# The Relations of Physics of Electrons to Other Branches of Science

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Congress of arts and science, universal exposition, St. Louis 1904, (1906), vol. 4, pp. 121-156, Online
Lecture delivered on September 22, 1904.
THE remarkable fertility shown by the new idea, based on the experimental fact of the discontinuous corpuscular structure of electrical charges, appears to be the most striking characteristic of the recent progress in electricity.
The consequences extend through all parts of the old physics; especially in electromagnetism, in optics, in radiant heat; they throw a new light even on the fundamental ideas of the Newtonian mechanics, and have revived the old atomistic ideas and caused them to be lifted from the rank of hypotheses to that of principles, owing to the proper relation which the laws of electrolysis have established between the discontinuous structure of matter and that of electricity.
Without seeking here to run through the whole field of their applications, I hope to indicate upon what solid foundations, both experimental and theoretical, rests at present the notion of the electron so fundamental to the new physics; to indicate the points which seem to require more complete light, and to show how vast is the synthesis which we can hope to attain, a synthesis whose main lines only are fixed to-day.

## I. The Electromagnetic EtherI. The Electromagnetic Ether

(1) Fields and Charges. One can say that the combined efforts of Faraday, Maxwell, and Hertz have resulted in giving us a precise knowledge of the properties of the electromagnetic ether, and of light; of a medium, homogeneous and void of matter, whose state is completely defined, with the exception of gravitation, when we know at any point the direction and magnitude of the electric and magnetic fields.
I insist, for the present, on the possibility of arriving at a conception of fields of force, as well as the related idea of electric charges, independently of all dynamics; I wish by this to imply only a knowledge of the laws of motion and of matter. The two fields possess this property, that their divergence is zero in all parts of the ether; that is to say, the flux of electric and magnetic force is rigorously zero across a closed surface which does not contain any matter in its interior. It is in fact always matter in the ordinary sense of the word which contains and can furnish the electric charges around which the divergence of field exists whose direction varies with the sign of the charges.
In extreme cases where the electric charges appear to be most completely separated from their material support, as in the case of the cathode rays for example, the experimental fact of the granular structure of these rays and the complete indestructibility of their charge, the fact finally that cathodic particles are charges possessing the fundamental property of matter, inertia, and experiencing acceleration in the electromagnetic field, these facts do not allow us to distinguish their charge from the so-called free charge of ordinary electrified matter.
Furthermore, we shall come to the idea not only that there can be no electric charge without matter, but that, in fact, there can be no matter without electricity, an aggregation of electrical centres of the two kinds. Electrons, analogous to the cathode particles, possess almost all the known properties of matter by the fact alone that these centres are electrified. We shall see within what limits this conception can be considered sufficiently known, and if it is necessary to superimpose other properties on those which result from electrically charged centres in order to obtain a satisfactory representation of matter; the ether alone, on the contrary, never contains any electricity. If experiment obliges us to admit the existence of electric charges, positive and negative, from the flux of electric force different from zero across a closed surface drawn entirely in the ether and containing matter, it is otherwise for the magnetic field. Experiment has never furnished an instance where a closed surface drawn in the ether was traversed by a magnetic field different from zero. One ​interesting phenomenon observed recently by P. Villard in the effect of an intense magnetic field on the production of the cathode rays, appears to receive a simple explanation in the hypothesis of free magnetic charges; but it is not certain that this hypothesis is necessary.
(2) The Equations of Hertz. The two fields, electric and magnetic, of which the ether can be the seat, are related to one another in such a manner that one of them can exist only on the condition that the other varies; all variations of an electric field produce a magnetic field; it is the displacement current of Maxwell: and all variations of the magnetic field produce an electric field; this is the phenomenon of induction discovered by Faraday. These two relations are expressed by Hertz's equations; they sum up completely our knowledge of the electromagnetic medium, and from these it results that all disturbances of this medium are propagated with the velocity of light. Hertz had the glory of proving this fact experimentally.
(3) Energy. We can now say that the ether is the seat of two distinct forms of energy, the electric and the magnetic, capable of transformation from the one into the other, but only through matter as an intermediary, that is to say, by means of the electrified centres which it contains.
In the ether alone, in fact, in the free radiation which it propagates, the electric and magnetic fields, transverse with respect to the direction of propagation, represent always equal energies in each element of volume, without oscillation of the energy from one form to the other. In the presence of matter, on the other hand, the electric energy can exist alone, and it is the motion of electrified centres which allows the transformation into magnetic energy, and vice versa. Matter only can be the source of radiation.
It is necessary, to the two preceding forms of energy, to add gravitation, which corresponds probably to a third mode of activity of the ether, whose connection with the two others is still obscure.
I insist here on the point that the principle of equivalence of various forms of energy, as far as the process allows of measurement, can be attained independently of all dynamical notions, by the process of using solely material systems in equilibrium.
One can find some information on this subject in a recent exposition by M. Perrin.
(4) The Theory of Lorentz. The ether being thus completely known to us from the electromagnetic and optical point of view, the problem which follows as a continuation of the work of Maxwell and of Hertz is that of the connection between ether and matter, inert matter, the source and recipient of the radiations which the ether ​transmits. The connection sought for is furnished us by the electron or corpuscle, an electrical centre movable with respect to the ether, and carrying with it its divergent electric field.
This was the fundamental idea which caused Lorentz to conceive of the possibility of a relative displacement of electrified centres of divergence of the electric field, and of the ether considered as immovable. This displacement takes place without any change in the amount of the charge, that is to say, that the surface which is displaced in the ether with the electron is crossed by an electric flux which is completely invariable. It is the fundamental principle of the conservation of electricity, which will perhaps absorb the principle of the conservation of matter, as we cannot have matter without electricity. It is, however, probable that electricity alone is not sufficient to constitute matter.
We have actually no very precise information of the relative displacement of charges and of the ether, of electrified centres in an immovable medium, no tangible form under which we can conceive it. The attempts which have thus far been made to obtain a concrete representation, in order to give a material structure to the ether, have all been sterile of results. Perhaps there is a difficulty which belongs to the actual constitution of our minds, habituated by our secular evolution to think through matter, unable to form a concrete representation which is not material; also it seems scarcely reasonable to seek to construct a simple medium such as the ether by considering it to spring from a complex and various medium like matter. I believe it will be necessary to think ether, to conceive of it independently of all material representations, by means of those electromagnetic properties which put us in contact with it. I will return to this point later in reference to the mechanical theories of the ether.
If the electric charge is assumed to have a volume distribution in a portion of the medium, the principle of the conservation of electricity, and also the possibility of relative displacement of electricity and ether, makes it necessary for us, in this portion of space, to modify the equations of Hertz relative to the displacement current by the addition of a convection current, a necessary consequence of the existence of a displacement current connected with a motion of charges, and implying the production of a magnetic field by the motion of electrified bodies across the medium. This consequence of Hertz's equations has now received complete experimental confirmation.
Moreover, the experimental facts impose on these movable charges a discontinuous, granular structure, and lead to the idea of the electron as a singular region of the ether, carrying a charge equal to that of the hydrogen atom in electrolysis, but of different sign, and distributed on the surface or in the volume of the electron ​according as the intensity of the electric field is supposed to present, or not, a discontinuity when it crosses the surface which limits the volume occupied by the electron. Inertia, of electromagnetic origin, which we are about to refer to a similar centre, is opposed also, under the difficulty of its becoming infinite, to the hypothesis of a finite electric charge condensed in a point without extension.
The various considerations, more and more precise, all converging toward this notion of the atomic structure of charges, form the starting-point of all recent works on electricity.

