blLH 
 
 A, CR^WTHER 
 
TEXT -BOOKS OF CHEMICAL RESEARCH AND ENGINEERING. 
 
 MOLECULAR PHYSICS 
 
 BY 
 
 JAMES ARNOLD CROWTHER, M.A. 
 
 FELLOW OF ST. JOHN'S COLLEGE, CAMBRIDGE, AND DEMONSTRATOR 
 IN PHYSICS AT THE CAVENDISH LABORATORY 
 
 PHILADELPHIA 
 
 P. BLAKISTON'S SON & CO. 
 
 1 01 2 WALNUT STREET 
 1914 
 
PREFACE 
 
 THE present volume is an attempt to give a 
 connected account of the constitution and properties 
 of the atom and molecule in the light which has 
 been thrown upon these particles by recent physical 
 research. From the great mass of experimental 
 observations which constitute what has been called 
 somewhat vaguely the " New Physics " I have 
 endeavoured to select those portions which have 
 a direct bearing on this important and fascinating 
 subject, and I have drawn freely on all available 
 sources of information, some of which are indicated 
 in the Bibliography at the end of the book. 
 
 To Professor Sir J. J. Thomson I owe a debt of 
 gratitude for his kindness in allowing me to select 
 from his experimental negatives, and to reproduce, 
 the Positive Ray photographs which illustrate 
 Chapter IV. I owe him still more for the privilege 
 which I have enjoyed during the past eight years in 
 the Cavendish Laboratory, of moving in daily 
 contact with much of the work, and of drinking in, 
 as it were at the fountain head, much of the theory 
 narrated in the present volume. To this must be 
 ascribed any merits which the following pages may 
 be found to possess ; for their errors and deficiencies 
 I, alone, am responsible. 
 
 J.A.C. 
 
 294689 
 
CONTENTS 
 
 CHAPTER I. INTRODUCTION ..... i 
 Historical survey. The old and the new physics. 
 The molecular theory of matter. Molecular 
 magnitudes. 
 
 CHAPTER II. THE PHYSICS OF THE ELECTRON . 10 
 The discharge of electricity through gases. 
 Cathode rays. Measurement of the ratio of 
 the mass to the charge for the cathode rays. 
 Measurement of the charge on an electron. 
 Photography of the tracks of ionizing particles. 
 
 CHAPTER III. THE POSITIVE PARTICLE . . 34 
 
 The a-particles from radio-active substances. 
 Counting the a-particles. The charge on an 
 a-particle. Production of helium from a-rays. 
 
 CHAPTER IV. THE NEW METHOD OF ANALYSIS . 42 
 Positive particles in the discharge tube. Sir J. J. 
 Thomson's experiments. Measurement of the 
 velocity and mass of the positive particles. Posi- 
 tive ray analysis. The new gases. Application 
 of the method to the study of chemical decom- 
 position. Electrical methods of measurement. 
 
 CHAPTER V. THE NATURE AND SIZE OF AN ELECTRON 67 
 The Faraday tubes. Electromagnetic mass. 
 Variation of electromagnetic mass with speed. 
 Kaufmann's experiments on the y8-rays from 
 radium. The radius of an electron. The num- 
 ber of electrons in the atom. The electron theory 
 of matter. 
 
 CHAPTER VI. THE CHEMISTRY OF THE MODEL ATOM 86 
 " Model " atoms. The stability of groups of 
 electrons. Cohesion and adhesion. The periodic 
 law. The electron theory of valency. Valency 
 and the dispersion of light. 
 
viii CONTENTS 
 
 PAGE 
 
 CHAPTER VII. THE ATOM IN VIBRATION . .in 
 Propagation of disturbances along a Faraday 
 tube. The wave theory of light. The Zeeman 
 effect. Spectral series. The origin of spectra. 
 
 CHAPTER VIII. THE MOLECULAR THEORY OF MATTE.R 131 
 Solids, liquids, and gases. The kinetic theory of 
 heat. Change of state. Van der Waal's equa- 
 tion. The size of the atom. Electron theory of 
 thermal and electrical conduction. 
 
 CHAPTER IX. THE ATOM IN DISSOLUTION . .147 
 Radioactive transformations . The decomposition 
 of an element. Radio-activity of ordinary 
 materials. Conclusion. 
 
 APPENDIX A. DEFLECTION OF THE POSITIVE RAYS 160 
 APPENDIX B. ELECTRO-MAGNETIC MASS . .161 
 APPENDIX C. THE ZEEMAN EFFECT . . .163 
 TABLE OF ATOMIC DATA . . . . 165 
 
 BIBLIOGRAPHY . . . . . . 166 
 
MOLECULAR PHYSICS 
 
 CHAPTER I. 
 INTRODUCTION. 
 
 THE history of the rise of molecular theory has 
 often been written. From Dalton, who first gave 
 to the conceptions of the early atomists a definite 
 meaning and a real experimental basis, through 
 Avogadro and his fertile hypothesis of the molecule, 
 and so on to the kinetic theory of Clausius and Max- 
 well, the story is told in almost every text-book of 
 Chemistry and Physics, and is familiar as household 
 words to all their readers. Here for a time science 
 seemed to pause in her progress. It seemed as if the 
 memoirs of these brilliant mathematicians were to 
 contain the last word in molecular theory. 
 
 If this had been so, the following pages would 
 have been superfluous. In the last few years, how- 
 ever, new fields have been opened to the student of 
 molecular phenomena ; new methods of approach 
 have been evolved so potent in character that sub- 
 jects about which we had until then barely sufficient 
 grounds for speculation are now laid open to direct 
 experimental attack. The molecule has been raised 
 from a conception only realisable experimentally in 
 millions to the rank of a definite particle whose entry 
 into our apparatus produces a definite and 
 measurable effect. At the same time the accuracy, 
 
 M.P. I 
 
.2 MOLECULAR PHYSICS 
 
 1 \ " ' > *^c -* s -fr c "^' 
 
 and what is still more important, the certainty, of our 
 measurements of molecular magnitudes have been 
 enormously increased. It seemed, therefore, neither 
 undesirable nor devoid of interest to attempt to 
 re- write the subject of molecular physics, not from 
 the standpoint of the kinetic theory, by which it was 
 approached historically, and which constituted for 
 many years the sole line of attack, but rather in the 
 light thrown upon these problems by the recent 
 developments in what has come to be known as the 
 " New Physics/' 
 
 In order to fix our attention upon the problems 
 to be dealt with, and to recall to our minds some 
 clear ideas of the magnitudes with which we shall 
 have to deal, it may be well to consider briefly the 
 position to which we had been brought by the 
 exponents of the kinetic theory. 
 
 The atom itself was a purely chemical conception. 
 It took its rise in an attempt to explain the laws of 
 chemical combination, and represents the smallest 
 mass of an element which can take part in a chemical 
 reaction. By its first exponents it was regarded as 
 homogeneous and indivisible. This view is no longer 
 held. We shall see later that we must conceive of 
 the atom as something approaching a planetary 
 system on an infinitesimal scale. A study of the 
 phenomena of radioactivity has driven us to believe 
 that in them we are dealing with a true decompo- 
 sition of a true chemical atom ; that the element 
 radium is in fact a decomposition product of the 
 atom of uranium, and is itself in the course of 
 transition into an atom of lead, with the emission 
 during the process of several atoms of helium. This 
 break up of an atom, however, is a process which we 
 are permitted to watch, but not to control. So far 
 we have not succeeded in either accelerating or 
 retarding its progress in any way whatever. 
 
 In compounds the atoms of the different elements 
 
INTRODUCTION 3 
 
 were supposed to be grouped together into similar 
 particles or molecules, the ratio of the masses of the 
 components being the same in each individual mole- 
 cule as in the compound as a whole. It was soon 
 found necessary to assume that even in the elements 
 the atoms were usually connected into groups of two 
 or more to form a larger particle, which, unless taking 
 part in a chemical reaction, always moved and acted 
 as a single system. This extension of the theory was 
 due to Avogadro, and his additional hypothesis that 
 the number of these molecules in a given volume of 
 gas under similar conditions is independent of the 
 nature of the gas was the first great generalisation 
 in the physics of the molecule. 
 
 It was soon realised that these molecules were 
 particles exceedingly small in size. Various 
 attempts to determine the approximate diameter of 
 the molecules all led to the result that it was not very 
 much greater than 2 X io~ 8 cms. Various illustra- 
 tions have been employed to assist us to grasp the 
 extreme minuteness of this quantity. If, for 
 example, a drop of water were to be magnified to the 
 size of the earth the molecules in it would be of the 
 size of footballs. Or again, as a recent writer has 
 suggested, we may say that the carbon atom in the 
 printed page subtends at the reader's eye the same 
 angle as would be subtended there by a man on the 
 moon. 
 
 The number of molecules in any visible portion 
 of matter is, of course, correspondingly large. 
 According to the latest determinations the number 
 of molecules in I cub. cm. of air under normal 
 conditions (o C. and 760 mm. pressure) is 2*7 X io 19 . 
 It is almost hopeless to attempt to conceive this 
 inconceivable swarm of particles. It may, perhaps, 
 be of some assistance to point out that in the highest 
 attainable vacua, when the pressure of the gas is not 
 more than TQOOO mm * f mercury, the number of 
 
 i 2 
 
4 MOLECULAR PHYSICS 
 
 molecules present in every cubic millimetre of the 
 space still exceeds 2,000,000,000. 
 
 In a solid body we must regard the molecules as 
 relatively fixed. They are indeed in rapid vibration 
 about their mean position, such vibration consti- 
 tuting the phenomenon which we know as heat. 
 The fact that ancient gems and coins have come 
 down to us through many ages still preserving their 
 sharp outlines and their beautiful and clear-cut 
 engraving shows that, in the absence of external 
 forces, the defection of a molecule in a solid from its 
 original station must be of exceedingly rare 
 occurrence. 
 
 In liquids, however, we must regard the molecules 
 as free to move. A liquid has no definite shape of 
 its own, and two liquids if left quite undisturbed will 
 gradually diffuse through each other with a velocity 
 which is in general small but quite measurable. The 
 different molecules possess sufficient energy to escape 
 from the attraction of neighbouring systems, but 
 move only a very short distance through the thickly- 
 crowded space before becoming entangled in other 
 clusters. 
 
 Gases differ from liquids in the fact that the space 
 occupied by a given number of molecules is very 
 much greater ; and a molecule therefore travels 
 much further before coming into collision with other 
 molecules. Thus a gramme of water substance when 
 transformed into steam occupies i, 600 times the 
 volume which it had in the liquid state. The mole- 
 cules are therefore J// 1,600 or, say, 12 times as far 
 
 apart in the gas as in the liquid. The actual volume 
 of the molecules themselves is thus only a very small 
 fraction of the volume filled by the gas, the mole- 
 cules occupying the space between their boundaries 
 not by filling it with their bulk, but by moving about 
 in it in all directions with considerable velocities. 
 The tendency of a gas to spread through the whole 
 
INTRODUCTION 5 
 
 of the space accessible to it thus represents the 
 tendency of each molecule to proceed 'on its path in 
 a straight line when not opposed by any obstacle, 
 while the pressure on the boundaries of the gaseous 
 space is due to the exceedingly rapid series of impacts 
 made on them by the innumerable swarm of mole- 
 cules in motion. 
 
 The velocity with which the molecules in a gas 
 are moving can easily be calculated when the pressure 
 and density are known. The mean velocity of a 
 molecule of oxygen at the freezing point of water is 
 about 425 metres per second, or about 1,000 miles per 
 hour. It is, therefore, somewhat greater than the 
 velocity of sound through air under the same con- 
 ditions (331 metres per second). In addition to 
 collisions upon the boundaries each molecule collides 
 from time to time with other molecules of the gas, 
 the number of collisions made by a single molecule 
 under ordinary conditions of temperature and 
 pressure being about 6,000,000,000 every second. 
 
 The distance travelled by the particle between 
 two collisions is known as its free path. Its actual 
 value between any two collisions depends, of course, 
 upon chance. Its mean value can, however, be cal- 
 culated from the viscosity of the gas. For air under 
 ordinary conditions it is about 7*6 X lo 6 cms.., or 
 roughly T ooooo of an inch - 
 
 This mean free path, although a giant among 
 molecular magnitudes, is still rather smaller than the 
 smallest distance we may ever hope to perceive. 
 Abbe has shown that two objects would have to be 
 separated by rather more than twice this distance 
 before they could be resolved by the best possible 
 microscope working under the best conditions. 
 
 The mass of each molecule is, of course, exceed- 
 ingly minute ; according to the recent determina- 
 tions of Rutherford, which we shall describe later, the 
 mass of a hydrogen atom is i'6i X io~ 24 gms., a 
 
6 MOLECULAR PHYSICS 
 
 number so minute that it can hardly be said to con- 
 vey to the mind any impression at all. This number, 
 it will be seen, represents the value in grammes of 
 the chemical unit of atomic weight ; the mass in 
 grammes of any atom or molecule can thus be calcu- 
 lated from a table of atomic weights by merely 
 multiplying the chemical atomic or molecular weight 
 by this factor. Small as is this quantity we shall see 
 that its value is known with certainty to within a 
 very few per cent. 
 
 Of the quantities with which we have been deal- 
 ing, the kinetic theory gave accurately the velocity 
 of the molecule and the mean free path. It threw 
 only a dim and somewhat uncertain light upon the 
 number and mass of the individual molecules. As 
 to the nature of the molecule it can hardly be said to 
 have given any information at all. It is at once the 
 strength and the weakness of the statistical methods 
 employed in the kinetic theory, that given a 
 sufficiently large number of molecules, their exact 
 number, size, mass and properties become for many 
 purposes matters of indifference. Thus many of the 
 properties of gases were successfully deduced, in the 
 first place, on the assumption that the molecule was 
 a hard sphere, an assumption which in the case, say, 
 of a molecule like that of oxygen built up of 
 two atoms is almost certainly incorrect. It will be 
 seen then how little light can be thrown upon 
 the individual molecule by investigations of this 
 nature. 
 
 As the moleeule itself lay far beyond the limits of 
 vision, and as the kinetic theory could afford so little 
 certain information, it might have seemed that we 
 must rest content with the knowledge already 
 attained. Speculation as to the nature of the atom 
 was not wanting, ranging from the simple hard atom 
 of the original theory to the centre of force, of 
 Boscovitch, and the vortex atom of Professor 
 
INTRODUCTION 7 
 
 Thomson, the early speculation of one who has done, 
 perhaps, more than any other to render possible a 
 true theory of the atom. These theories, ingenious as 
 they were, withered for lack of experimental support, 
 and the subject became gradually to be regarded as 
 being in the realm of the unknowable. Meanwhile 
 the great success of the statistical methods of the 
 kinetic theory, the extension of thermodynamics, and 
 the study of phenomena from a consideration of 
 their equilibrium conditions which followed on the 
 work of Willard Gibbs, were leading further and 
 further away from atomic and molecular hypotheses. 
 Fortunately one loophole remained into this 
 region of the infinitely small. The kinetic energy 
 of a particle is equal to the product of one-half its 
 mass into the square of its velocity. However small 
 the mass of the particle, therefore, we can theoreti- 
 cally by sufficiently increasing its velocity endow it 
 with an appreciable amount of energy. In the case 
 of a molecule the velocity required will, of course, be 
 very large. The energy of a molecule in the air 
 under normal conditions of temperature and pressure 
 is about 5 X io~~ u ergs, assuming the mass and 
 velocity already given. This is far too small to be 
 detected. Let us suppose, however, that we can 
 endow our molecule with a velocity much greater 
 than this, approaching 2 X io 9 cms. per second. The 
 energy of an oxygen molecule moving with such a 
 speed would be J (32 X i'6i X io~ 24 ) . (2 X io 9 ) 2 ergs, 
 or about io~ 4 ergs. This, though small, is not less 
 than can be appreciated in other forms of energy. 
 Thus Lord Rayleigh has estimated that the faintest 
 sound which can be heard transmits every second 
 across a square centimetre of area at right angles to its 
 path about 2*3 X io~ 5 ergs. The energy in the 
 faintest perceptible beam of light is not far dif- 
 ferent from this. Thus the energy of impact of a 
 single molecule travelling with the velocity we have 
 
8 MOLECULAR PHYSICS 
 
 suggested would be comparable with the energy in a 
 faint beam of light or a just audible sound. 
 
 The velocity ascribed to the molecule in this 
 calculation might seem impossibly large. It is 
 in fact about -^ of the velocity of light, and a 
 particle travelling with this speed would, therefore, 
 cover the distance from the earth to the sun in 2 
 hours. Such particles, however, actually exist, and 
 it is the discovery of these particles and the measure- 
 ments made upon them that have led to the great 
 advances in molecular physics which we are about to 
 describe. Particles having this velocity are shot out 
 in large numbers from radioactive bodies. To 
 anticipate a little we may say that the a-particles 
 from radium consist of atoms of helium shot out with 
 a speed of this order of magnitude, and bearing a 
 positive charge. Thus it is that a single a-particle 
 is able to cause a flash of light when it strikes upon a 
 screen covered with a suitable material. 
 
 The a-particles consist of helium atoms only. 
 Velocities approaching that of the a-particles can 
 be given to atoms and molecules of other substances 
 by passing an electric discharge through them in the 
 gaseous state at very low pressures. The phenomena 
 of the discharge tube have indeed afforded the best 
 means of investigating the properties of moving 
 electrified particles, and we shall proceed to their 
 consideration immediately. 
 
 In order to complete our survey we will anticipate 
 so far as to say that the first experimental investiga- 
 tion of these phenomena led to results of a startling 
 nature. Professor Sir J. J. Thomson, as the result 
 of a brilliant series of researches and deductions, 
 which may truly be said to mark a fresh era in the 
 progress of science, showed that the most conspicuous 
 set of particles in the discharge tube, namely, those 
 constituting the cathode rays, had a mass not more 
 than 7^00 P ai "t f that of a hydrogen atom. 
 
INTRODUCTION 9 
 
 It was found, moreover, that whatever the nature 
 of the gas through which the discharge was passing, 
 whatever the nature of the electrodes used, the mass 
 of the cathode particle produced and the magnitude 
 of the charge carried by it was always the same. 
 These cathode particles, corpuscles or electrons, as 
 they came to be called, must thus be regarded as 
 forming an integral part of the atom of every kind of 
 substance. They are therefore even more funda- 
 mental than the atom itself, since they form part of 
 the material from which the atom is built up. The 
 methods used in their investigation are similar in 
 principle to those which have recently been applied 
 to atoms and molecules, but the special properties of 
 the electrons rendered their experimental investiga- 
 tion less difficult than that of the atom or molecule, 
 so that for a time it could truly be said that far more 
 was known of the electron than of the atom itself. 
 For these reasons we will commence our study of 
 molecular physics with the consideration of the 
 electron. 
 
CHAPTER II. 
 THE PHYSICS OF THE ELECTRON. 
 
 THE general appearance of an ordinary discharge 
 tube is perhaps familiar to most of my readers. It 
 is represented somewhat diagrammatically in Fig. i. 
 Covering the cathode C is a velvety light known as 
 the cathode glow. Beyond this is a comparatively 
 dark space, named after its discoverer Sir William 
 Crookes. If the pressure in the tube is fairly high 
 this Crookes dark space will be so close to the 
 cathode and so small as to be hardly visible. Beyond 
 
 c 
 
 FIG. i. THE DISCHARGE TUBE. 
 
 this dark space is another luminous area, the 
 negative glow, bounded on the side remote from 
 the cathode by still another obscure area, the Faraday 
 dark space. The length of the tube occupied by 
 these phenomena depends mainly on the pressure 
 of the gas, and is practically independent of the 
 size of the tube, the remainder of which, however 
 long, is filled with a bright light known as the 
 positive column, which is frequently, though not 
 necessarily, divided into numerous striae. It is the 
 
THE PHYSICS OF THE ELECTRON n 
 
 light from this positive column that is generally 
 employed in the spectroscopic examination of gases 
 in the discharge tube. 
 
 If the pressure is fairly low another phenomenon 
 may be distinguished. Proceeding normally from 
 the cathode and penetrating in straight lines across 
 one or more of the dark spaces may be seen faint 
 bluish streams of light, known as the cathode rays. 
 As the pressure is still further reduced these rays 
 become relatively more and more important, and 
 penetrate further and further, until finally they 
 fall upon the glass walls of the discharge tube, 
 exciting there a greenish phosphorescence. Mean- 
 while the Crookes dark space has grown until it 
 occupies practically the whole of the tube, the 
 remaining parts of the ordinary discharge being 
 represented by the glow on the cathode and a single 
 patch of light near the anode itself. 
 
 The nature of the cathode rays remained for 
 some time in doubt. However, in 1895 Perrin 
 showed that they transported a negative charge, 
 and in the following year Professor Sir J. J. Thomson 
 proved conclusively that they consisted of streams 
 of negatively charged particles, moving with 
 extremely high velocities and having a mass in all 
 probability much less than that of a hydrogen 
 atom. 
 
 Let us continue for a moment the study of the 
 discharge tube. It had long been known that if a 
 solid obstacle were placed in the path of the discharge 
 a shadow of the object was cast by the cathode rays 
 on the opposite wall of the tube. It was noticed 
 that if the obstacle was placed within the Crookes 
 dark space a shadow was also cast on the cathode. 
 That is to say, there must also be rays in the tube 
 proceeding in the opposite direction to the cathode 
 rays and falling upon the cathode itself. By using 
 a perforated cathode, as shown in the diagram. 
 
12 MOLECULAR PHYSICS 
 
 these rays become visible as faintly luminous 
 streaks of light, coming from each of the per- 
 forations, and exciting a faint mauve phosphor- 
 escence where they strike the walls of the tube. 
 These rays which carry a positive charge and have 
 a mass comparable with that of an atom, form the 
 positive particles to which we have already alluded. 
 
 The high velocities of these particles give them, 
 as we have seen, sufficient energy to produce 
 luminous effects when they fall upon suitable screens. 
 The additional fact that they carry an electric charge 
 enables us to determine not only the velocity, but 
 also the ratio of the mass of the particles to the 
 charge which they carry. 
 
 The general problem of the motion of an electri- 
 fied particle when moving under the action of electric 
 and magnetic forces is one of some little complexity, 
 though complete solutions have been given by 
 various mathematicians. Fortunately the special 
 cases which are required for our present purpose 
 lend themselves readily to the simplest treatment. 
 
 Suppose that a particle of mass m and charge e is 
 moving with a velocity v at right angles to a magnetic 
 field of strength H. In one second the charge e will 
 have moved through a distance v cms. We may 
 therefore regard the path of the particle as a sort of 
 conductor v cms. long, carrying an electric current 
 whose strength is e. The mechanical force on such 
 a conductor when placed in a magnetic field is known 
 from the laws of electro-magnetic induction to be 
 equal to the strength of the field multiplied by the 
 current and the length of the conductor, that is to 
 the product H . e . v. Further, this force is at right 
 angles to the direction of the current and to the lines 
 of force in the magnetic field. A little consideration 
 will show that under these circumstances the path 
 of the particle is changed from a straight line to a 
 circle described in a plane at right angles to the 
 
THE PHYSICS OF THE ELECTRON 13 
 
 direction of the lines of force in the magnetic 
 field. 
 
 Let r be the radius of this circle. A particle of 
 mass -m moving round a circle with a velocity v 
 exerts a centrifugal force tending to urge it away 
 from the centre of the circle. The value of this is 
 known to be 
 
 m . v*/r. 
 
 Now for equilibrium the force tending to urge the 
 particle away from the centre must equal the force 
 due to the magnetic field tending to draw it in. 
 Thus we have 
 
 H . e . v = m . v^/r 
 
 M TT / \ 
 
 - . v = H . r . . . (a) 
 
 Again the particle carries an electric charge. It 
 can therefore be deflected by an electric field. Let 
 X be the strength of the electric field. Then the 
 force experienced by the particle is equal to X . e and 
 acts upon the particle in the direction of the lines of 
 electric force. If now we arrange our apparatus 
 so that the electric field and the magnetic field are 
 at right angles to each other, the forces upon the 
 particle due to the two fields will act along the same 
 straight line, and by properly adjusting the sign of 
 the electric field we can make the two forces oppose 
 each other. It will then be possible to find a value 
 for the electric field such that the two forces just 
 neutralise each other and the particle goes on its 
 path without deflection. When this is so we know 
 that the mechanical forces on the particle due to 
 electric and magnetic fields just balance each other. 
 That is 
 
 . . . (b) 
 Thus if we apply to the moving electrified particle 
 
14 MOLECULAR PHYSICS 
 
 simultaneously an electric and magnetic field of such 
 magnitudes that the particle pursues its path without 
 any deviation, the ratio of the strengths of the two 
 fields will give us directly the velocity of the particle. 
 If, further, we can measure the radius of the circle 
 into which the path of our particle is bent by the 
 action of the magnetic field alone, we can, by 
 equation (a), determine the value of the ratio 
 m/e, or the mass to the charge for the particle we are 
 investigating, since the value of v is now known 
 from the previous experiment. 
 
 This ratio of the mass to the charge is one of the 
 utmost importance in molecular physics. It may 
 be noted that for ions in solutions it is the quantity 
 of matter associated with the transference of unit 
 quantity of electricity, that is to say, the electro- 
 chemical equivalent. According to the latest values, 
 the electro-chemical equivalent of hydrogen ions in 
 solution is '0000109 m - P er coulomb. The values 
 of the ratio for other ions can be deduced from this 
 and a table of combining weights in the usual way, 
 since every ion in solution carries by Faraday's laws 
 either the same charge as the hydrogen ion or some 
 simple multiple of it. 
 
 Owing to the way in which the volt and the ohm 
 have been defined, the former as io 8 and the latter 
 as io 9 absolute electro-magnetic units, the absolute 
 unit of electro-magnetic charge is ten times the 
 coulomb or practical unit of charge. The value of 
 m/e for hydrogen in absolute units of charge is, 
 therefore, "000109, or J us ^ a little greater than 
 io~ 4 gms. per absolute electro-magnetic unit of 
 charge. 1 
 
 i The science of electricity is burdened with two distinct systems of 
 units for the measurement of electrical magnitudes, the one founded on 
 the consideration of the force with which two similar charges repel each 
 other, the other on considerations of the induction of currents by mag- 
 nets. The practical system of units is founded upon the latter, the volt 
 being io8 and the ohm io9 absolute electro-magnetic units. The ampere 
 
THE PHYSICS OF THE ELECTRON 15 
 
 The principles just explained found their first 
 application in the experiments of Professor Sir J. J. 
 Thomson, on the cathode rays, experiments which 
 may well be said to mark a new era in science. The 
 experimental methods used by him have been 
 
 FIG. 2. CATHODE RAY DEFLECTION TUBE. 
 
 modified and improved upon in the light of subse- 
 quent discoveries, and the accuracy attained in the 
 measurements greatly increased. In principle, how- 
 
 and coulomb are thus i/ioth of the absolute units of current and charge. 
 To make confusion worse confounded, it has become usual in works and 
 original papers on these subjects to give the value of mje in electro-mag- 
 netic units, while the value of e itself is usually given in electrostatic 
 units. Our statement that the force on the electron due to the magnetic 
 field is equal to H.e.v implies that we are using the absolute electro- 
 magnetic system of units, as this system has been denned in such a way 
 as to make this statement true. As this system is the one more closely 
 related to the units in actual use, we shall employ it throughout, except 
 where the contrary is explicitly stated. 
 
16 MOLECULAR PHYSICS 
 
 ever, the experiments remain the same, and on 
 account of its historic interest the original apparatus 
 used in these experiments will be described. Fig. 2 
 is taken (by kind permission of Professor Sir J. J. 
 Thomson) from a photograph of one of the tubes 
 used by him for the experiment. The arrangement 
 of the various parts will be seen more clearly from 
 the diagrammatic representation in Fig. 2A. 
 
 The cathode of the discharge tube is at C, and 
 consists of an aluminium disc supported by a rod 
 of the same metal and connected with the outside of 
 the tube by a platinum wire sealed through the 
 glass. The anode R is an aluminium rod placed in 
 
 uii (1 
 
 -I ~Lrr 
 
 D 
 
 
 J 1 1 r 
 
 ~E"~- 
 
 
 C A B 
 
 FIG. 2A. DIAGRAM OF CATHODE RAY TUBE. 
 
 a side tube, while facing the cathode is a thick metal 
 disc A, filling the tube but pierced with a small hole 
 through which the cathode rays can pass in a narrow 
 pencil. To define this beam of rays still further, a 
 second metal disc B pierced with a still finer hole is 
 placed some distance behind A. For convenience 
 these two discs are mounted in a metal tube as shown 
 in the figure. This tube and the anode R are con- 
 nected to earth, while R and C are connected to the 
 terminals of a large induction coil as shown in the 
 photograph. 
 
 Thus, when the discharge is passed between C 
 and D, a very fine well-marked pencil of cathode 
 rays emerges from B. It is then made to pass 
 
THE PHYSICS OF THE ELECTRON 17 
 
 between two parallel plates D and E of aluminium 
 which can be charged to any required difference of 
 potential by connecting them to a large battery of 
 small accumulators. 
 
 This part of the tube is also placed between the 
 poles of the little electro-magnet shown in the 
 photograph, the lines of magnetic force being at 
 right angles to the plane of the paper and therefore 
 at right angles to the electric field. Finally, the 
 stream of cathode particles falls upon the walls of 
 the bulb Z which are covered with powdered zinc 
 blende, its presence being marked by a spot of bright 
 green phosphorescent light at the point of impact. 
 The position of the spot in the original experiments 
 was read off on a scale pasted on the outside of the 
 tube. 
 
 To perform the experiment the magnetic field is 
 first applied and the deflection of the spot of light 
 measured. From this deflection and the dimensions 
 of the different parts of the tube it is possible to 
 calculate the radius of the circle into which the path 
 of the rays has been bent by the magnetic field. 
 The deflected and undeflected paths of the particles 
 are indicated by the dotted lines in the diagram. 
 The electric field is then applied and the difference 
 of potential between the two plates gradually 
 increased until the spot of light is brought back to 
 its original position. The ratio of the electric to the 
 magnetic field is then equal to the velocity of the 
 cathode particles. The value of the ratio m/e can 
 be calculated from this velocity and the known 
 magnetic deflection as explained above. 
 
 The experiments were not without difficulty. It 
 was at first found very difficult to obtain any deflec- 
 tion of the particles by means of an electric field. 
 This was found to be due to the fact that the 
 passage of the cathode rays through the residual 
 gas in the discharge tube rendered it more or less 
 M.P. 3 
 
i8 MOLECULAR PHYSICS 
 
 
 
 conducting, so that the particles were moving 
 through what was practically a closed conductor 
 and were thus hardly affected by the external electric 
 field. It was necessary in order to eliminate this 
 effect to work with very high vacua. 
 
 On making the calculations it was found that the 
 velocity of the particles depended principally upon 
 the potential of the discharge, and to some extent 
 also on the pressure of the residual gas in the tube 
 and the nature of the electrodes and the gas in the 
 tube. Even in the same tube the velocity of all the 
 rays was not the same, so that on applying the 
 magnetic field the single spot of light made by the 
 cathode beam on the zinc blende screen was spread 
 out into a little magnetic spectrum, as we may call 
 it, each point of which corresponded to cathode rays 
 moving with a definite velocity. In tubes at an 
 exhaustion suitable for these experiments the 
 velocities range, as a rule, from 2 X io 9 to 3 X io 9 
 cms. per second, or about i/ioth of the velocity of 
 light. 
 
