obtained are in agreement with those of Lorentz on all important points; I was only led to modify and supplement them in some points of detail; one will further see the differences which are of secondary importance.
The idea of Lorentz can be summarized as follows: if we can bring the whole system to a common translation, without modification of any of the apparent phenomena, it is because the equations of the electromagnetic medium are not altered by certain transformations, which we will call Lorentz transformation; two systems, one motionless, the other in translation, thus become exact images of one another.
Langevin[1] had sought to modify the idea of Lorentz; for both authors the moving electron takes the shape of a flattened ellipsoid, but for Lorentz two of the axes of the ellipsoid remain constant, while for Langevin on the contrary it is the volume of the ellipsoid which remains constant. Besides, both scientists showed hat these two hypothesis are in agreement with the experiments of Kaufmann, as well as the original hypothesis of Abraham (undeformable spherical electron).
The advantage of the theory of Langevin is that it uses only electromagnetic forces and binding forces; but it is incompatible with the postulate of relativity; this is what Lorentz had shown, this is what I find again in another way by relying upon the principles of group theory.
It is thus necessary to return from here to the theory of Lorentz; but if one wants to preserve it and avoid intolerable contradictions, it is necessary to suppose a special force which explains at the same time the contraction and the constancy of two of the axes. I sought to determine this force, I found that it can be compared to a constant external pressure, acting on the deformable and compressible electron, and whose work is proportional to the variations of the volume of the electron.
So if the inertia of matter is exclusively of electromagnetic origin, as it is generally admitted since the experiment of Kaufmann, and except that constant pressure from which I come to speak, all forces are of electromagnetic origin, the postulate of relativity can be established in any rigour. It is what I show by a very simple calculation founded on the principle of least action.
But this is not all. Lorentz, in the quoted work, considered it to be necessary to supplement his hypothesis so that the postulate remains when there are other forces as the electromagnetic forces. According to him, all the forces, whatever is their origin, are affected by the Lorentz transformation (and consequently by a translation) in the same way as the electromagnetic forces.
It was important to examine this assumption more closely and in particular to seek which modifications it would oblige us to bring to the laws of gravitation.
It is found at first sight, that we are forced to suppose that the propagation of
- ↑ Langevin was preceded by M. Bucherer from Bonn, who had put forward the same theory before. (See: Bucherer, Mathematische Einführung in die Elektronentheorie; August 1904. Teubner, Leipzig).