## II. The Atom of ElectricityII. The Atom of Electricity

(6) The Electron. The remarkable laws of electrolysis discovered by Faraday establish an intimate and necessary connection between the atomic structure of matter and that of electricity. They were sufficient to lead Helmholtz to conceive the latter as constituted of distinct, indivisible portions, elements of charge, all identical from the point of view of the quantity of electricity which they carry, and differing only in the sign. This elementary charge is equal to that carried by a monovalent atom or radical in electrolysis; a polyvalent atom or radical carries an equivalent number of such charges.
It was Johnstone Stoney who first used the word electron to designate atoms of electricity as distinct from matter, with which they combine to furnish the electrolytic ions. The presence of similar electrons combined with material atoms allows us to represent certain peculiarities of the spectrum, the existence of doublets of like frequencies; the electron, in motion, is thus considered as the origin of the emission of all luminous rays.
(7) Gaseous Conductors. But there are the researches on the electrical conductivity of gases, which have presented to us in a forcible manner the idea of electrical atoms, which have made this notion more tangible by allowing us to count these electric centres, to lay hold of them individually, and to measure for the first time the charge of each of them in absolute value.
As early as 1882, Giese, in observing the peculiarities of the conductivity of gases escaping from flames, the departure from Ohm's law, the impossibility of drawing from the gas, whatever might be the electric field employed, more than a limited amount of electricity of each kind, the progressive recombination of the free charges in the gas, had expressed in a precise manner the idea, that as in electrolytes the free electric charges in a gas are carried by distinct positive and negative centres in limited numbers, capable of moving in opposite directions under the action of an external electric field in order to discharge the electrified body which produces the field.
It is difficult, in fact, to conceive how, on the hypothesis that the ​charges are distributed in a continuous manner in space, a mass of gas electrically neutral could furnish a limited quantity of electricity of each kind, decreasing with the time by progressive recombination if one delays the establishment of the electric field in the gas.
It is indeed necessary to admit, for the two electricities, a discontinuous structure in order to allow their coexistence without completely neutralizing one another. The progressive recombination of the charged particles or ions of two kinds would produce this neutralization at the moment of their mutual collisions.
The phenomena of the saturation current, of the limited quantity of free electricity in a gas, were obtained under conditions most favorable to experimental study, when, immediately after the discovery of Roentgen rays and like radiations, one had recognized their property of making the gas they traversed a conductor of electricity. The limited charge which we can extract from a gas thus modified, the velocity, finite and easily measured, with which they move under the action of an electric field, their progressive recombination, are interpreted in an admirable manner on the hypothesis that the radiations, as well as the intense heat agitations in a flame, dissociate a certain number of the molecules of the gas into electrified parts carrying charges of opposite kinds.
(8) The Phenomena of Condensation. We know how the phenomena of condensation of supersaturated water vapor in the presence of a conducting gas, already referred by H. von Helmholtz to the presence of ions, has given the preceding hypothesis a brilliant confirmation. As a result of the researches of J. J. Thomson, Townsend, C. T. R. Wilson, and H. A. Wilson, these droplets of visible water, each formed by condensation around an electrified centre, bring forward a tangible witness to the existence of these centres, and furnish a means of measuring the individual charge, present on each drop of water formed, and equal to about 3.4 x 10$^{-10}$ electrostatic units of electricity according to the recent measurements of J. J. Thomson and H. A. Wilson.
The fundamental idea in these kinds of measurements, applied for the first time by Townsend to the charged drops which are produced in the presence of saturated water vapor in recently prepared gases, consists in deducing the mass of each drop from its velocity of fall under the action of gravity by means of Stokes's formula, which gives the frictional resistance of a sphere moving through a viscous medium, and which expresses the velocity of fall in terms of the radius of the drop and consequently of its mass. We can obtain from this the electric charge carried by each drop if we know the ratio of this charge to the mass.
This ratio can be obtained, as was done by Townsend and J. J. Thomson, by measuring or calculating the total mass of water carried ​by the droplets, considered as uniform, as well as the total quantity of electricity carried by the ions which have served as centres for the formation of the drops. The charge thus obtained by Townsend was found to be 3 × 10$^{-10}$ electrostatic units for each centre in the case of gases of electrolysis, and to 6.5 × 10$^{-10}$ by J. J. Thomson from the first series of measurement on gases ionized by Roentgen rays.
H. A. Wilson obtained the ratio of charge to the mass of a drop more simply by comparing the velocity of fall under the action of gravity alone with the velocity of fall in a vertical electric field. He obtained thus directly the ratio sought for. This method has the advantage of showing that the electric charges are really carried by the drops, and of separating those drops which carry a single elementary charge from those which, by diffusion of the ions toward one another, carry a double or triple charge.
Wilson gives as the mean result of his measurements 3.1 × 10$^{-10}$, a value very near to that of Townsend.
A second series of experiments by Professor J. J. Thomson, in which he used radioactive substances as sources of ionization more constant than the Crookes tube, and in which he took care to cause the drops to form on all the ions present in the gas, by producing a supersaturation of the water vapor by a rapid expansion of sufficient magnitude to cause the condensation on the ions of both kinds, gave as a mean result 3.4 × 10$^{-10}$, a value in complete agreement with the other two experimenters. The principles of thermodynamics account perfectly for the influence of electrified centres on the condensation of water vapor: the electric charge of a drop in fact diminishes the pressure of water vapor in equilibrium with it. Moreover, the least supersaturation found necessary, by C. T. R. Wilson, for the formation of drops of water on the ions, which are the same whatever may be the means of producing them (Roentgen rays, Becquerel rays, brush discharge, action of ultra-violet light on metal negatively charged), allows us by purely thermodynamical reasoning to calculate approximately the charge carried by each of the ions, and this calculation, entirely distinct from direct measurement, gives in the case of the positive centres a value of 4 × 10$^{-10}$ E. S. units.
(9) The Radiation Integral. More surprising still is the result recently obtained by H. A. Lorentz, who succeeded in basing a precise measurement of the elementary charges carried by the electrified centres present in metals on the experimental study of the radiation integral or black body radiation.
We will see how the emission and absorption of heat- and lightwaves by matter are dependent on the presence in it of electrons in motion. The ratio, for a radiation of given wave-length, between the emissive and absorptive power, a ratio independent of the nature ​of the substance, represents the emissive power of the radiation integral, which bolometric measurements give directly.
Now this ratio can be calculated, as Lorentz has shown, for wavelengths which are long in comparison with the mean path of free electrons in the metal, as a function of the charge carried by each of them. The comparison of these results with those of Kurlbaum furnishes an entirely new method of obtaining this charge, and gives 3.7 × 10$^{-10}$ E. S. units.
(10) The Kinetic Theory. Finally, the last confirmation, which states more precisely still our knowledge of the electric atom, and our confidence in this fundamental idea, Townsend, through comparing by the simple reasoning of the kinetic theory the velocities of ions in a gas under the action of an electric field with their coefficient of diffusion through the interior of the gas, two quantities directly measurable by experiment, has been able to demonstrate the identity of the charge of one of these gaseous ions with the electric atom of Helmholtz, the charge of a monovalent atom in electrolysis.
From this comes directly a new confirmation of the values previously obtained, for it allows us to know, owing to Townsend's results, the charge on an atom in electrolysis, and from it to deduce immediately the constant of Avogadro, the number of molecules contained in a given volume of a gas. The results are well in agreement with the values of this constant (in general a little greater), which we can directly deduce from the kinetic theory of gases.
Here is an important group of concordant indications, all of absolutely distinct origin, which show without doubt the granular structure of electric charges, and consequently the atomic structure of matter itself. The measurements which I have just enumerated allow us to establish, in great security, the hypothesis of the existence of molecular masses.
I seek to point out here this extremely remarkable result, which belongs without doubt to some fundamental property of the ether and of the electrons, that all these electrified centres, whatever may be their origin, are now identical from the point of view of the charge which they carry.