 On evaluating the ratio m/e it was not found to 
 suffer similar variations. The original experiments 
 showed and this has since been confirmed by many 
 subsequent experiments, that, whatever the nature 
 of the gas in the discharge tube, whatever the 
 material of the cathode, whatever the working 
 potential of the tube, the value of the ratio of the 
 mass of the cathode particle to its charge is always 
 the same. According to the latest determinations 
 the value of this constant is 5*65 X io~ 8 gms. per 
 unit of charge. 
 
 Again, although we have so far considered only 
 the case of the cathode rays, they are not by any 
 means the only source of these corpuscles, or elec- 
 trons as they are now called. Similar electrons are 
 given off in quantities from a clean metal surface 
 when illuminated by ultra-violet light, or from the 
 
THE PHYSICS OF THE ELECTRON 19 
 
 surface of the liquid sodium-potassium alloy under 
 the action of the light from an ordinary candle. 
 Rontgen rays produce them whenever they fall upon 
 any material object, and it is interesting to note that 
 the velocity of the electrons thus produced is the 
 
 FIG. 3. MAGNETIC DEFLECTION OF THE CATHODE RAYS. 
 
 same as that of the cathode rays in the Crookes tube 
 from which the Rontgen rays proceed. Electrons 
 are also emitted from incandescent metals at a high 
 temperature, and in very large quantities when 
 certain metallic oxides and notably those of barium 
 and calcium are raised to a red heat. These elec- 
 
 2 2 
 
20 MOLECULAR PHYSICS 
 
 Irons have very little velocity of their own, but may 
 very readily be given one by acting upon them with 
 an electric field. If the heated oxide is raised to a 
 potential P in absolute units, the work done on the 
 electron by the field will be P . e. liv is the velocity 
 acquired by the electron, its kinetic energy is ^mv 2 . 
 Hence, by the principle of the conservation of 
 energy P . e = %mv 2 or v 2 = 2P . e/m. Thus by 
 suitably altering the potential of the hot oxide we can 
 give to these electrons a suitable and known velocity. 
 
 Fig. 3 is a reproduction of an actual photograph 
 of such a discharge. The cathode is a platinum strip 
 carrying a minute speck of barium oxide, raised to 
 a red heat by means of an electric current and 
 charged to a potential of 240 volts from a cabinet of 
 small accumulators. The electrons given out by 
 the heated BaO are projected by the field in a 
 narrow pencil and are rendered visible by their action 
 on the residual molecules of air in the exhausted 
 tube. In the photograph a magnet has been placed 
 behind the tube so that there is a magnetic field at 
 right angles to the paths of the electrons, which are 
 thus bent into the arc of a circle as shown in the 
 figure. The fact that the circle is not completed is 
 due to the gradual diffusion and absorption of the 
 electrons by collision with the molecules of the gas 
 in the tube. 
 
 The value of the ratio m/e for these electrons has 
 been measured by their discoverer Wehnelt and 
 others. It may be noticed that as the potential 
 P to which the cathode is raised is equal to ^v 2 . m/e, 
 it is only necessary to measure the radius of the 
 circle into which the rays are bent by a magnetic 
 field of known strength H in order to be able to 
 calculate both v and m/e. This fact has been applied 
 by Lenard and others to measure the value of m/e 
 for the electrons given off by metallic surfaces under 
 the action of ultra-violet light. 
 
THE PHYSICS OF THE ELECTRON 21 
 TABLE I. 
 
 Observer. 
 
 Source of electrons. 
 
 ejm e.m.u. per gra. 
 
 Kaufmann 
 
 /3-rays (slow) from Radium 
 
 177 x io 7 
 
 Simon . 
 
 Cathode rays 
 
 1-72 x io 7 
 
 Ewers 
 
 -rays from Polonium 
 
 17 x io 7 
 
 Classen . 
 
 Cathode rays . . 
 
 1774 X IO 7 
 
 t 
 
 Hot lime .... 
 
 1-776 X io 7 
 
 Woltz ; . 
 
 /3-rays (slow) from Radium 
 
 1767 X io 7 
 
 Bestelmeyer 
 
 Hot lime .... 
 
 1766 X io 7 
 
 The above table (Table I.) gives a few of the 
 more recent determinations of the ratio e/m for 
 electrons from different sources. It will be seen 
 that within very narrow limits indeed, especially 
 considering the difficulties of the experiments, the 
 ratio of *the charge to the mass is the same for all 
 electrons, whatever their origin and whatever their 
 velocity, and differs very little from 1*77 X io 7 . 
 The value of m/e or the electro-chemical equivalent 
 of the electron, if we may so call it, is therefore 
 5*65 x io~ 8 . For the hydrogen atom, as we have 
 seen, the value is about io~ 4 . If we could assume 
 that the charge e is the same for the electron as for 
 the ion in solution we see at once that the mass of 
 the electron must be only about T ^oo P ar ^ of that of 
 the hydrogen atom. 
 
 For this assumption, however, very little direct 
 evidence could be adduced at the time it was made. 
 It was one of those strokes of genius which have 
 proved to be correct. To determine absolutely the 
 mass of an electron we must find some method of 
 determining the value of the electronic charge e. 
 Fortunately this also has proved possible, owing to 
 a discovery made in the Cavendish laboratory by 
 Mr. C. T. R. Wilson. 
 
 If a space saturated with water vapour is 
 
22 MOLECULAR PHYSICS 
 
 suddenly chilled the surplus water over and above 
 that which would saturate the space at the lower 
 temperature in general separates out in little par- 
 ticles of water, forming within the space a thick mist 
 or cloud. It was, however, shown many years ago 
 by Aitken that this condensation always commenced 
 round minute particles of dust, particles often far 
 too small to be visible, yet sufficiently material to be 
 caught by a well-packed tube of cotton wool. In 
 the absence of these particles he found that a very 
 considerable degree of supersaturation could be 
 produced without any deposition of water and 
 without any appearance of cloud or mist, and that 
 it was only when the supersaturation became at 
 least eightfold that a mist or cloud was produced. 
 It appeared then that for a lesser degree of super- 
 saturation than this the water vapour must have 
 some nucleus about which to condense before a drop 
 could be formed. 
 
 Gases under ordinary conditions are almost 
 perfect insulators. Under the action of certain 
 agents, such, for example, as Rontgen rays or any of 
 the rays from radio-active substances, a gas becomes 
 more or less conducting. It has been shown that 
 this is due to the creation in the gas of systems, 
 some negatively, some positively charged. In all 
 probability these are produced by the ionising agent 
 expelling a negative electron from the atom through 
 which it passes, leaving the remainder of the mole- 
 cule positively charged. The negative electron 
 thus set free soon attracts to itself one or more 
 atoms just as an uncharged pith ball is attracted by 
 an electrified ebonite rod. The gas thus becomes 
 filled with oppositely electrified systems consisting 
 of clusters of three or four atoms together, which 
 move under the action of an electric field in exactly 
 the same way as the ions of an electrolyte move in 
 the electrolysis of a solution. There is this difference, 
 
THE PHYSICS OF THE ELECTRON 23 
 
 however, that, whereas the electrolytic ions are 
 stable, the gaseous ions if left to themselves, gradually 
 re-combine to form neutral molecules. Thus unless 
 the supply is kept up by the continuous action of 
 the ionising agent the conductivity will soon die 
 away. 
 
 The mechanism of ionisation by the electrons 
 emitted by a metal plate under the action of ultra- 
 violet light is somewhat different. Here the elec- 
 trons have not sufficient energy to expel an electron 
 from the atom and thus no positive ions are produced 
 in the gas. The negative electrons, however, attract 
 to themselves neutral molecules to form negative 
 ions. It will be evident from the mode of formation 
 that these ions bear the same charge as the electron 
 which gave rise to them, that is to say, their ionic 
 charge is the same as the electronic charge e. It 
 may be pointed out in passing that since the ions are 
 all of the same sign and produced at the same place, 
 namely, the surface of the metal plate, a current can 
 only be sent through the gas in one direction. If 
 the metal plate is negative the ions will be repelled 
 and thus carry a negative current from it to the 
 positive electrode. If, however, the plate is posi- 
 tively charged the ions will be attracted back to it 
 by the field and the gas will remain an insulator. 
 
 It occurred to C. T. R. Wilson that these ions 
 might possibly serve as nuclei for the production 
 of a fog or cloud in supersaturated air, and this was 
 found on experiment to be the case. He was able 
 to show that drops of water would condense on these 
 negative ions when the supersaturation was only 
 fourfold, while condensation occurred on the positive 
 ions also when the supersaturation was sixfold. It 
 was found that when the supersaturation was 
 increased to the proper extent each negative ion 
 became the centre of a single drop of water, and if 
 the conditions were fairly uniform these drops were 
 
24 MOLECULAR PHYSICS 
 
 all of the same size. It will be remembered that in 
 the case of the ions formed by ultra-violet light each 
 of these drops will carry with it the electronic charge 
 e, the magnitude of which we wish to determine. 
 
 Every drop in a cloud is falling through the air 
 under the action of gravity with a definite velocity. 
 Clouds do not float in the air, though, if the drops 
 are sufficiently small they fall very slowly, owing to 
 the great surface they present in comparison with 
 their mass to the viscous drag of the air. Sir G. G. 
 Stokes has shown that if r is the radius of a small 
 drop of water and q the viscosity of the air, the 
 velocity with which the drop will fall relative to the 
 
 2 ft'fi 
 
 air is -^ , where g is, as usual, the acceleration 
 
 due to gravity. The drops formed round the ions 
 are all of the same size and fall at the same rate. 
 We can thus measure the velocity v of their fall by 
 watching the rate at which the surface of the cloud 
 settles. This will enable us to calculate the radius 
 r of the drop, and hence its mass M. 
 
 So far the cloud has been falling freely under the 
 action of gravity. Let us apply a field of strength X 
 in such a direction as to oppose the action of gravity, 
 that is to say, with the positive plate above the cloud. 
 The force on each drop due to the electric field is 
 then X . e, while that due to gravity is M . g. We can 
 adjust the field X until these two forces exactly 
 balance each other, and the drop remains suspended 
 in air like Mahomet's coffin. When this stage is 
 reached we have 
 
 X . * = M . g 
 
 or e = M . g/X. 
 
 But all these quantities are known, and thus the 
 charge on the drop of water, which we have shown to 
 be the same as that on the original electron, can be 
 determined. 
 
 It remains to describe the apparatus devised for 
 
THE PHYSICS OF THE ELECTRON 25 
 
 the experiment. It is shown in Fig. 4. It is well 
 known that if a mass of gas is expanded in such 
 a way that no heat is allowed to enter or leave it, 
 the temperature will fall. The lowest temperature 
 reached in any given expansion can be calculated 
 
 t 
 
 R 
 
 t 
 
 FIG. 4. C. T. R. WILSON'S EXPANSION APPARATUS. 
 
 from the gas laws if the ratio of the specific heats of 
 the gas is known. As gases are bad conductors of 
 heat we can satisfy the conditions of the experiment 
 by making the expansion sufficiently rapid. The 
 mass of the gas is then cooled down to the calculated 
 
26 MOLECULAR PHYSICS 
 
 temperature before any appreciable amount of heat 
 has had time to enter the system. 
 
 The method of making the expansion will be 
 clear from the diagram. The tube H connects 
 with a large bulb of some litres capacity kept 
 exhausted by means of a water pump. It is closed 
 by a rubber stopper C which can be suddenly with- 
 drawn by means of the rod R, thus creating practi- 
 cally instantaneously a partial vacuum in this part 
 of the apparatus. The air being thus suddenly 
 withdrawn from beneath it, the light glass plunger P 
 which had been adjusted to a suitable height in 
 the cylinder D is forced down with great rapidity, 
 thus producing within the experimental chamber L 
 a very rapid expansion of an amount which depends 
 only upon the initial position of the plunger P. The 
 temperature in L is therefore suddenly lowered to a 
 degree which can be calculated, and if the air in L 
 was previously saturated it will now be super- 
 saturated to an extent which is measured by P/p 
 where P and p are the vapour pressures of water at 
 the initial and final temperatures. 
 
 In making an experiment the air in L is freed 
 from all material nuclei by repeated expansions ; 
 the plunger is adjusted so as to make the super- 
 saturation after expansion rather more than fourfold, 
 the upper plate E, which is usually of zinc, is illu- 
 minated with ultra-violet light for a moment in 
 order to produce a suitable supply of negative ions 
 in the gas and the expansion is made. A cloud is 
 formed on the negative ions and the rate at which 
 the surface of it settles is taken. After it has fallen 
 some little distance the upper plate E, which had 
 been previously uncharged, is raised to a positive 
 potential, and its potential adjusted until the surface 
 of the cloud is seen to remain stationary. If V is 
 this potential and the lower plate at a distance d from 
 the upper one is earthed, the strength of the electric 
 
THE PHYSICS OF THE ELECTRON 27 
 
 field is V/d and the electronic charge e is equal to 
 Mgrf/V, where M has been calculated by Stokes' 
 law from the rate of fall of the cloud. 
 
 The method was first applied in a rather different 
 form by Professor Sir J. J. Thomson. In the form 
 described, which is the one which has been used with 
 the greatest success, it was performed by H. A. 
 Wilson. We have, for the sake of making our 
 argument logically complete, considered the case of 
 the electrons produced by ultra-violet light, for in 
 this case we have evidence that the charge we are 
 measuring is really that carried by an electron. It has 
 been shown, however, experimentally, that the value 
 of the charge e is the same no matter how the ions 
 are produced. Experiments carried out with ions 
 produced by Rontgen rays or the various rays from 
 radio-active materials gave exactly the same values 
 for the charge e. Like the ratio m/e, the charge e is 
 a universal constant. Some recent determinations 
 of it are given in the following table. 
 
 TABLE II. 
 
 Roux 
 
 Planck . 
 
 server. 
 
 Carrier. 
 
 t (electrostatic 
 units). 
 
 nan 
 
 ihaft . 
 an 
 
 Water drops (original method) 
 Sulphur drops 
 Metallic dust .... 
 Oil or mercury spray 
 
 4-67 X io- 10 
 4-17 X io- 10 
 4*65 X io- 10 
 4-89 X io- 10 
 
 ;rford . 
 k. 
 
 [Counting the a-rays] 
 Theory of radiation 
 
 4-65 X io- 10 
 4-69 X io- 10 
 
 It will be seen from Table II. that the values 
 obtained for the electron charge e by different 
 observers working in different ways, though not so 
 consistent as those obtained for the ratio e/m, yet 
 
28 MOLECULAR PHYSICS 
 
 do not differ much from a mean value of about 
 47 X 10 ~ 10 electrostatic units, or 1-57 X io~ 20 in 
 the absolute electromagnetic unit of charge which 
 is equal to 10 coulombs. 
 
 The most extensive survey of the subject has 
 been made by Millikan (see Physical Review, 1911). 
 Instead of water drops he used very fine globules 
 of oil or sometimes mercury produced by an atomiser 
 or fine spray. These drops could be passed as 
 required into his apparatus, which very much 
 resembled the chamber L in Fig. 4, through a small 
 hole made in the top plate. These globules did not 
 evaporate appreciably, so that an individual drop 
 could be isolated and kept under observation 
 through a microscope for several hours consecu- 
 tively. The microscope was fitted with an engraved 
 glass scale in the eyepiece, on which the whole 
 of the measurements on the motion of the drop 
 could be made very accurately and conveniently. 
 By properly adjusting the difference of potential 
 between the upper and lower plates the drop could 
 be kept in the field of view during the whole of the 
 experiment. The measurements made and the 
 calculation of the charge are precisely the same for 
 the oil globule as for the water drop. 
 
 These drops were not originally charged, but 
 picked up their charges from the surrounding air, 
 which was ionised either by Rontgen rays or by 
 radium. These comparatively large globules could 
 collect and carry more than one electronic charge, 
 seven or eight being a very usual number, though 
 some drops had many more than this. The inter- 
 change of charges between the globule and the air 
 could be easily observed with the microscope. The 
 drop which had been poised almost motionless in the 
 air for some time by the balanced action of gravity 
 and the electric field would be seen to dart suddenly 
 upwards, showing that the drop had captured 
 
THE PHYSICS OF THE ELECTRON 29 
 
 another charge and thus caused the electric force to 
 increase, or perhaps on the other hand the drop 
 would be seen to fall, having parted with one of its 
 charges to some colliding molecule. 
 
 The important point brought out by the experi- 
 ment is that in every case it was found that the 
 magnitude of the charge thus exchanged, which 
 could be calculated by a simple application of the 
 principles already explained, was exactly the 
 electronic charge e, and the total charge on the 
 globule at any time was always very exactly some 
 integral multiple of this charge. An examination 
 of the mass of figures collected by Professor Millikan 
 leaves no room for doubting that the charge which 
 we have denoted by e is a universal constant, and 
 that every electrical charge is made up of an 
 integral number of electrons, just as every fragment 
 of an element is made up of a whole number of 
 atoms. 
 
 From Table I. we have the ratio e/m, equal to 
 177 X io 7 , - for all electrons. Combining this 
 result with the value just obtained for e we are 
 driven to the conclusion that whatever the source 
 from which they come all electrons have identically 
 the same mass and charge, the former being 8 '8 X 
 io~ 28 gms., the latter 1*57 X io~ 19 coulombs. Such 
 particles must form a constituent part of all matter. 
 
 The value of e ascribed to Professor Rutherford 
 and also included in Table II. was obtained irom 
 experiments of an entirely different nature made on 
 the a-particles. Before passing to these we must 
 refer very briefly to an exceedingly beautiful 
 extension of the method of drops which has recently 
 been brought to perfection by the originator of the 
 experiments. 
 
 In the experiments already described, the clouds 
 obtained were fairly uniform, as the ionisation was 
 intense and time was given for the ions formed to 
 
30 MOLECULAR PHYSICS 
 
 diffuse through the body of the gas. Suppose, how- 
 ever, that we allow, say, a single a-particle to cross 
 our expansion chamber and at the same time make 
 an expansion of the air in the chamber by the method 
 
 FIG. 5. THE TRACKS OF THE 
 
 already described. The particle passes through the 
 air, ionising it as it passes, and thus leaving behind it 
 a trail of charged ions. Water drops at once form 
 upon these from the now supersaturated air before 
 they have had time either to diffuse into the rest of 
 
THE PHYSICS OF THE ELECTRON 31 
 
 the gas or to recombine. If the expansion chamber 
 is suitably illuminated these drops appear as 
 brilliant points of light all 
 along the path traversed 
 by the particle. In the 
 case of the a-particle the 
 ions are so numerous that 
 the track of the particle 
 becomes visible as a con- 
 tinuous shining streak of 
 light. In the case of an 
 electron where the ioriisa- 
 tion is less intense the ap- 
 pearance presented is that 
 of a string of bright beads. 
 We are thus able not 
 merely to detect, but even 
 to follow the path of a 
 single particle of any kind 
 providing it produces ioni- 
 sation in a gas. 
 
 By the kindness of 
 Mr. C. T. R. Wilson, I 
 am able to reproduce 'two 
 of the photographs taken 
 by him in this way. In 
 Fig. 5 are shown the paths 
 of a number of a-particles. 
 These have their origin in 
 a small sample of radium 
 placed just outside the 
 chamber and shoot across 
 the chamber as shown in 
 the photograph until finally 
 
 their energy, which is being spent in the work of 
 separating the ionic charges along the whole of the 
 path, finally becomes too small to produce ionisation, 
 and the particles disappear from human ken. 
 
 A 
 
 FIG. 6. RONTGEN RAYS. 
 
32 MOLECULAR PHYSICS 
 
 Fig. 6 is a photograph of the passage of a 
 narrow beam of Rontgen rays through the expansion 
 chamber, from A. to A/ We have mentioned before 
 that the Rontgen rays produce rapidly-moving 
 cathode rays when they fall upon matter ; in this 
 remarkable photograph these cathode rays are 
 made visible to us by the ions they produce. Here 
 upon the dark background their tracks may be seen 
 as a tangled skein of bright threads radiating out 
 from the invisible track of the Rontgen rays. Each 
 single thread represents the whole path of a single 
 electron from its expulsion from the parent molecule 
 under the action of the Rontgen rays, to the place 
 where it finally becomes too weak to ionise. In some 
 of the brighter threads the individual drops are 
 clearly to be seen. The twists and turns in each 
 little path are due to collisions between the cathode 
 particle and the molecules of the surrounding air, 
 or, rather, perhaps, with the individual electrons 
 contained in these molecules. 
 
 These photographs will perhaps do more than 
 any argument, however cogent, to remove any doubt 
 which may still be felt as to the objective reality 
 of the electrons and other particles with which we 
 have been dealing. Nothing but an actual particle 
 could leave behind it such tracks as those shown in 
 the photographs we have reproduced. 
 
 We have not space to deal with the many 
 difficulties of the experiment or with the skill and 
 ingenuity with which they have been overcome. 
 Those interested may be referred to the original 
 paper in the Proceedings of the Royal Society for 1912. 
 
 The method is still in its infancy, and the photo- 
 graphs so far obtained are hardly more than trial 
 exposures. Already, however, several heated con- 
 troversies have been settled, and many cherished 
 hypotheses dethroned, as the result of the photo- 
 graphs obtained. To those of us who have been 
 
THE PHYSICS OF THE ELECTRON 33 
 
 working by indirect methods on some of the more 
 obscure problems still left to us for solution, the 
 method has come as a veritable giving of sight to 
 the blind, and now that Mr. C. T. R. Wilson has 
 perfected his apparatus and can turn his attention 
 to using it as an instrument of research we may hope 
 for many interesting and important results in the 
 near future. 
 
 M.p. 
 
CHAPTER III. 
 THE POSITIVE PARTICLE. 
 
 WE have already seen that positively charged 
 particles are projected with high velocities from 
 radium and other radioactive substances, and that 
 they are also to be found in discharge tubes. Unlike 
 the electron the positive particle has a mass com- 
 parable with that of an atom, no positive charge 
 having yet been detected in association with any 
 mass less than that of an hydrogen atom. The 
 charge on a positive particle is, however, either the 
 same as that on an electron or some simple multiple 
 of it. The a-rays, as the particles from radioactive 
 substances are still called (a relic of the time when 
 their nature was unknown) always carry a charge 
 of 2 . e. In discharge tubes, however, positive 
 particles are found with all integral multiples up to 
 8 . e. We shall see that we may regard the 
 positive particles as atoms travelling with a high 
 speed from which one or more electrons have been 
 removed. 
 
 The positive particle can be deflected by electric 
 and magnetic fields in the same way as the negative 
 electron, and obeys the same laws. The deflection 
 is in each case in the opposite direction to that of 
 the electron, while, owing to the greater mass, the 
 deflection is less than that for a similarly moving 
 electron. The great ionising power of the positive 
 particles makes the detection of the electrical 
 deflection difficult. For these and other experi- 
 mental reasons it is only recently that much light 
 
THE POSITIVE PARTICLE 35 
 
 has been thrown on their nature and properties. 
 These difficulties have now been overcome, and 
 the positive particle also is beginning to yield up 
 its secrets. As the positive particle is always an 
 atom of some kind, its investigation is, perhaps, 
 from some points of view of even greater interest 
 than that of the electron. 
 
 The greater energy of these particles is, however, 
 in some ways an advantage. It enables us to deal 
 with individual particles, whereas in the case of 
 the electron we can only deal with large numbers. 
 Thus our measurements gain, perhaps, in definiteness 
 although they may lose somewhat in numerical 
 precision. 
 
 If e be the charge on a single a-particle, the total 
 charge carried by N particles is N . e, and if N is 
 sufficiently large this charge will be large enough to 
 be directly measured by an electroscope or electro- 
 meter. If we can further determine the number of 
 particles carrying this charge we shall have made a 
 direct determination of the charge e. 
 
 The experiments are best performed using the 
 a-particles from radium, polonium, or some other 
 radioactive substance. They were carried out 
 almost simultaneously by Rutherford, and by 
 Regener. In Rutherford's experiments the a-par- 
 ticle was detected by the ionisation it produced in a 
 special chamber ; the entry of each a-particle into 
 the apparatus -being notified by a kick of the needle 
 of a sensitive electrometer. In Regener's experi- 
 ments the number of scintillations produced by the 
 particles in a given time on a fluorescent screen was 
 counted. The former method was the more satis- 
 factory from a theoretical view, as there was at the 
 time no direct evidence that every particle produced 
 a scintillation when it struck a screen, although this 
 has since been shown to be the case by Rutherford. 
 It was also proved by the fact that the two experi- 
 
 32 
 
36 MOLECULAR PHYSICS 
 
 menters reached almost exactly the same value for 
 the charge on the a-particle. The experiment of 
 Regener is simpler to carry out than the electrical 
 method of Rutherford, and granting his assumptions, 
 is probably capable of greater accuracy. 
 
 Regener's apparatus is shown in Fig. 7. Fig. 7a 
 shows the " counting " apparatus, Fig. 7b the 
 
 FIG. 7. REGENER'S APPARATUS. 
 
 apparatus for measuring the total charge carried by 
 the rays. 
 
 The counting apparatus is very simple. It 
 consists of a long tube closed at one end by a brass 
 plate c, c, bored with a circular hole some centimetre 
 in diameter. Across this is sealed a thin glass cover- 
 slip bearing on its under surface the fluorescent 
 screen D, in this case a thin plate cut from a crystal 
 of brown diamond, a substance chosen by Regener 
 after many trials as the most suitable for the 
 
THE POSITIVE PARTICLE 37 
 
 purpose. Rutherford has since used prepared 
 screens of powdered willemite with equal success. 
 
 A high power microscope was focussed on the 
 diamond plate for viewing the scintillations which, 
 numbering about one every two seconds, were 
 easily counted. The source of the a-particles in 
 Regener's experiments was a plate of polonium, 
 placed at P, some 127 cms. from the diamond screen. 
 The whole tube was carefully exhausted so that there 
 should be no absorption of the particles before 
 reaching the screen. 
 
 The number of scintillations in a given time was 
 counted, and the area A of the aperture in the brass 
 plate and its distance R from the polonium carefully 
 determined. If n is the number of particles hitting 
 the screen in a time t seconds, then the number of 
 particles emitted by the polonium per second across 
 a hemisphere drawn about its upper surface is 
 
 27iR 2 n 
 
 N = ^--p 
 
 assuming that the particles are given out equally in 
 all directions. This assumption was verified by 
 Rutherford in a separate experiment. For the disc 
 used by Regener N was found to be 3*935 X io 5 . 
 
 To measure the total charge carried by the 
 a-particles from the disc a Faraday cylinder was 
 used. This consisted of a partially closed brass 
 cylinder F (Fig. 7b) enclosed in a glass chamber 
 exhausted to a very high vacuum to avoid any loss 
 of charge by ionisation in residual air. The polo- 
 nium was mounted at P so that the a-particles from 
 its upper surface entered the cylinder. Here they 
 gave up their charges to it, gradually raising it to a 
 positive potential, which could be measured by an 
 electrometer or electroscope connected to the metal 
 electrode E. 
 
 This method of measuring small currents by the 
 electrometer is one in e very-day use in this class .of 
 
38 MOLECULAR PHYSICS 
 
 experimental work and deserves a little further con- 
 sideration. Let C be the electrical capacity of the 
 Faraday cylinder and its connections, and suppose 
 the cylinder is placed at zero potential by connecting 
 it to earth. Insulate and note the reading after 
 some suitable interval of time, say t seconds. .Let 
 V be the potential corresponding to this reading ; 
 this can easily be determined by calibrating the 
 instrument with suitable known potentials. The 
 charge given to the electrode in the time t is then 
 CV. so that the current between P and F is CV/t. 
 
 Since the capacity of a system can be made very 
 small the method is far more sensitive than the most 
 delicate galvanometer. The capacity of an electro- 
 scope of the C. T. R. Wilson type with its electrode 
 and all its connections need not be greater than 4 or 
 5 cms. ; or, say, 5 X 10 - 12 farads. The electroscope 
 will easily give a deflection of 100 divisions for a 
 potential of I volt, while a movement of the gold 
 leaf of a division per minute can be detected with 
 certainty. This corresponds to a current of 10 - 15 
 amperes. The best galvanometers give a perceptible 
 deflection for a current of about io- n amperes. 
 The electroscope method is, therefore, about ten 
 thousand times as sensitive as the most delicate 
 galvanometer. 
 
 In the present case the value of C.V.// gives the 
 charge carried by the a-particles per second from the 
 upper surface of the polonium disc. In electro- 
 static units it was found to be -000377. This was 
 the charge carried by the 3*935 X io 5 a-particles 
 emitted by the polonium. The charge on each 
 particle was therefore "000377/3 -935 X io 5 or 
 9-58 X io - 10 in electrostatic units. Rutherford's 
 value was 9*30 X io ~ 10 in the same units. 
 
 It will be seen that these numbers are almost 
 exactly twice the value 47 X io~ 10 e.s.u., which 
 represents the mean value for the electronic charge e. 
 
THE POSITIVE PARTICLE 39 
 
 In fact the value of 2 . e is almost midway between 
 these experimental numbers. The charge on the 
 a-particle is therefore exactly twice the charge on 
 the electron. The a-particle is therefore an atom 
 which has lost two electrons. This is characteristic 
 of all the a-particles emitted by radioactive 
 substances which appear to differ from each other 
 only in velocity. 
 
 We have stated that the a-particle is an atom ; 
 the question arises of what element is it an atom ? 
 The ratio of the mass to the charge can be determined 
 for the a-particle in the same way as for the electron, 
 neglecting the different experimental arrangements 
 required. No great accuracy has, however, been 
 reached, as Ihe deflection of these particles from 
 radioactive substances even in the strongest magnetic 
 fields is small. According to Rutherford, the ratio 
 of mass to charge for the a-particle from radium is 
 1*97 x io~ 4 , and we have seen that they carry two 
 charges, or in the language of electrolysis, are di- 
 valent. The electrochemical equivalent of hydrogen 
 is io~ 4 , so that if we can assume that the ion in 
 solution carries the electronic charge e, the atomic 
 weight of the a-particles would be 3*84, which is 
 very near 3*96, the atomic weight of helium. Con- 
 versely, if we can show that the a-particle is an atom 
 of helium we shall have direct evidence that our 
 assumption that the monovalent ion carries the 
 same charge as an electron is correct. 
 
 The proof of the nature of the a-particle has been 
 given by Rutherford to whom we owe so much of 
 our knowledge of these rays. The experiment is 
 based on the fact that the a-rays, owing to the great 
 speed with which they are projected by the parent 
 molecule, are able to pass through thin sheets of 
 solid substances which are perfectly impervious to 
 the molecules of ordinary gases. 
 
 The substance used as the source of a-particles 
 
40 MOLECULAR PHYSICS 
 
 was radium emanation, the radioactive gas which is 
 the first decomposition product of radium, and on 
 which Professor Ramsay proposes to bestow the 
 name of niton. This gas, which is disengaged from 
 solutions of radium in water, after being purified in 
 various ways, is finally passed into a fine thin- walled 
 glass tube, the end of which has been carefully 
 sealed. This is enclosed by a wider thick-walled 
 glass tube which is also made quite air-tight and has 
 in its upper portion two electrodes. The spectrum 
 of the discharge between these two electrodes 
 enables us to determine the nature of the gases in 
 this outer tube. There is no connection between the 
 inner and outer tubes, so that nothing can pass from 
 the one to the other, except the a-rays. This point 
 was tested by filling the inner tube with helium and 
 allowing the apparatus to stand for some days. No 
 trace of the helium spectrum was obtained in the 
 outer tube under these circumstances. When, how- 
 ever, the inner tube was filled with emanation, the 
 a-particles emitted were able to pass through the 
 thin glass walls and, being stopped by the thicker 
 tube beyond, collected in the space between the two 
 tubes. 
 
