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 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.