## III. Inertia and RadiationIII. Inertia and Radiation

(11) The Electromagnetic Wake. Before going farther it is important to point out what we can draw from the point of view to which we have now come. Electrified centres, whose existence is experimentally proven, whose charge we know in absolute units, are movable with respect to a fixed ether defined according to the equations of Hertz, without its having been necessary for us to have recourse to dynamic principles to arrive at this point of view.
To what extent can the known properties of matter be deduced from these two ideas of the electron and the ether, and is it necessary to add something to them in order to build up a synthesis? We are going to see rapidly and definitely from our idea of the electron, how it is sufficient to represent at the same time the inertia of matter, its dynamic properties, also how it can emit and absorb the radiations which the ether transmits.
The possibility of conceiving of inertia, mass, not as a fundamental idea, but as a consequence of the laws of electromagnetism, is a conception which owes its origin to an important memoir published in 1881 by Professor J. J. Thomson. He studies there, basing his assumptions on the existence of the displacement currents of Maxwell, the electromagnetic field accompanying an electrified sphere in motion. This motion implies a change in the electric field at a point fixed with respect to the medium, and this displacement current immediately produces a magnetic field according to the ideas of Maxwell. The necessity of a convection current is pointed out later. The magnetic field thus produced, identical with that of an element of current parallel to the velocity of the moving charge, is proportional at each point to that velocity, at least, if it does not approach too nearly to that of light.
The creation of a magnetic field at the time of setting the charged centre in motion implies an expenditure of energy, energy of selfinduction of the convection current, proportional to a first approximation to the square of the velocity, for those velocities which are small compared to the velocity of light. It is thus an expression of the same form as that of ordinary kinetic energy. A part, at least, of the inertia of an electrified body, of its capacity for kinetic energy, is thus a consequence of its electric charge.
Moreover, the magnetic field thus produced, and the electric field as well, modified by the velocity as it approaches more nearly to that of light, constitute around the electrified centre in translation a wake which accompanies it in its translation through the ether without change so long as the velocity remains constant. It is besides necessary ​that an external action should intervene in order to modify the energy of this wake and consequently to increase or diminish the velocity. This implies, in the absence of all other kinetic energy than this of electromagnetic origin, corresponding to the production of the wake, by the law of Galileo on the conservation of the velocity acquired, in the absence of action of all external fields of force, that an electrified centre possesses inertia by the fact alone that it is electrified.
It is the immovable ether, the electromagnetic medium, which serves as a fixed support for the axes with respect to which the principle of inertia is applicable, and of which the ordinary mechanics limits itself in affirming the existence by saying: there exists a system of axes, determined by a nearly uniform translation with respect to which the principle of Galileo is exactly verified.
(12) The Absolute Motion. If we are able, from the actual point of view, to conceive of the ether as supporting these Galilean axes, it does not necessarily follow that the electromagnetic phenomena enable us to arrive at this absolute motion. It seems, on the contrary, so far, that static experiments, carried on in a material system by an observer carried along with it with a uniform motion of translation, do not allow, whatever may be the degree of accuracy of observation, the detection of a relative motion of the ether with respect to matter.
Larmor, and more completely Lorentz, have shown that there exist in the system actions of electromagnetic origin; it is possible to establish in a complete manner a static correspondence (relating to the positions of equilibrium or to the black fringes in optics) between the system in motion and a system fixed with respect to the ether, by means of a change of variables which preserves for the equations of the medium for a moving system the exact form which they possess for a system at rest.
The two systems differ from one another in that the moving system is slightly contracted compared with the fixed system in the direction of the resultant motion by an amount always very small, proportional to the square of the ratio of the velocity of motion to the velocity of light. This contraction affects equally all the elements of the moving system, i. e. the electrons themselves, if we admit with Lorentz that the interior actions of these electrons are solely electromagnetic actions or are modified in the same manner by the translation, - with the result that observation cannot prove this contraction any more than it can prove the general dragging of the ether. These elements behave as though they belonged to a corresponding fixed system. Thus is found an explanation of the negative results of experiments undertaken to show the absolute motion of the earth, by Michelson and Morley, Lord Rayleigh, Brace, Trouton, and Noble, if one admits ​that all the internal forces of matter are of electromagnetic origin, and that the energy is entirely divided between the two fields, electric and magnetic.
We shall see, however, farther on that it Is difficult to eliminate in this way all other forms of energy, all other forces, such as gravitation; and it would then be necessary to admit with Lorentz, in order that the correspondence between the two systems should actually subsist, that in the moved system the forces and masses of different origins are modified exactly as the electromagnetic forces and masses, an hypothesis too complicated and arbitrary in the actual state of the question.
But this does not seem to be a necessary consequence: it appears probable that these actions, foreign to electromagnetism, and necessary at the interior of the electron in order to give stability and in order to represent gravitation, and which are probably connected with one another, do not intervene in a sensible manner in the negative experiments referred to above, and that everything transpires as if the electromagnetic forces alone played a role, alone existed.
We shall see farther on that perhaps experiments of another kind than those referred to here, for example, some dynamic measurements bringing in a relative motion of the system moved, or some static experiments bringing in gravitation, would enable us to understand the absolute motion, the axes bound to the ether, instead of conceiving simply of their existence.
(13) Electromagnetic Inertia. The problem of the electromagnetic wake accompanying an electrified sphere or ellipsoid in the ether has been taken up since J. J. Thomson by Heaviside and Searle.
Max Abraham has shown their results to consist approximately of a numerical factor when, instead of supposing the body to be a conductor having a surface charge, we suppose its charge to have a uniform volume distribution.
Among the more important results contained in this solution of J. J. Thomson's problem, I will point out these: that in the case of a conducting sphere, the charge remains uniformly distributed on the surface whatever may be the velocity, and that in all cases the electric field at a distance tends to become more and more concentrated in the equatorial plane with respect to the direction of the velocity in proportion as this velocity approaches that of light.
Moreover the kinetic energy which it is necessary to expend at the moment of putting it in motion in order to create the electromagnetic wake ceases to be proportional to the square of the velocity, and increases indefinitely as the velocity approaches the velocity of lightwaves; the law of the increase of this kinetic energy with the velocity, the energy of self-induction of the current to which the charged body in motion is equal, may be easily deduced by Searle's solution.
​Without any other hypothesis than that of its electric charge, the electron is found to have inertia defined as capacity for kinetic energy, but with a particular law of variation of this as a function of the velocity, and this inertia appears to approach infinity as the velocity approaches that of light.
The behavior of this law depends very little on the hypothesis made as to the form of the electron and the distribution of the electric charge which it carries. In all cases it is found to be impossible to give the electron a velocity equal to that of light, at least permanently.
Instead of considering with Max Abraham the electron to be spherical at all velocities, Lorentz admits it to be spherical when at rest and to have a uniform distribution of charge; but if all internal forces are solely electromagnetic or act as such, we have the view that the electron is flattened in the direction of motion by a quantity proportional to the square of the ratio (β=v/V). of its velocity to that of light, becoming an ellipsoid of revolution, the equatorial diameter remaining equal to that of the original. This leads, as we shall see, to a law of inertia different from that of an invariable sphere.
We shall likewise see that it does not appear to be necessary to assign to the electrons, the negative ones at least, any other inertia than this in order to account for the dynamic properties of the cathode rays; however, experiments are not yet sufficiently exact to allow us to infer the form of the electron itself, which depends on the law of the variation of the kinetic energy with the velocity.
(14) Two Problems. We have examined, so far, only the case of an electron in uniform motion in the absence of any external electromagnetic field capable of modifying the motion of the electron by giving it an acceleration.
The general problem of the connection between the ether and the electron, which probably represents the most important of the connections between ether and matter, is double.
In the first place, what is the electromagnetic disturbance in the ether accompanying any given motion of the electrons whatsoever?
In the second place, what motions would free electrons have if displaced in an external magnetic field superimposed on that which constitutes their wake?
(15) The Velocity Wave - The Acceleration Wave. We actually possess all the elements necessary for the solution of the first problem, in which the motion is uniform in a particular case. Lorentz has given in a very simple form the general solution by the use of a delayed potential.
Each element of the charge in motion is determined by its position, its velocity, and its acceleration at the time T, the electric and magnetic fields at the time T + t, on a sphere having for its centre the ​position at the time T and for radius the path passed over by light during the time t.
Lorentz has given in this way the expressions for the two electric and vector potentials from which the fields can be deduced by the well-known formula. The complete expressions for these fields have been given for the first time, I believe, by Lenard; I obtained them independently at the same time as Schwartzschild by putting them in the following form.
The expressions for the two fields consist of two parts: the first depends solely on the velocity of the element at the time T and contributes to form the wake (sillage) which accompanies the electron in its motion; I shall call this the velocity wave. This velocity wave, which exists only in the case of uniform motion, has its electric field always directed toward the position which the element of charge will occupy at the time T + t, if it had retained from the time T the velocity which it had at that moment. Schwartzschild calls this position the point of aberration. It coincides with the true position of the moving element at time T if the motion has been uniform. The other part of the two fields is proportional to the acceleration projected on the direction of propagation, and the directions of the two fields are there perpendicular to one another, and perpendicular to the radius, at the same time the two electric and magnetic fields represent equal energies per unit volume; they have all the characteristics of a radiation which is freely propagated in the ether. I shall call this part the acceleration wave. Moreover, the intensities of the fields in this case vary inversely as the distance from the centre of emission, the energy represented by this wave does not tend toward zero as the time T increases indefinitely; there is thus energy radiated to infinity by the acceleration wave.
The velocity wave, on the contrary, in which the fields vary inversely as the square of the radius Vt, does not carry any energy to infinity: the energy of the velocity wave accompanies the electron in its motion and corresponds to its kinetic energy.
(16) Radiation implies Acceleration. We can conclude from this that when an electrified centre experiences an acceleration, and only then, it radiates to infinity in the form of a transverse wave, electromagnetic radiation, a definite quantity of energy, proportional per unit of time to the square of the acceleration.
The origin of electromagnetic radiation, of all radiation, is, then, in the electron undergoing acceleration. It is through the electron that matter acts as the source of Hertzian or light waves. All acceleration, all change which takes place in the state of motion of electrons, result in the emission of waves. The character of the emitted waves changes naturally according as the acceleration is abrupt, discontinuous, or periodic.
​In the first case, realized, for example, in the sudden stopping of the negative electrons, or corpuscles, by the anti-cathode, the radiation consists of an abrupt pulse whose thickness is equal to the product of the velocity of light into the time taken to stop them, and which gives us a good representation of the Roentgen rays or of the rays from radioactive substances.
If the acceleration is periodic, on the contrary, as in the case when the electron revolves around an electrified centre of opposite sign to itself, the acceleration is periodic, and the radiation emitted constitutes a light-wave whose length is determined by the period of revolution of the electron.
The solution of the first of the two fundamental problems thus appears complete and raises no difficulty.