 Slowly, as the experiment went on, the spectrum 
 of helium began to appear, becoming brighter and 
 more complete as more and more of the rays passed 
 through the inner tube, until at the end of a few 
 hours the complete helium spectrum was obtained. 
 The blank experiments were far more in number and 
 severity than has been described here. They left 
 no doubt that the a-particles were indeed atoms of 
 helium, differing from the ordinary atoms of the gas 
 only in their velocity and charge. We have seen 
 above that this result leads directly to the conclusion 
 that the charge on a monovalent ion in solution is 
 the atom of electricity which we denote by e. 
 
 This is one of the most direct proofs of this very 
 
THE POSITIVE PARTICLE 41 
 
 important fact. There are, however, many others 
 of very diverse natures, some of which we shall 
 have occasion to discuss when dealing with the 
 phenomena on which they are founded. 
 
 The charge carried by a monovalent ion in 
 solution and the electronic charge are thus the same; 
 the value for the latter is, as we have seen, very 
 near 47 X io~ 10 .s.^., or 1*57 x io~ 20 in our electro- 
 magnetic units. The ratio of the mass to the 
 charge for the hydrogen atom is, as we have seen, 
 1-04 X io~ 4 . Thus the mass of the hydrogen atom 
 is 1*04 X 10 ~ 4 e, or 1-63 x io~ 24 gms. This is there- 
 fore the value in grammes of the chemical unit of 
 atomic weight, and we can at once calculate from it 
 the actual mass of any atom of which the chemical 
 atomic weight is known. The accuracy of the 
 result depends only on the accuracy with which the 
 value of e can be determined. A reference to 
 Table II. (see page 27) will show that the error in 
 the value we have used probably does not exceed 
 2%, or 3% at most. 
 
 Since the mass of a cubic centimetre of hydrogen 
 at normal temperature and pressure is almost 
 exactly 9 x io~ 5 gms., the number of hydrogen 
 molecules contained in I cub. cm. of a gas under 
 these conditions is 9 X io~ 5 /2 X 1*58 X io~ 24 , or 
 275 X io vl9 . By Avogadro's hypothesis this 
 number is independent of the nature of the gas. 
 
CHAPTER IV. 
 
 THE NEW METHOD OF ANALYSIS. 
 
 WE have considered so far the case of the 
 positively charged particles from radioactive sub- 
 stances, and have seen how their mass, charge, and 
 chemical nature have been determined, and how 
 these determinations have given us the most certain 
 and accurate estimate of the actual mass of a hydrogen 
 atom. The information obtainable was, however, 
 limited by the fact that these particles are all of one 
 kind, consisting always of atoms of helium. 
 
 We have already mentioned that it is possible, 
 in a discharge tube, to endow atoms and molecules 
 of ordinary matter with those properties of high 
 velocity and electric charge which have made the 
 a-particles so amenable to experiment. The pro- 
 cess may be regarded as follows. When the two 
 electrodes of the discharge tube are connected to 
 the poles of an induction coil, the molecules of the 
 rarefied gas in the tube are subjected to a very 
 strong electric tension. This tension acting upon 
 the negative electrons, which, as we have seen, are 
 contained in all molecules, causes one or more of 
 them to be displaced from the molecule, leaving the 
 remainder positively charged. This positive particle, 
 as we may now call it, is driven with great velocity 
 towards the cathode by the action of the electric 
 field which produced it. 
 
 If the cathode is suitably perforated, the positive 
 particle will pass through it, and emerge on the 
 
THE NEW METHOD OF ANALYSIS 43 
 
 further side with this velocity unimpaired. It can 
 then be detected by allowing it to fall either on a 
 fluorescent screen, or preferably on a photographic 
 plate, where it will produce a permanent record, 
 which can be measured at leisure with suitable 
 instruments of precision. 
 
 The experiments, for reasons to which we have 
 already alluded, presented many difficulties. It 
 
 FIG. 8. THOMSON'S POSITIVE RAY APPARATUS. 
 
 is only after several years of experiment that 
 Professor Sir J. J. Thomson has at last perfected 
 an apparatus which allows him to measure these 
 particles with accuracy and certainty. 
 
 A general idea of the apparatus can be obtained 
 from Fig. 8, which is reproduced from a photograph 
 of one of Professor Thomson's tubes. The details 
 are shown more clearly in the accompanying 
 
44 MOLECULAR PHYSICS 
 
 diagram, Fig. 9, which represents a section of part 
 of the apparatus as seen from above. 
 
 The apparatus consists of two parts : the dis- 
 charge tube proper, where the particles are produced 
 and the " camera/' where their presence is detected 
 and their masses determined. The discharge tube 
 proper consists of a large bulb T, some 30 cms. in 
 diameter. The anode A (Fig. 8) is placed in a side tube, 
 while the cathode C (Fig. 9) occupies the neck of the 
 bulb. The gas to be experimented on enters the 
 
 FIG. 9. THOMSON'S POSITIVE RAY TUBE. 
 
 bulb through the tubes at e, and is removed through 
 the tube g by a Gaede pump, which is worked 
 sufficiently rapidly to keep the gas in T at a suitably 
 low pressure. 
 
 The cathode C (Fig. 9) is an aluminium rod 
 pierced with a very fine copper tube about 8 cms. 
 long and less than i-ioth mm. in diameter. An 
 exceedingly fine pencil of positive rays is thus 
 obtained. It is evident that with a tube so narrow 
 any stray magnetic field will cause the particles to 
 hit the walls of the tube and be lost. To prevent 
 
THE NEW METHOD OF ANALYSIS 45 
 
 this the copper tube is enclosed for the greater part 
 of its length in a thick iron tube S, shaded in the 
 diagram, while thick iron screens I, I, protect the 
 main discharge from the influence of the magnet. 
 
 Owing to the intensity of the discharge, the 
 cathode becomes very hot, and it is necessary, in 
 order to protect the numerous sealing wax joints, 
 to surround them with a water cooling jacket, as 
 shown in Fig. 8. 
 
 On leaving the copper tube, the rays pass between 
 M and N, two soft iron blocks let in through the sides 
 of the tube (which is here made of ebonite) and 
 carefully waxed round, so as to be completely 
 vacuum tight. These blocks serve two purposes. 
 In the first place, they form the pole pieces of the 
 electromagnet E, E, from which, however, they are 
 electrically insulated by two thin strips of mica m, m. 
 This insulation enables them to be charged positively 
 and negatively respectively, by means of a cabinet 
 of small storage cells, and thus to serve as electrodes 
 for the application of an electrostatic field. 
 
 In this way the positive particles can be sub- 
 jected at the same time to a magnetic and an electric 
 field. It will be noticed that, whereas in the case of 
 the cathode ray experiments described in an earlier 
 chapter the two fields were at right -angles to each 
 other, in this case the two fields are parallel, and the 
 corresponding deflections therefore at right angles 
 to each other. 
 
 After passing through these fields, the rays fall 
 either upon the glass plate Z, which is covered with 
 powdeied willemite, or upon a photographic plate, 
 which can be introduced when required immediately 
 in front of Z by suitable devices. 
 
 The side tube L leads to a tube filled with char- 
 coal and immersed during the experiment in liquid 
 air, a device due originally to Sir James Dewar for 
 absorbing as completely as possible the gases in this 
 
46 MOLECULAR PHYSICS 
 
 part of the apparatus. This detail, apparently 
 insignificant in itself, has had much to do with the 
 success of the method. If the gas in the camera is 
 at the pressure most suitable for the production of 
 positive rays in the discharge tube, the effects 
 observed on the screen are found to be almost 
 entirely secondary. The residual gas in the camera 
 becomes strongly ionized by the action of the 
 positive rays upon it. The latter are thus travelling 
 through an atmosphere charged with negative 
 electrons, with which they readily combine to form 
 neutral molecules again. When this has taken place, 
 the particle is no longer acted upon by electric or 
 magnetic fields. The exact extent of its deflection 
 will depend upon the length of time during which it 
 succeeded in retaining its charge. These secondary 
 effects still make their appearance upon some of the 
 photographs taken. They can, however, always be 
 detected by the fact that they either disappear or 
 alter in position or appearance, if the pressure in the 
 camera is slightly lowered or slightly raised. 
 
 The charcoal and liquid air method enables us to 
 remove the residual gas so rapidly that it is possible 
 to have the pressure in the camera considerably 
 lower than that in the discharge tube, the diffusion 
 along the long narrow copper tube, which is their 
 only connection, being comparatively slow. In this 
 way the production and the measurements of the 
 particles can both be carried on under the most 
 favourable conditions. 
 
 Let us consider the course of the positive particle 
 from its genesis in the discharge tube to its stoppage 
 on the photographic plate. Particles formed near 
 the anode will fall through practically the whole of 
 the difference of potential between the electrodes of 
 the discharge tube, some 30,000 or 40,000 volts. 
 The energy they acquire will thus be V X E where V 
 is this difference of potential, and E the charge on 
 
THE NEW METHOD OF ANALYSIS 47 
 
 the particle. Their velocity v, on reaching the 
 cathode, will thus be given by j"- 
 
 This is the maximum velocity the particles can 
 
 X n 
 
 K 
 
 
 
 N 
 
 X 
 
 \ 
 
 \ 
 
 \ 
 
 \ 
 
 FIG. 10. POSITIVE RAY PARABOLAS. 
 
 attain. Those commencing their existence nearer 
 the cathode than this, only fall through a fraction of 
 the full potential V, and thus acquire only a fraction 
 of this maximum velocity. Thus, the stream of rays 
 
48 MOLECULAR PHYSICS 
 
 passing through the cathode will contain particles 
 moving with all velocities up to a certain maximum. 
 On passing into the electric and magnetic fields 
 at MN they will be acted upon by forces equal to 
 XE and HE?; respectively where X is the electric 
 and H the magnetic field, exactly as in the case of the 
 cathode particles, the only difference being that the 
 directions of the deflections will be in the opposite 
 directions to those of the negative particles. It can 
 be shown* that these forces will cause the point 
 at which the particle strikes Z to be deflected through 
 
 HE 
 
 distances equal to ki -- in the case of the magnetic 
 mv 
 
 XE 
 
 field, and k 2 * i n tne case f tne electric field, ki 
 2 
 
 and &2 being constants which depend only on the 
 relative dimensions of the various parts of the 
 apparatus. It must be remembered that the fields 
 have been so disposed that these two deflections 
 will take place at right angles to each other. 
 
 Thus if O (Fig. 10) represents the position on 
 the plate of the undetected rays, and OX, OY are 
 the directions of the electric and magnetic deflec- 
 tions, the particle after passing through the two 
 fields, will be deflected to some point P such that 
 
 PK = x = k* ^ (electric deflection) . (a) 
 
 PJ = y = ki 5^ (magnetic d 
 We see from these equations that 
 
 PJ = y = ki (magnetic deflection) . (b) 
 
 Thus, if the strengths of the two fields are kept 
 
 * Appendix A. 
 
THE NEW METHOD OF ANALYSIS 40 
 
 the same throughout the experiment, all the 
 quantities within the brackets will be constant. 
 Thus, y/x will be a measure of the velocity of the 
 deflected particle, while the ratio y 2 /x will measure 
 the ratio of the mass to the charge. 
 
 If all the particles were identical, and had the 
 same velocity, the spot O would simply be shifted 
 to the point P. As we have seen the velocities of 
 the particles vary considerably. The rays will 
 therefore not be deflected to a single spot, even if 
 their mass and charge are identical, but will be 
 drawn out into a line or band. By equation (d) 
 all the particles for which m/E is the same will, 
 however, lie on some curve for which the value of 
 y*/x is constant ; such a curve is known as a parabola. 
 
 If the particles emerging from the cathode con- 
 sist of atoms of differing atomic weight, they will be 
 sorted out into a series of parabolas one above the 
 other, each curve corresponding to some definite 
 value of m/Mt. Since the velocity which is propor- 
 tional to y/^ cannot exceed a certain value, these 
 curves will not be complete, but will stop short at 
 some definite distance from the axis O Y. The appear- 
 ance of the plate after exposure should therefore be 
 somewhat as shown in the top left hand quadrant 
 Fig. 10, where two such parabolas are shown. 
 
 To measure the curves, drop any perpendicular 
 on OXrcutting the curves in / and m, and the axis in 
 n. Then, from equation (b) it can be seen that 
 
 since the value of x is the same for all points along 
 the line Imn. Thus, if EX = E 2 , that is to say, if the 
 two particles carry the same charge, the ratio of the 
 masses of the two sets of particles is simply equal to 
 
 The line OX has no real existence on the plate, 
 but the apparatus can be arranged so that the 
 M.P. 4 
 
50 MOLECULAR PHYSICS 
 
 direction of the deflections are parallel to the 
 edges of the photographic plate, while the position 
 of O is always marked by a very bright spot 
 caused by rays which come through the cathode 
 uncharged, and are therefore undeflected. A more 
 
 FIG. ii. PARABOLAS DUE TO MULTIPLE-CHARGED 
 MERCURY ATOMS. 
 
 accurate method is to reverse the field halfway 
 through the exposure. The direction of the 
 deflection is thus reversed, and symmetrical para- 
 bolas are formed on the opposite side of OX as 
 shown in Fig. 10. The distance between the two 
 branches of the same curve is then twice the distance 
 of either from the line OX. 
 
THE NEW METHOD OF ANALYSIS 51 
 
 It will have been noted that the ratio of the 
 squares on these ordinates does not give directly 
 the ratio of the masses of the particles, but only 
 the ratio of what we may term their electrochemical 
 equivalents. Fortunately, however the majority 
 
 FIG. 12. TYPICAL POSITIVE RAY PHOTOGRAPH. 
 
 of the particles carry the single electronic charge e y 
 while in any case the charge E on the positive particle 
 cannot be more than a small integral multiple of 
 this. Very little uncertainty is as a rule introduced 
 from this cause, though it does occasionally arise. 
 Mercury is the greatest offender in this respect, as 
 
 42 
 
MOLECULAR PHYSICS 
 
 mercury atoms carrying as many as eight charges 
 are sometimes to be detected. Thus, five of the 
 six parabolas on Fig. n, which is reproduced from 
 one ol Prof, Thomson's photographs, are due to 
 atoms of mercury, carrying respectively one, two, 
 
 TABLE III. 
 
 Atmospheric nitrogen. Potential across discharge tube, 
 30,000 volts ; current through magnet, 3*5 amperes ; 
 potential difference in electric field, 200 volts. 
 
 M 
 
 WE. 
 
 Probable cause of line. 
 
 7-2 
 
 2OO 
 
 Hg + 
 
 Mercury atom with single 
 
 
 
 
 charge. 
 
 10*3 
 
 IOO 
 
 Hg+ + 
 
 Mercury atom with two 
 
 
 
 
 charges. 
 
 12-4 
 
 67 
 
 Hg+ + 
 
 -f- Mercury atom with three 
 
 
 
 
 charges. 
 
 IT4 
 
 44 
 
 CO 2 + 
 
 Molecule of carbon dioxide. 
 
 16-5 
 
 TT 
 
 39 
 
 A + 
 
 Argon atom (40) with 
 
 * 
 
 
 
 single charge. 
 
 19*4 
 
 28 
 
 No + 
 
 Nitrogen molecule with 
 
 
 
 
 single charge 1 . 
 
 2VI 
 
 20 
 
 Ne + 
 
 ? Neon with single charge. 
 
 J 
 25-6 
 
 
 f 
 
 Atom of oxygen with single 
 
 
 
 
 
 charge. 
 
 27-6 
 
 14 
 
 N + 
 
 Nitrogen atom; with single 
 
 / 
 
 
 
 charge. 
 
 3O'O 
 
 12 
 
 C -f- 
 
 Carbon atom with single 
 
 } 
 
 
 
 charge. j 
 
 38-7 
 
 7 
 
 N + + 
 
 Nitrogen atom with two 
 
 *J / 
 
 / 
 
 
 charges. 
 
 three, four, and eight charges. The latter line, 
 though clear on the negative, is too faint to show 
 up clearly in the reproduction. 
 
 The measurement and interpretation of the 
 results can best be illustrated by an actual example. 
 
THE NEW METHOD OF ANALYSIS 53 
 
 Fig. 12 represents a fairly typical photograph 
 obtained with the apparatus. The gas in the 
 discharge tube in this case was atmospheric nitrogen, 
 that is to say, air from which the oxygen had been 
 extracted. Table III. contains the actual measure- 
 ments made on this plate. 
 
 The first column gives the distance of the different 
 parabolas from the axis OX, measured along some 
 common ordinate as explained above. The second 
 column gives the value deduced from these figures 
 for the relative masses of the particles, assuming 
 that they all carry the same charge. If the charge 
 carried is double or treble this value, the corre- 
 sponding mass so obtained Will be half, one-third 
 and so on, of the actual mass of the particle. The 
 standard line on this plate was the innermost one 
 of all, which as its appearance shows, is due to 
 mercury carrying a single charge. The mass of this 
 particle is for convenience taken as being equal to 
 its atomic weight (200). 
 
 Examining the table, it will be seen that the three 
 inner parabolas represent particles having a value of 
 m/E of 200, \ . (200), and (200). They are due 
 to mercury atoms having, respectively, one, two, and 
 three charges. Mercury vapour is always present 
 in the tube unless special precautions are taken to 
 exclude it, as it is used in the vacuum pumps 
 attached to the apparatus. The next line is made 
 by particles having a mass of 44 ; these are singly 
 charged molecules of carbon dioxide ; carbon com- 
 pounds being usually present as impurities in small 
 quantities. 
 
 The argon line (39) is the long bright parabola, 
 immediately below the very thick bright line (28), 
 due to molecules of nitrogen with a single positive 
 charge. This, as might be expected, is the brightest 
 line in the photograph. The parabola for which d 
 is 23 . i, is very faint on the reproduction. It 
 
54 MOLECULAR PHYSICS 
 
 probably represents Neon (20) though there is also the 
 possibility that it is formed by argon atoms with a 
 double charge, as the argon line (40) is very bright. 
 
 FIG. 13. POSITIVE RAY PARABOLAS. 
 
 Our method does not enable us to distinguish 
 between these alternatives. 
 
 The triplet of lines which follow is due to atoms 
 of oxygen, nitrogen, and carbon. The last line on 
 the plate, indicating a value 7 is the nitrogen atom 
 with a double charge. The hydrogen line which is 
 
THE NEW METHOD OF ANALYSIS 55 
 
 nearly always present, has been deflected entirely 
 off the plate by the large magnetic field applied in 
 order to separate the heavier constituents. 
 
 It will thus be seen that all the lines on our plate 
 correspond to elements which we might expect to find 
 present from the nature of the gas employed. There 
 are no lines unexplained, and the values obtained 
 for the relative masses of the particles correspond 
 very closely to the atomic and molecular weights 
 determined from chemical considerations. 
 
 The faint lines seen on Fig. 12 joining some of 
 the parabolas to the origin, are due to the secondary 
 effects which we have already mentioned. The 
 mercury parabolas, however, as will be seen from 
 the figure, do actually extend to within a very short 
 distance of the origin. This is due to quite a 
 different cause. Turning back to equation (a), it 
 will be seen that the electric deflection is propor- 
 tional to the charge EI carried by the particle in the 
 electric field divided by %mv 2 , the kinetic energy of 
 the particle. We have seen that the maximum 
 value of the latter is equal to V . E 2 , where V is the 
 potential of the discharge, and E 2 the charge carried 
 by the particle in the discharge tube. The minimum 
 value of the electric deflection, that is to say, the 
 nearest point to which the parabolas can extend 
 will be proportional to Ej/E 2 and will thus be the 
 same for all particles, whatever their mass and 
 charge, if each particle carries the same charge in the 
 tube as in the camera. Thus all the curves will 
 stop short at a certain line drawn parallel to OY. 
 This is well shown in Figs. 13 and 14. 
 
 If, however, a particle in the discharge tube 
 having a double or treble charge, loses one or more 
 of these extra charges before the electric field at MN 
 is reached, the value of E 2 /Ei will be greater than 
 unity, and the parabola will extend further towards 
 the axis OY. 
 
56 MOLECULAR PHYSICS 
 
 These extensions of the parabolas are very 
 clearly shown in the three inner curves of Fig. 13, 
 where an almost complete break occurs between the 
 termination of the original parabola and its con- 
 tinuation by particles which have parted with one 
 of their original charges. These three parabolas are 
 due respectively to Mercury (200), Xenon (132), and 
 Krypton (83). The two outer curves, representing 
 
 FlG. 14. GAS EVOLVED FROM PLATINUM. 
 
 Argon (40) and the Nitrogen molecule (28), end 
 abruptly at the normal distance from OY. 
 
 The best example of the effect is, however, shown 
 by the mercury lines in Fig. n. The normal 
 mercury atom in the discharge tube apparently 
 carries a charge of 8e, and approaches the cathode 
 with an amount of energy equivalent to this. The 
 innermost mercury parabola (Fig. n) gives a value 
 for the mass just 200 times that of the hydrogen 
 atom. It is therefore due to a mercury atom carry- 
 ing a unit charge, and having thus only one-eighth 
 
THE NEW METHOD OF ANALYSIS 57 
 
 of the charge it carried in the discharge tube. The 
 value of Ei/E 2 is thus | and the parabola extends to 
 one-eighth of the usual minimum distance from the 
 vertical axis. The next line (m = 100) is due to 
 atoms with two charges, and extends to one-quarter 
 of the usual minimum distance, and so on, until the 
 last parabola which corresponds to a mercury atom 
 with eight charges (the same number as in the dis- 
 charge), ends up at the usual distance from the axis. 
 
 This gradual shortening of the parabolas for the 
 differently charged mercury atoms, is beautifully 
 shown in Fig. n, where the terminations of the five 
 mercury parabolas can be seen to lie exactly on a 
 straight line through the point O inclined at an angle 
 to OY, as would be expected on the above theory. 
 
 It will be noticed that the lines decrease in 
 intensity as the number of charges carried is 
 increased. This is always to be observed on the 
 photographs, and is a fact which sometimes helps 
 us to the right interpretation of a doubtful line in 
 a photograph. For example, if the line indicating 
 a mass of 20 on Fig. 12 had been brighter than the 
 Argon line (40) we should have been able to say 
 definitely that it was due to atoms of Neon, and not 
 to Argon atoms with a double charge. 
 
 The plates so far described were all taken using 
 large magnetic fields in order to obtain a suitable 
 dispersion of the heavier atoms. The last plate of 
 the series (Fig. 14) was taken with a smaller magnetic 
 dispersion, and shows the lines due to some of the 
 lighter elements. It is of peculiar interest at the 
 present moment, as it is one of the photographs 
 which shows the mysterious line due to particles for 
 which the ratio of the mass to the charge is exactly 
 three times that for the singly charged hydrogen 
 atom. On this account it may perhaps be of 
 interest to give the actual measurements made on 
 this plate (Table IV.). The first column of the 
 
MOLECULAR PHYSICS 
 
 table gives the actual measurements of a common 
 ordinate of the different parabolas, the second 
 column the corresponding values of m/E, the ratio 
 for the hydrogen atom being taken as unity. 
 
 The gas used in the experiment was a sample of 
 that mysterious gas which is evolved in considerable 
 quantities when any metal is heated, or better still, 
 as in the present case, bombarded with cathode rays 
 in a vacuum tube. That gases were evolved under 
 these circumstances had been known for some 
 considerable time, but their analysis had not been 
 
 Gases evolved from 
 rays for 6 hours. 
 
 TABLE IV. 
 
 Platinum bombarded 
 (See Fig. 14.) 
 
 with Cathode 
 
 d m.m. 
 
 ;/E. 
 
 Probable cause of line. 
 
 27'O 
 
 I'OO 
 
 H + Hydrogen atom. 
 
 19-1 
 
 2'O 
 
 H 2 -j- Hydrogen molecule. 
 
 15-6 
 
 3 -0 
 
 ? Unknown element. 
 
 7-8 
 
 12 
 
 C + Carbon atom. 
 
 6-7 
 
 16 
 
 O + Oxygen atom. 
 
 5*8 
 
 21 
 
 Ne + Neon atom (20). 
 
 4-8 
 
 32 
 
 O 2 + Oxygen molecule. 
 
 previously effected. As will be seen from the table, 
 the gas consists principally of hydrogen, but helium 
 and neon are also present ; while the plate also shows 
 traces of carbon and oxygen, probably due to 
 impurities in the apparatus. 
 
 In addition to these known substances there is 
 also 'very clearly marked a line, the third from the 
 top of the plate, which cannot be assigned to any 
 known element or compound. There was at first 
 the possibility that it might be due to a carbon atom 
 carrying four elementary charges, but this hypothesis 
 was found to be untenable. In the first place the 
 
THE NEW METHOD OF ANALYSIS 59 
 
 line under consideration is much brighter than that 
 due to the singly charged carbon atoms, while we 
 have seen that on a given plate the curves due to 
 multiply charged atoms are invariably fainter than 
 those due to atoms of the same substance having a 
 single charge. In the second place, when pre- 
 cautions were taken to exclude carbon compounds 
 from the apparatus the carbon line (12) completely 
 disappeared, while the line 3 remained as bright as 
 ever. 
 
 Only two possibilities remain. The line may be 
 due to a previously unknown element of atomic 
 weight 3, or it is due to a hitherto unknown modifica- 
 tion of hydrogen H 3 corresponding to ozone. If the 
 latter is the case, the substance has some quite unex- 
 pected properties, as it is certainly not destroyed by 
 sparking with excess of oxygen. Professor Sir J. J. 
 Thomson is still actively pursuing his experiments on 
 this substance, and some very interesting results 
 may be expected. Until these experiments are 
 completed it would be premature to venture any 
 further opinion as to the real nature of this new gas. 
 
 Another parabola which is found when the gases 
 from liquid air residues are introduced into the tube 
 suggests interesting possibilities. This is a line 
 giving a value for w/E equal to 22. This might 
 possibly be a molecule of carbon dioxide (44) with a 
 double charge, but from the fact that it appears only 
 in these mixtures of the rarer atmospheric gases, 
 and that it is quite well marked even when the 
 CO 2 and CO lines are absent seems to point to it 
 being a new compound NeH 2 of neon and hydrogen. 
 
 A few further points of interest in the photo- 
 graphs may be noted. The bright central spot 
 shown in all the figures is due to the particles which 
 have lost their charge during their passage through 
 the long copper canal tube, and are therefore unde- 
 flected by any combination of electric and magnetic 
 
60 MOLECULAR PHYSICS 
 
 fields. The atoms of some elements have such 
 a strong attraction . for the surrounding negative 
 electrons that they actually take up more of them 
 than would be sufficient to neutralise the original 
 positive charge. They thus enter the deflecting 
 fields with a negative instead of a positive charge, 
 and so give rise to parabolas in the opposite quadrant 
 to those due to the positive particles, but giving, of 
 course, the same values for m/'E. At least two of 
 these " negative " parabolas appear on Fig. 13. 
 Oxygen and the halogens if present in any quantity 
 almost invariably give these negative curves, 
 Strangely enough hydrogen, which is generally 
 reckoned among the more electro-positive elements, 
 also frequently shows the same effect. It has never 
 been found with nitrogen or helium. 
 
 We have so far only been considering the relative 
 values on the ratio m/E for the different particles. 
 By measuring the dimensions of the different parts 
 of the apparatus and calculating the actual values 
 of the constants ki and & 2 , the absolute value of this 
 ratio for any given parabola can be deduced. Such 
 a determination was made by Professor Sir J. J. 
 Thomson, and it was found that the absolute value 
 for the outermost parabola of all was almost exactly 
 io~ 4 . We have seen that this is the value of the 
 ratio for a hydrogen ion in solution or a hydrogen 
 atom carrying a single charge. The particles with 
 which we have been dealing are therefore actual 
 atoms and molecules of the substances in the 
 discharge tube, as we have tacitly assumed in the 
 foregoing pages. 
 
 We have now described in some detail the prin- 
 cipal features of the new method of molecular 
 analysis. Its importance can hardly be exaggerated. 
 In the first place it enables us to detect with certainty 
 the presence in a gaseous mixture of far smaller 
 quantities of an element than could be accomplished 
 
THE NEW METHOD OF ANALYSIS 61 
 
 by any other method known to science. Professor 
 Thomson has given the following striking illustration 
 of the delicacy of the method. It was found that the 
 photographs taken with atmospheric argon in the 
 apparatus always showed the helium line faint but 
 quite distinct. In this particular experiment the 
 volume of the discharge tube was about 2 litres, 
 and the pressure of the gas in the tube 1/300 m.m. of 
 mercury. The gas experimented on would therefore 
 have had a volume of about i/ioo c.c. at atmospheric 
 pressure. This is approximately the quantity of 
 argon in i c.c. of air at atmospheric pressure. We 
 are thus able to detect the helium present in a single 
 cubic centimetre of air. According to the deter- 
 minations of Professor Ramsay this amounts to no 
 more than four millionths of a cubic centimetre. 
 
 The new method has the further advantage over 
 spectroscopic analysis that it gives directly the 
 atomic or molecular weight of the substance under 
 experiment. Thus the photograph of Fig. 14 not 
 only reveals the existence of a new gas but gives at 
 once its molecular weight. 
 
 Lastly, and this is perhaps most important of 
 all from the point of view of an intimate study of 
 the modes and methods of chemical combination 
 and decomposition, the time taken for each single 
 particle to register its presence and mass is 
 exceedingly minute. A very moderate value for 
 the speed of the positive particles is io 8 cms. per 
 second (about 620 miles per second). Their path 
 in the discharge tube is not more than 50 cms. in 
 all. Thus a particle when caught by the discharge 
 will register itself on the photographic plate in 
 considerably less than one millionth of a second. 
 
 We might therefore reasonably expect to find on 
 the photographs curves corresponding to temporary 
 combinations of atoms so unstable that their whole 
 period of existence is not greater than one millionth 
 
62 MOLECULAR PHYSICS 
 
 of a second, if any such combinations are formed in 
 the discharge tube. Thus in the case of chemical 
 reactions taking place within the discharge tube we 
 might expect to find on the plate traces not merely 
 of the stable products of the reaction but also of 
 any intermediate stages occurring in the course of 
 the reaction. The field thus opened up for an 
 intimate study of the mechanism of chemical 
 reactions is illimitable. 
 
 Though little has as yet been accomplished along 
 these lines, the experiments already made show that 
 this expectation is not unfounded. As a very simple 
 illustration of the application of the method we may 
 take the case of phosgene, COC1 2 . When this was 
 introduced into the apparatus the photographs 
 showed that, in addition to the molecules of unde- 
 composed phosgene (99), the carriers of positive 
 electricity were molecules of carbon monoxide (28) 
 and atoms of chlorine (35*5). The lines due to 
 single atoms of carbon and oxygen were very faint 
 indeed, thus showing that the decomposition" of the 
 compound by the discharge consisted of the separa- 
 tion of the chlorine atoms from the CO molecule, 
 the bond between the carbon and oxygen atoms 
 remaining intact. 
 
 This is a simple case where the results obtained 
 might easily have been predicted. Another inter- 
 esting case is that of methane, CH 4 . When this gas 
 is subjected to the discharge a group of five lines 
 appears on the photographic plate, indicating the 
 presence of particles having masses 12, 13, 14, 15 and 
 16 times that of the hydrogen atom. These corre- 
 spond to particles having the composition C, CH, 
 CH 2 , CH 3 , and CH 4 respectively. 
 
