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.