## IV. Dynamics of the ElectronIV. Dynamics of the Electron

(17) Maxwell's Idea. The inverse problem is less simple. It consists in finding the motion, the acceleration which a movable electron experiences in electric or magnetic fields of given intensities; it is, properly so to speak, the problem of the dynamics of the electron.
The equations which solve this problem ought to consist, like the equations of ordinary dynamics, of two kinds of terms: one of these dependent on the external fields, which produce their actions on the electron, and are analogous to the external forces in dynamics; the other, representing forces dependent on the motion itself, and producing a resistance to motion, similar to the forces of inertia.
The terms corresponding to external actions, the forces, have been obtained by Lorentz following a method which was the natural continuation of Maxwell's idea as to the possibility of a mechanical explanation, otherwise indeterminate, by the facts of electromagnetism. The analogy to the equations of electrodynamic induction, and to the equations of Lagrange, appeared to justify such an explanation, and it was natural to continue to look upon the ether-electron system as a mechanical system, and to apply to the motions of electrified centres Lagrange's equations, deducing thus the forces exerted on the electrons by its electric and magnetic energies considered as corresponding to the potential and kinetic energies of a mechanical system, substituted in the ether. We are thus led to apply to the medium, ether, in consideration of the fundamental notions of force and mass, which they imply, the equations of material dynamics, deduced from principles founded on observations of matter only, always taken in mass and without an appreciable amount of radiation.
​(18) Ether in Matter. We extend thus, by a bold deduction, these principles to a region for which they have not been designed, and thus admit implicitly the possibility of a material representation of the ether. However, as I have already pointed out, an attempt at such a representation raises many difficulties, and the efforts so far made to extend these principles in a more precise manner have not been successful. The most profound attempt, that of Lord Kelvin, the gyrostatic ether, lends itself rigorously only to the representation of the propagation of periodic disturbances in the ether, but makes impossible the existence of a permanent deformation, necessary, however, for the representation of a constant electrostatic field. The gyrostats would turn back again at the end of a finite time, and the system would cease to react against a deformation which has been imposed. Moreover, it would appear impossible to include in this conception the permanent existence of electrons, centres of deformation in the medium.
To get around this difficulty, Larmor had occasion, in the material image which he proposed for the ether, to superimpose on the gyrostatic system of Lord Kelvin the properties of a perfect fluid, of which the displacements representing the magnetic field should be at each instant irrotational in order not to produce an electric field by the rotation of the gyrostats present in the medium. But a great difficulty is added to the preceding: if the motion of a fluid satisfies at every moment the condition of being irrotational for infinitely small displacements, it is not so for finite displacements, and a magnetic field could not continue to exist without giving rise to an electric field.
I believe it impossible to overcome these difficulties and to give a material image of the ether, whose properties are entirely distinct, and probably much more simple than those of matter.
(19) Action and Reaction. Let us, however, retain this view in order that we may meet new difficulties. By means of Lagrange's equations Lorentz obtains two external forces acting on each electron in motion, two terms representing the action of the electromagnetic field. One force is parallel to the electrostatic field; it is the ordinary electric force, due to the superposition of the electric field produced by the electron on the external electric field: the other is perpendicular to the direction of the velocity of the electron and of the external magnetic field; it is the electromagnetic force analogous to the force of Laplace exerted by a magnetic field on an element of current, and due to the superposition on the external magnetic field of the magnetic field produced by the electron during its motion. This double result includes all the elementary laws of electromagnetism and of electrodynamics, if we consider the current in ordinary conductors as due to the displacement of electrified particles.
​We easily see that the forces thus obtained, exerted on the electrons by the ether, i. e. on the matter which contains them, do not satisfy the principle of the equality of action and reaction, if we consider all the forces which act at the same moment on all the electrons constituting matter. In the case of a body which radiates in an unsymmetrical manner, a recoil, an acceleration, is produced which is not compensated at the same moment by an acceleration set up in another portion of the matter. Later, at the time that the emitted radiation meets an obstacle, the compensation is made (but only in a partial manner if all the radiation is not absorbed) by means of the pressure which the radiation exerts on the body which receives it; a pressure whose existence is shown by experiment.
The equality of action and reaction has never been verified in similar cases, and it adds no difficulty to this subject if we do not seek to extend the principle beyond the facts which suggested it.
(20) Quantity of Electromagnetic Motion. If we could nevertheless realize this extension of the principle, an extension somewhat arbitrary, we should be led not only to apply this principle to matter, but to suppose the ether to have a quantity of motion which would be that of a material system to which we compare it.
Poincare has shown that this quantity of electromagnetic motion ought to be, at every point in the ether, in direction and in magnitude, proportional to Poynting's vector, which gives at the same time a definition of the energy transmitted through the medium.
By starting with this idea of the quantity of electromagnetic motion, Max Abraham has been able to calculate the terms, put to one side by Lorentz, which depend on the motion of the electron itself, its force of inertia, by the variation of the quantity of electromagnetic motion contained in its train. He was led for the first time, by the form of the terms which represent this force of inertia, to the notion of an unsymmetrical mass as a function of the velocity.
(21) Quasi-Stationary Motion. The calculation can be completely made only in the case, always realizable from the experimental point of view, where the acceleration of the electron is so small that its train can be considered at each instant as identical with that of an electron having the actual velocity, but whose motion has been uniform for a long time. This is what Abraham calls a quasi-stationary motion. In this case, the train is entirely determined at each moment by the actual velocity of the electron, also the quantity of electromagnetic motion which it contains, and consequently the variation of this quantity which represents the force of inertia. The condition of quasi-stationary motion is simply that in the neighborhood of the electron, where the quantity of electromagnetic motion is localized, the wave of acceleration may be neglected in comparison with the velocity wave.
​(22) Longitudinal Mass and Transverse Mass. We find under these conditions that the force of inertia is proportional to the acceleration with a coefficient of proportionality analogous to mass, but which is here a function of the velocity, and increases indefinitely, like the kinetic energy, as the velocity tends to approach that of light. Moreover, this electromagnetic mass differs for the same velocity, according as the acceleration is parallel or perpendicular to the direction of the velocity. There is, corresponding to the direction, a longitudinal and a transverse mass. Mass is then no longer a scalar quantity, but has the symmetry of a tensor parallel to the velocity. No experimental fact yet allows us to verify this dissymmetry of the mass of the electrons, which becomes evident only when the velocity is of the same order as that of light, but the variation of the transverse mass with the velocity has been proven by Kaufmann for the β rays of radium, which consist of particles identical with the cathode rays. It is sufficient to compare the deviations of these rays in the electric and magnetic fields perpendicular to their direction in order to deduce, by application of the equations of the dynamics of the electron, their velocity and the ratio of the charge to the transverse mass of the particles which compose them. This ratio decreases as the velocity increases, and, if we consider as fundamental the principle of the conservation of electricity, we conclude from it an actual increase of the transverse mass according to a law easy to compare with that which the theory gives for the electromagnetic mass.
(23) Matter of the Philosophers. But before discussing the result of this comparison, I wish to point out a logical difficulty raised by the course which we have followed: we are accustomed to consider as fundamental the ideas of mass and force, built up in order to represent the laws of motion of matter; we, a priori, conceive of mass as a perfectly invariable scalar quantity.
Now, let us suppose the possibility of a material representation of the ether: we apply to it the equations of material dynamics, and we are led to admit for the electrons, which form a part of matter, and consequently for matter itself, a dissymmetrical mass, tensorial and variable.
To what, then, should the equations of ordinary dynamics apply, and what are the ideas considered as fundamental which they imply? To an abstract matter, the matter of the philosophers, which could not be ordinary matter, since it is inseparable from electric charges, and which is probably made up of an agglomeration of electrons in periodic motion, stable under their mutual actions? Or to the ether? But we have no idea of what can be its mass or motion.
It is, indeed, rather the ether which it is necessary to consider as fundamental, and it is then natural to define it initially by those properties ​of it which we know, that is to say, by the electric and magnetic fields, which it is possible to arrive at, as I have already remarked, without admitting at any time the laws of dynamics, the ideas of mass and force under their ordinary form. We will find this last to be a derived and secondary idea.