 We have been dealing so far with the many 
 advantages of the method. Some of its limitations 
 should perhaps be pointed out. In the first place 
 the substance to be exeprimented on must be either 
 
THE NEW METHOD OF ANALYSIS 63 
 
 gaseous or capable of exerting a vapour pressure at 
 ordinary temperatures. A more important defect, 
 and one which is shared by the spectroscopic method, 
 is that an element may be present in considerable 
 quantity in the discharge tube without producing a 
 corresponding trace upon the photographic plate. 
 Thus, although many metals have compounds suffi- 
 ciently volatile for the purpose of the experiment, 
 mercury and nickel are the only metallic elements 
 which have so far been detected by the method. 
 
 One word may be added as to the relative inten- 
 sity of the different lines on a given photograph. 
 
 B 
 
 tk 
 
 FIG. 15. APPARATUS FOR THE ELECTRICAL MEASUREMENT OF 
 THE POSITIVE RAYS. 
 
 It is found that in general this is far from repre- 
 senting the actual proportion of the particles in the 
 stream having masses corresponding to the different 
 lines. For some reason at present unexplained, a 
 given number of atoms of a light element produce 
 far greater effect on a photographic plate or wille- 
 mite screen than an equal number of the atoms of a 
 heavier element. Thus the parabola corresponding 
 to the hydrogen atom will often be the most intense 
 line on the plate when the amount of that element 
 present forms less than i% of the contents of the 
 tube. 
 
64 MOLECULAR PHYSICS 
 
 This has been very clearly demonstrated by 
 Sir J. J. Thomson by substituting an electrical for 
 a photographic method of detecting the positive 
 particles. It must be remembered that as all the 
 particles with which we are dealing carry an electric 
 charge they can be measured by collecting them in 
 a Faraday cylinder in the way described for the 
 a-particles in the preceding chapter. 
 
 To carry out the experiment a brass plate B 
 (Fig. 15) was substituted for the glass screen Z of 
 Fig. 9. If the brass plate is covered with powdered 
 willemite a series of bright parabolic curves will of 
 course appear upon it when the tube is running 
 somewhat as indicated in Fig. I5a, where three such 
 curves are shown. If a slit SS is cut in the brass 
 plate so as to coincide with one of the parabolas the 
 particles forming this parabola will pass through the 
 slit and can be collected by a Faraday cylinder F 
 (Fig. I5b) placed immediately behind it. As 
 explained in Chapter III., the rate of charging up 
 of an electrometer connected to the Faraday 
 cylinder will be proportional to the number of 
 particles entering the latter per second, that is to 
 say, to the relative number of molecules in the 
 positive rays which have a mass corresponding to 
 that indicated by the parabola coinciding with the 
 slit SS. 
 
 If the slit could be made to coincide successively 
 with each of the different parabolas indicated by the 
 glowing willemite, the relative rates of deflection of 
 the electrometer for the different positions would be 
 proportional to the number of particles of corre- 
 sponding mass in the positive rays from the discharge. 
 The experiment can be performed much more 
 conveniently without moving the slit by varying the 
 intensity of the deflecting magnetic field, H. If this 
 is increased it can easily be seen that the corre- 
 sponding magnetic deflections of the particles will 
 
THE NEW METHOD OF ANALYSIS 65 
 
 also.be increased and the various parabolas will move 
 outwards from the centre of the screen. In this way 
 each of them in turn can be brought to coincide with 
 the parabolic slit SS. It can easily be seen from 
 equations (a) and (b) that if the other conditions of the 
 experiment remain the same the value of m/E for a 
 given set of particles is proportional to the square 
 of the strength of the magnetic field necessary to 
 deflect them to a given position. Thus from the 
 various rates of deflection of the electrometer 
 corresponding to different values of the magnetic 
 field we can at once determine the relative 
 number of particles in the beam of positive rays 
 corresponding to definite values of the ratio w/E. 
 In other words, we can determine the relative pro- 
 portions of the different kinds of atoms and 
 molecules which make up a given beam of positive 
 rays. 
 
 On making the experiment it was found that 
 there was practically no movement of the needle of 
 the electrometer connected to the Faraday cylinder 
 except when one ol the bright parabolas was made 
 to coincide with the slit. If a fairly narrow slit was 
 used, the appearance and disappearance of a deflec- 
 tion of the electrometer as such a line passed across 
 the slit was surprisingly sharp, and lines quite close 
 together could easily be separated. 
 
 Although we can thus perform a quantitative 
 analysis of the beam of positive rays it cannot be 
 assumed without further experiment that the 
 number of atoms of an element in the beam is 
 necessarily proportional to the quantity of the 
 substance present in the discharge tube. Preli- 
 minary experiments, however, seem to indicate that 
 this is very approximately the case at any rate for 
 the non-metallic elements. If so, this latest modifi- 
 cation of the method of molecular analysis will 
 enable us to carry out not merely a qualitative but 
 M.P. 5 
 
66 MOLECULAR PHYSICS 
 
 also a quantitative analysis of any gas introduced 
 into the . discharge tube. The quantitative deter- 
 mination of traces of a gaseous substance too small 
 to be detected by the spectroscope will then have 
 become an accomplished fact. 
 
 \ 
 
CHAPTER V. 
 
 THE NATURE AND SIZE OF AN ELECTRON. 
 
 WE must now turn from these triumphs of 
 experimental skill to some theoretical considerations, 
 and discuss briefly the new views of the atom to 
 which they have given rise. It would be idle to 
 pretend that we have as yet any theory of the 
 structure of the atom which absolutely and com- 
 pletely sums up all the known phenomena of Science. 
 The scientific philosophers of an earlier age hoped 
 that at no very distant date they might be able to 
 include in one or more ponderous tomes all that 
 could be known in the realm of physical phenomena. 
 Looking down the long vistas which the new dis- 
 coveries have so recently opened up, we expect no 
 such immediate end. We are not yet within 
 sight of a mechanical or electrical theory of the 
 universe wherein all the chemical and physical pro- 
 perties of the material universe shall be explicable 
 in terms of the electrons and their motions. Still, 
 while w r e cannot say that we have such a theory, 
 there are certain sign-posts pointing out the direction 
 in which we may hope for ultimate success. Even 
 now it is possible to construct " models " of the 
 atom which, however crude and insufficient they 
 may be, enable us to link together many most 
 diverse phenomena. 
 
 In the realm of science an insufficient, or even a 
 false, hypothesis is better than none at all, and it 
 will be useful to take the best approximation we can 
 devise to serve us as a clue through the labyrinth of 
 
 52 
 
68 MOLECULAR PHYSICS 
 
 experimental facts which we have still to consider. 
 At the same time, it will be well to point out care- 
 fully where we are treading the solid ground of 
 experimental fact and legitimate deduction, and 
 where we rise to the higher but more precarious 
 flights of scientific imagination. 
 
 We have seen that electrons are contained in all 
 atoms, and many phenomena lead us to believe that 
 they play a most important part in determining 
 both the chemical and the physical properties of the 
 substance. The question naturally arises, what is 
 an electron ? Fortunately to this question also we 
 are able to give some answer. An electron is an 
 atom ,of electricity free from association with any- 
 thing in the nature of matter as we know it. It not 
 merely has a charge, it is a charge, and apart from 
 its charge has no existence and no properties, not 
 even that of mass. 
 
 The exact proof of this statement has involved 
 long and intricate mathematical analysis. It will, 
 however, be possible, without going at all deeply 
 into these abstruse calculations, to make clear the 
 nature of the proofs advanced, and the experimental 
 evidence upon which they rest. 
 
 In the first place, since we have already deter- 
 mined the mass of an electron, we must show that 
 such a moving electric charge will possess mass, a 
 property which we have been accustomed to associate 
 only with what we call matter. The proof follows 
 directly from the ordinary laws of electric and mag- 
 netic induction, and was first given by Professor 
 J. J. Thomson, in 1881, many years before the dis- 
 covery of the electron rendered possible any practical 
 application of the result. 
 
 Consider a small sphere charged with electricity 
 of either sign moving through space with a velocity v. 
 We have already pointed out that this moving sphere 
 will be equivalent to an electric current element 
 
NATURE AND SIZE OF AN ELECTRON 69 
 
 coinciding with the path of the particle. By the 
 usual laws of electro-magnetic induction this current 
 element will produce a magnetic field, at a distance r 
 from the particle, equal to ev sin 0/r*, where 6 is the 
 angle between the direction of motion of the particle 
 and the direction of r. Thus, the moving particle is 
 surrounded not only by an electro-static field due to 
 its charge, but also by a magnetic field due to the 
 motion of that charge. It will be seen that this 
 field has its greatest value in a direction at right 
 angles to the motion of the particle, and falls to zero 
 in the direction in which the particle is travelling. 
 
 It is a well-known fact that a magnetic field is 
 the seat of energy, the energy in a field of strength H 
 
 H 2 
 
 being ^ times the volume. The magnetic energy 
 
 in a small space of volume u at a distance r from our 
 moving charge is thus 
 
 (ev sin 0\ 2 u ue 1 sin 2 # 
 
 The total energy of the magnetic field surround- 
 ing the particle is the sum of the energy in all these 
 little volumes, from the surface of the particle away 
 to infinity. The summation of this quantity does 
 
 not present any difficulties. It is equal to --- , 
 
 where a is the radius of the sphere. 
 
 If m is the ordinary mechanical mass of the 
 particle, the kinetic energy due to its motion will be 
 
 - mv 2 . In addition to this there is, as we have shown, 
 
 2 
 
 a quantity of energy due to its charge. The total 
 energy of the moving particle and its charge is thus 
 
 I mv * + 1 
 
 2 r 3 <* ' 
 
 1 / 2 2 \ 
 
 If we write this in the form ( m + - - ) v 2 , and 
 
 2 V 3 & * 
 
70 MOLECULAR PHYSICS 
 
 compare it with the ordinary Newtonian expression 
 for the kinetic energy of a particle (- mv*\ we see 
 
 that the particle behaves as if its mass m had been 
 
 2 e 2 
 
 increased by an amount equal to . This is the 
 
 3 a 
 
 extra or " electrical " mass, due to the fact that the 
 
 particle carries a charge. It is evident that, even 
 
 if m, the " mechanical " mass of the particle, is zero, 
 
 the " electrical " mass due to the moving charge 
 
 will still persist. Thus, even if our electron is a pure 
 
 charge unassociated with any mechanical mass, it 
 
 will still have an electrical mass equal to 
 
 2 X (electrical charge) 2 
 
 3 X radius. 
 
 Since this " electrical " mass is really that of the 
 magnetic field surrounding the particle, it resides 
 not in the particle itself but in the medium sur- 
 rounding it, that is, in that mysterious fluid which 
 we call the ether. As soon, however, as we attempt 
 to alter the motion of the particle this energy flows 
 into it from all sides, so that, as far as experiments 
 upon the particle itself are concerned, the results 
 obtained are precisely the same as if it resided 
 permanently there. 
 
 To make this somewhat novel idea a little clearer 
 we may consider a close and very serviceable analogy, 
 where the mechanism of the extra mass is a little 
 clearer than in the electrical case. If any body is 
 moving through water, or any viscous fluid, it carries 
 with it a certain amount of the liquid through which 
 it is moving. In the case of a sphere, for example, 
 the quantity carried along by the motion of the body 
 amounts to half the volume of the sphere itself. A 
 long cylinder moving at right angles to its own length 
 will carry with it a quantity of fluid equal to 
 its own volume. On the other hand, if it moves in 
 the direction of its own length the fluid entangled 
 
NATURE AND SIZE OF AN ELECTRON 71 
 
 is practically nil. Thus, in order to set the body 
 in motion with a velocity v, we have to supply to 
 it energy enough to give this velocity, not only to 
 the sphere itself, but also to the mass of fluid which 
 it carries with it. That is to say, if M is the mass of 
 the sphere itself, and M' the mass of the attached 
 
 fluid, the work done in starting the body is - (M +M') .v 2 . 
 
 In other words, the body will behave as if its mass 
 were increased by the mass of the fluid entangled by 
 it. Just as in the electrical case, this extra mass 
 resides in the surrounding medium. 
 
 It makes itself apparent at the surface of the 
 sphere when the motion of the latter is altered in 
 any way. 
 
 We may very profitably extend this analogy 
 further in that part of our proof which still remains 
 to be considered, by thinking of our electric field in 
 terms of tubes of electric force. This conception we 
 owe to the genius of Faraday. Untrained in the 
 methods of mathematicians, he found the mere 
 algebraical expression for the laws of electrical 
 attraction both unsatisfying and unstimulating. 
 He felt that if two bodies attracted each other it 
 could only be because of some vital bond between 
 them. Thus he imagined that every positive charge 
 was the beginning of a certain number of tubes of 
 force stretching out through space until, somewhere 
 or other, they ended up on an equal but opposite 
 negative charge. 
 
 By assuming that these tubes were in a state of 
 tension so that they tended to shorten themselves 
 as much as possible, and, further, that two similar 
 tubes repelled each other, he was able to give 
 a clear explanation of the various electrical pheno- 
 mena. Thus the attraction between two oppositely 
 charged bodies was the result of the tendency 
 of the tubes connecting them to contract ; the 
 
?a MOLECULAR PHYSICS 
 
 repulsion between two like charges was due to 
 the mutual repulsion between the tubes of force 
 radiating from each of them. An electric current 
 was the motion of one of the ends of the tubes of 
 force along the conductor, while the magnetic effect 
 in the neighbourhood of the current was due to 
 
 FIG. 16. DISTRIBUTION OF TUBES OF ELECTRIC FORCE ROUND 
 AN ELECTRON AT REST. 
 
 the motion of the tubes of force through the 
 surrounding medium. 
 
 The concentration of attention upon the pheno- 
 mena of currents which marked the latter half of last 
 century tended to throw somewhat into oblivion this 
 conception of Faraday. The recent researches with 
 which we are dealing have, however, found in it a 
 most powerful weapon, and are tending to give to 
 these tubes of force a definite significance and con- 
 
NATURE AND SIZE OF AN ELECTRON 73 
 
 Crete existence of which even their originator per- 
 haps hardly dreamed. 
 
 Let us add to the postulates already made by 
 Faraday this additional assumption, that a tube of 
 force when moving through the ether is able to grip 
 a certain quantity of that subtle fluid, in much the 
 same way that a cylinder carries along with it a 
 definite mass of any liquid through which it moves. 
 For a single charged particle at a considerable dis- 
 tance from any other attracting bodies the lines of 
 force will radiate out in straight lines from its surface, 
 and, if the latter is spherical, the tubes will space 
 themselves evenly around it owing to their mutual 
 repulsion. In section, therefore, they will appear 
 somewhat as in Fig. 16. 
 
 Suppose this system to be moving through space 
 in the direction OA with a velocity v. If our 
 analogy with the case of a body moving through 
 water holds, the tubes, like OB, which move at right 
 angles to their length, will grip the maximum amount 
 of the ether through which they are moving, while 
 tubes like OA, which are moving along their length, 
 will carry none. It will thus be seen that the dis- 
 tribution of energy in the field surrounding the par- 
 ticle will correspond exactly with the distribution of 
 energy in the electro-magnetic field of which it is 
 supposed to be a visualisation. The electrical mass 
 of the particle will then be the whole mass of the 
 ether gripped by these radiating tubes. 
 
 Now it is a well-known fact that a cylinder 
 moving through a fluid in the direction of its own 
 length is not in stable equilibrium. In accordance 
 with the well-known principle of least action, the 
 cylinder will tend to turn so as to offer the greatest 
 possible resistance to the motion, that is to say, it 
 will tend to set itself at right angles to the direction 
 in which it is being compelled to move. If this 
 holds for tubes of force travelling through the ether, 
 
74 
 
 MOLECULAR PHYSICS 
 
 then tubes like OA are not in stable equilibrium, but 
 will tend to turn into the plane of OB, which we may 
 call the equatorial plane. It can be shown from the 
 principles of electricity that such a tendency does 
 indeed exist. The repulsion between the different 
 tubes will, of course, tend to keep OA in position, 
 and, as this repulsion is very great, at moderate 
 
 p IG 
 
 DISTRIBUTION OF TUBES OF ELECTRIC FORCE ROUND 
 A MOVING ELECTRON. 
 
 velocities the effect we are considering will be quite 
 negligible. The force, however, tending to displace 
 the tubes increases with the velocity of the particle, 
 so that at speeds approaching that of light there is 
 a very perceptible shifting of the lines of force into 
 the equatorial plane, as indicated in Fig. 17. But 
 we have noted that the mass of ether gripped by the 
 
NATURE AND SIZE OF AN ELECTRON 75 
 
 tubes in this position is greater than that which they 
 originally held. Thus we arrive at the somewhat 
 startling result that the electrical mass of a particle 
 is not a constant, but depends, at any rate at high 
 velocities, upon the speed with which it is moving. 
 
 We have followed out the theory of the variation 
 of electrical mass from the standpoint of Faraday's 
 tubes of force, because in the first place it gives us 
 at once a clear and vivid picture of the processes 
 which are going on in the field, while in the second 
 place we are being gradually driven to the con- 
 clusion that some such entities do play a very 
 important part in the phenomena of the electric 
 field. The fact of the variation of electric mass with 
 the speed, however, does not depend in the least 
 upon the particular way in which we choose to 
 regard the electric field, but is a direct though obscure 
 consequence of the fundamental facts of the science. 
 
 The exact relation between the electrical mass of 
 a moving charge and its velocity depends somewhat 
 on the assumptions we make as to the distribution 
 and geometrical configuration of the charge. Thus, 
 starting from different ideas of the shape of the 
 electron and the way in which its charge is arranged, 
 different mathematicians have arrived at somewhat 
 different formulae for this relation. Fortunately, 
 when these are reduced to figures the differences 
 between the best of them are so small that our 
 experiments are scarcely accurate enough to settle 
 definitely between them. One of the most success- 
 ful is that of Dr. Abraham, who deduces that 
 
 electrical mass ;;/ at a velocity v 3 (\ + fl 2 . i -h \ 
 electrical mass m f or small velocities "4 )8 2 \ " 2/8 & i - /' 
 
 where /3 is the ratio of the velocity of the particle 
 to the velocity of light. 
 
 Let us see now how these results assist us to 
 discover the nature of an electron. The total mass 
 
76 MOLECULAR PHYSICS 
 
 of the electron may be made up of two parts : its 
 mechanical mass, which is constant and independent 
 of the velocity, with which the electron is moving ; 
 and an electrical mass, which increases with the 
 velocity in the way we have just considered. If the 
 electrical mass of the electron is small compared 
 with its ordinary mechanical mass, then there will be 
 very little variation in the total mass of the electron 
 as the speed is increased. If, on the other hand, the 
 whole of the mass is electrical in its nature, the total 
 mass of the electron should increase at the rate given 
 by the formula of Abraham. If part of the mass is 
 mechanical and part electrical, the rate of increase 
 of the whole mass of the electron with increasing 
 velocity will be somewhere between these two 
 values. 
 
 If we substitute numerical values in the equation 
 given above, it will be found that the difference 
 between m and m is quite inappreciable unless the 
 speed of the particle is very high indeed. Thus 
 when the velocity is as much as one-tenth that of 
 light, the increase in the electrical mass only amounts 
 to about i%, while even when the velocity reaches 
 one-third that of light, that is to say, over 60,000 
 miles per second, the increase in the mass is only 
 about 5%. As this is the maximum velocity 
 attainable in a discharge tube it might have been 
 thought that the experimental investigation of the 
 variation of mass with speed lay forever beyond our 
 reach. 
 
 Fortunately this is not the case. Experiments 
 have shown that the /3-particles from radium, while 
 otherwise similar to cathode rays, travel with 
 velocities enormously greater even than those of the 
 particles in a discharge tube, in some cases approach- 
 ing within 4% of the velocity of light itself. For 
 speeds such as this the electrical mass should be 
 nearly three times its ordinary value, and thus, by 
 
NATURE AND SIZE OF AN ELECTRON 77 
 
 4 cms. 
 
 FIG 18. KAUFMANN'S APPARATUS FOR DETERMINING THE 
 MASS OF A /3-PARTICLE. 
 
 careful experiments on these particles, we might 
 well hope to put to the test the theories we have 
 propounded. 
 
 Such experiments have been made with exquisite 
 
78 MOLECULAR PHYSICS 
 
 skill and care by Kaufmann. In principle the 
 methods he employed were identical with those 
 
 Y 
 
 
 
 FIG. 19. KAUFMANN'S EXPERIMENTAL CURVE FOR THE 
 ELECTRIC MAGNETIC DEFLEXION OF THE /8 RAYS FROM 
 RADIUM. 
 
 already -described. The /3-particles given out by 
 a small quantity of radium placed at R (Fig. 18), 
 passed through a fine hole in a lead screen at A, 
 before finally falling on a photographic plate at P. 
 
NATURE AND SIZE OF AN ELECTRON 79 
 
 Before reaching the hole at A the particles passed 
 between two parallel plates, which could be very 
 carefully adjusted by means of a series of levelling 
 screws, and which were charged to a high difference 
 of potential. The whole of the apparatus was placed 
 between the poles of a strong electromagnet N, S, 
 arranged so that the electric and magnetic fields were 
 parallel to each other and therefore the correspond- 
 ing deflections they produced at right angles to each 
 other, exactly as in Professor Sir J. J. Thomson's 
 experiments on the positive rays. Apart from the 
 differences in velocity all the /3-particles are identical. 
 Thus, for every value of the velocity v there is only 
 one corresponding value for the mass m. Hence 
 the beam of rays is drawn out on the plate into 
 a single curve (Fig. 19), every point on which corre- 
 sponds to particles with a particular mass and speed. 
 
 This curve can be measured up with a micrometer 
 in exactly the same way as has been described for 
 the positive ray curves, and the mass and speed of 
 the particles deduced by equations (c) and (d) 
 (Chapter IV.). The values of the constants ki and 
 2 for the apparatus were very accurately deter- 
 mined, as were also the strengths of the electric and 
 magnetic fields. In this way Kaufmann obtained 
 results which he regarded as being accurate to 
 within i*5%, a very notable achievement. 
 
 Some of the results obtained are given in Table V. 
 The first column of the table gives the velocity of 
 the particles, the second the value of ft in Abraham's 
 formula, that is to say, the ratio of the velocity 
 of the particle to the velocity of light. In the 
 third column we have Kaufmann's experimental 
 values for the ratio of the whole mass of the particles 
 to their mass at small velocities. The last column 
 gives the theoretical value of this ratio, deduced 
 from Abraham's equation, on the assumption that 
 the whole of the mass is electrical. 
 
8o 
 
 MOLECULAR PHYSICS 
 
 It will be seen how very closely, all things 
 considered, the two sets of figures agree. The 
 experimental values for the ratio m/m ti increase, 
 if anything, even more rapidly than theoretical. 
 This would imply that, if anything, the mechanical 
 mass of the electron is negative, which is, of course, 
 an impossibility. The small discrepancy between 
 the two sets of figures is no doubt due to a lack of 
 
 TABLE V. 
 
 Kaufmann's values for the variation of the mass of a 
 /3-particle with change of velocity. 
 
 Velocity of the j3-particle. 
 
 - 
 
 of particle 
 
 bp 
 O 
 
 Experimental 
 value of 
 ntlm for the 
 
 ///// for 
 Abraham's 
 
 
 1 
 
 velocit 
 
 j3-particle. 
 
 equation. 
 
 2-88 x io 10 cm. per sec. 
 
 9<: 
 
 >3 
 
 2-70 
 
 2-52 
 
 2-85 
 
 9z 
 
 19 
 
 
 2*24 
 
 2-80 
 
 '9: 
 
 13 
 
 2*09 
 
 2*I4 
 
 2-65 
 
 8^ 
 
 >3 
 
 I '96 
 
 1-81 
 
 2*49 
 
 8- 
 
 *o 
 
 I "70 
 
 1-61 
 
 2-41 
 
 8c 
 
 )i 
 
 1-61 
 
 1*54 
 
 2'20 
 
 7: 
 
 *2 
 
 1-41 
 
 1-41 
 
 knowledge as to the exact nature of the distribution 
 of the electronic charge. 
 
 We have now discussed the evidence for our 
 original statement that the whole mass of the 
 electron is electrical in origin and due entirely to 
 the charge it carries. Granting this conclusion, 
 we can at once determine the dimensions of the 
 electron, and so complete our knowledge of its 
 properties. 
 
NATURE AND SIZE OF AN ELECTRON 81 
 We have seen that the electrical mass of a charge 
 
 2 P 
 
 e for moderate speeds is equal to - - where a is the 
 
 3 * 
 
 radius of the space occupied by the charge. The 
 mass of an electron is 8*8 X io~ 28 gms., while the 
 value of the charge it carries is 1*57 X io~ 20 units. 
 Substituting these values in the formula we find that 
 the radius of an electron is 1*87 X io~ 13 cms. 
 
 We have stated elsewhere that the radius of an 
 atom is of the order of io~ 8 cms., and have attempted 
 to form some idea of the exceeding smallness of 
 this magnitude. We may now say that small as 
 the atom is, the electron is so much smaller that 
 the electron bears to the atom which contains it 
 very much the same relation as a pea to a 
 cathedral. 
 
 We have seen that the whole of the mass of the 
 electron is due to the charge which it carries. The 
 thought at once suggests itself : Are there indeed 
 two kinds of mass or is all mass electrical in its 
 origin ? Probably most physicists cherish this 
 belief at the bottom of their hearts, but it cannot 
 at present be said to be much more than a pious 
 hope. The mass of a negative electron is about 
 TTOO P ar t f the mass of a hydrogen atom. 
 Neglecting the positive charge of the atom, of which 
 we know practically nothing, it would require 
 1,700 electrons to make up the mass of a single 
 hydrogen atom. This of course is not a priori an 
 impossible number considering the smallness of 
 the electron ; and speculations along these lines 
 were for a time freely indulged in. In this case, 
 however, experiment failed to confirm the bold 
 conjecture. The number of electrons in the atom 
 has been determined at any rate approximately, 
 and affords no support for such a theory. 
 
 As this number is one of considerable theoretical 
 importance, we may perhaps be allowed to describe, 
 M.P. 6 
 
82 MOLECULAR PHYSICS 
 
 very briefly, one of the methods by which attempts 
 have been made to determine it. Consider a 
 single electron flying through a sheet of metal. With 
 the huge velocity which it possesses a sheet of 
 aluminium, say Jth mm. thick, is not a very serious 
 obstacle to a /3-particle. Neglecting for a moment 
 the positive charge which keeps the atom together, 
 the various atoms which our particle encounters 
 must present to the particle the appearance of a 
 series of large chambers, empty save for a certain 
 number of particles, minute in comparison with 
 the atom, and similar to itself. 
 
 At a considerable distance these fixed electrons 
 will have little effect on the moving corpuscle. If, 
 however, in its flight it approaches one of them 
 closely it will be repelled, as the two particles each 
 carry a negative charge. The nearer it approaches 
 the greater will be the repulsion, and the further the 
 moving particle will be deflected from its original 
 path. We may call this a collision. It is, in fact 
 the same sort of collision as we imagine to take place 
 between two gas molecules. The direction in which 
 the particle will be deflected will be perfectly arbi- 
 trary, and a second collision may actually undo the 
 work of the -first. On the whole, however, the 
 greater the number of collisions the greater will be 
 the deflection, and it is not beyond the possibilities 
 of mathematics to determine the most probable 
 effect of a given number of these deflections. The 
 problem is indeed mathematically equivalent to the 
 well-known theorem of the drunkard's walk. Sup- 
 pose a drunkard walks so many yards before falling 
 down, and after each fall, having lost all sense of 
 locality, sets out again in some new and arbitrary 
 direction, at what distance from his starting point 
 will he be most likely to be found after a given 
 number of falls ? This problem, under a somewhat 
 different title, has been solved by Lord Rayleigh 
 
NATURE AND SIZE OF AN ELECTRON 83 
 
 in that marvellous compendium of mathematical 
 physics, the "Theory of Sound/' 
 
 If then we can find experimentally the most 
 probable deflection of a /3-particle after passing 
 through a certain thickness of solid matter, we can 
 deduce the number of collisions it has made in its 
 passage through the solid, and hence the number of 
 electrons in unit volume of the substance. Since 
 the number of atoms per cubic centimetre of any 
 substance can readily be deduced from the data 
 given in Chapter III., the number of electrons in 
 each atom can at once be determined. 
 
 A series of experiments upon these lines was 
 recently performed by the author. By various 
 experimental devices, which it would take us too far 
 from our course to describe, the mean angle through 
 which an originally parallel pencil of /3-rays was 
 scattered in passing through sheets of various sub- 
 stances was determined. By experimenting on 
 sheets of different thicknesses the author was able 
 to show that the mathematical treatment outlined 
 above was applicable to this particular case, and 
 hence to deduce the number of electrons in the 
 atoms of the various elements experimented upon. 
 
 The matter is, perhaps, hardly so simple as we 
 have described it. We have neglected so far the 
 effect of the positive electrification which we know 
 must be present in the atom if the latter is to be 
 electrically neutral. This will exert a certain 
 attraction on the flying electrons. 
 
 Unfortunately, we are not yet acquainted with 
 the nature of positive electricity. Professor Sir 
 J. J. Thomson's experiments on the positive rays, 
 brilliant as they have been, have not at present 
 thrown much light upon this exceedingly difficult 
 problem. For the present the term "positive elec- 
 trification " remains for the physicist very much 
 what the term " catalytic action " is for the chemist 
 
 62 
 
84 MOLECULAR PHYSICS 
 
 a not too humiliating method of confessing 
 ignorance. If we suppose that the positive electri- 
 city is distributed uniformly over a sphere the size 
 of the atom (a hypothesis which lends itself very 
 readily to mathematical treatment), the author's 
 result would indicate that the number of electrons 
 in an atom is almost exactly three times its atomic 
 weight. That is to say, the number of electrons 
 in a hydrogen atom would be three. If we go to 
 the other, extreme, and suppose that the positive 
 electrification is a sort of nucleus at the centre of the 
 atom, and that the electrons revolve round it some- 
 what after the manner of the rings of Saturn, the 
 number of electrons in a hydrogen atom works out 
 at unity, the number in any other atom being equal 
 to its atomic weight. The assigning of unit atomic 
 weight to hydrogen would then have a very definite 
 physical significance, as it would be the lightest 
 atom which could possibly exist. In either case 
 the number of electrons in an atom is only a very 
 small multiple of its atomic weight. We cannot, 
 therefore, assign any appreciable fraction of the mass 
 of the atoms to the negative electrons it contains. 
 
 There still remains, of course, the possibility that 
 the mass is electrical, but that it resides in the 
 positive portion of the atom. If the formula for the 
 electric mass be examined, it will be seen that for a 
 given charge the mass is inversely proportional to 
 the radius of the sphere upon which it is concentrated. 
 If we suppose that the positive charge on the 
 hydrogen atom to be concentrated upon a sphere 
 only xt'oo f the size of the negative electron, its 
 mass would be 1,700 times as great, that is to say, 
 equal to that of the hydrogen atom. Our perfect 
 ignorance of the nature of positive electricity renders 
 the suggestion not untenable, though evidence for it 
 is sadly lacking. For the present our belief in the 
 electro-magnetic nature of all mass remains an 
 
NATURE AND SIZE OF AN ELECTRON 85 
 
 expression of our faith that all the varied phe- 
 nomena with which we have to deal are manifesta- 
 tions of some single principle or essence which 
 underlies them all. To what extent future experi- 
 ment will realise our belief in the present instance 
 remains to be seen. 
 
