134 PHYSICS OF THE ELECTRON 



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 con- 

 stitutes 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 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 intens- 

 ities; 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 dynam- 

 ics; the other, representing forces dependent on the motion itself, 

 and producing a resistance to motion, similar to the forces of in- 

 ertia. 



The terms corresponding to external actions, the forces, have been 

 obtained by Lorentz following a method which was the natural con- 

 tinuation of Maxwell's idea as to the possibility of a mechanical 

 explanation, otherwise indeterminate, by the facts of electromag- 

 netism. The analogy to the equations of electrodynamic induction, 

 and to the equations of Lagrange, appeared to justify such an ex- 

 planation, 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 con- 

 sidered 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 ma- 

 terial dynamics, deduced from principles founded on observations of 

 matter only, always taken in mass and without an appreciable amount 

 of radiation. 