## V. Electromagnetic DynamicsV. Electromagnetic Dynamics

(24) Change of Point of View. It seems thus much more natural to reverse the conception of Maxwell and to consider the analogy which he has pointed out between the equations of electromagnetism and those of dynamics under Lagrange's form as justifying much more the possibility of an electromagnetic representation of the principles and ideas of ordinary, material mechanics, than the inverse possibility.
It is necessary then for us to solve our second problem, that of the dynamics of the electron, of its motion in a given external field, without having recourse to the principles of mechanics, by purely electromagnetic considerations.
Hertz's equations, which permit a solution of the first problem, are here not sufficient, and we have need of a more general principle, which assumes not the motion of the electrons given, but that determines it.
(25) The Law of Stationary Energy. We will use this principle under a form indicated by Larmor, and which we can look upon as a generalization of the known laws of electrostatics and of electrodynamics. We know that the distribution of electric charges and electric fields in a system of electrified bodies is always such that the electrostatic energy W$_e$, contained in the medium modified by the field, is a minimum. The analogous principle holds for the magnetic field produced by currents of given intensities. The energy W$_m$ localized in the magnetic field is less for the real distribution of it than for all other distributions satisfying the condition that the integral around a closed line is equal to 4π times the intensities of the currents inclosed by the line.
If displacements are possible, the conductors maintained at constant potential are in stable equilibrium if the electrostatic energy is a maximum, and the currents of given intensities are likewise in stable equilibrium if the energy of their magnetic field is a maximum. In all cases of maxima and minima, an infinitely small modification of the system from the configuration of equilibrium produces a zero variation in the energy: it is stationary.
(26) General Principle. When, instead of remaining permanent, the state of the system is variable, and if there are represented necessarily at the same time the two kinds of fields, we seek to find how, ​as in the permanent case, an expression which remains stationary. that is to say, the variation of which is zero when supposed slightly modified, can start from its real state. We are thus led to replace the energies W$_e$, W$_m$) which play this role in the permanent case, by an integral taken with respect to the time, and which represents not the sum of the energies, since this quantity, equal to the total energy, ought to remain constant if only electromagnetic action come in, but their difference:
$\int _{t_{0}}^{t_{1}}(W_{e}-W_{m})dt$,
an integral which remains stationary for all virtual modifications of the system, such modifications being subject to the condition of disappearing at the limits t$_0$ and t$_1$ of the integral, exactly as in the analogous principle of Hamilton in mechanics. The principle of zero variation just announced, and which we will consider as the result of an induction based entirely on electromagnetic principles, allows us in fact to find three of Hertz' s equations, if we admit the three others as an imposed interconnection of the system, and furnishes in the most simple manner the solution which we have obtained for the first problem by means of these equations. Moreover, the motion of the electrons supposed given only at the times t$_0$ t$_1$ comes into the integral, and the condition that this must be stationary allows us to find the law of the motion during the interval, by starting from a principle whose signification is purely electromagnetic. We obtain thus exactly the results of Max Abraham; the equations of motion contain terms which depend first on the motion of the electron, and are proportional, in the hypothesis of quasi-stationary motion, to its acceleration, having coefficients that are functions of the velocity which we will call the longitudinal and transverse masses of the electron; also some terms depending on the charge, and on the external fields, which we will call the forces, and we find that they coincide with those given by Lorentz. The external motion of the electron is thus determined by the actual electromagnetic state of the system.
(27) The Process in the Electron. In order to simplify the analysis and to avoid considering the motion of rotation of the electron, I will consider it as a cavity in the ether; the volume integrals which express the energies W$_e$, W$_m$ of the electric and magnetic fields extend only over the space external to the surface which bounds the cavity. We can suppose as a special condition outside of the electric charge that the form of this surface is fixed, spherical for example, due to an unknown action of nature, and we find the equations of Abraham for the longitudinal and transverse masses of a spherical electron.
But we can suppose a more simple condition, implying only a fixed volume of the cavity on account of the incompressibility of the external ​ether; if we seek, then, what is, in the case of uniform translation, the form that the electron would spontaneously take in order to satisfy the condition of zero variation, we find precisely the oblate ellipsoidal form assumed by Lorentz, with this difference, that the equatorial diameter increases with the velocity instead of remaining constant, as Lorentz considers it; this constancy implies a diminution of the volume as the velocity increases. The equations which express in this case the variation of the longitudinal and transverse mass with the velocity are different from those of Abraham and Lorentz, although giving always an indefinite increase of the two masses as the velocity approaches that of light.
The equations thus obtained for the ratio m/m$_0$ of the transverse mass m, the only one so far accessible to experiment, to the mass mm/m$_0$ for very small velocities, as a function of the ratio β=v/V of the velocity of the electron to that of light are:
(1) Invariable spherical electron,
${\frac {m}{m_{0}}}{\frac {3}{4}}\psi (\beta )={\frac {3}{2\beta ^{2}}}\left[{\frac {1+\beta ^{2}}{2\beta }}L{\frac {1+\beta }{1-\beta }}-1\right]$
(2) Variable Electron
${\begin{cases}\mathrm {Equatorialdiameter\ constant} &{\frac {m}{m_{0}}}=(1-\beta ^{2})^{-1/2}\\\\\mathrm {Volume\ constant} &{\frac {m}{m_{0}}}=(1-\beta ^{2})^{-1/3}\end{cases}}$
(28) Comparison. The researches of Kaufmann are not yet exact enough to determine which of these equations represents most nearly the experimental variation of the ratio e/m with the velocity. In order to make the comparison, I have used a process similar to that of Kaufmann, who eliminated the two electric and magnetic fields used to deviate the β rays, seeking to obtain the best concordance possible between the experimental variation of e/m and the theoretical variation calculated on the hypothesis that the mass is entirely electromagnetic.
It would be extremely important to determine the longitudinal mass by the use of an intense electric field parallel to the velocity of the electron, furnishing to it a known energy and producing a variation of the velocity, which if measured would give the longitudinal mass.
(29) Matter and Electrons. But if the accuracy of experiment is not sufficient to determine completely the law, the agreement with the equations, obtained by supposing the mass to be entirely electromagnetic, is so good that we can reasonably conclude that cathode particles constituting the β rays have no mass other than that due to their electric charges or the train which they carry with them in their motion through the ether.
It is interesting to extend the same result to ordinary matter by conceiving it as made up of an aggregation of electrons of both signs; it is unreasonable on the other hand to apply to two phenomena so nearly identical as inertia of ordinary matter and that of the cathode particles, two entirely distinct explanations, of which the one, the electromagnetic explanation, is definite and confirmed by experiment, while the other remains entirely unknown.
The inertia of a similar aggregation of electrons should be equal to the sum of the partial inertias because of the great distance of the electrified centres from one another compared to their radii, which one can calculate by supposing all their inertia electromagnetic.
In these conditions, the trains of the different electrons do not interfere appreciably, and we find thus the law of the conservation of inertia as a consequence of the conservation of the electrons in the transformations to which matter is subject. But the theory is not incompatible, on account of the interference of trains, with a slight disagreement between the inertia of an assemblage and the sum of the partial inertias.
The complexity of the atomic system to which we are led, each atom of the molecule containing probably a very great number of electrons, seems also to be a necessary consequence of the complexity of the luminous spectrum sent out from the atoms, by the electrons which they contain, when an external disturbance displaces the system from its state of stable periodic motion. In such a state the radiations emitted by the various electrons on .account of the acceleration which keeps them in their intermolecular orbits compensate one another almost completely from the point of view of energy radiated; so that there is in general no decay of the periodic intermolecular motion.
​This conception, this electronic theory of matter in which matter becomes, at least partially, synonymous with electricity in motion, appears to account for an enormous number of facts, which increase constantly under the efforts of physicists impatient to contemplate in a less primitive form the synthesis which it promises to bring forward.
(30) Stability of the Electron. The fundamental conception, that of the electron, does not go without raising difficulties still further, besides the impossibility already pointed out of representing to ourselves by material images its displacement with respect to the ether. It seems necessary to admit something else in its structure than its electric charge, an action which maintains the unity of the electron and prevents its charge from being dissipated by the mutual repulsions of the elements which constitute it. The form of the electron is determined by some relation which insures its stability, the condition of incompressibility of the medium being insufficient, since the spherical form corresponds only to unstable equilibrium for an electrified body of given volume in which no force opposes the deformation.
This condition, which belongs to some fundamental property of the medium, determining the charge carried by the electrons, all identical from this point of view, is perhaps closely connected with the third mode of activity of the ether, a third form of energy, the gravitational form, of which our principle of stationary energy ought to take account by the addition of terms to those expressing the electrostatic energy, but of infinitely smaller magnitude.
(31) Gravitation. Gravitation remains obstinately outside of our electromagnetic synthesis; the Newtonian forces not only do not appear to be propagated with the velocity of light, but also it seems difficult to found them on electromagnetism without modifying profoundly our fundamental ideas in regard to field and quantity of electricity and the possibility of an attraction of one aggregation of neutral electrons for another aggregation of the same nature.
It appears probable that gravitation results from a mode of activity of the ether and a property of electrons entirely different from the electromagnetic mode, and we must admit besides electric and magnetic energies, a third distinct form, that of gravitation.
It remains to understand how it is possible, and what is the significance of the equivalence, the passage of this third form into one of the first two. Also we are no more capable of understanding, outside of the formal equations which express it, the connection between the electric and magnetic energies themselves and their transformations, the one into the other, by means of the electrons.
(32) An Experiment Necessary. It does not seem impossible to connect the forces of cohesion with electromagnetism, especially ​from the point of view of the mutual attractions which orientation causes in the constitution of crystalline media, on account of the complex electric and magnetic fields which surround a system of electrons in its immediate vicinity.
Gravitational forces alone remain distinct, superimposed on the electromagnetic forces, and no difficulty comes from this on account of the negative results of the experiments undertaken to show the absolute motion of the earth.
The negative results can be explained, as we shall see, if all the internal forces of matter are of electromagnetic origin; but gravitational force, alone different, can be superimposed on them without introducing an appreciable modification of this result, for its intensity is extraordinarily small compared to electromagnetic actions, even if there is no mutual compensation between them, and in all the experiments in question, interference of light or equilibrium of an elastic system, the gravitational forces play no appreciable role.
It would be, indeed, important to obtain a condition in a case of equilibrium where the forces of gravity would play an important part, and if the equilibrium remains independent of the total motion to nearly the second order, if we could only observe the mutual motion to this order of precision, it would be necessary to conclude that the forces of gravitation also are modified by motion of translation in the same manner as the electromagnetic forces, since the equilibrium between the two kinds of forces is not disturbed, and this would be an important indication of the necessity of an electromagnetic representation of gravitation. We would be able, for example, if the sensibility allowed it, to perform the experiment of Trouton and Noble by suspending the condenser with a bifilar to the pan of a balance instead of by an elastic fibre.
Since this test has not been made, since experiments designed to show the absolute motion have not involved weight, it would be more reasonable to consider gravitation as a force distinct from electromagnetic action, which acts at the interior of the electrons in order to insure their stability, without its being possible actually to imagine in what manner we can seek a more profound knowledge of the ether and of the electrons which it incloses.
It does not seem, in any manner and for many reasons, that this can be of the nature of a material and mechanical representation of the ether.