CHAPTER VI. 
 THE CHEMISTRY OF THE MODEL ATOM. 
 
 WE have now learned all that is to be known 
 about electrons, their nature, their mass, their 
 charge, and their dimensions. We have seen that 
 they form a part of all atoms, and have discovered, 
 at any rate approximately, how many of them we 
 may expect to find in an atom of any given element. 
 We have seen also that electrons form a very minute 
 part of the mass, and a still smaller part by volume 
 of the whole atom. 
 
 It might be thought therefore that their influence 
 in determining the properties of the atom would be 
 proportionately small. There is much evidence 
 however that this is not the case, as we shall have 
 occasion to see during our further survey of molecular 
 physics. The electrons are small but they are 
 fmobile. It is entirely owing to this mobility that 
 we are so well acquainted with their properties. 
 It is owing to this same mobility that they exercise 
 such a marked influence upon the chemical and 
 physical character of the atom. 
 
 Our difficulties in constructing a satisfactory 
 model of an atom lie, as we have already seen, in 
 our almost complete ignorance of the nature of the 
 residue of an atom from which the electrons have 
 been extracted. The atom can lose at any rate 
 | some of its electrons without any serious change of 
 properties, and as the normal atom is neutral, the 
 residues aiter extracting the electrons must possess 
 
CHEMISTRY OF THE MODEL ATOM 87 
 
 positive electrification. Beyond this we know little , 
 or nothing. 
 
 Three views are possible. In the first place we 
 may assume of our residues what the earlier atomists 
 assumed of their atoms, that they are fundamentally 
 different in character, that copper is copper, and 
 tin is tin, and that there is no more to be said about 
 it. This would be to abandon all hope of attaining 
 any explanation of those recurring similarities 
 between the properties of the different elements 
 which are so clearly brought out in that greatest 
 of the generalisations of descriptive chemistry, the 
 periodic classification of the elements. This is a 
 policy of despair. 
 
 Assuming, then, that the remainder of all the" 1 
 atoms is composed of different amounts of the same 
 stuff, call it matter or positive electrification as 
 we will, this substance may be either continuous 
 or divided up into larger or smaller particles. The 
 fact that the a-particles given out by all radio- 
 active substances are identical might suggest that 
 these particles are the stones from which the edifice 
 of the atom is built up. The a-particle is, however, 
 too complex a structure to serve as a protyle ; it 
 is, for example, four times as heavy as our lightest 
 atom, and, in all probability contains at least two 
 electrons. Professor Nicholson has built up an 
 interesting chemical system from protyle atoms of 
 atomic weight, i, 2, 3, and 4, but these in themselves 
 would in all probability be complicated structures, 
 and in the absence of further evidence on which to 
 work it seems better to proceed at once to thej 
 fundamentals. 
 
 The existence of a positive electron is not quite^ 
 beyond the realms of possibility. It may be that 
 there is some sort of undetected one-sidedness about 
 our experiments which accounts for our complete 
 failure to observe it. If at any time it makes its 
 
88 MOLECULAR PHYSICS 
 
 appearance, it is possible that something of the 
 argument which follows may have to be referred to 
 the positive rather than to the negative electron. 
 
 Taking all the facts into consideration, the most 
 probable hypothesis at the present moment is the 
 one which regards the positive part of the atom as 
 forming either a uniform sphere, coterminous with 
 the atom, or a dense nucleus at its centre. In the 
 first hypothesis the electrons would move about 
 within the- positive sphere and would be attracted 
 with a force varying directly as their distance 
 from the centre of the sphere. On the second 
 hypothesis some, at any rate, of the electrons would 
 be outside the positive charge and revolve as 
 satellites around it, like the rings round the planet 
 Saturn, being attracted to it in this case with a 
 force varying inversely as the square of the distance. 
 
 The latter suggestion has very much to recommend 
 it, but it has also the very great defect from our 
 immediate point of view that it does not lend itself 
 at all readily to mathematical treatment. In other 
 words we cannot easily determine from the laws 
 governing such a system the way in which the 
 electrons would be arranged, and hence we cannot 
 easily deduce the properties to be expected in such 
 an atom. It is most probable that the arrangement 
 of the electrons in the two cases would exhibit the 
 same general features, though, of course, the actual 
 values in any given case would be different. As it 
 is not at all likely that either of these simple 
 systems will eventually be found adequate to 
 represent the atom of any real substance, we may, 
 without any loss of generality, confine our attention 
 ; to the simpler case. 
 
 The grouping of a number of electrons in a 
 sphere of positive electrification which is just 
 sufficient to neutralise their charges at points 
 outside the sphere, has been investigated theoreti- 
 
CHEMISTRY OF THE MODEL ATOM 89 
 
 cally by Professor Sir J. J. Thomson. A single 
 electron if at rest will place itself at the centre of 
 the sphere, or if in motion will describe a circle 
 around that point with a radius depending on its 
 velocity. Two electrons would occupy the opposite 
 ends of the diameter of a circle whose radius is 
 equal to half the radius of the positive sphere while 
 three electrons would arrange themselves at the 
 points of an equilateral triangle. The arrangement 
 of four electrons at the corners of a square is, however, 
 not a stable grouping if the ring of electrons is at 
 rest, but becomes possible if they are revolving 
 round the centre with a speed which exceeds a 
 certain critical value. If their velocity falls below 
 this the system collapses into a tetrahedron with an 
 evolution of energy. 
 
 The determination of the arrangement of any 
 number of electrons in a space of three dimensions 
 becomes at first difficult and finally impossible. 
 A few cases have, however, been worked out. Thus 
 six electrons would arrange themselves at the 
 corners of a regular octahedron, but, on the other 
 hand, the arrangement of eight at the corners of a 
 cube is not stable and will collapse into two tetra- 
 hedra, one inside the other, unless we station at least 
 one other electron within it. We are thus brought 
 face to face with one of the most important generali- 
 sations in electron grouping, namely, that it is quite 
 impossible for any system to make a large display 
 of electrons near its surface without a corresponding 
 stock within. The presence of a given number of 
 electrons near the outside of the atom demands 
 that there shall be a certain definite number of 
 electrons within in order that the system may be 
 stable. To use a commercial metaphor, an atom 
 cannot have all its goods in the shop window. 
 Otherwise there will be inevitable collapse into some 
 less pretentious system. 
 
MOLECULAR PHYSICS 
 
 The analysis becomes simpler, and leads to the 
 same general results, if we consider the electrons as 
 confined to a single plane instead of being able to 
 move in three dimensional space, a supposition 
 which is not altogether without justification on 
 experimental grounds. This case has the further 
 
 1 
 
 FIG. 20. A "MODEL" ATOM. 
 
 advantage that it can be studied experimentally in 
 a variety of ways. Of these the very beautiful experi- 
 ments of Mayer, though designed for quite other 
 purposes, are perhaps the simplest to reproduce. 
 
 A large number of needles are magnetised 
 together in a solenoid, and are floated vertically in 
 a basin of water by pushing all their (say) north 
 
CHEMISTRY OF THE MODEL ATOM 91 
 
 poles into small corks, their south poles being at 
 the same depth below the water. These latter repel 
 each other, just as do the electrons, according to an 
 inverse square law. To represent the action of the 
 positive sphere we may place a strong electro-magnet 
 beneath the bowl with its north pole upwards. 
 It can be shown that the attraction of this magnet 
 for the tiny south poles is (for the horizontal plane 
 in which alone they are able to move) approxi- 
 mately proportional to their distance from a point 
 immediately above the pole. Fig. 20 is a photo- 
 graph showing ten of these small magnets. It will 
 be seen that they are arranged in two rings of seven 
 and three respectively. The attracting electro- 
 magnet is concealed below the board. 
 
 On making the experiment it is found that the 
 greatest number of magnets which we can have in 
 an empty ring is five. If a sixth is added the 
 ring breaks up, the magnets gradually settling down 
 into an arrangement of five on the outside with one 
 in the middle. The number which must be placed 
 in the middle rapidly increases with the number in 
 the outer ring. Thus an outer ring of twelve 
 requires at least eight inside, and one of thirty no 
 less than one hundred and one for stability to be 
 possible. As these inner magnets are subject to 
 exactly the same laws as the outer ones, the whole 
 system, whether of magnets or electrons, splits up 
 into a series of concentric rings, with a perfectly 
 definite number of particles in each. 
 
 A complete mathematical solution has been 
 obtained by Professor Thomson. Table VI. con- 
 tains his results foi the model atoms in which the 
 number of electrons is not more than fifty-two. I 
 would point out very emphatically at this point 
 that no stress must be laid on the exact numbers 
 given in this Table. The simplifications we have 
 made are too many to render it even possible that 
 
92 MOLECULAR PHYSICS 
 
 these arrangements represent actual atoms of any 
 real substance. Neither does the weight of the 
 argument rest on any numerical relations between 
 the numbers of electrons in the different rings. The 
 general law of electron grouping enunciated above 
 when discussing three dimensional systems is amply 
 sufficient for all that follows, and is all we have at 
 present any right to make. It is, however, of the 
 greatest assistance in following the arguments to 
 clothe our abstract principles in concrete form and 
 to consider some definite case where the relationships 
 can be expressed in numerical form. The system 
 chosen is the simplest for the purpose. 
 
 The first row in Table VI. contains, with these 
 limitations, the " atoms " for which there is only 
 one ring of electrons, the second those with two, 
 and so on, the upper number being in each case that 
 contained in the outer ring. Thus n, 5, i, which 
 commences series C, implies that this atom contains 
 an outermost ring of eleven electrons with an inner 
 ring of five and a single electron at the centre. 
 Remembering that the number of electrons in the 
 atom is proportional to the atomic weight, it will be 
 seen that this Table represents a series of model 
 elements arranged according to their ascending 
 atomic weight. 
 
 A very cursory glance at this Table at once 
 reveals a very striking similarity to Mendeleef's 
 periodic classification of the elements. Thus, for 
 example, if we assign any chemical or physical 
 property to the existence in the atom of an arrange- 
 ment of electrons such as (5, i) this property will 
 disappear as we pass along the series to atoms with 
 different groupings, and consequently different 
 properties. Proceeding still further, however, we 
 come to a place where the original grouping (5, i) is 
 restored with the addition of an extra outer ring of 
 eleven electrons (n, 5, i). '- 3 
 
CHEMISTRY OF THE MODEL ATOM 93 
 
 This grouping again disappears as we pass along 
 series C, to reappear again with an extra ring of 
 fifteen at the beginning of series D, and with a 
 further ring of seventeen in series E. 
 
 Thus any property associated with a given 
 grouping of electrons will recur again and again at 
 intervals, as the number of electrons in the model 
 atom is increased. It can hardly be necessary to 
 point out how closely this resembles the arrangement 
 of the elements according to atomic weight where 
 the properties of the element sodium, for example, 
 disappear as we proceed to elements of higher 
 atomic weight, only to make their appearance again 
 with slight modifications when we arrive at the 
 element potassium. 
 
 There are many other resemblances which may 
 be pointed out between the periodic Table and our 
 scheme of electrons. In the first place it will be 
 seen that in the same group the atoms of series D and 
 E have four rings in common with each other, 
 while those in series B and C have only two. The 
 elements of higher atomic weight will resemble each 
 other more closely than the elements of lower 
 atomic weight. This again is a commonplace of 
 the periodic classification. Further, it will be seen 
 that at certain places in the Table the groupings are 
 in rapid change, while at others the configuration 
 alters much more slowly. This again corresponds 
 very closely with what actually occurs in the 
 arrangement of the elements where starting, for 
 example, at sodium, the alkaline properties gradually 
 disappear as we pass through magnesium and 
 aluminium, to be replaced by acid ones at sulphur 
 and chlorine. As we proceed further, however, there 
 is a sudden recurrence of the alkaline properties at 
 the next element, potassium. 
 
 Again, although the groupings shown in the Table 
 are all stable, they are not the only possible arrange- 
 

 H IO 
 
 IO M >O 
 
 I^x IO M IO 
 
 M HI HI 
 
 - 
 
 ; 
 
 O iO 
 
 M 
 
 O O iO 
 
 M HI 
 
 rj-o o 
 
 M HI 
 
 M HI M 
 HI HI HI 
 
 P< 
 
 - 
 
 Th 
 
 M 
 
 Tf Tf 
 
 M M 
 
 CO O Tj- 
 
 M H 
 
 t^ ^ O "^" 
 
 M M H 
 
 1>* CO O rj- 
 
 H M HI 
 
 
 
 
 O CO 
 
 CO O CO 
 
 HI HI 
 
 t^ CO O CO 
 
 H HI M 
 
 a 
 
 CO 
 
 ON co 
 
 CO O> CO 
 
 M 
 
 1^ CO O\ CO 
 
 HI H 
 
 O co O^ CO 
 
 M HI 
 
 
 
 00 CO 
 
 cooo co 
 
 HI 
 
 N 00 CO 
 
 H 
 
 MD COOO CO 
 
 H HI 
 
 VO N 00 CO 
 
 HI HI 
 
 
 
 
 00 <N 
 
 M 00 <N 
 
 H 
 
 VO CJ 00 M 
 
 H H 
 
 
 
 00 H 
 
 <N OO H 
 
 HI 
 
 vo N oo Hi 
 
 HI H 
 
 1 
 
 H 
 
 !> H 
 
 M (NH 
 
 H 
 
 HI t^ H 
 HI 
 
 1 
 
 O N J>. H 
 
 M H 
 
 \O HI t^ H 
 
 H H 
 
 10 HI r^ H 
 
 HI M 
 
 OO IO M O H 
 
 HI HI HI 
 
 
 *,; 
 
 M O H 
 HI 
 
 M M 
 
 OO >O HI VO M 4J 
 HI HI H 
 
 j 
 
 IO H 
 
 HI IO H 
 
 IO M IO H 
 
 M M 
 
 P 
 
 HI H H 
 
CHEMISTRY OF THE MODEL . ATOM 95 
 
 ments of electrons. Thus, while we cannot have a 
 ring of six electrons unless there is at least one 
 electron inside it, we may conceivably have more 
 than this without disturbing the equilibrium. Thus 
 an atom with ten electrons might be represented 
 either by (8, 2) as in the Table, or by the grouping 
 (7, 3). The latter grouping is the one actually seen 
 in the photograph (Fig. 20). In general, one of these 
 arrangements would be more stable than the other, 
 that is to say, its energy would be greater and it 
 would be more likely to survive. At certain points, 
 however, the different configurations might be so 
 evenly balanced as to be almost equally stable. In 
 this case we should have a series of elements of 
 almost exactly the same atomic weight, but differing 
 somewhat, though probably not markedly, in 
 properties ; a case corresponding very closely to the 
 puzzling series of rare earths which occur in the 
 middle of the Periodic Table. 
 
 It may be asked, what properties can be asso- 
 ciated with a grouping of electrons in a sphere of 
 positive electrification ? If we are on the right 
 track, we may expect sooner or later to be able to 
 interpret every phenomenon associated with the 
 atom in terms of such a system. But this is a far 
 cry, and it must be confessed that our present know r - 
 ledge does not extend very far in this direction. 
 We can, however, suggest several important pro- 
 perties which may, and one or two which can be 
 proved to be due to causes of this kind. 
 
 In the first place, we may almost certainly 
 include all those forces of cohesion, adhesion, and 
 the like which go by the name of molecular : those 
 attractions which, quite insensible at any appreci- 
 able distance, are yet at distances comparable with 
 the diameter of a molecule strong enough to rivet 
 together the atoms and molecules in a solid so firmly 
 that in some cases it requires stresses of many tons to 
 
96 .MOLECULAR PHYSICS 
 
 the square inch to drag them asunder. Since these 
 molecular forces determine tenacity, elasticity, and 
 melting point for solids, and surface tension and 
 vapour pressure for liquids, it will be seen that a 
 very considerable and important set of properties 
 are thus brought within the scope of our hypothesis. 
 The most probable and, indeed, at present, the 
 only explanation of these molecular attractions, is 
 that they represent the resultant force between the 
 different parts of the two electrical systems which 
 make up the atoms, each of which is neutral as a 
 whole. Let us take as an illustration a very simple 
 concrete case. Suppose the black dots in Fig. 21 
 
 o 
 
 O 
 
 o 
 o 
 
 FIG. 21. DIAGRAM TO ILLUSTRATE COHESION. 
 
 represent the outer rings of electrons in two ad- 
 jacent atoms, and that the effect of the positive 
 electricity around them may, for the sake of sim- 
 plicity, be regarded as .concentrated in the white 
 circles between them. 
 
 Since each of the atoms, as a whole, is electri- 
 cally neutral, the attractions and repulsions between 
 the different parts at any distance which at all 
 greatly exceeds the diameter of the atom will be 
 vanishingly small. If, however, as in the illustra- 
 tion, the two atoms are brought so close together 
 that their distance is only a fraction of this diameter, 
 this is no longer the case. It can readily be shown 
 that the atoms will turn so that a negative electron 
 in the one is faced by the positive portion of the 
 
CHEMISTRY OF THE MODEL ATOM 97 
 
 other. There would thus be an attraction between 
 them which would increase with great rapidity as 
 the distance between the atoms was diminished. 
 The law of force would thus be similar to that 
 actually found for these molecular forces. 
 
 The magnitude of the forces obviously depends 
 on the number and arrangement of the electrons in 
 the atom. A complete theory of cohesion is not 
 possible in the present state of our knowledge. 
 There is little doubt that it will be found to proceed 
 on lines not very different from the explanation 
 suggested above. 
 
 Although our methods of analysis do not enable 
 us to pursue this problem further, another very 
 important characteristic of the atom, namely, its 
 emission spectrum, has proved more amenable to 
 investigation. The evidence obtainable from a 
 study of spectral lines is so important that we shall 
 deal with it more fully in a later chapter. For the 
 present it may be noted that, before the electron 
 had been isolated and its properties determined by 
 direct experiment, it had been shown by Lorentz 
 that the systems emitting the vibrations which con- 
 stitute ordinary light were negatively charged 
 particles, and further, that the ratio of the charge 
 to the mass was of the order of 1*7 X io 7 . It was 
 also shown that these same electrons were the 
 cause of the absorption of light and its dispersion in 
 transparent media. Thus, practically the whole 
 range of optical phenomena of the atoms are due 
 to the electrons which they contain. 
 
 This point is so important that we shall return 
 to it in a separate chapter. In the remainder of 
 the present chapter we will confine our attention to 
 that important, fascinating and mysterious quality 
 of the atom which determines its chemical pro- 
 perties, namely, valency. 
 
 Ever since the time of Berzelius, the view has 
 M.P. 7 
 
98 MOLECULAR PHYSICS 
 
 been held that the forces binding the different atoms 
 together within the molecule were electrical in their 
 origin, that, for example, the molecule NaCl was 
 formed by the mutual attraction of a positively 
 charged sodium atom for a negatively charged atom 
 of chlorine. This view was, of course, based on the 
 phenomena of electrolysis. When an electric cur- 
 rent is passed through a solution of sodium chloride 
 in water, it is found that the sodium makes its way 
 to the negative electrode, the chlorine to the positive. 
 Thus, the salt behaves as if the sodium atoms bore a 
 positive charge and the chlorine a negative. The 
 conclusion seems irresistible, that the force binding 
 together these opposites in the same molecule is the 
 electrical attraction between their charges. 
 
 It was found necessary, from consideration of 
 the electrolysis of such compounds as CuCl 2 , etc., 
 to assume that the atoms of certain elements carried 
 charges amounting to twice, three times, etc., the 
 charge carried by a sodium or chlorine atom, and 
 thus the notion of valency arose, the valency of the 
 element being the number of times its charge in the 
 ionic state exceeded that of sodium or chlorine. 
 For elements such as carbon and nitrogen, which 
 are never found in the free ionic state, the valency 
 was deduced from their chemical analogy to ele- 
 ments of known valency. We may say, then, that 
 positive valency represents the tendency of the 
 neutral atom to part with its electrons, while nega- 
 tive valency is the tendency of the neutral atom to 
 absorb electrons into itself from without. If 
 electro-positive and electro-negative atoms are pre- 
 sent together, these tendencies can both be satisfied 
 by the mutual interchange of one or more electrons. 
 The passage of an electron from one atom to the 
 other will make the former positively the latter 
 negatively charged, and the attraction of the posi- 
 tive atom for its lost electron will constitute on our 
 
CHEMISTRY OF THE MODEL ATOM 99 
 
 hypothesis the force of chemical combination 
 between the two atoms. 
 
 Although these ideas in one form or another are 
 as old as Davy and Berzelius, chemists have made, 
 up to the present, little direct use of them, finding 
 the notion of bonds of affinity sufficient for all 
 practical purposes. So long as the electric charge 
 was regarded as something apart and distinct from 
 the atom itself, something of a different nature 
 superadded to it by external means, the electrical 
 theory, except in so far as it explained the phe- 
 nomena of electrolysis in which it had its rise, was 
 no more fundamental than the theory of a mys- 
 terious chemical bond. 
 
 With the electron theory of matter, the situation 
 is quite changed. It is evident that the question 
 whether a given atom will tend to lose or gain 
 electrons, and how many electrons can be so lost 
 or gained, will depend upon the number and arrange- 
 ment of the electrons within it, and the forces with 
 which they are retained in the atom. If we can 
 determine these, and if we can show that they lead 
 to a similar distribution of valency with atomic 
 weight to that actually demanded by chemical 
 considerations, we shall feel that we have made a 
 very hopeful start in the solution of this funda- 
 mentally important question. 
 
 In the first place, it must be pointed out that all 
 the electrons in the atom are not held in the same 
 way. The majority of the electrons are too firmly 
 held to be displaced by anything short of a dis- 
 ruption of the whole atom. A certain number, 
 however, are held comparatively loosely. Optical 
 experiments have shown that the number per cubic 
 centimetre of the comparatively mobile eelctrons 
 which determine the dispersion of the substance is 
 not many times greater than the number of atoms 
 present. Similar results are obtained from a con- 
 
 72 
 
ioo MOLECULAR PHYSICS 
 
 sideration of the numbers of free electrons in a 
 metallic conductor. It will obviously be these 
 free electrons that determine the valency of the 
 atom. It seems very probable that the greatest 
 number of these that any atom can gain or lose does 
 not exceed eight, and it may be noted that this is the 
 greatest charge ever found to be carried by a positive 
 particle. 
 
 Since valency is a property of the simplest 
 atoms, it seems probable that the valency electrons 
 form the innermost ring of the atomic system. Let 
 us suppose, now, that the maximum number of 
 electrons which can be contained in this inner shell 
 is eight, the minimum, of course, being zero, and 
 let us suppose, further, that there is a tendency in 
 every atom to give this inner ring either its maxi- 
 mum or minimum value. An atom with an inner 
 ring of five electrons would then either part with its 
 five valency electrons, in which case it would have 
 a positive charge and, consequently, a positive 
 valency of five, or attract three more electrons from 
 without, making up its complement to eight. In 
 this case it would be electro-negative in character 
 with a charge and a valency of three. It will be 
 .noted that the sum of the two valencies is equal to 
 the maximum number of particles in the inner ring, 
 namely, eight. 
 
 Which of these two actions would take place 
 would depend on the nature of the atoms with which 
 it was placed in contact. If surrounded by atoms 
 which tended to part with electrons, it would be 
 electro-negative, if by atoms with a strong attraction 
 for free electrons, it would eventually give up some, 
 or all of its five to the stronger atom and remain 
 electro-positive with a maximum valency of five. 
 The atom would correspond closely to such a sub- 
 stance as phosphorus, which forms compounds 
 such as PH 3 , in which it shows a negative valency 
 
CHEMISTRY OF THE , 
 
 of three, while, with the strongly electro-negative 
 element, chlorine, it forms compounds such as 
 PCl 3 ^and PC1 5 , in which it has a maximum positive 
 valency of five. 
 
 To compare our results with the periodic table, 
 we must suppose the elements of Group I., lithium, 
 sodium, etc., to possess, when in their neutral state, 
 only one valency or free .electron, which they give 
 up with the greatest readiness. The elements of 
 the next group should have two free electrons and a 
 positive valency of two. At the same time, there 
 would be the possibility of their taking in sufficient 
 electrons to bring their total up to eight, in which 
 case they would possess a possible maximum 
 negative valency of six. I am not aware that any 
 compounds have been prepared in which this 
 valency is exercised. It might, in any case, be 
 expected to be very feeble. 
 
 The number of valency electrons in the atom, 
 then, increases uniformly as we pass along the series, 
 until we reach the halogens with a total number of 
 seven. These have a possible positive valency of 
 seven, as they might conceivably lose the whole 
 number they possessed. This valency is probably 
 exercised in compounds, such as I 2 O 7 . As they con- 
 tain very nearly the maximum number possible, 
 they are, however, much more likely to acquire the 
 one necessary electron to make their total up to 
 eight, and thus act as strongly electro-negative 
 elements, as in the great majority of their stable 
 compounds, e.g., NaCl, we know they do. From 
 energy considerations we should expect that 
 the number of electrons in the inner ring would 
 tend to that stable number to which it was nearest 
 to begin with. Thus, elements possessing fewer free 
 electrons than four would be electro-positive, those 
 with more would tend to make their complement up 
 to eight, and be electro-negative. The elements of 
 
ica 
 
 MOJlECULAR PHYSICS 
 
 the carbon group (Group IV.), with four valency 
 electrons would be almost indifferently positive or 
 negative ; as we find them to be, both CO 2 and CH 4 , 
 being stable compounds. Our complete valency 
 scheme is thus represented by Table VII., where 
 the Roman numerals indicate the group in the 
 periodic classification. It is most interesting to note 
 that Professor Abegg, in a very illuminating paper 
 on valency, arrived at a precisely similar scheme 
 from purely chemical considerations. He suggssted 
 that every element had two valencies, a normal and 
 a contra valency, the normal being supposed to be 
 the stronger. The positive valencies were the normal 
 
 TABLE VII. TABLE OF VALENCIES OF THE PERIODIC 
 GROUPS. 
 
 Group. 
 
 i. 
 
 ii. 
 
 in. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 Normal valency . 
 
 + i 
 
 + ? 
 
 + 3 
 
 
 _ 3 
 
 2 
 
 i 
 
 
 
 
 
 4 
 
 
 
 
 Additional or 
 
 
 
 
 
 
 
 
 contra- valency . 
 
 - 7 
 
 - 6 
 
 - 5 
 
 
 + 5 
 
 + 6 
 
 + 7 
 
 for elements of Groups I. to III., the negative for 
 Groups V. to VII., Group IV. being indifferently plus 
 or minus. The sum of the normal and contra 
 valencies for any element was eight. It will be seen 
 that this suggestion is exactly embodied in our 
 theoretical table. 
 
 The phenomena of variable valency and valen- 
 cies of different signs have no difficulties on our 
 hypothesis. It is, in fact, exactly what we should 
 expect. It is not necessary that the whole of the 
 available electrons should be extracted in one step. 
 It is evident that the work done in extracting an 
 electron from the atom will be greater for the second 
 than for the first, and it is quite easy to imagine 
 
CHEMISTRY OF THE MODEL ATOM 103 
 
 circumstances under which the ionising force was 
 sufficient to produce the expulsion of one, but not 
 of two electrons, while under more favourable 
 conditions, both might escape. 
 
 The inert gases of the helium group possess no 
 valency and, hence, presumably, no free electrons. 
 We have already remarked that the phenomenon of 
 the dispersion of light is due to these free electrons, 
 which are thus sometimes spoken of as dispersional 
 electrons. It is interesting to note, in support of 
 the hypothesis we have advanced, that the dis- 
 
 TABLE VIII. NUMBER OF FREE ELECTRONS IN THE ATOM 
 DEDUCED FROM THE DISPERSION OF LIGHT. 
 
 Substance. 
 
 Calculated 
 Number of 
 Free Electrons. 
 
 Number 
 Assumed 
 (maximum 
 positive value). 
 
 Hydrogen 
 
 
 
 
 i'4 
 
 I 
 
 Calcium 
 
 
 
 
 
 1*5 
 
 2 
 
 Carbon 
 
 
 
 
 
 37 
 
 4 
 
 Siliccfe 
 
 
 
 
 
 3*9 
 
 4 
 
 Oxygen 
 
 
 .,. 
 
 
 
 4*4 
 
 6 
 
 Chlorine 
 
 
 
 
 
 
 6'2 
 
 7 
 
 persion of light in helium is abnormally small, while 
 that of the halogen gases, which, on our theory, 
 possess the maximum number of valency electrons, 
 is very large. 
 
 Drude, by means of a rather abstruse and some- 
 what approximate calculation, has deduced from 
 these considerations the number of free electrons 
 in the atoms of different elements. Some of the 
 results are given in Table VIII. Remembering that 
 the number of electrons in the atom must be an 
 integer, and that the calculations are only approxi- 
 mate, his calculated values seem fully to bear out 
 the assumption we have made above. 
 
104 MOLECULAR PHYSICS 
 
 Again, our hypothesis explains directly the 
 curious connection between the sign of the valency 
 and electrical conductivity. With the exception of 
 hydrogen, every electro-positive element conducts 
 electricity when in the solid state. This fact is such 
 a commonplace, that an explanation, perhaps, at 
 first sight, hardly seems necessary. On any other 
 theory of valency, however, it would be difficult to 
 account for this invariable co-existence. On the 
 assumption, however, that electro-positive elements 
 are those which easily give up electrons, it is evident 
 that since these electrons will be free to move under 
 the electric field, these elements will be able to con- 
 duct electricity, while, since the electro-negative 
 elements tend to absorb electrons, there will be few 
 electrons present in them in a free state, and since 
 the atoms themselves are not able to move through 
 the solid, the current will find no carriers, and so will 
 be unable to pass. 
 
 One further direct deduction from our hypo- 
 thesis is of interest. It can be shown that when 
 two atoms of different sizes come into contact, the 
 attraction of the smaller atom for the electrons con- 
 tained in the larger exceeds that of the larger atom 
 for the electrons in the smaller. There is thus a 
 resultant force tending to drive the electrons from 
 the larger to the smaller atom. It has been shown 
 that in the simplest possible case an electron will 
 actually pass between two similar atoms if the 
 radius of the smaller is less than seven-tenths that 
 of the larger. 
 
 Thus, among atoms of the same type, those with 
 a smaller volume will tend to acquire, those with a 
 larger volume will tend to lose, electrons. In the 
 same group, therefore, the elements of greater 
 atomic volume will be more electro-positive (or less 
 electro-negative, as the case may be) than the 
 elements with the smaller atomic volume. In any 
 
CHEMISTRY OF THE MODEL ATOM 105 
 
 one group of elements the atomic volume increases 
 with the atomic weight. Hence, we arrive at the 
 general result, that the electro-positiveness of the 
 elements in any group increases with increasing 
 atomic weight. This relation has often been pointed 
 out. A very striking example of it is seen in 
 Group V. of the^ periodic classification, where the 
 lightest element, nitrogen, is usually electro-nega- 
 tive, while the heaviest, bismuth, is generally 
 electro-positive. 
 
 We have now traced out some of the conse- 
 quences of the hypothesis that valency is deter- 
 mined by the number of loosely bound or valency 
 electrons contained in the atom, these electrons 
 being identical with those which determine the 
 dispersion of light. We have also made the addi- 
 tional assumption that the maximum number of 
 such electrons which can be contained in any atom 
 is eight, and that in every case there is a tendency 
 to make this number either eight (negative valency), 
 or zero (positive valency). 
 
