, if they are the 
 cause of gravitation, must be enormous so great 
 that the energy emitted by radium would be but 
 an exceedingly small fraction of the energy being 
 transformed within it. From these considerations 
 I think that the magnitude of the energy radiated 
 from radium is not a valid argument against the 
 energy being derived from radiation. The reason 
 which induces me to think that the source of the 
 energy is in the atom of radium itself and not ex- 
 ternal to it is that the radio-activity of substances 
 is, in all cases in which we have been able to local- 
 ize it, a transient property. No substance goes on 
 being radio-active for very long. It may be asked 
 how can this statement be reconciled with the fact
 
 IQ2 ELECTRICITY AND MATTER 
 
 that thorium and radium keep up their activity 
 without any appreciable falling off with time. 
 The answer to this is that, as Rutherford and 
 Soddy have shown in the case of thorium, it is 
 only an exceedingly small fraction of the mass 
 which is at any one time radio-active, and that this 
 radio-active portion loses its activity in a few 
 hours, and has to be replaced by a fresh supply 
 from the non-radio-active thorium. Take any of 
 the radio-active substances we have described, the 
 ThX, the emanations from thorium or radium, 
 the substance which produces induced radio- 
 activity, all these are active for at the most a few 
 days and then lose this property. This is what 
 we should expect on the view that the source of 
 the radio-activity is a change in the atom ; it is 
 not what we should expect if the source were ex- 
 ternal radiation.
 
 DATE DUE 
 
 MAR:. H979 
 
 MAY 3 

 
 PhysSci QC721 T48 1 
 .Thomson, Joseph John 
 
 1856-1*40. 
 Electricity and matter 
 
 n, SiJ^H 
 
 EOONM. LIBRARY FACILITY 
 
 A 001 450 478 1 
 
 FEE 
 
 I 6 19T9 
 
 A