## VI. Cathode RaysVI. Cathode Rays

(33) The Ratio e/m. Before examining the consequences involved in the electronic conception of matter, I should like to examine a few points relative to the electrons of two kinds. Those which we know the better, the more intimately, are the negative electrons, which ​are always identical with one another in all their properties, whatever may be the matter which has furnished them. We have already seen how the direct measurement of the charge leads always to the same result, The mass, both the longitudinal and transverse mass, having the same value for small velocities, can be determined by the measurement of the ratio of the charge to the mass.
The results obtained for this ratio in the case of cathode rays show some quite marked divergences when different methods of measurement are employed. The first values were given by J. J. Thomson by combining the magnetic deviation of the rays with a measurement of the energy which they possess by means of the heat produced in a thermoelectric couple which receives them, or by combining this magnetic deviation with the deviation in an electrostatic field. The ratio e/m furnished by this second method, the more accurate of the two, is approximately 10$^7$ electromagnetic units C.G.S.
Another method first pointed out by Schuster was used successively by Kaufmann and Simon. It consists in combining the magnetic deviation with the measurement of the difference of potential under which the rays are produced, considering that this difference of potential is that which exists between the cathode and anode. This hypothesis admitted, the method is capable of great accuracy, and the results which it gives appear to agree with the limiting values, for small velocities of the ratio e/m for the β rays, although the method employed by Kaufmann in this last measurement is different from that of Schuster. The number obtained by Simon is 1.865 x 10$^0$, nearly double that of J. J. Thomson. The explanation proposed by the latter for this disagreement, according to which the cathode rays are not produced by the total difference of potential between the cathode and the anode, but originate in a region situated in front of the cathode, does not, however, appear satisfactory, since it does not account for the constancy of the results of Kaufmann and Simon when the conditions of the experiment, the difference of potential in particular, were varied between large limits.
A means of deciding the question would consist in performing a type of experiment already used by Lenard, by subjecting the cathode rays, after their production, to a supplementary and known fall of potential, and determining by the modification which would result in their magnetic deviation the initial fall of potential under which they had been produced.
(34) The Cathode Corpuscle. However it may be, we can, owing to the results of Kaufmann, affirm the identity of the cathode rays already found independent of the gas and the electrode contained in the Crookes tube, with the β rays of radium. The measurements ​by J. J. Thomson and Lenard of the negative charges emitted by a negatively charged metallic surface under the action of light and of those spontaneously emitted by incandescent bodies also show an identity with the cathode rays. Wehnelt has recently shown that the oxides of the alkaline earths possess in an extraordinary degree this property of spontaneously emitting cathode rays at high temperatures, and furnishes a means of performing, on this particular kind of rays, simple and exact measurements.
Finally, we know that the magnitude of the Zeeman effect, in the case where the spectrum lines considered present the appearance of a normal triplet, leads to the conclusion that the light corresponding to these lines is emitted by negatively electrified centres, present in matter and having the same ratio e/m as the cathode rays.
Moreover, the magnitude of this ratio, one thousand to two thousand times greater than for the hydrogen atom in electrolysis, leads us, as a consequence of the identity of charges established by Townsend, to consider the mass of the cathode corpuscle as one thousand times smaller at least than an atom of hydrogen; a result in perfect agreement with the conception which makes material atoms an agglomeration of electrons of two kinds. On the hypothesis that the mass is entirely of electromagnetic origin, the knowledge of the ratio e/m gives for the electron a sufficiently small radius (10$^{-13}$ centimeters about) in order to be, conformably to our conception also, negligible in comparison with atomic dimensions.
(35) Flames. The small mass of the cathode corpuscle, and the possibility of separating from matter electrified centres a thousand times smaller than the smallest atom, is confirmed by the mobility of the negative ions in flames. We obtain enormous mobility compared to that observed in gases at ordinary temperatures, and the methods of the kinetic theory of gases permits us to calculate, by means of this experimental mobility, that the movable negative centres in flames have a mass about a thousand times smaller than the hydrogen atom, and should consequently be identical with the cathode corpuscles. At ordinary temperatures the negative ions are less mobile because the cathode corpuscles surround themselves with neutral molecules by simple electrostatic attraction, and form an agglomeration which the feeble agitation allows to remain stable.

## VII. Positive Electrons - α RaysVII. Positive Electrons - α Rays

(36) Goldstein Rays. α Rays. Our knowledge of the structure of positive charges is much less advanced than for the negative. Two important cases show us the existence of positively charged particles, besides the positive ions in conducting gases, which at ordinary temperatures consist of an agglomeration of neutral molecules around ​a charged centre: these are the Kanalstrahlen of Goldstein, an efflux of positive charges toward the cathode, the electric and magnetic deviations of which lead to values for the ratio of e/m varying between wide limits, but always several thousand times smaller than for the cathode rays. The mass of these positive centres is of the order of that of the atoms. The α rays of radioactive bodies, easily absorbed, and particularly easy to observe in the case of polonium and the active bismuth of Marckwald, appear to be, in fact, Kanalstrahlen. The mass of the positively charged particles which constitute these rays is of the same order as that of the hydrogen atom, and their velocity does not exceed 20,000 to 25,000 kilometers per second, so that it is impossible to verify whether their mass is entirely electromagnetic or not. Can we consider them as electrons as simple as the negative corpuscle itself, or are they of much more complex structure; are they, for example, atoms or molecules which have lost a cathode corpuscle?
(37) Electrons or Atoms. On the first hypothesis, the great mass of the positive centres would lead us to assign them dimensions much smaller than the cathode corpuscles themselves, the electromagnetic mass of an electrified sphere being inversely proportional to its radius. One is thus led to the result that an electron possesses inertia, I will not say weight, inversely proportional to its radius. H. A. Wilson thinks to find an argument in favor of this conception of a very small and consequently very inert positive electron in the observation that the α rays are much less easily absorbed than the β rays of the same velocity.
Many other reasons lead us to adopt the contrary hypothesis that an α particle is very complex and little different from an atom. Rutherford has given serious reasons for identifying the α particle with the helium atom deprived of a cathode corpuscle; also Stark gives experimental reasons referring to the emission spectra of positive centres in vacuum tubes, which imply a complex structure. Finally the theory of the disruptive discharge attributes the production of cathode rays in part at least to the impact against the cathode of particles which constitute the Goldstein rays; an electron smaller than the cathode particle itself seems scarcely able to produce a surface disturbance sufficiently intense, while on the other hand, an atom, unable to penetrate another atomic structure, and projected with a high velocity, would produce by its impact a considerable local disturbance.
(38) The Positive charge of the a Rays. It is perhaps by this considerable disturbance produced by the α or canal rays in matter which they meet that one can explain the interesting fact that the positive charge of the α rays has not been directly shown so far by the negative charge which a polonium salt should spontaneously ​acquire if it emits only α rays. However high may be the vacuum around a piece of radioactive bismuth, or polonium, it does not acquire any charge, and loses rapidly, on the contrary, its positive or negative charge. Possibly one might explain this discharge by the ionizing action of the α rays on the gas, however rare. The passage of α particles, projectiles of large dimensions, through the surface of radioactive bodies from which they come, can play the same part as the impact of Kanalstrahlen on the surface of the cathode, and cause the emission of cathode rays of very little penetrating power, whose presence would suffice, added to that of the α rays, to prevent any permanent charge of the radioactive body, whatever may be its sign.
(39) The Positive Electrons. If the positive centres, as we know, ought not to be represented as free electrons, it seems, however, necessary to admit the presence of probable electrons which cause the neutralization of the negative charges in the atomic structure, but which for some reason come out of this structure with extreme difficulty, contrary to what is the case for the negative centres. Moreover, it would appear necessary in order that the theory of metals, which ascribes their conductivity to the presence of free electrified centres moving under the action of a field can take account of all the facts, the Hall effect in particular, of variable sign in different metals, that the centres of two kinds coexist in the metal, free to move about in all directions. These positive centres do not appear to be the metallic atoms themselves, necessarily immovable in order to maintain the solid framework of the metal. It is possible that the positive electron, which no known action in a gas can maintain separate from the atomic material, may be free in large numbers in the entirely different medium which constitutes the metal. Many problems present themselves here on the subject of the nature of the positive charges.