 This latter hypothesis has, it must be confessed, 
 somewhat of an a posteriori air about it, and it may 
 be interesting to investigate, briefly, whether there 
 is any property of electron grouping from which 
 this apparently arbitrary assumption can be 
 deduced. 
 
 Qualitatively, at least, we can show that some 
 such quality is a direct consequence of the laws of 
 electron groupings which we have formulated above. 
 It was shown that for any ring or shell of electrons 
 to persist, there must be contained within it a certain 
 definite number, at least, of other electrons. 
 
 Let us suppose now, that for an outer ring of A 
 electrons this number is a, while for a ring of A + i 
 electrons it is b. Consider an atom with a ring 
 of A electrons having n other electrons within 
 it w T here n is some number greater than a, but less 
 
io6 MOLECULAR PHYSICS 
 
 than b. By suitable means we may extract from 
 this atom a number of electrons equal to n a, 
 without destroying the equilibrium of the outer 
 ring A. If, however, we succeeded in extracting 
 one further electron, the system would become 
 unstable and the atom would collapse. 
 
 Now we know that any real atom is a very stable 
 structure indeed. Certain atoms, it is true, owing 
 to circumstances we shall have to consider later, 
 spontaneously break up into simpler substances, but 
 there is no known agency by which we can bring 
 about the dissolution of an atom of ordinary matter. 
 The phenomena of radio-activity have furnished us 
 with the clue to our failure : the energy required is 
 too great. On the other hand, the energy required 
 to extract single electrons from a neutral atom has 
 been determined, experimentally, and is triflingly 
 small. A single a-particle, for example, has suffi- 
 cient energy to produce many thousands of ions. 
 Thus, the work required to reduce the number of 
 electrons in the atom below the critical value a 
 would be out of all proportion greater than that 
 necessary to extract the electrons above this number. 
 In effect, the value a would be a barrier which 
 we could not overstep. 
 
 Similarly, we could add to the atom sufficient 
 electrons to make its number up to b, without 
 bringing about any change in atomic structure. 
 Beyond that point, a further electron would neces- 
 sitate an outer ring of A + z electrons, with a re- 
 arrangement of the atomic structure. 
 
 Thus, the two critical values a and b constitute, 
 as it were, barriers which we cannot pass. We may 
 extract n a electrons, at most, giving the element 
 a positive valency of n a, or we may add b n 
 electrons, giving the atom a negative charge and 
 negative valency of this amount. More than this 
 we cannot achieve. The sum of these two valen- 
 
CHEMISTRY OF THE MODEL ATOM 107 
 
 cies is obviously b a, which is a constant for all 
 elements with a ring of A electrons. 
 
 We have presented the argument in general 
 terms, rather than from a consideration of the model 
 scheme in Table V., because we did not wish to 
 suggest that it depended in any way upon the 
 numerous simplifications and approximations which 
 were necessary in calculating that table. This 
 granted, however, a concrete example taken from 
 that table may serve to make the argument more 
 clear. 
 
 Consider the elements with an outer ring of seven- 
 teen. We have lettered them from / to s in Table VI. 
 The number of electrons within the ring in element m 
 is twenty-six, which is one more than is absolutely 
 necessary for the stability of the ring. Thus, the 
 element m might lose one, and only one electron 
 without any violent rearrangement of the system 
 taking place. Moreover, as the system is not much 
 more than stable, the forces retaining the electron 
 within the atom are not very strong, and this 
 electron would be very easily displaced. The 
 element m would thus be monovalent and strongly 
 electro-positive. The next element, n, could lose a 
 total of two electrons without derangement of the 
 system. It would thus be divalent and electro- 
 positive, but as it would naturally be more stable 
 than m, its activity would be less marked. Thus, 
 as we pass along the series, the positive valency 
 increases numerically while, at the same time, it 
 decreases in intensity. 
 
 At the other end of the series the element r 
 could take in one extra electron without raising its 
 total number sufficiently to necessitate an outer ring 
 of eighteen. It would thus be monovalent and 
 electro-negative. Theoretically, it might also lose 
 six electrons and be hexavalent and electro-positive. 
 From energy considerations, however, this would 
 
io8 
 
 MOLECULAR PHYSICS 
 
 only occur in exceptional circumstances. Similarly, 
 the element q preceding it would be divalent and 
 electro-negative, though less actively so than r. 
 Thus, our series of model atoms gives us a valency 
 system very similar to that already described. 
 
 In conclusion, it may be noted that the electron 
 theory of valency, while more fundamental and 
 complete, has yet a very close resemblance to the 
 " bond " theory, and is thus capable of including in 
 itself all the very important and interesting results 
 which have been achieved on that hypothesis. For 
 consider an electro-positive atom which has lost one 
 
 FIG. 22. STRUCTURE OF ETHANE. 
 
 electron. It will be the starting point of a Faraday 
 tube of force, which, when a compound is finally 
 formed, will end up upon the extra electron con- 
 tained in the electro-negative partner of the com- 
 bination. Similarly, a divalent atom would be the 
 starting point of two such tubes, and would require 
 two monovalent or one divalent atom for its satura- 
 tion. Thus, we may say that the chemical bonds 
 represent the Faraday tubes linking up the different 
 atoms in the molecule. 
 
 There is this difference, however, between the 
 two theories, that while a bond is not usually 
 regarded as implying direction, a Faraday tube is 
 essentially different at its two ends, and implies a 
 
CHEMISTRY OF THE MODEL ATOM 109 
 
 finite difference of potential. Take, now, the case 
 of ethane, C 2 H 6 . Regarding all the hydrogen atoms 
 as positive, three Faraday tubes have their negative 
 ends upon each of the carbon atoms (Fig. 22). 
 If the bond between the carbon atoms is a Faraday 
 tube it must run from one atom to the other. The 
 atom on which it starts will then have a total nega- 
 tive charge of 2.e, while the other has a total charge 
 of 4.0. The two carbon atoms are thus not in 
 precisely the same electrical state. 
 
 No change in properties has yet been observed, 
 attributable to this difference. In the case of 
 
 FIG. 23. STRUCTURE OF ETHYLENE. 
 
 ethylene, however (Fig. 23), where the difference 
 between the atoms is more marked, one carrying a 
 charge of 4.0, while the other is electrically neutral, 
 such differences have been noted. Take, for 
 example, the property of the refraction of light. 
 It has been found that the refraction produced per 
 molecule by many organic compounds can be 
 calculated by assigning certain definite values to 
 the atoms of carbon, hydrogen, and the rest, the 
 molecular refraction of any compound being then 
 equal to the sum of the values for all the separate 
 atoms which go to make up its molecule. It has 
 been found, however, that if the carbon atom is 
 present in the ethylene linking, a certain additional 
 
no MOLECULAR PHYSICS 
 
 amount must be added in for every atom so linked 
 up. Thus, the atomic refraction of the carbon atom 
 is apparently not the same in its neutral as in its 
 charged state. A precisely similar result is obtained 
 if we consider other additive properties, such as 
 molecular volume. Thus, there seems to be a 
 distinct difference in the properties of the carbon 
 atom in these two electrical conditions. 
 
 We have developed this subject of valency at 
 considerable length, because it is one of the most 
 fundamental, and, at the same time, has been one 
 of the most mysterious of all atomic properties. 
 While it would be idle to pretend that the hypo- 
 thesis which we have advanced, which is due, in the 
 main, to Professor Sir J. J. Thomson, is at present 
 entirely adequate to include the whole of these 
 puzzling phenomena, it does, on the whole, correlate 
 so successfully the more fundamental facts of 
 valency that we cannot but feel that, at any rate, 
 we are working along right lines and may look with 
 some confidence to a complete solution in the 
 perhaps not very distant future. 
 
CHAPTER VII. 
 
 THE ATOM IN VIBRATION. 
 
 IT can easily be shown that when a moving electric 
 charge is accelerated or retarded in any way, a wave 
 of electro-magnetic disturbance radiates out through 
 the surrounding space. Consider an electron with 
 its Faraday tubes moving along in the direction 
 AB (Fig. 24) . If the electron is moving with uniform 
 
 FIG. 24.- 
 
 -PRODUCTION OF ELECTRO-MAGNETIC DISTURBANCES 
 BY THE STOPPAGE OF AN ELECTRON. 
 
 velocity these tubes will travel along with the 
 electron as if they were rigidly attached to it. 
 Suppose, however, that this electron on reaching a 
 point C is suddenly stopped in its career. The ends 
 of the Faraday tubes attached to the electron are 
 suddenly brought to rest. 
 
 Now a Faraday tube is in some respects very 
 like a stretched rope. For instance, it has a tension 
 
ii2 MOLECULAR PHYSICS 
 
 along its length, and possesses, as we have seen in a 
 previous chapter, mass. Thus, just as when one 
 end of a rope is jerked, a certain definite time 
 elapses before the displacement reaches the other 
 end, so a displacement in a Faraday tube does not 
 reach all points of it simultaneously, but is propagated 
 along it with a definite velocity. In the case of the 
 
 /T" 
 
 stretched rope the velocity is equal to /y where 
 
 T is the tension on the rope and m its mass per unit 
 length. On similar principles it can be shown that 
 the velocity of a disturbance along a Faraday tube 
 
 is equal to , where ^ is the magnetic per- 
 V/^K 
 
 meability and K the specific inductive capacity of 
 the medium through which the disturbance is 
 travelling. We will call this velocity V. 
 
 Now, during the time it has taken for the jerk 
 to travel from the electron O to a point P, the 
 portion of the tube beyond P, not having received 
 the signal that the electron has been stopped, has 
 been travelling on with its original velocity and is 
 now in the position P', where PP' is the distance 
 which the electron would have gone in the time 
 taken for the disturbance to travel along the tube 
 from O to P. Thus a kink is developed in the tube 
 which travels outward along it with the velocity V. 
 
 The bent portion of the tube PP' is moving 
 perpendicular to its length and will thus, by the 
 principles we have already developed, produce a 
 magnetic field in the medium which will also travel 
 out with the kink. If we consider all the tubes 
 surrounding the particle, it will be seen that these 
 bent portions will form a kind of sheet of disturbance 
 travelling outwards as an expanding spherical shell 
 or wave. 
 
 If we can determine for any medium the values 
 of /x and K in the same system of units, we can 
 
THE ATOM IN VIBRATION 113 
 
 calculate the velocity V with which the disturbance 
 is propagated in that medium. It will be remem- 
 bered that the electrostatic system of units was 
 obtained by defining K the specific inductive 
 capacity of air as unity. The electro-magnetic 
 system on the other hand assigns this value to ^ the 
 magnetic permeability of air. The comparison of 
 the two systems can best be performed by measuring 
 the capacity of the same condenser according to both 
 systems of units. This operation is described in 
 most text-books of electricity, and its details are 
 outside the scope of our present work. The results 
 obtained are, however, most striking and important. 
 The result of a long series of experiments at the 
 American Bureau of Standards extending over 
 several years has given a value for V of 2*997 X io 10 
 cm. per second. This is, within the limits of 
 experimental error, identical with the best deter- 
 minations of the velocity of light, which have given 
 a mean value of 2*998 xio 10 cm. per second. The 
 agreement between the values obtained for the two 
 velocities is too close to be accidental. It affords 
 a convincing proof of the electro-magnetic nature 
 of light. 
 
 In the case we have considered where the particle 
 is suddenly brought to rest a single pulse is formed 
 the thickness of which is equal to the distance 
 through which the disturbance can travel in the 
 time taken to stop the particle. Such pulses are 
 given out when cathode rays in a discharge tube 
 impinge on a solid anticathode. They give rise to 
 the well-known phenomena of Rontgen or X-rays. 
 
 If instead of stopping the particle dead we cause 
 it to oscillate about a mean position, a series of un- 
 dulations will be set up in the Faraday tubes attached 
 to it, such, for example, as are seen when one end 
 of a long rope is shaken regularly to and fro. Thus 
 a series of electro-magnetic waves move out from the 
 M.P. 8 
 
H4 MOLECULAR PHYSICS 
 
 vibrating electron, their frequency being equal to 
 the number of vibrations made by the particle per 
 second. Their wave length is equal to the distance 
 travelled by the disturbance during the time of one 
 complete vibration. If this lies between -0004 and 
 0008 mm. these waves will produce on our eyes the 
 impression of light. This, in its crudest form, is 
 the Faraday-Maxwell electro-magnetic theory of 
 light. 
 
 Not only may light originate in the vibration 
 of electrons; all our experiments drive us to the 
 conclusion that such vibration is the only way in 
 which light can be produced. Uncharged matter 
 is apparently quite incapable of setting up any kind 
 of disturbance in the sether. It is the electric charge 
 which serves as the only link between the two. 
 
 We can, however, proceed further than this. 
 Modern research has enabled us to identify with 
 certainty the vibrating systems which emit the 
 myriad lines in the spectra of the elements with the 
 electrons, with the properties of which we are now 
 growing familiar. 
 
 Michael Faraday, with almost uncanny prescience, 
 seems to have felt that the relation between mag- 
 netism and light must be of the closest, and sought 
 for it with unremitting diligence. It is one of the 
 little ironies of life that the only effect which he 
 did discover (the magnetic rotation of the plane of 
 polarisation) was one of the very few phenomena 
 which the theory even now is hardly adequate to 
 explain. The effect he sought for was not discovered 
 until, more than thirty years later, his experiments 
 were repeated with stronger magnetic fields and far 
 more powerful methods of spectrum analysis by 
 Zeeman. 
 
 He found that if a source of light was placed 
 between the poles of a strong electro-magnet and the 
 light emitted was examined spec! rose opically, a 
 
THE ATOM IN VIBRATION 
 
 curious change took place in the appearance of the 
 different lines in the spectrum, each being split up or 
 decomposed into two components when the light 
 was viewed along the lines of force in the magnetic 
 field, or three when viewed at right angles to this 
 direction. 
 
 Let us consider briefly the effect of applying a 
 magnetic field to the charged particles emitting the 
 vibrations as they oscillate about their mean 
 positions. In general the path described by the 
 particle will be somewhat complicated. We can, 
 however, resolve its motion in the usual way into 
 
 Q 
 
 FIG. 25. ILLUSTRATING THE DECOMPOSITION OF A HARMONIC 
 MOTION INTO TWO CIRCULAR VIBRATIONS. 
 
 vibrations parallel to and at right angles to the lines 
 of force in the magnetic field. The vibrations 
 performed along the lines of the field will be unaltered 
 by the application of the field since the latter produces 
 no mechanical effect on a particle moving in its 
 own direction. 
 
 It will be quite different with those vibrations 
 which are executed in directions at right angles to 
 this. It is shown in works on mechanics that any 
 harmonic vibration can be regarded as the sum of 
 two circular motions of properly chosen amplitude 
 and phase. For example, the harmonic motion of a 
 particle A vibrating along the straight line BC 
 
 82 
 
n6 MOLECULAR PHYSICS 
 
 (Fig. 25) is exactly equivalent to the motions of two 
 equal particles P and Q describing the circles shown 
 in the diagram with equal velocities but in opposite 
 directions. 
 
 It will be sufficient, therefore, and will lead to 
 no loss of generality if we consider the charged 
 particles as describing circles at right angles to the 
 magnetic field, under the action of forces directed 
 towards the centres of the circles. Since the motion 
 of the charged particles is now everywhere at right 
 angles to the magnetic field there will be a mechanical 
 force acting on the particles which will be everywhere 
 at right angles to the magnetic field, and to the 
 direction of motion of the particles. A little 
 consideration will show that it must always act in 
 the line joining the position of the particle at any 
 moment to the centre of the circle. 
 
 Particles such as P and Q are, however, 
 describing their circles in opposite directions. Thus 
 the magnetic force will be in one case directed 
 towards, in the other away, from the centre of the 
 circle. In the first case the total force dragging the 
 particle towards the centre is increased ; the circle 
 is contracted and the time of vibration becomes 
 more rapid. In the latter the effective force is 
 diminished, with the result that the orbit expands 
 and the vibrations become slower. 
 
 An apple whirling round at the end of a string 
 will furnish a very useful analogy. If the tension 
 of the string is increased the apple is drawn in and 
 its revolutions become more rapid. If, on the other 
 hand, the tension is relaxed, the apple takes a 
 wider sweep, while the time it takes to complete a 
 single revolution becomes longer. 
 
 Thus, instead of all the particles describing their 
 orbits in exactly the same time and thus producing 
 light of one frequency only, one set have been 
 accelerated, the other retarded by the magnetic 
 
THE ATOM IN VIBRATION 
 
 117 
 
 field, so that instead of a single line the spectroscope 
 will reveal two, one on each side of the original 
 position of the line. By optical means we can 
 distinguish between clockwise and counter clockwise 
 rotations, and can thus determine which of the 
 two has been accelerated and which retarded by the 
 magnetic field. Since the effect on a positive 
 particle would be exactly the reverse of that on a 
 negative, we can thus determine the sign of the 
 
 FIG. 26. ILLUSTRATING THE ZEEMAN EFFECT. N, S ARE POLES 
 OF ELECTRO-MAGNET. A, B REPRESENT THE APPEARANCE 
 OF A SINGLE LINE EMITTED BY THE FLAME AS SEEN 
 THROUGH A SPECTROSCOPE PLACED IN THE TWO POSITIONS. 
 
 charge carried by the vibrating particle. In every 
 case so far examined it has been found to be 
 negative. 
 
 If we view the flame along the lines of force, 
 these two new lines are the only ones seen, as the 
 vibrations taking place in the line of sight produce 
 no effect on the eye. If, however, we look across 
 the field, the vibrations executed along the lines of 
 the field will also produce their effect in the spectro- 
 scope, and since their period is unaltered by the 
 field they will give a line in the position of the original 
 
n8 MOLECULAR PHYSICS 
 
 undecomposed line. Since all the circular paths 
 are being now viewed end on, all three lines will 
 appear to be plane polarised. These results are 
 shown diagrammatically in Fig. 26. 
 
 This in its simplest form is exactly the effect 
 discovered by Zeeman in 1896. He found that if 
 a source emitting a line spectrum were placed be- 
 tween the poles of a very powerful electro-magnet 
 
 FIG. 27. THE ZEEMAN EFFECT. (a) UNDECOMPOSED LINE. 
 (6) SAME LINE VIEWED ALONG THE LINES OF FORCE OF A 
 MAGNETIC FIELD, (c) LINE VIEWED AT RIGHT ANGLES 
 TO LINES OF FORCE. 
 
 and viewed with an interference spectrometer of 
 high resolving power the line was split up into three 
 components when viewed at right angles to the 
 magnetic field and into two when seen along the 
 lines through a hole in the pole piece. This is very 
 well shown in the photograph reproduced in Fig. 27. 
 When, at the suggestion of Lorentz,who at once saw 
 the correct explanation, the polarisation of the 
 
THE ATOM IN VIBRATION 119 
 
 different components was examined, it was found 
 to agree exactly with that described above. 
 
 -We have seen that these observations have shown 
 that the vibrating system is negatively charged. 
 We can, however, go further than this. Following 
 up the argument given above it can easily be shown* 
 that if \ a and A c are the wave lengths of the two 
 outer components into which a single line of wave 
 length A is split up 
 
 where e/m is the ratio of the mass to the charge for 
 the particles and V is the velocity of light. Now 
 Runge and Paschen found that for a certain series 
 
 of mercury lines, for example, the value of -^ - - 
 
 A o 
 
 was 2*14 for a magnetic field of 24,600 units, while 
 V is of course 3 x io 10 cms. per second. Substituting 
 these values in the equation we have 
 
 , 2-14 X 2 TT X 3 X io 10 
 e ' m ~- 24,600 - or r6 5 x Io7 " 
 
 Considering that the displacement produced by 
 even the strongest fields amounts generally to some- 
 where about one-fifth of the distance separating the 
 two D lines of sodium, it will be seen that this result 
 agrees even better than might have been expected 
 with the value of the same ratio 1-77 x io 7 deduced 
 for the negative electron from experiments on 
 cathode rays. The identity of the light-emitting 
 systems with the cathode ray particles must be 
 regarded as established beyond all challenge. 
 
 Many spectral lines show the Zeeman effect in 
 this simple form. Others, however, give more com- 
 plicated effects, some of the lines of Molybdenum, for 
 example, splitting up into seventeen and even 
 nineteen components. We have, in assuming that 
 
 * See Appendix C. 
 
120 MOLECULAR PHYSICS 
 
 the vibrating electron executed harmonic vibrations, 
 neglected the possibility of its motion being disturbed 
 by the forces due to neighbouring electrons in the 
 same atom. If these are not negligible complications 
 ensue, and the time of vibration is no longer indepen- 
 dent of the direction in which it takes place. The 
 matter has been discussed at length for certain 
 simple systems of electrons by Professor Sir J. J. 
 Thomson, and his paper may be found in the 
 Proceeding? of the Cambridge Philosophical Society, 
 Vol. 39, by any who are interested in pursuing the 
 matter more deeply. 
 
 The lines in the spectra of an element thus 
 represent the different modes of vibration of the 
 electrons connected with it. It might seem that 
 with a complete knowledge of these periods at our 
 disposal it should be possible to reconstruct the atom 
 with certainty. Theoretically, no doubt, this should 
 be so. The mathematical difficulties are, however, 
 appalling, and only in the case of a few very simple 
 systems is the analysis at all possible. Thus the 
 results to be looked for from spectroscopy are at 
 present qualitative rather than quantitative. 
 
 Even so, however, a study of spectra is most 
 luminously suggestive. A careful analysis of the 
 innumerable lines which are dotted apparently at 
 random through the spectra of the elements has 
 shown that they are by no means the confused 
 jumble of periods which at first sight they appear to 
 be. It has been found that in very many cases they 
 can be grouped into definite series, every line of 
 which can be obtained by substituting particular 
 whole numbers for a variable quantity " m" in a 
 general equation the form of which is the same for 
 all elements. 
 
 This was first pointed out by Balmer for the 
 hydrogen spectrum, but it was afterwards shown by 
 Rydberg that Balmer's equation was merely a 
 
THE ATOM IN VIBRATION 121 
 
 particular case of a very general law which could be 
 stated so as to apply to all the elements giving 
 series spectra. He showed that if n is the frequency 
 of the vibrations corresponding to a given line (the 
 frequency is the number of vibrations made per 
 second by the particle emitting the light) then the 
 frequency of all the lines in a given series can be 
 represented by the equation 
 
 _N_ 
 (m + /x) 2 
 
 the different lines composing the series being 
 obtained by putting m equal successively to the 
 whole numbers, 1,2,3,... Nisa constant so 
 universal in its character that it applies not merely 
 for all the series of a given element but for all the 
 series of all elements giving series spectra at all. 
 The constants n and /x differ for different elements 
 and are characteristic of the particular series. 
 
 That this method of classifying a spectrum is no 
 mere mathematical fiction is very clearly brought 
 out when the character of the lines making up a 
 single series is closely observed. It is found that 
 all the lines of a single series are exactly similar in 
 appearance. Thus all of them appear sharp and 
 distinct with definite clear-cut boundaries, or else 
 they are all indistinct and diffuse. The two types 
 of lines are never associated in the same series. 
 Again, any physical change which we bring about in 
 one of the lines of a series is reproduced simul- 
 taneously in all the others. Thus, all the lines 
 split up in the same way under the action of a 
 magnetic field. If one of the lines is broadened by 
 the application of pressure to the gas emitting the 
 spectrum, all the others are broadened to a similar 
 degree, and when the method of producing the 
 spectrum is altered, all the lines have their bright- 
 ness either enhanced or diminished at the same 
 
122 MOLECULAR PHYSICS 
 
 time. We can hardly avoid the conclusion that they 
 are all different modes of vibration of the same system. 
 
 An analogy may make this clearer. It is well 
 known that when an organ pipe is sounded it gives 
 out in addition to its fundamental note a series of 
 overtones, the fullness and richness of the organ 
 notes being due to the presence of these extra tones. 
 In such a simple system the overtones are always 
 harmonics, that is to say, their frequencies are 
 always exact multiples of the lowest mode of 
 vibration. In mathematical language we can say 
 that the different frequencies are obtainable by 
 substituting various whole numbers for the quantity 
 m in the equation, n = m . n . 
 
 In more complicated vibrators the relationship 
 becomes more complicated while at the same time 
 the importance of the overtones becomes even more 
 pronounced. In the case of a sounding bell the 
 relation between the different modes of vibration 
 is so complicated that it has not yet been completely 
 worked out. 
 
 This is not all, however. Not only do the 
 spectra of a single element show these close numerical 
 relationships. They are also found to exist 
 between the spectra of different elements belonging 
 to the same group of the periodic table. The 
 spectra of the different elements of the alkali metals, 
 for example, are so closely connected that it is 
 actually possible to calculate the whole spectrum 
 of, say, rubidium or caesium, from that of potassium, 
 and a knowledge of the relative atomic weights of 
 the three elements. The spectrum of caesium is 
 practically the same as that of potassium but is 
 shifted bodily towards the violet end of the spectrum. 
 We are thus driven to the conclusion that the 
 vibrating, systems in the two cases are identical in 
 form, and differ from each other only in being placed 
 in slightly different environments. 
 
THE ATOM IN VIBRATION 123 
 
 In terms of our model atom, if we regard the 
 series spectra as being given out by the inner rings 
 of electrons, these rings are identical for the three 
 elements, but in the case of the two latter the extra 
 outer rings added on to increase the atomic weight 
 produce some alteration in the external forces acting 
 on the rings and so cause a shift in the absolute 
 frequencies of the vibrations without altering the 
 relation between them. In the words of astro- 
 nomical theory, the outer electrons perturb the 
 vibrations of the inner ring without destroying 
 their character. Or, returning to our analogy of 
 the bell, it is the same bell which is sounding but in 
 a somewhat different medium. 
 
 One difficulty, a very formidable one, remains, 
 and may, perhaps, already have occurred to the 
 reader. The spectra of many of the elements is 
 exceedingly complicated, containing in some cases 
 many hundreds of well-defined lines. A contem- 
 plation of the iron spectrum wrung from the great 
 American spectroscopist Rowland the exclamation 
 that, compared with an atom of iron, a grand piano 
 must be a very simple affair indeed. 
 
 We have seen, however, in a former chapter that 1 
 the number of electrons in an atom is, on the whole, 
 not very large. In all probability the hydrogen 
 atom contains only one electron, and certainly not 
 more than three. A single electron has only three 
 degrees of freedom and therefore only three modes 
 of vibration, and in the simple atom these three 
 w r ould all have the same period and thus coalesce 
 into a single line. As a matter of fact, the ordinary 
 spectrum of hydrogen contains a fair number of 
 lines while what is known as its secondary spectrum 
 is very complicated. The difficulty seems at first 
 sight almost insuperable. 
 
 To solve the riddle, Professor Sir J. J. Thomson 
 has hazarded the bold but almost certainly correct 
 
124 MOLECULAR PHYSICS 
 
 conjecture that the lines in the spectrum of hydrogen 
 and, indeed, of many other elements are not emitted 
 by the atoms of the element at all but by systems 
 which only exist when the gas is thrown into a 
 luminous condition. When we consider the absolute 
 identity of the spectrum of an element whether 
 situated on the earth or away on the furthest star 
 of which we have spectroscopic data, this hypothesis 
 may seem to be the most startling we have yet 
 advanced., It is, however, not without a very 
 v -considerable experimental basis. 
 
 Consider for a moment the phenomena known as 
 selective absorption of light, of which the well-known 
 experiment of the reversal of the sodium lines is a 
 good example. If white light is passed through 
 sodium vapour enclosed in an iron tube and the 
 transmitted light examined with a spectroscope 
 there can be seen across the ordinary coloured 
 spectrum two sharp, dark lines, corresponding 
 exactly in position with the two bright lines, which 
 would be seen if the sodium were raised to incan- 
 descence. This is the cause of the dark Fraunhofer 
 lines which are to be seen crossing the spectrum of 
 the light from the sun. 
 
 These effects are due to a form of resonance. 
 The sodium atom contains systems of electrons 
 which, when suitably excited, give out light of the 
 frequency corresponding to the two sodium lines. 
 To use an analogy from sound or from wireless 
 telegraphy the sodium atom is tuned to this 
 frequency. It will therefore begin to vibrate 
 violently if oscillations of this period fall upon it. 
 In doing so it abstracts the energy of the radiation 
 in tune with itself, so that the latter is very rapidly 
 absorbed, while light of frequency remote from this 
 passes on almost unaffected. Thus, after passing 
 through a very small thickness of material the light 
 is robbed of all the constituents which have 
 
THE ATOM IN VIBRATION 
 
 125 
 
 frequencies corresponding to those of the radiating 
 systems within it. Conversely all the electronic 
 systems which have natural periods falling within 
 the limits of the visible spectrum must produce a 
 dark band when white light is passed through 
 them. 
 
 Now, it is remarkable that such absorption lines 
 are not seen when white light is passed through a 
 
 FIG. 28. LADENBURG'S EXPERIMENT. 
 
 A, discharge tube containing hydrogen at high pressure. B, dis- 
 charge tube containing hydrogen at low pressure. C, induc- 
 tion coil working both tubes. Sp, spectrometer for viewing 
 the light transmitted. The inset shows the appearance seen 
 in spectrometer when the tubes are working, aa, broadened 
 band due to hydrogen in A. bb, spectrum due to the tube 
 B alone. The dark line where the- two bands cross shows 
 the reversal of the line by the systems formed in B by the 
 discharge. 
 
 column of hydrogen, or indeed of most other simple 
 gases. There are, for example, no dark lines to be 
 seen in the spectrum when examined after passing 
 through a long tube of hydrogen gas, corresponding 
 to, say, the brilliant lines of the hydrogen spectrum 
 in the red or in the blue. Indeed, the laws of the 
 absorption and dispersion of light in hydrogen are so 
 simple that they can be explained on the assumption 
 
126 MOLECULAR PHYSICS 
 
 of a single absorption band far away beyond the 
 
 violet end of the spectrum. This is, of course, 
 
 what we should expect from the simple nature of 
 
 the hydrogen atom. There is thus no escape from 
 
 I the conclusion that the vibrating systems which 
 
 ; emit the hydrogen spectrum are not present in the 
 
 gas in its normal condition. 
 
 A very interesting experiment made not long 
 ago by Ladenburg has shown, however, that they 
 can be manufactured in the gas under suitable 
 conditions. He passed the light from a very bright 
 discharge in hydrogen at fairly high pressure through 
 a long tube of hydrogen at much lower pressure, 
 fitted with terminals for the passage of a discharge, 
 and examined the light transmitted with a spectro- 
 scope. His apparatus is indicated very di.agram- 
 matically in Fig. 28. The effect of the high pressure 
 on the discharge is to widen out all the lines in the 
 spectrum so that, instead of a narrow line a broad 
 band of light is seen overlapping the original line 
 on each side. When there was no discharge passing 
 through the long tube of hydrogen there was no trace 
 of any absorption of any part of this broadened band. 
 If, however, a feeble discharge was sent through 
 this long tube of gas it was seen that the centre portion 
 of the broad line corresponding to the original line 
 and hence having the period of the light emitted by 
 the tube at low pressure became distinctly less bright 
 than the outer portions, showing that the long 
 column of feebly glowing gas was now absorbing 
 from the light emitted by the brighter hydrogen 
 tube those wave lengths corresponding in period 
 to the light it was itself giving out. There are some 
 difficulties in the experiment, and a certain syn- 
 chronism of the two discharges seems to be necessary 
 for its success. On the whole, the conclusion seems 
 irresistible. The hydrogen line spectrum is emitted 
 by systems of electrons which are not present in the 
 
THE ATOM IN VIBRATION 127 
 
 gas in its normal condition, but which are formed 
 when the gas is thrown into a luminous state. 
 
