The more important values from the point of view of choice of equations are those corresponding to values of the velocity very near to that of light, and which amounted to ninety-five per cent of it in Kaufmann's experiments. But the β rays are then very little deviated, and exact measurements are extremely difficult.
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.