## VIII. Theory of Matter. RadioactivityVIII. Theory of Matter. Radioactivity

(40) Atomic Instability. Let us examine now a little more closely the consequences to which we are led by the conception of matter as made up of electrons of two signs, of atoms formed of electrified bodies in motion under their mutual actions. From the first, - outside of gravitation, whose intensity is infinitely small compared to the electromagnetic forces in the interior of atoms which determine all the physical and chemical changes of state, - the elementary laws of action reduce to the forces of Lorentz, which allow us, as we have seen, to calculate the acceleration to which an electron is subjected as function of the electric and magnetic fields produced by the other electrons at the point where the first electron is situated. In the case ​where the acceleration is sufficient for it to radiate an appreciable energy to a distance by means of the acceleration wave, it is probably necessary to bring in, by other terms in the equation of motion of the electron, some forces by which it can receive again the energy which it radiates, and which disappear in the case of quasi-stationary motion. It does not seem, however, in any experimental case that these corrective terms can become appreciable.
From the same point of view, the electrons in periodic motion in the material atom are necessarily subject throughout their closed orbits to accelerations which are accompanied by a radiation of energy borrowed from the internal electric and magnetic energy of the atom. This radiation must be extremely small, as in the simple case of several cathode corpuscles circulating at equal distances in the same orbit, and can be compensated for by energy obtained from external radiation. We can suppose that this continual radiation, much more important naturally when the atom, as the result of external shock, is displaced from its most stable equilibrium, is a cause of decay to the atomic structure and which at the end of a certain length of time ought necessarily to give the structure a fundamental rearrangement, as a top falls when its rotation has sufficiently diminished in velocity. A condition of instability is thus reached, the consecutive rearrangement being accompanied by a violent projection of certain electrified centres from the atom. This conception furnishes at least an image of radioactive phenomena, and the successive transformations in the life of an atom, an hypothesis of which has been advanced by Rutherford. It seems, however, that it is not necessary to admit a probable decay of atomic structures, sensible only for radioactive substances. The fact that the dispersion takes place as a function of the time according to a rigorous exponential law, the quantity which is destroyed in a given time being exactly proportional to the quantity present, seems to indicate that the substance not destroyed remains identical with itself. Perhaps the reorganization of the atomic structure might result from its accidental passage through a particularly unstable configuration, the probability that a like configuration should be reproduced being independent, in the mean, of the previous history of the atom, and the mean life of the latter would be short in proportion as this probability is great.
(41) Internal Energy and Heat set Free. A very simple calculation shows also that the stock of energy represented by the electric and magnetic fields surrounding the electrons contained in an atom is sufficiently great to supply for ten million years the evolution of heat discovered by Curie in the radium salts. As it appears now well established that the mean life of a radium atom is of the order of a thousand years, it results that the ten-thousandth part only of this reserve of energy is utilized during this especially active period in ​the life of the atom. There is then no difficulty in conceiving how the enormous evolution of heat by radium can be ascribed to its internal energy.
No atom being free from this loss of energy due to the radiation of the electrons, one ought to expect on this hypothesis of decay a universality of radioactive phenomena, the atoms which we consider as actually stable suffering only an extraordinarily slow waste.

## IX. Electric PropertiesIX. Electric Properties

(42) Polarization. It remains now to show in a few words how the preceding conceptions lend themselves easily to a representation of the principal electric and magnetic properties of matter and make possible for the first time a theory of the disruptive discharge and of metallic conduction.
A common property of all forms of matter is electrostatic polarization arising from the variation of the specific inductive power with the nature of the substance.
This polarization results in a manner quite natural by the modification which an external electric field produces in the motions of the electron which constitute the atom. This modification is caused in the mean by an excess of positive centres on the side where the field tends to displace them and by an excess of negative centres on the opposite side. The system takes then on the average an electrostatic polarization.
(43) Corpuscular Dissociations. If the electric field becomes sufficiently intense, as, for example, during the passage of one of those brief pulsations which constitute the Roentgen rays, or during the passage through the atomic structure of an α or β particle of very great velocity, the modification produced may be very great, a cathode corpuscle may be separated from the structure which remains positively charged; there is produced thus a corpuscular dissociation which explains the conductivity acquired by insulating mediums under the action of Roentgen or Becquerel rays, and which manifests itself especially in gases, where the electrified centres thus freed can move more easily, although by electrostatic attraction on the neutral molecules, electrically polarizable, they surround themselves with a group of molecules which accompany them during their motion.
It seems well established that the negative ions in particular, also produced in a gas, have a cathode corpuscle for centre, since the penetration of cathode rays into a gas produces in it negative ions identical with those of Roentgen rays, at least from the point of view of their mobility or of their power of condensing supersaturated water vapor. It seems, nevertheless, important to make sure, by measuring the mobility of ions produced by different causes in the interior of gases, ​whether the differences which appear to exist are real and are caused by the difference in the molecules which adhere to them, or are due to the electrified centres which serve as the nuclei for them.
(44) Mobility and Recombination. It is equally important to be able, by measurement of mobility, to follow the modification which a change of temperature produces in the size of the agglomeration and to connect the ions observed at ordinary temperatures with the incomparably more mobile ions which we observe in flames, and which appear to be made up of single electrical centres, cathode corpuscles and perhaps α particles.
The rate of recombination of ions is as yet not well known in respect to the variations with pressure and temperature, although it certainly plays an essential part in the phenomena of disruptive discharge through gases at low pressures; it would be desirable if this point were better fixed.
(45) Ionization by Impact. Every actual theory of the disruptive discharge rests on the conception that the impact of an electrified particle in sufficiently rapid motion against a molecule can cause corpuscular dissociation.
This idea was a natural consequence of the known fact that cathode and Becquerel rays, made up of similar particles, make a gas through which they pass a conductor. If the corpuscular dissociation produces in the gas, separated from the molecule, a cathode corpuscle and a positive residue, these fragments can, if a sufficiently intense electric field exists in the gas, acquire a velocity great enough to act as β or α rays and cause from point to point a rapid increase in conductivity.
Townsend has shown how this consequence is capable of exact experimental verification, and he has found that between certain limits of velocity, each impact between the cathode corpuscle and a molecule results in a corpuscular dissociation of the same kind. The velocity acquired ought not, however, to exceed a certain limit beyond which the negative corpuscle or β particle passes through the atomic edifice without producing a sensible disturbance in it.
In order that a disruptive discharge may exist without an external cause to maintain the production of the first electrified centres, it is necessary that the positive centres should be able, like the negative, although with more difficulty, to produce corpuscular dissociation at the moment of their impact with the molecules, as this latter causes the conductivity produced in gases by the α rays.
Townsend has been able, in support of this hypothesis, to determine the exact moment when the disruptive phenomenon is produced, and to analyze the mechanism of it.
In addition to this fundamental conception of ionization by impact, the theory of the disruptive discharge has yet much progress to make. ​The extremely varied aspects which this discharge takes, the production of striations, an explanation of which was first given by J. J. Thomson, the influence of a magnetic field on the conditions of the discharge, the phenomena that are produced when the electrodes are only of the order of a micron apart, where the molecules do not appear to take part in the production of the spark, are many of the essential points which to-day attract attention.
(46) The Electric Arc. By the side of the ordinary disruptive discharge, by brush or spark, the electric arc, with an entirely different aspect, brings in the new phenomenon of the emission of cathode corpuscles by the surface of incandescent bodies. This incandescence of the electrode, of the cathode especially, is, in fact, characteristic of the arc discharge; the cathode is raised to a sufficiently high temperature by the impact of the positive ions which flow toward it, so that the corpuscles present in the electrode, and which give it its conductivity, experience a true evaporation and carry the greater part of the current. In fact, a filament of incandescent carbon is able to emit, at a much lower temperature than that of the voltaic arc, cathode corpuscles representing a current density of two amperes per square centimeter.
(47) Evaporation of the Cathode. This phenomenon, known under the name of the Edison effect, is very general and has been connected in a quantitative manner by Richardson on the fundamental hypothesis of the kinetic theory with the presence of freely moving cathode particles in the interior of conductors.
At ordinary temperatures this emission of corpuscles is diminished to such an extent that electrostatics is possible and a metal can keep a permanent charge. Every corpuscle present in the metal is immersed in a medium of high specific inductive capacity, and a finite amount of work is necessary to make them pass from this medium to a region where the specific inductive capacity is equal to unity. Only the corpuscles having a sufficient velocity would be able to supply this work on leaving the conductor, and their number, absolutely negligible at ordinary temperatures, increases with extreme rapidity with the rise in temperature. Richardson has shown that the variation obtained by experiment agrees very well with that predicted by theory.
(48) Metals. The spontaneous dissociation of atoms which the kinetic theory implies, the separation of electrified centres free to move in the interior of the metal, is a consequence of the high specific inductive capacity of the medium, of the ease of electrostatic polarization of metals, owing to the ease with which the metallic atoms lose corpuscles in order to remain positively charged. The potential energy of an electrified particle in such a medium is much smaller than anywhere else, and conformably with the laws of the distribution of ​energy given by the kinetic theory, the free particles ought to be more numerous in it.
(49) Chemical Phenomena. It is by an action of the same kind that water, of great specific inductive capacity (smaller, however, than that of metals) causes the electrolytic dissociation of salts that are dissolved in it; it would be of great interest to determine the relation between this electrolytic dissociation, especially of liquid conductors, and the corpuscular dissociation common probably to gases and metals.
In electrolytic dissociation, the cathode corpuscles lost by the metallic atoms, instead of remaining free as in corpuscular dissociation, remain united to an atom or to a radical to form the negative ion in electrolytes. This question touches the relations between our actual ideas and chemistry, relations still very obscure, and which it would be very important to clear up. The electric dissociation produced in gases by Roentgen rays does not appear connected with any chemical modification; however, in air all intense ionization is accompanied by the formation of ozone. Here is a domain almost entirely unexplored.