 Let us consider for a moment the ways in which 
 an atom can be made to emit luminous vibrations. 
 Experiments have shown that for an atom to emit 
 its characteristic spectrum it is necessary that it 
 should be in a region of intense ionisation or 
 recombination. It seems that nothing short of 
 driving an electron into or out of the atom will 
 suffice to set in vibration the light emitting systems 
 of electrons. It is obvious that this condition is 
 fulfilled when the spectrum is excited electrically, 
 either by sparking between terminals of the 
 substance or by a low pressure discharge through a 
 gas. It is interesting in this connection to note in 
 the latter case that experiments have shown that, 
 in the dark portions of the discharge the ionisation 
 is very feeble, while it is most intense in the brightest 
 portions of the positive column. The ordinary 
 method of producing a spectrum by placing the 
 substance in a Bunsen flame is also merely a rough- 
 and-ready way of producing ionisation in the 
 substance, Professor H. A. Wilson having shown 
 that a Bunsen flame, especially if it contains salt 
 vapours, is the seat of very intense ionisation. 
 
 Consider an atom placed within this ionised 
 space. It meets the ionising agent and an electron 
 is ejected, leaving the atom with a positive charge. 
 The loss of this electron will alter the forces within 
 the atom and the remaining electrons will oscillate 
 about their new positions of equilibrium before 
 finally settling down. These vibrations, if of 
 suitable periods, will set up luminous radiations 
 and give rise to a set of lines in the spectrum. The 
 positively charged atom is now surrounded by a 
 cloud of negative electrons which fill the surrounding 
 space. It attracts them and, normally, one would 
 enter to take the place of the lost member. If 
 
128 MOLECULAR PHYSICS 
 
 however, the mutual kinetic energy of the two is 
 sufficient the electron will revolve round the attracting 
 atom without falling into it in exactly the same 
 way as the earth revolves around the sun. The 
 revolutions of this electron, being isochronous, will 
 give rise to a single line in the spectrum with a 
 period corresponding to the time taken by the 
 electron to describe the circle. 
 
 If the law of force between the atom and the 
 electron were the simple one of the inverse squares, 
 an orbit of any size would be possible under suitable 
 conditions. Taking into account the fact that the 
 electron is losing speed owing to the fact that it is 
 all the time radiating away its energy in the form 
 of light waves, it will be gradually drawn nearer and 
 nearer the atom so that its path would be a sort of 
 spiral ending up in collapse into the atom. Since 
 slightly different times would be occupied in 
 describing each part of the curve the spectrum thus 
 produced would be continuous. 
 
 The neighbourhood of the electrons within the 
 atom and their repulsion of the external one would 
 complicate the simple law of force, and in general 
 the attraction of the atom for its satellite would 
 depend not only on the distance but also on the 
 direction of the line joining the satellite to the atom. 
 The actual law of force would thus depend upon the 
 number and arrangement of the electrons within the 
 atom, just as much as if the electron were revolving 
 inside it. 
 
 Sir George Darwin, in his monumental work on 
 Periodic Orbits has shown that, if the single 
 system of a satellite revolving round its planet is 
 disturbed by the presence of a third body, the number 
 of orbits which the satellite may describe is no 
 longer infinite, but that there are certain regions 
 through which the particle must not pass if it is to 
 continue to revolve as a satellite around the planet. 
 
THE ATOM IN VIBRATION 129 
 
 In the simple case considered by Darwin this space 
 did not quite enclose the planet, but in more compli- 
 cated cases such as we have to deal with when we 
 come to a consideration of the atom, hg was of the ^ 
 opinion that it might very well take the form of 
 a series of closed rings surrounding the atom. 
 In this case there would be a series of separate rings 
 in which alone the electron could revolve, and 
 each of which it would describe in a definite time 
 peculiar to that ring. Each of these rings would 
 thus give rise to a separate line in the spectrum. 
 Since the atom would only attract one electron at 
 a time each atom would at one time be only 
 emitting one of these extra lines. 
 
 These systems would, of course, not be permanent, 
 as the electron would constantly be losing energy 
 by radiation. After a time its energy would fall 
 below that necessary to keep it in rotation in the 
 ring it was describing, and it would collapse through 
 ring after ring, until finally it was reabsorbed into 
 the atom. Fresh systems would, however, be 
 constantly being formed in the ionised gas, and the 
 supply would be kept up as long as the exciting 
 conditions were maintained. 
 
 The return of the lost electron into the atomic 
 fold would obviously stir up fresh vibrations among 
 the electrons already present. Since the atom is 
 now neutral and not positively charged as it was 
 when the electron left it these vibrations would not 
 have the same periods as those set up when the 
 electron was expelled. There is some evidence for 
 the suggestion that the vibrations corresponding to 
 the return of the electron form the band spectrum of 
 the element, while those set up on its expulsion, 
 together with those due to the special systems, make 
 up the different series of line spectra. 
 
 Very recently an ingenious Danish mathe- 
 matician, Dr. Bohr, has worked out mathematically 
 M.P. o 
 
130 MOLECULAR PHYSICS 
 
 a theory of spectra very much on the lines described 
 above, and has in this way obtained a formula for 
 the spectral series identical in form with the 
 empirical formula of Rydberg which we have already 
 discussed. He has from his theory deduced an 
 expression for the universal constant N of Rydberg's 
 equation in terms of the mass and charge on an 
 electron and other known physical quantities, which 
 gives a numerical value for that quantity within 
 about 5 %, of the value obtained from direct spectro- 
 scopic observations. His assumptions will require 
 further consideration before they can be unreservedly 
 adopted. They appear to involve the abandonment 
 not merely of Newtonian mechanics, but also of the 
 ordinary Faraday-Maxwell electro-magnetic theory. 
 The closeness of the agreement between the results 
 of 'the theory and of experiment is, however, at 
 least remarkable, and seems to show that, at any 
 -rate in its general outlines, the theory of the origin 
 of spectra which we have propounded above is a 
 step in the right direction. 
 
 We have, however, wandered far from the solid 
 certainties of the Zeeman effect and its consequences, 
 with which we commenced this chapter, into the 
 dark and mysterious hinterland where science is in 
 the making. In a few more years we may hope that 
 this will be transformed into plain and open ground. 
 At present we must pause here, lest we lose ourselves 
 altogether in a quagmire of fascinating but ground- 
 less speculations. 
 
CHAPTER VIII. 
 THE MOLECULAR THEORY OF MATTER. 
 
 WE have now surveyed very briefly what is 
 known and surmised of the nature and properties of 
 the atom and molecule. In the brief space of the 
 present chapter let us indicate one or two of the many 
 points of interest which arise when we come to con- 
 sider the molecule, not as standing by itself, but as 
 massed together in myriads to form a fragment of 
 what we know as matter. 
 
 In solids, we must regard the molecules as 
 fixed relatively to each other, and we have in an 
 earlier chapter considered briefly the nature of the 
 molecular forces, cohesion, adhesion, and the like, 
 which bring about this result. But though the 
 molecules are fixed, in the sense that they are not 
 free to move about in the solid, we cannot consider 
 them as being altogether motionless. Every body, 
 unless it is at the absolute zero of temperature (a 
 temperature which has not yet been reached in 
 any experiment, although the brilliant researches 
 of Kamerlingh Onnes have brought us within 4 
 of it), contains a certain definite amount of heat. 
 Now heat is merely energy in a molecular form. 
 The work which we do in raising the temperature 
 of a substance is in reality spent in increasing the 
 energy of the individual molecules of the substance, 
 and thus in every body which is not at the absolute 
 zero, the molecules must be in some sort of motion, 
 the rapidity of which increases as the temperature 
 is raised. 
 
 92 
 
132 MOLECULAR PHYSICS 
 
 The molecules of the solid are not free to move 
 from their positions, but two forms of motion are 
 possible to them. They may either spin round 
 like a top, or oscillate backwards and forwards 
 about their mean position, like the bob of a pen- 
 dulum, or like a heavy weight suspended by an 
 elastic cord. 
 
 In the case where the molecule is a system made 
 up of two or more atoms, both these kinds of motion 
 take place., The atoms spin round their common 
 centre at a rate which increases as the body gets 
 hotter, while at the same time the molecule as a 
 whole, oscillates backwards and forwards about its 
 mean position with ever-increasing amplitude. If, 
 however, the molecule consists of a single atom, 
 only the latter form of motion seems to be possible, 
 all the evidence going to show that thermal energy 
 is unable to set a single atom spinning about its 
 own centre. 
 
 For the sake of simplicity we will consider the 
 case of the non-atomic molecule, where the thermal 
 energy is all used in the second kind of motion. 
 As the body gets hotter and hotter, the molecule 
 moves faster and faster, and the swings which it takes 
 on each side of its normal position get larger and 
 larger. The molecular forces which keep it in 
 position, however, fall off very rapidly as the dis- 
 tance between the neighbouring molecules is 
 increased, while at the same time the force required 
 to retain the molecule in position increases with 
 every increase in velocity. Hence, sooner or later, 
 a point is reached when the molecular forces are 
 no longer able to retain the atoms in position. The 
 solid loses its cohesion and its rigidity. In other 
 words it melts. 
 
 It is obvious that melting sets in when the tem- 
 perature is just sufficient to give the molecules the 
 necessary minimum of velocity to overcome the 
 
MOLECULAR THEORY OF MATTER 133 
 
 molecular forces retaining them in position, that is 
 to say, it will be a constant for any definite substance. 
 Also as work must be done to break down these 
 inter-molecular bonds it is evident that energy 
 must be supplied to the body in the form of heat 
 to enable it to melt. This is the latent heat of 
 liquefaction. 
 
 Though the molecule has broken its old bonds, 
 it is still within the range of molecular attraction 
 of many of its neighbours, and has hardly escaped 
 from one cluster before it is attracted into another. 
 Its rate of progress is thus comparatively slow. 
 In time, however, any given group of molecules 
 will be found dispersed throughout the whole of 
 the liquid and thus diffusion is brought about. 
 
 Consider now the state of affairs at the surface 
 of the liquid. Every molecule as we know attracts 
 every other molecule which may happen to be 
 within a certain distance from it which we denote 
 as the sphere of molecular attraction. In the 
 body of the liquid, this attractive force is more or 
 less neutralised by the fact that the molecule we 
 are considering is surrounded on all sides by others, 
 all pulling in different directions. Hence the com- 
 bined effect is practically zero. At the surface, 
 however, all the molecules are below it, and there 
 are none above to neutralise the force which they 
 exert. There is thus a strong downward force 
 tending to drag the molecule into the surface. 
 This force makes itself manifest in the phenomenon 
 known as surface tension or capillarity. 
 
 A molecule will thus require a definite and in 
 most cases, a considerable velocity to succeed in 
 escaping from the surface of the liquid. Now the 
 mean velocity of the molecules depends only on 
 the temperature, and is fixed for any given sub- 
 stance when the temperature is known. The actual 
 velocity of any given molecule at a given instant 
 
134 MOLECULAR PHYSICS 
 
 may, however, differ very considerably from this 
 average speed. The molecules in the liquid are 
 constantly bumping against each other, and at 
 every collision one of the molecules will probably 
 gain speed, and the other lose it, and a difference 
 in velocity is thus set up. The law of the distribu- 
 tion of speeds among an infinite number of colliding 
 molecules has been worked out by Maxwell, for the 
 simpler case of a gas, and is known as Maxwell's 
 law. He showed that at any given instant the 
 great majority of the molecules would have velo- 
 cities not widely removed from the average, but 
 that there would always be a few which, owing to 
 special circumstances, would have velocities very 
 much greater, and others with velocities very much 
 less, than the normal value. 
 
 Thus for oxygen at C., in which the mean 
 velocity of the molecules is 425 metres per second, 
 out of every 1,000 molecules of the gas, about half 
 have velocities between 300 and 500 metres per 
 second, but there are 77 with a velocity greater 
 than 700 metres per second, and 30 with a velocity 
 greater than 900 metres per second. 
 
 The case of a liquid is much more complicated 
 than that of a gas, but there is no doubt that a 
 similar state of affairs prevails in the liquid state 
 also. Hence, even at temperatures far below the 
 boiling point of the liquid, there will be a few 
 molecules which have temporarily sufficient speed 
 to escape from the attraction of the mass of liquid 
 below them. 
 
 Thus even at low temperatures, a certain number 
 of molecules escape every second from the free 
 surface of the liquid. If the space above the 
 liquid is free there will thus be a constant evapora- 
 tion going on until all the liquid disappears into 
 vapour. 
 
 If, however, the liquid is contained in a closed 
 
MOLECULAR THEORY OF MATTER 135 
 
 vessel, the escaping molecules are unable to get 
 away altogether and after perhaps many reflections 
 at ^the enclosing walls will sooner or later strike 
 the surface of the liquid and be reabsorbed. The 
 number so returned to the liquid will depend on 
 the number of molecules present in the vapourous 
 state above the liquid. Evaporation will go on 
 until the number of molecules in unit volume of the 
 vapour is so great that the number returned per 
 second is exactly equal to the number which escape 
 per second owing to their high velocity. Thus for 
 every temperature there will be a corresponding 
 vapour pressure which will be constant for that 
 temperature and that pressure. If the temperature 
 is raised, the average speed of the molecules is 
 increased, and more of them will attain a velocity 
 sufficient to enable them to escape from the surface. 
 The vapour pressure thus rises. When the vapour 
 pressure reaches that of the atmosphere the liquid 
 will begin to boil, and if the supply of heat is main- 
 tained, will all pass into the state of a gas. 
 
 The difference between a liquid and a gas is 
 that in the latter all the molecules are moving 
 with sufficient speed to escape completely from the 
 attraction of their neighbours, and are thus able 
 to avoid those molecular aggregations which take 
 place in the liquid state. On this account the 
 behaviour of a molecule in a gas lends itself much 
 more readily to mathematical analysis than the 
 more complicated phenomena of the liquid and 
 solid states. The kinetic theory of gases has been 
 very completely worked out by Maxwell, Clausius, 
 and their successors. Unfortunately, even with the 
 simplifications thus introduced, the theory needs 
 considerable mathematical ability for its elucida- 
 tion, and does not lend itself at all readily to non- 
 mathematical treatment. 
 
 The pressure which a gas exerts on its boundaries 
 
136 MOLECULAR PHYSICS 
 
 is made up of the innumerable shocks given 
 to the bounding walls by the many impacts upon 
 them of the molecules of the gas, which are moving 
 as we have seen with considerable speeds. It will 
 obviously depend on the number of molecules 
 present per unit volume, and the speed with which 
 they are moving. The higher the temperature, the 
 faster the molecules move, and the greater, there- 
 fore, will be the pressure they exert. It can be 
 shown that this pressure is simply proportional to 
 the temperature, if we begin to measure the latter 
 not from the freezing point of water, but from the 
 absolute zero of temperature, that is, the tempera- 
 ture at which the molecules would all be reduced to 
 rest. This temperature is about 273 below the zero 
 on the Centigrade scale. 
 
 Again, if we halve the volume occupied by the 
 gas, we double the number of molecules present in 
 every cubic centimetre, and hence double the 
 pressure which they exert on the enclosing walls. 
 The pressure is thus inversely proportional to the 
 volume occupied by the gas and directly propor- 
 tional to its absolute temperature ; thus, if P is 
 the pressure, V the volume and T the temperature, 
 of a given mass of substance in the gaseous form, 
 P .V/T is a constant. This is the well-known gas 
 equation embodying the laws of Boyle and Charles. 
 
 These laws are obeyed approximately by all 
 gases, but perfectly by none. We have assumed 
 in calculating the formula that the molecules exert 
 no attraction upon each other in the gaseous state. 
 This is of course only approximately true. Hence 
 the velocity with which the molecules strike the 
 boundary is always a little smaller than the normal 
 velocity at that temperature, owing to the attraction 
 of the molecules behind it. This effect will obviously 
 be greater if the molecules are closely packed together 
 than if they occupy a large volume. It has been 
 
MOLECULAR THEORY OF MATTER 137 
 
 shown that to get the true pressure we must add 
 to the observed pressure an amount equal to #/V 2 , 
 where a is constant for a given gas. 
 
 Again the actual space in which the molecules 
 are free to move is less than the whole space of 
 the vessel, owing to the fact that the molecules 
 are not mere mathematical points, but have a 
 definite volume of their own. Thus if b is the 
 whole volume occupied by all the molecules in a gas, 
 the actual free space in which they are free to move 
 is not V the volume of the vessel, but V b. 
 
 To be accurate, therefore, we should write our 
 gas equation in the form 
 
 where R is a constant for the gas. 
 
 This equation was first given by Van der Waals, 
 and is found to represent the behaviour of real 
 gases with a considerable degree of accuracy. In 
 fact it is even capable of representing with some 
 degree of success the transition state from liquid to 
 gas. It has the further advantage that it offers 
 us a simple method for determining the one mole- 
 cular dimension with which we are still unacquainted, 
 namely, the radius of the molecule. 
 
 By accurate experiments on the behaviour of the 
 gas under varying conditions, we can determine the 
 value of the constant b in any given case. Since 
 one molecule cannot pass between two others if the 
 space between them is less than the diameter of a 
 molecule, the volume b occupied by the molecules 
 in the gas will be somewhat greater than the sum of 
 their individual volumes. If r is the radius of each 
 molecule, and N the total number of molecules 
 present in the gas, a number which we have already 
 determined it can be shown that 
 
138 
 
 MOLECULAR PHYSICS 
 
 assuming that the molecules are spheres. In com- 
 pound gases where there are several atoms in the 
 molecule this can hardly be the case, but in the case 
 of monatomic gases where the atom is also the 
 molecule, it seems a probable assumption. Hence 
 knowing N, we can calculate the value of r the radius 
 of the molecule of the gas we are considering. A 
 few of the values so obtained are given in Table IX. 
 It will be seen that they are of the order of io~ 8 or 
 one hundred millionth of a centimetre. The radius 
 of an electron is io~ 13 cms., or about one ten thou- 
 sandth part of this. The size of an electron thus 
 
 TABLE IX. 
 
 The Radius of the Molecule. 
 
 Substance. 
 
 From Van der Waals' 
 Equation. 
 
 From the Viscosity. 
 
 From the Thermal 
 Conductivity. 
 
 Hydrogen 
 
 i-i6x io *cm. 
 
 1*23 x io 8 cm. 
 
 i*2o^< io 8 cm. 
 
 Helium . 
 
 i'i5 
 
 1-09 
 
 
 
 Nitrogen . 
 
 1*76 
 
 J '75 
 
 1-66 
 
 Oxygen . 
 
 
 
 1*70 
 
 I *55 
 
 Argon 
 
 i'43 
 
 1-68 
 
 
 Carbon 
 
 
 
 
 dioxide . 
 
 1-70 
 
 2-09 ,; -- 
 
 2-16 
 
 bears to the size of the molecule in which it moves 
 very much the same relationship that the diameter 
 of our earth bears to the diameter of its orbit round 
 the sun. A molecule is therefore a system very 
 similar in its relative dimensions to the solar system 
 but on an infinitesimal scale. 
 
 The kinetic theory affords other methods of 
 estimating the dimensions of a molecule, but their 
 theory is too complicated to be attempted in the 
 space that remains. The results obtained are in- 
 cluded for the sake of comparison in Table IX. 
 The second column of figures gives the value of the 
 
MOLECULAR THEORY OF MATTER 139 
 
 radius deduced from considerations of the viscosity 
 of the gas ; the last column the value deduced 
 from its thermal conductivity. The three values 
 agree among themselves as well as could be expected. 
 
 Let us return now for a brief space to our solid 
 again. Solids may be divided into two classes, 
 according as they do or do not conduct electricity. 
 It is also found that conductors of electricity are 
 also good conductors of heat, while electrical insu- 
 lators are generally very poor conductors of heat. 
 We have by now come to connect electricity with 
 electrons, and hence an electric current is a flow of 
 electrons from a place of high to a place of low 
 potential. We may regard a conductor, then, 
 as a substance containing electrons which are free 
 to move under the action of an electric field, while 
 in non-conductors the electrons are fixed and unable 
 to follow the impulse of the field. 
 
 How are these electrons set free ? In the first 
 place it may be noticed that the only good con- 
 ductors of electricity are metallic, that is to say, 
 electro-positive in character, substances which we 
 know from other phenomena readily part with an 
 electron under the slightest provocation. Now in 
 a solid such provocation may well be supplied by 
 the close propinquity of the neighbouring mole- 
 cules. It is well known that a charged body will 
 attract light uncharged substances. The attraction 
 of a well-rubbed stick of sealing wax for small 
 pieces of paper is generally our first introduction 
 to the science of electricity. The attraction is of 
 course mutual, the force on the charged body being 
 equal to that on the uncharged paper. Hence an 
 electron in one atom is attracted by a neighbouring 
 uncharged atom, and under favourable circumstances, 
 and especially in the case of an atom only too ready 
 to part with its electrons, the attraction may well 
 be sufficient to enable it to make its escape; 
 
140 MOLECULAR PHYSICS 
 
 That some such assistance is necessary and is 
 so given, is shown by the fact that a metallic vapour 
 is no better a conductor than any other gas at the 
 same temperature. Thus while metallic mercury 
 at its boiling point is an excellent conductor of 
 electricity, the mercury vapour above it conducts 
 little better than the air it displaces, that is prac- 
 tically not at all. 
 
 The evolution of electrons by the molecules of 
 a metal is very similar to the evaporation of a liquid 
 into a closed space a phenomenon we have already 
 described. It will go on until the number of 
 electrons which are attracted by the positively 
 charged residues and so recombine, is equal to the 
 number of. electrons which are given off by the 
 neutral molecules in the same time. Thus for a 
 given temperature there will be a definite pressure 
 of electrons per unit volume in the metal, and we 
 may in fact look upon the electrons as a kind of 
 tenuous gas filling up the interspaces between the 
 molecules of the solid. We must regard them as 
 moving about in all directions in the solid with 
 considerable velocities. The principles of thermo- 
 dynamics would lead us to imagine that when 
 equilibrium is established each of these electrons 
 will have the same average energy as the molecules 
 around it, that is to say, the energy corresponding 
 to the temperature of the body at the time. This 
 is an important point to which we shall return later. 
 
 These electrons, if no electric force be acting, 
 will be moving in all directions, so that if we take 
 any cross section of the metal the number of elec- 
 trons crossing it in one direction will be the same as 
 the number crossing in the opposite direction, and 
 so the total transference of electricity across the 
 section will be zero. 
 
 If, however, we apply an electric field to the body 
 there will be a force on each electron urging it in 
 
MOLECULAR THEORY OF MATTER 141 
 
 the direction of the field. Thus in addition to the 
 irregular motion due to the heat energy of the body, 
 there will be a steady drift of the electrons as a 
 whole in the direction of the electric force. 
 
 Let us consider for the sake of simplicity, a 
 regular conductor such as a uniform wire. Let us 
 apply an electric field X, to the wire along its length. 
 Then the force on every electron is equal to X0, 
 where e is the charge on an electron, and it can be 
 shown that the average velocity of the electron 
 due to the electric field is K.X0, where K is some 
 constant which for the moment we will leave 
 undetermined. 
 
 In one second all the electrons which are less 
 than v cms. from a given cross section of the con- 
 ductor will be forced across it under the action of 
 the field. The volume of this space is vA. if A is 
 the area of cross section, and thus if there are N 
 electrons per unit volume, each carrying a charge e 
 the total charge passing through the given cross 
 section will be N<?.vA units per second. But this 
 is by definition the current along the conductor. 
 Hence remembering that the velocity v is K.X0 we 
 have the current i is equal to K.# 2 N.A.X. 
 
 If d is the length of the wire and E the difference 
 of potential between its ends, the field X in the 
 wire is. equal to E/d. Hence finally 
 
 i = (K. 2 N)^. E. 
 ct 
 
 The current through a given conductor is thus 
 directly proportional to the difference of potential 
 between its ends which is the well known law of 
 Ohm. We see that it is also proportional to the 
 cross section of the conductor, and inversely pro- 
 portional to its length. We may thus write it 
 
 where a- is written for the quantity in the bracket. 
 
142 MOLECULAR PHYSICS 
 
 This is a well-known expression for the current 
 through a wire. The quantity o- which is a con- 
 stant for a given substance at a given temperature, 
 is known as its specific electrical conductivity. Com- 
 paring the equations we see that the conductivity a 
 is equal to K.e^N. 
 
 Now the constant K can be evaluated on certain 
 probable assumptions and has been shown to be 
 equal to V A/6 RT, where V is the velocity of the 
 turbulent motion of the electrons, A is the average 
 distance traversed by the electron between one 
 collision with a molecule and the next, R is the 
 well known constant from the gas equation, and T 
 is the temperature of the conductor on the absolute 
 scale. Hence finally the electrical conductivity of 
 a substance is given by the expression 
 
 N e* A V 
 6.R.T. 
 
 This relation contains several quantities which 
 are at present unknown to us, and so we cannot 
 put it directly to the test. Let us proceed, however, 
 a little further. 
 
 Suppose now that instead of applying an electric 
 field to the metal, we begin to heat one end of it. 
 We have seen that the turbulent velocity of the 
 electrons depends only on the temperature, and 
 hence the electrons in contact with the heated area 
 will begin to move with a greater speed than those 
 in the colder parts of the substance. These elec- 
 trons are moving in all directions, and so in course 
 of time, some will move away into the colder 
 regions, carrying their increased velocity with them. 
 Their places near the hot end will of course be 
 taken by electrons from the colder parts which in 
 turn will have their motion accelerated by contact 
 with the hot face. 
 
 Thus there will be a constant stream of quickly 
 
MOLECULAR THEORY OF MATTER 143 
 
 moving electrons from the hot end into the cold 
 parts of the body, sharing their energy with, and 
 thus increasing the velocity of, the molecules 
 there. But the temperature at any point in the 
 body depends only on the speed with which the 
 particles are moving. Thus to translate the pro- 
 cess from molecular to molar physics, heat has been 
 conducted from the hot to the cold parts of the body, 
 and the rate at which this process takes place 
 measures what is called the thermal conductivity 
 of the substance. 
 
 Since then the free electrons play the principal 
 role both in the conduction of electricity, and the 
 conduction of heat we should expect to find some 
 sort of relation between the conductivity of a sub- 
 stance for heat and its conductivity for electricity. 
 
 It has long been known that good conductors 
 of the one are also good conductors of the other, 
 and as long ago as the middle of last century, 
 Wiedemann and Franz, by comparing the experi- 
 mental results for a number of metals, discovered 
 that the ratio of the thermal to the electrical 
 conductivity had the same value for all metallic 
 substances. Somewhat later Lorenz, by making 
 the comparison at different temperatures, found 
 that the magnitude of this ratio was simply propor- 
 tional to the temperature at which the comparison 
 was made, reckoned from the absolute zero of tem- 
 perature. These results are well brought out in 
 Table X. The second column gives the ratio of 
 the thermal to the electrical conductivities at 
 18 C. for the metals given in the first column of the 
 table. The last column gives the observed tem- 
 perature coefficient of the ratio. If Lorenz' law is 
 true, this coefficient should have the value '00366. 
 
 For many years this empirical law of Wiedemann 
 and Franz remained without explanation. The 
 electron theory of conduction would, however, as 
 
144 
 
 MOLECULAR PHYSICS 
 
 we have seen, lead us to expect with confidence 
 some such relationship. We can, however, go further 
 than this. We have already seen how to calculate 
 the electrical conductivity of a metal. Its thermal 
 conductivity can also be calculated if we assume 
 that the heat is all carried by electrons. This 
 assumption cannot be strictly true, bscause sub- 
 stances which are non-conductors of electricity 
 still conduct heat to a small but finite degree. In 
 this case the transference of heat is carried on by the 
 molecules themselves, the heated molecules trans- 
 
 TABLE X. 
 
 
 Ratio of Thermal 
 
 Temperature 
 
 Metal. 
 
 to Electrical 
 
 Coefficient of the 
 
 
 Conductivity. 
 
 Ratio. 
 
 Copper . 
 
 
 
 6'7I X IO 10 
 
 0039 
 
 Silver . 
 
 
 
 6-86 X io 10 
 
 0037 
 
 Gold . 
 
 .. 
 
 
 7-09 x io 10 
 
 0037 
 
 Nickel . 
 
 ' . ": 
 
 
 6*99 X io 10 
 
 0039 
 
 Zinc 
 
 
 
 6-72 X io 10 
 
 OO^S 
 
 Cadmium 
 
 
 
 7'o6 X io 10 
 
 0037 
 
 Lead . 
 
 
 
 7*15 X io 10 
 
 0040 
 
 Tin 
 
 
 
 7-35 X io 10 
 
 0034 
 
 Platinum 
 
 
 
 7*53 X io 10 
 
 0046 
 
 
 i 
 
 ferring their increased velocity to their immediate 
 neighbours by the somewhat tedious process of 
 repeatedly bumping against them. This method 
 is necessarily slow compared to that of the freely 
 moving electrons, and the very small thermal con- 
 ductivities possessed by electrical insulators leads 
 us confidently to suppose that the amount of heat 
 transmitted in this way in a metallic conductor is 
 very small, compared with that carried by the 
 electrons. 
 
 The free electrons in a metal behave, as we have 
 seen, like a rarefied gas. We can therefore apply 
 
MOLECULAR THEORY OF MATTER 145 
 
 the results obtained for gases to them. The thermal 
 conductivity of a gas has been worked out by Max- 
 well and others. The mathematical analysis of the 
 problem would lead us too far. It is contained in 
 all treatises on the dynamical theory of gases. It 
 is found that the thermal conductivity of a gas is 
 represented by 
 
 |N A V.R 
 
 where N, A, V, and R have the same meaning as in 
 the equation for electrical conductivity. 
 
 Hence comparing the two equations we have 
 
 Thermal conductivity . i /AJ\ vi^ 
 Electrical conductivity ~ 6 R.T 
 
 This is a very simple relation indeed. All the 
 quantities with which we are unfamiliar have gone 
 out, leaving only R the constant of the gas equation, 
 e the ubiquitous electronic charge, and T the tem- 
 perature on the absolute scale at which our com- 
 parison is made. Let us substitute for these symbols 
 their numerical values, and so bring our theory to 
 a critical numerical test. R in absolute units is 
 equal to 1*40 X io~ 16 , while e in electro-magnetic 
 units is 1-57 X io~ 20 . If the comparison is made 
 at 18 C., as in Table X., T is (18 + 273) or 291 
 on the absolute scale. 
 
 Hence, the ratio of the two conductivities should 
 be equal to 
 
 3 X ^ >< ~Z X 2 9 I, 
 
 (1-57 x lo- 20 ) 2 
 
 or 6-95 X io 10 . 
 
 The agreement with the experimental values 
 given in Table X. is satisfactory beyond the bounds 
 of expectation. Since R and e are both independent 
 M.P. io 
 
146 MOLECULAR PHYSICS 
 
 of the temperature it is evident from our equation, 
 that the ratio varies directly as the absolute tempera- 
 ture as was discovered experimentally by Lorenz. 
 
 The electron theory of conduction has many 
 other triumphs and at present also not a few unsolved 
 difficulties, which would need a treatise rather than 
 a chapter to expound. Let us, therefore, leave the 
 subject here, and take a final and farewell glance at 
 our atom, this time in the throes of dissolution. 
 