## X. Magnetic PropertiesX. Magnetic Properties

(50) Ampère and Weber. However, the complex phenomena of magnetism and diamagnetism have seemed so far to lead us to expect more difficulties, although the electrons gravitating in the atom in closed orbits furnish at first sight a simple representation of the molecular currents of Ampere, capable of turning under the action of an external magnetic field in order to give birth to induced magnetism, or of reacting by induction, according to the idea of Weber, against the external field so as to make the substance diamagnetic.
Those who have tried to follow out this idea have found it so far sterile; independently, different physicists have come to the conclusion that the hypothesis of electrons in undiminished motion cannot furnish a representation of the permanent phenomena of magnetism or diamagnetism.
I am enough of a parvenu to attempt to show, contrary to the preceding opinion, that it is possible to give, by means of the electrons, an exact signification to the ideas of Ampere and Weber, to find for para- and diamagnetism completely distinct interpretations, conforming to the laws experimentally established by Curie: weak magnetism, an attenuated form of ferromagnetism, varies inversely as the absolute temperature; on the other hand diamagnetism is shown to be, in all observed cases with the exception of bismuth, rigorously independent of the temperature. The theory which I propose takes ​entire account of these facts and clears up at the same time the complex question of magnetic energy.
I shall give here only the principal results of this work which will, be published in full elsewhere.
(51) Molecular Currents. An electrified particle of charge e moving with a velocity v is equivalent to a current of moment ev. One easily deduces from this that a molecular current made up of an electron which describes in the periodic time t an orbit inclosed by the surface S is equivalent from the point of view of the magnetic field produced to a magnet of magnetic moment $M={\tfrac {eS}{t}}$ normal to the plane of the orbit.
There would be a corresponding current for each of the electrons present in a molecule, and the magnetic moment resulting from these would be zero or different from zero, according to the degree of symmetry of the molecular structure.
(52) Diamagnetism. If on a group of such molecules we superimpose an external magnetic field, all the molecular currents experience a modification independent of the manner in which the superposition is obtained, whether by the establishment of the field or by motion of the molecule in a preexisting field. The direction of this modification, due to the induction experienced by the molecular currents, corresponds always to diamagnetism, the increase of the magnetic moment being $\Delta M=-{\tfrac {He^{2}}{4\pi m}}S$ in the case of a circular orbit. H is the component of the magnetic field normal to the plane of the orbit and m the mass of the electron which describes the orbit.
(53) The Magnetic Energy. When the molecule is supposed immovable, the work necessary for the modification of the molecular currents is furnished by the electric field produced, according to the equations of Hertz, during the establishment of the magnetic field.
In the opposite case, where the modification is due to the motion of the molecules, the work is furnished to the molecular currents by the kinetic energy of the molecule or by the action of neighboring molecules. The diamagnetic modification produced at the moment of the establishment of the field continues in spite of the molecular agitation.
This modification is manifested in three distinct ways:
1. If the resulting motion of the molecules is zero, the substance is diamagnetic in the ordinary sense of the word, and the order of magnitude of the experimental diamagnetic constants is in good agreement with the hypothesis of molecular currents circulating in intra-molecular paths.
This conception leads to the law of independence established by Curie between the diamagnetic constants and the temperature or the physical state.
​2. If the resulting motion of the molecules is not zero, the initial diamagnetic modification is followed by an orientation of the molecules under the action of the external field, which cause a paramagnetism to appear that masks the underlying diamagnetism, the new phenomenon being considerable compared to the first, when the symmetry permits it to appear.
In slightly paramagnetic bodies, such as gases, the heat agitation is opposed to the complete orientation of the molecular magnets, to saturation, and one finds, in seeking what permanent condition is established, the law of Curie, that the variation of paramagnetic constants is in inverse ratio to the absolute temperature.
3. Finally, the change of period of revolution in consequence of the diamagnetic modification corresponds to the Zeeman effect, as general as diamagnetism itself; iron, certain rays of which show the Zeeman effect, is diamagnetic before the orientation of the molecular magnets under the action of the external field makes it appear paramagnetic.
The orbits considered, which represent the molecular currents of Ampère, are also the circuits of zero resistance of the diamagnetism of Weber, with this remarkable peculiarity that the flux which passes through them is not constant, as Weber supposed, if the inertia of the electrons is entirely of electromagnetic origin.
I have shown, on the other hand, that the orbits of the electrons supposed circular, and described under the action of central forces, experience no deformation during the diamagnetic modification, this latter consisting only in a change of velocity of the electrons in their orbits. We can thus form an exact and simple conception of the facts of magnetism and diamagnetism by considering the molecular currents as non-deformable but movable currents, of zero resistance and of enormous self-induction, to which all the ordinary laws of induction are applicable.

## XI. ConclusionXI. Conclusion

The rapid perspective which I have just sketched is full of promises, and I believe that rarely in the history of physics has one had the opportunity of looking either so far into the past or so far into the future. The relative importance of parts of this immense and scarcely explored domain appears different to-day from what it did in the preceding century: from the new point of view the various plans arrange themselves in a new order. The electrical idea, the last discovered, appears to-day to dominate the whole, as the place of choice where the explorer feels that he can found a city before advancing into new territories.
The mechanical facts, the most evident of all those of which matter is possessed, from the first attracted the attention of our ancestors, ​and led them to conceive of the notions of mass and force which appeared a long while the most fundamental, those from which all the others ought to raminate. As the means of investigation have increased, as the more hidden facts have been discovered, we have thought for a long while to be able to reduce them to the old laws, to be able in fact to find an explanation of mechanical origin.
The actual tendency, of making the electromagnetic ideas to occupy the preponderating place, is justified, as I have sought to show, by the solidity of the double base on which rests the idea of the electron; on the one hand by the exact knowledge of the electromagnetic ether which we owe to Faraday, Maxwell, and Hertz, and on the other hand by the experimental evidence brought forward by the recent investigations into the granular structure of electricity. Moreover, this assurance which we express when considering the past is increased, if it is possible, when we consider the future.
Already all views, not only of the ether, but of matter, source and receiver of luminous waves, obtain an immediate interpretation which mechanics is powerless to give, and this mechanics itself appears to-day as a first approximation, largely sufficing in all cases of motion of matter taken in mass, but for which a more complete expression must be sought in the dynamics of the electron.
Although still very recent, the conceptions of which I have sought to give a collected idea are about to penetrate to the very heart of the entire physics, and to act as a fertile germ in order to crystallize around it, in a new order, facts very far removed from one another.
Falling in ground well prepared to receive it, in the ether of Faraday, Maxwell, and Hertz, the idea of the electron, an electrified movable centre which experiment to-day allows us to lay hold of individually, constitutes the tie between the ether and matter formed of a group of electrons.
This idea has taken an immense development in the last few years, which causes it to break the framework of the old physics to pieces, and to overturn the established order of ideas and laws in order to branch out again in an organization which one foresees to be simple, harmonious, and fruitful.
* ↑ I. Perrin, Traité de chimie Physique. Les Principes. Gauthier-Villars, Paris.
* ↑ Le Sillage Electro-magnétique.
* ↑ J. J. Thomson, Phil. Mag. t. 11, p. 229. 1881.
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