CHAPTER IX. 
 
 THE ATOM IN DISSOLUTION. 
 
 IF the ideas which have been developed in the 
 preceding chapters have any sort of foundation in 
 fact, the title of the present chapter will hardly 
 come as a shock to any reader. It may seem at 
 first sight much more surprising that a system s"o 
 complex as the one we have described, and in such 
 constant motion, when subjected to all the shocks 
 mechanical, chemical, and electrical, which an 
 atom must undergo, should continue to exist in such 
 a persistent and unchangeable way as is actually 
 found to be the case. 
 
 The cause is probably to be found in the rela- 
 tively enormous amount of energy associated with 
 an atom, an amount which is quite out of proportion 
 to the energy liberated by chemical reactions. It 
 has been shown that the heat liberated by the 
 transformation of one gram of radium into its 
 final product is about 4 X io 9 gram calories. Com- 
 pared with this enormous quantity the heat liberated 
 in the most energetic of chemical reactions fades 
 into insignificance. The formation of a gram of 
 water for example, is attended by the emission of 
 about 4 x io 3 gram calories. And yet this enor- 
 mous quantity must only be a small fraction of 
 the total energy in the radium atom. Radium, 
 as we shall see, has an atomic weight of 225 ; the 
 final product of its decomposition one of about 206. 
 This atom, whatever it may be (modern speculation 
 
 IO 2 
 
148 MOLECULAR PHYSICS 
 
 points to lead, but the proof is far from complete) 
 is stable and must possess a very large amount of 
 energy of its own. The total energy in an atom 
 must therefore be enormous, and it is for this reason 
 that all efforts to transmute one element into 
 another have failed. 
 
 Great as this energy is, however, our theory 
 indicates that there is a steady and continuous 
 drain upon it which sooner or later must bring 
 about instability, and the dissolution of the system. 
 We saw in the last chapter that an electron in motion 
 round a circle is a source of radiation. The rate of 
 radiation depends on several factors. A single 
 electron moving in a circle is a very efficient radiator, 
 and would quickly drain any atom of its enormous 
 supply. It can be shown, however, that if several 
 electrons are moving round the same circle the 
 amount of radiation is very considerably reduced, 
 so that for a continuous ring of electrons the effect 
 would be very small indeed. Small or great, 
 however, it is a constant source of loss which in 
 the course of ages must, in the absence of some 
 counteracting force with which we are at present 
 unacquainted, bring about the downfall of the 
 atom. 
 
 It is doubtful how far this deduction and the 
 theory on which it is based would have found any 
 acceptance had it not been for the discovery, almost 
 simultaneously with the rise of the electron theory, 
 of a series of phenomena which found in it their 
 only possible explanation. 
 
 The main outlines of the new science of radio- 
 activity are perhaps familiar to all readers. The 
 subject is one of profound interest, but it lies almost 
 wholly outside the scope of such a work as this. 
 We will, however, summarise such of the main facts 
 of that science as bear on our immediate subject, 
 leaving the proof of the various statements and the 
 
THE ATOM IN DISSOLUTION 149 
 
 description of the often very beautiful experiments 
 from which they were deduced to other hands. 
 
 The metal uranium and its compounds were 
 found by Becquerel to give off continuously par- 
 ticles capable of affecting a photographic plate at 
 a considerable distance. These are the /3-rays 
 which, as was mentioned in an earlier chapter, are 
 identical except in speed with the cathode rays. 
 
 If the uranium salt is subjected to certain 
 chemical processes it is possible to separate the 
 uranium compound into tw r o fractions. In one 
 fraction, an almost imperceptible part of the whole, 
 all the power of emitting /3-rays is concentrated. 
 The other, containing practically all the original 
 salt, is completely inactive. For example, if we 
 follow Sir William Crookes and shake up crystals of 
 uranium nitrate in ether, the water of crystalliza- 
 tion, which settles out beneath the ethereal solution 
 and can be separated from it by a separating funnel, 
 is found to contain by far the greater part of the 
 /3-ray activity of the whole, the great mass of the 
 salt now dissolved in the ether being comparatively 
 inactive. 
 
 Let us take these two solutions and keep them 
 under observation for some time. It will be noticed 
 that the watery solution is gradually losing its 
 /3-ray producing powers, the rate of emission of 
 these rays falling in fact to half its original value in 
 about twenty-five days. At the same time the ethereal 
 solution which we had rendered inactive, gradually 
 begins to radiate again, so that at the end of twenty- 
 five days it has recovered one-half of its original 
 activity. Fig. 29 shows in a graphic way the exact 
 correlation between the loss of radio-activity by the 
 active fraction and the growth of activity in the in- 
 active mass. It will be seen that the total activity is 
 constant throughout the experiment. From these 
 results we may draw the following conclusions. 
 
150 
 
 MOLECULAR PHYSICS 
 
 In the first place, the property of ejecting these 
 electrons with enormous speeds resides not in the 
 uranium itself, but in some substance which is mixed 
 with it but which can be separated from it by 
 suitable chemical processes. Secondly, this sub- 
 stance is not a stable substance but loses its 'activity 
 
 FIG. 29. Growth and decay of $-ray activity with time for 
 uranium and uranium X. 
 
 with time. Lastly, this substance is not of the 
 nature of an impurity in the uranium, but is so 
 vitally bound up with it that when the latter is 
 completely freed from its presence it can reproduce 
 this strange substance again at a steady and per- 
 fectly definite rate. The conclusion seems irresistible. 
 
THE ATOM IN DISSOLUTION 151 
 
 Some new substance is being produced out of 
 uranium itself, and in turn is decomposing with 
 considerable celerity into some other substance 
 which for the moment we are unable to pursue. 
 
 I have discussed the case of uranium because 
 that metal is a recognised element belonging to a 
 well-known and respectable family, and might have 
 been expected to behave in a rational and orthodox 
 manner. The case of radium (which is actually a 
 decomposition product of uranium) is still more 
 striking. Rutherford discovered that radium and 
 its salts are constantly giving off a heavy, chemically 
 inert gas known as the "emanation," a non-committal 
 name bestowed upon it before its nature had baen 
 determined. This emanation collects in the radium, 
 but can be extracted from it by heating under 
 reduced pressure or better still, by dissolving the 
 salt in water and boiling the solution. In either 
 way the radium can be completely freed from this 
 new gas. On allowing the gas and the radium to 
 stand, however, it is found that fresh emanation 
 makes its appearance in the radium, while the 
 collected emanation gradually disappears, the rela- 
 tion between the growth and decay of the emanation 
 being precisely similar to that of uranium and its 
 /3-ray producing product. It is impossible to escape 
 the conclusion that the element radium is evolving 
 out of its own substance the heavy gas known as 
 the emanation. 
 
 The properties of both radium and its emanation 
 are now quite well known. Radium is a metal of 
 the calcium group, with an atomic weight of 226*5. 
 It has been prepared in a metallic state, and its 
 properties are found to agree with the place we have 
 assigned to it in the periodic table. The emanation 
 on the other hand is, as we have said, a chemically 
 inert gas resembling the members of the helium 
 group. It can be liquefied at 150 C. Sir William 
 
152 
 
 MOLECULAR PHYSICS 
 
 Ramsay has even succeeded in determining its 
 density, an achievement which as a triumph of skill 
 and refinement of experimental method is beyond 
 all praise. The difficulties of the work will be 
 realised when it is mentioned that the total volume 
 
 TABLE XI. 
 
 Element. Average Life. 
 
 Rays emitted. 
 
 Uranium 
 
 1 
 Uranium X 
 
 1 
 
 238-5 
 (230*5) 
 
 6 x io 9 years 
 24*6 days 
 
 a, a 
 
 P. y 
 
 Ionium 
 
 i 
 
 Radium 
 
 i 
 
 230*5 
 226*5 
 
 200,000 years 
 2,000 years 
 
 a 
 a 
 
 Emanation 
 
 1 
 Radium A 
 
 i 
 
 223 
 
 (222-5) 
 (218-5) 
 
 3*85 days 
 3 minutes 
 
 a 
 a 
 
 Radium B 
 
 i 
 
 (214*5) 
 
 26*8 minutes 
 
 none 
 
 Radium C 
 
 (214*5) 
 
 19-5 minutes 
 
 , ft 7 
 
 i 
 
 Radium D 
 
 i 
 
 (210-5) 
 
 40 years 
 
 none 
 
 Radium E 
 
 i 
 
 (210-5) 
 
 4*8 days 
 
 
 
 Polonium 
 
 ! 
 
 (210-5) 
 
 140 days 
 
 a 
 
 ?' 
 
 (206-5) 
 
 ' 
 
 
 
 of emanation available for the determination was 
 less than one-tenth of a cubic millimetre. 
 
 The molecular weight of the emanation deduced 
 from this determination is 223. Assuming the 
 gas to be monatomic like the gases it most resembles, 
 this is also its atomic weight. 
 
 What happens to that fragment of the radium 
 
THE ATOM IN DISSOLUTION 153 
 
 atom which represents the difference between 
 226*5, the atomic weight of radium, and 223, that of 
 its emanation ? The answer is not far to seek. It 
 will be remembered that radium is constantly 
 giving off what are known as a-rays which, as we 
 saw in an earlier chapter, have been proved to be 
 helium atoms with a high velocity and an electric 
 charge. The atomic weight of helium is 4-0. 
 Within the limits of experimental error this is the 
 difference between the weight of an atom of radium 
 and that of the emanation. 
 
 The break up of the radium atom therefore 
 takes place as follows. Its energy content becomes 
 too small for its mass and a small fragment of it 
 which we must regard as having been whirling round 
 in the atom with a great velocity, is projected like 
 a stone from a sling, or rather, like one of the 
 fragments of a bursting flywheel. This fragment 
 is always an atom of helium why, we do not know. 
 The residue of the atom, its atomic weight now 
 reduced by four, forms a new substance, which in 
 this case happens to be gaseous. 
 
 The emanation itself is very far from being 
 stable. It is half decomposed in a little less than 
 four days, the new decomposition product being 
 in this case a solid. We cannot follow here the 
 changes undergone by the atom in its attempts to 
 reach a stable state. They are, however, sum- 
 marised in Table XL, which gives at a glance the 
 whole of the interesting but pitiful story from the 
 break up of the original uranium atom to that of 
 polonium, the last member of the chain to be 
 definitely identified. 
 
 The first column gives the name of the element, 
 and its probable atomic weight. Those enclosed 
 in brackets have not been actually determined, but 
 are deduced on the assumption that each emission 
 of an a-particle involves a loss of atomic weight of 
 
154 MOLECULAR PHYSICS 
 
 four units. The second column gives the time taken 
 for the element to lose one-half of its mass, or in 
 other words for one-half of its atoms to decompose. 
 It may be called the average life of the atoms of 
 the element. The third column indicates the nature 
 of the rays emitted by the substance on its decom- 
 position. 
 
 Polonium itself is radio-active, but its decompo- 
 sition product has not yet been identified. The 
 worn out atom has probably found peace at last, 
 and hence no longer emits those radiations which 
 in most cases afford our only means of following 
 its changes. It will be seen from the table that 
 five a-particles are given out in the passage from 
 radium to this final product. If each of these is a 
 helium atom the atomic weight of the final element 
 should be 226-5 (5 x 4) or 206-5. This is very 
 approximately the atomic weight of lead, and it 
 has been conjectured with some degree of proba- 
 bility that lead is the final stable product of this 
 great series of changes. At present, however, the 
 evidence can hardly be said to amount to a proof. 
 
 Most of these radio-active changes, as they are 
 called, result in the expulsion of an a-particle, and 
 consequent change in atomic weight. Others, 
 however, for example, that of Uranium X, the decom- 
 position product of uranium with which we com- 
 menced our survey of the subject, give off only 
 /3-particles, and hence differ inappreciably in atomic 
 weight from their immediate successor. The 7-rays 
 which always accompany /3-radiation are merely 
 electro -magnetic pulses due to the sudden ejection 
 of the negatively charged particles, and do not 
 concern us here. In some cases, there is apparently 
 no emission of any kind of radiation by the atom, 
 the change in this case consisting of a mere re- 
 arrangement of the electrons within the atom itself. 
 
 So far we have been treading on safe ground. 
 
THE ATOM IN DISSOLUTION 155 
 
 There can be no doubt that the scheme we have 
 outlined so briefly above represents the true relation 
 between the various radio-active substances. The 
 disintegration theory which is due to the genius of 
 Professor Rutherford, as much of the work embodied 
 in the table is due to his experimental skill and 
 energy, is the only theory which can in any x way 
 explain this novel series of facts. It is now univer- 
 sally accepted. It is when we come to consider the 
 mechanism of the change that difficulties arise. 
 
 Of actual knowledge we can hardly be said to 
 have any, but something may be conjectured. We 
 saw that the rings of electrons of which we built up 
 the atom were in many cases only stable if they 
 were revolving round the atom with a velocity 
 exceeding a certain critical value. Owing to radia- 
 tion from the system the velocity of the electrons 
 must be gradually but constantly decreasing, and 
 a time must come when it will be insufficient to 
 ensure stability. 
 
 It seems probable that when this stage is reached 
 one of the electrons leaves the ring and commences 
 an orbit on its own account. The radiation from a 
 single electron, is however, very much greater than 
 from a number of electrons moving in the same 
 orbit, and the loss of energy from the atom is 
 greatly increased. This brings about a state of 
 instability which results in the expulsion of an 
 a-particle or helium atom, though why the expulsion 
 should always take this form is a question we are 
 far from having solved. In some cases the breaking 
 off of this positive portion enables the atomic forces 
 to expel the disturbing /3-particle, in which case 
 there is at any rate a temporary lull in the pro- 
 ceedings. In other cases, as in that which follows 
 the break up of the radium atom, four helium atoms 
 are ejected in quick succession, one of the stages 
 lasting only three minutes, until finally radium C 
 
156 MOLECULAR PHYSICS 
 
 expels the disturbing electron, and the succeeding 
 element radium D enjoys an average life of forty 
 years. 
 
 Whether this account is correct or no, there is 
 distinct evidence that it is the /3-particle which is 
 the disturber of the atomic peace for in every case 
 the expulsion of a /3-particle seems to bring about 
 an increase in the stability of the system, the suc- 
 ceeding change having a much longer half period 
 than the changes immediately preceding it. 
 
 The subject is one full of difficulties, but where so 
 much has been done we may well expect still more. 
 We are marching with a triumphant army, and are 
 not inclined to set any bounds on the extent of our 
 possible conquests in the future. 
 
 In addition to the radium-uranium series, two 
 other elements, thorium and actinium are strongly 
 radio-active, giving rise to series of decomposition 
 products, similar to the chain we have already 
 considered. The question now arises, are all the 
 elements suffering from this slow decay, or are these 
 few heavy elements alone in their spontaneous 
 decomposition ? 
 
 Extensive researches have been made to answ r er 
 this question, but the results are perhaps not quite 
 as definite as might be desired. Potassium has been 
 found to give off appreciable quantities of /3- 
 radiation, its activity in this respect being about i% 
 of that of uranium. Its radio-activity, if such it 
 is, seems to be of a peculiar kind, as in spite of very 
 prolonged and drastic experiments, both by Camp- 
 bell who discovered the phenomenon, and by others, 
 it has not been found possible to separate from the 
 potassium any substance bearing the same relation 
 to the potassium as Uranium X bears to uranium. 
 Rubidium and possibly caesium show similar effects. 
 
 With all other elements the effect, if it exists, 
 is very small. There is, however, considerable 
 
THE ATOM IN DISSOLUTION 157 
 
 evidence for the radio-activity of all kinds of matter, 
 although it hardly amounts to a formal proof. 
 
 If we examine a quantity of air enclosed in a 
 metal vessel we find that, even in the absence of 
 any specific ionizing agent a certain number of 
 ions are always being formed in the air, which 
 enable us to send a small but measurable current 
 through the air. It has been shown that a great 
 part of this ionization is due to radium which 
 disseminated through the atmosphere as emanation, 
 or present in solid form in the soil, seems to be quite 
 ubiquitous. It is found, however, that the amount 
 of this ionization depends on the substance of which 
 the walls of the vessel are made, it is for example, 
 greater in a lead than in a copper vessel. This 
 would certainly seem to point to the emission from 
 the walls themselves of an ionising radiation of 
 some sort, which is greater in amount for lead than 
 for copper. 
 
 The matter is complicated by the fact that a 
 certain amount of secondary radiation is set up 
 when radium rays impinge on various metals, and 
 these might very well depend for their intensity on 
 the nature of the metal used. Dr. N. R. Campbell 
 who has made this subject his own, decides against 
 this explanation. I cannot do better than quote 
 his deliberate conclusions. 
 
 " It has been proved beyond doubt that the 
 emission of ionizing radiation is an inherent pro- 
 perty of all the metals investigated. It is not of 
 course necessary that this ray emission should be 
 identified at once with radio-activity if that word 
 is taken to mean a process of ray emission accom- 
 panied by atomic decomposition. But the constant 
 intensity of the rays, and the probability that the 
 larger portion of them are a-rays, afford considerable 
 support for that hypothesis ; while I know of no 
 other process which affords any analogy/' 
 
158 MOLECULAR PHYSICS 
 
 The process is not proceeding at such a rate as 
 to give cause for legitimate alarm. As we have 
 seen, the aveiage life of a uranium atom is about 
 six thousand million years ; from a comparison of 
 the relative intensities of the radiation from uranium 
 and from ordinary materials we may conclude that 
 the average existence of the latter cannot be less 
 than ten thousand times longer still. If, however, 
 we accept Dr. Campbell's conclusion that all sub- 
 stances are emitting a-particles then, whether 
 quickly or slowly, all matter is in the process of 
 gradual dissolution into helium, and perhaps 
 hydrogen. 
 
 It is curious that in this case the conclusions to 
 be drawn from a sister science, that of astronomical 
 physics, diametrically contradict those which we 
 have arrived at from a consideration of radio- 
 activity. It is a well-known fact that the very 
 hottest and therefore presumably the newest stars, 
 when examined by the spectroscope are seen to 
 consist of very little else than hydrogen, helium, 
 and two other elements, the spectra of which have 
 not yet been identified on the earth. Coming to 
 some of the slightly cooler stars fresh elements all 
 of low atomic weight gradually make their appear- 
 ance, the list increasing, and elements of higher 
 and higher atomic weight coming into existence 
 as cooler and cooler stars are examined. As we 
 have no reason whatever to suppose that the uni- 
 verse was anything save homogenous in the begin- 
 ning, we are led to the conclusion that all the ele- 
 ments as we have them on this earth are in reality 
 aggregates of hydrogen, helium, and these two 
 unknown elements. 
 
 In these stars progress is obviously from the 
 simple to the complex. Little by little new elements 
 are created by the gradual aggregation of the lighter 
 atoms. Oil earth, so far as we can follow it the 
 
THE ATOM IN DISSOLUTION 159 
 
 change is in the opposite direction, the heavier atoms 
 such as uranium and thorium spontaneously breaking 
 down into simpler and simpler systems. It must be 
 remembered that so far as we know the decomposi- 
 tion of the radio-active elements is quite uninfluenced 
 by any change of conditions which can be applied 
 to them. The substance can be heated up in the 
 electric furnace or cooled to the temperature of 
 liquid hydrogen without in anyway altering its slow 
 but steady rate of decomposition. It is true that 
 the highest temperatures which we can attain are 
 small compared with those of the hotter stars, but 
 it is difficult to conceive that a rise in temperature 
 should assist aggregation, its tendency being always 
 in the direction of disintegration. 
 
 The question suggests itself, are the elements 
 as we know them merely a part of a great cycle of 
 growth and decay ? Is the atom born, to grow old, 
 decay, and die ? Are new atoms being formed in 
 the secret places of the universe to take the place 
 of those that have passed away ? The facts have 
 been briefly stated above, but of explanation there 
 appears at present to be none. We are brought 
 not for the first time to one of those mysteries 
 which science has so far failed to illuminate. 
 
 We have weighed and measured the atom ; we 
 have analysed it and learned something of the 
 stuff of which it is made and a little of its inner 
 structure, and the way in which it behaves. We 
 have now watched its dissolution and attended its 
 obsequies. Whether it will ever be granted to us 
 to sit as spectators at a new birth time alone can 
 show. 
 
APPENDICES 
 
 APPENDIX A. 
 
 (See page 48.) 
 
 DEFLECTION OF THE POSITIVE RAYS BY ELECTRO- 
 STATIC AND MAGNETIC FIELDS. 
 
 (i) Electrostatic Deflection. 
 
 Let d be the length of the path of the particles 
 over which the field is applied, and D the distance 
 of the photographic plate Z (Fig. 9) from the centre 
 of the field MN. In the apparatus used d is small 
 compared with D. 
 
 Since the field is uniform the particle is acted 
 upon by a force X.E, and acquires an acceleration 
 XE/m in a direction perpendicular to its initial 
 velocity. This acts for the time t taken by the 
 particle to describe the path d, that is for a time d/v. 
 Hence velocity v r acquired under the action of the 
 field ' 
 
 d 
 
 ' m m ' v' 
 
 The particle describes the remainder of its path 
 from the field to the plate under these two velocities. 
 Hence the deflection x is to the horizontal distance 
 travelled D as the acquired velocity v r is to the initial 
 velocity v of the particle. Thus 
 
 * = * = XE d 
 D v m i? 
 
APPENDICES 161 
 
 ~ . XE 
 
 x D . d . s. 
 
 mv 2 
 
 (2) Magnetic Deflection. 
 
 The path of the rays in the field is bent into the 
 arc of a circle of radius r where r = 
 
 H.E' 
 
 On leaving the field the particles continue to 
 move along the tangent to this circle at the point 
 where the field ends. Hence the angular deflection 
 6 of the beam is the angle between the tangents to 
 this circle where the path enters and leaves the field 
 respectively. This is obviously the same as the 
 angle between the normals to the circle at those 
 points. 
 
 Hence, if d is small compared with r, as is the 
 case in practice, we have 
 
 d , HE 
 
 - = d . -. 
 r mv 
 
 But, if y is the deflection as measured on the 
 photographic plate, 
 
 .. 
 
 D mv 
 
 Hence 
 
 T^ * 
 y = D . d . 
 
 mv 
 
 APPENDIX B. 
 
 (See page 69.) 
 ELECTRO-MAGNETIC MASS OF AN ELECTRON. 
 
 With the electron as centre describe two spheres 
 of radius, r and r + dr, and draw two radii making 
 
 M.P. II 
 
APPENDICES 
 
 angles and + d6 with the direction of motion. 
 If these radii are supposed rotated about the direc- 
 tion of motion of the electron, they will sweep out a 
 hollow cone, cutting from the sphere of radius r a 
 circular zone, the area of which is 
 
 277?- sin . rd0. 
 
 The volume of the space included between the 
 two spheres and the hollow cone is thus 
 
 27iT 2 sin d0 . dr. 
 
 The magnetic field due to the moving electron 
 is obviously constant throughout the annular space 
 so defined and equal to 
 
 ev sin 
 
 The energy of the magnetic field in the space is thus 
 
 ^l . ^ sin d de . dr> or ew^ede.dr 
 
 O7JT ^ 
 
 Hence the total magnetic energy in the space 
 between the two spheres is 
 
 eW sin 3 6, eWdr 
 
 4r -2 .dr.d0=- s -X2\ 
 
 ev 2 2 
 
 = o -^ dr - since sin 3 0d0 = -. 
 
 J . 3 
 
 The total energy in the field is therefore the 
 integral of this quantity from the surface of the 
 electron of radius a to infinity. 
 
APPENDICES 163 
 
 I.e., total magnetic energy associated with the 
 moving electron 
 
 APPENDIX C. 
 
 THE ZEEMAN EFFECT. 
 
 The mechanical force on the rotating electron P 
 (Fig. 25, p. 115) is H.e.v, where H is the magnetic 
 field supposed directed down through the paper, 
 e the charge, and v the velocity of the particle. If 
 P is positively charged, it will act towards the 
 centre O, thus increasing the force retaining the 
 particle ; if negative, it will oppose it. The 
 mechanical force on Q will obviously be in the 
 opposite direction to that on P. 
 
 Let /be the retaining force in the absence of any 
 magnetic field. Then, since the motion is simple 
 harmonic, we may write 
 
 f=k.r 
 
 where r is the radius of the circle described by the 
 particle. Also, by the laws of mechanics, 
 
 mv 2 
 
 /= ;> || | W 
 
 If T is the time taken to complete the circle once 
 
 271T , . 
 
 V 
 
 m /4-V 
 
 (3) 
 
164 APPENDICES 
 
 Now, if TI, r x , Vi are the values of T, r, and v for 
 P when the field is applied, and T 2 , r 2 , f 2 the corres- 
 ponding values for Q, we have 
 
 l forP 
 
 forQ 
 
 2 
 
 where the charge e is supposed to carry its own sign. 
 Substituting in these equations for the velocities 
 ^i and v 2 from (2), and for k from (3), and dividing 
 the equations by r\ and r 2 respectively, we have 
 
 4^m_4^m 27r 
 
 qp 2 ' T^ T" rL( ^ T-i ''- '' ' V4/ 
 47T 2 m _ 477 2 W TT 277 / \ 
 
 " : ~ r e ' ' 
 
 Subtracting (5) from (4) 
 
 f I I ) 
 
 ~ 
 
 .- f_l 
 *)TI i 
 
 ^_2rr T 2 TI 
 w - H ' TjT 2 
 
 or writing T 2 for Ti.T 2 , which is permissible since 
 the change in the periods produced by the magnetic 
 field is very small and T lies between TI and T 2 , 
 
 e _ 27T T 2 TI 
 m ~ H T 2 
 
 But if A is the wave length of the light emitted, 
 and V is the velocity of light, 
 
 Thus, if A is the original unaltered wave length, 
 
APPENDICES 165 
 
 A c that of the clockwise rotation, \ a that of the 
 counter-clockwise rotation, 
 
 6 _ 2J7T V ~~' V 
 
 > ~~~ "H ' ~A7~ 
 
 V 2 
 
 277 A c \ a 
 
 tr n ^* 
 
 JTl AQ 
 
 Thus, if the particles are positively charged, the 
 clockwise rotation will have the greater wave length ; 
 if negative, the counter-clockwise, as viewed along 
 the lines of magnetic force. The latter is found 
 experimentally to be the case. 
 
 TABLE OF ATOMIC DATA. 
 
 (Calculated from the most recent observations. ) 
 Mass of an electron m 8 99 x 1028 g m . 
 
 Charge On an electron e } 477 X 10 I0 e s. units 
 or monovalent ion j 1-59 x 10 20 e m. units 
 
 Ratio of charge to mass ) 1*774 X 10 7 e.m. units 
 e/m for an electron ) per gm. 
 
 Radius of an electron 1-87 x 10 1 3 cm. 
 
 Electrochemical equi- \ >_ 
 
 valent of hydrogen 1*04 X 10^ e.m. units 
 (Mass/charge) ) P er &"' 
 
 Mass of a hydrogen atom 1*66 x 10 _ 24 gm. 
 
 Radius of hydrogen atom 1-21 X 10 8 cm. 
 
 Gaseous molecules in \ 
 
 i c.c. at o C. and 2-705 x io4 I( > 
 
 760 mm. pressure 
 
 ( 1-40 x 10-16 ergs, per 
 " Gas Constant, R I degree 
 
 Velocity of light, V 2-998 x io-\- cm. per sec. 
 
BIBLIOGRAPHY 
 
 THE following brief list of books and scientific 
 papers may be found of use by readers wishing to 
 pursue further the subjects treated of in the foregoing 
 pages. It lays no claim to completeness. 
 
 BOOKS. 
 
 Professor Sir J. J. Thomson's Conduction of 
 Electricity through Gases, and Professor Sir E. 
 Rutherford's Radioactivity are the standard works on 
 the physics of the electron and on radioactivity 
 disintegration respectively, while Dr. N. Campbell's 
 Modern Electrical Theory is a fascinating and original 
 treatise on the electron theory as a whole. For the 
 older kinetic theory of matter, students cannot do 
 better than consult Professor O. E. Meyer's treatise. 
 
 The above books are of an advanced character and 
 postulate some considerable mathematical and 
 physical knowledge on the part of their readers. Of 
 books of a more popular type Professor Sir J. J. 
 Thomson's Electricity and Matter, or his more recent 
 Corpuscular Theory of Matter may be consulted, 
 while for a detailed account of the experiments 
 described in Chapter IV. the same author's mono- 
 graph on Positive Rays should be referred to. 
 
 SCIENTIFIC MEMOIRS. 
 
 For those who may wish to consult the original 
 authorities a list of a few of the most important 
 papers is appended. 
 
BIBLIOGRAPHY 167 
 
 Sir J. J. THOMSON. " Kathode Rays." Phil. Mag., 
 October, 1897. ' The Charge of Electricity 
 carried by the Ions produced by Rontgen Rays/' 
 Phil. Mag., Vol. xlvi., 1898. ' 
 
 R. A. MILLIKAN. " Charge on an Electron/' 
 Physical Review, 1911. "Elementary Electric 
 Charge/' Physical Review, p. 109, August, 
 
 IQZS- 
 C. T. R. WILSON. ' The Photography of Particles 
 
 ejected from Atoms/' Proceedings of Royal 
 
 Society (Proc. Roy. Soc.), A. 1913. 
 E. RUTHERFORD and H. GEIGER. ' The Charge and 
 
 Nature of the a-particle." Proc. Roy. Soc., 
 
 A. 1908. 
 Sir J. J. THOMSON. " Rays of Positive Electricity/' 
 
 Phil. Mag., February, 1911. Further experi- 
 ments, Phil. Mag., August, 1912. 
 KAUFMANN. " Ratio of Charge to Mass for High 
 
 Speed Electrons." Gottingen Nach., November, 
 
 1901. 
 Sir J. J. THOMSON. " The Structure of the Atom." 
 
 Phil. Mag., March, 1904. Phil. Mag., October, 
 
 1913. ' The Zeeman Effect/' Proc. Camb. 
 
 Phil. Soc., Vol. xxxix. 
 E. RUTHERFORD and F. SODDY. " Radioactive 
 
 Change/-' Phil. Mag., 1903. 
 Dr. R. W. GRAY and Sir W. RAMSAY. "The 
 
 Density of Radium Emanation." Chemical 
 
 News, 1911. 
 
THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW 
 
 AN INITIAL FINE OF 25 CENTS 
 
 WILL BE ASSESSED FOR FAILURE TO RETURN 
 THIS BOOK ON THE DATE DUE. THE PENALTY 
 WILL INCREASE TO SO CENTS ON THE FOURTH 
 DAY AND TO $1.OO ON THE SEVENTH DAY 
 OVERDUE. 
 
 
 !50ct'83SC 
 
 . 1 n 1^3*5 
 
 F?EC'n I PI 
 
 M /tf 10 IS* 
 
 ***rts LJ L.U 
 
 &EC 17 is 
 
 JCI 16 '63 -7PM 
 
 *B 10 
 
 
 10 1936 
 
 
 SP 17 J97- 
 
 
 rg >h 
 
 
 
 
 
 
 f*. 4-AOO 
 
 
 HOV 2 193 9 
 
 
 
 
 APR 10 1942.E 
 
 
 AU6 27 1942 
 
 
 
 
 13Mar'49PJ 
 
 
 24Wa/ r oAV 
 
 r 
 
 tnivv 1 1954 uVi 
 
 
 
 LD 21-100m-8,'34 
 

 UNIVERSITY OF CALIFORNIA LIBRARY