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Translated from Recherches critiques sur l'Ėlectrodynamique Générale,
Annales de Chimie et de Physique, Vol. 13,   p. 145, 1908.

Annales 244 (Oeuvres 400)

      When a condenser discharges through a wire, one obtains, as we know, a first approximation,

Annales 245

sufficient in many cases, for calculating electromagnetic effects (for example, the impulse felt by a magnetized needle in the experiment of Weber and Kohlrausch for the determination of the relation between the units) and self-induction, as if the current was closed, while naturally taking into account the electrostatic actions of the charges of the condenser. These calculations will therefore continue to be applicable in the new theory; they lead, in accord with the experiment, to the very rapid phenomena, for which the accelerations w are quite considerable in relation to the speeds v. In the case, for example, where one would have n sinusoidal oscillations per second, the maximum value of w is 2πn times greater than that of v. In these experiments, the electrostatic term, the resistance, and the induction proportional to, that is to say, to w, play only a role, which concerns the movement of electricity in the conductors. These terms are identical in both theories. As for the couples acting on the magnetized needles or coils, we have seen that it suffices, for the identity of the theories, that one of the currents be closed, which is certainly the case.

      The effects of a movement of the conductors, which will always be slow in relation to these phenomena, would not noticeably influence them; more generally, the terms in v’, small compared to those which contain w', will be without an induction effect in these phenomena. The oscillations of such circuits (oscillations which are often designated by the expression quasi-stationary) and their effects on neighboring circuits will therefore be the same in both theories.  It is only when the oscillations become extremely rapid (Hertzian oscillations) that the serial developments which have led to formula (13) cease to be very (Oeuvres 400) convergent; the propagation then plays an explicit role, and one must have resort to new

Annales 246

considerations which I will show later on; the agreement with the formulas of Maxwell and Lorentz will stay the same.

      In summary, no noticeable divergence from Lorentz’s theory and from experiment was revealed for slowly varying phenomena; this fact is not without interest, in light of the great difference in elementary laws, and shows that despite recent progress, these laws can still be deduced from experiments.[1]  

[1] For more details on the interpretation of the resistance, the magnetism, and so on, in the theory of electrons, see the already cited article by M. Lorentz: Elektronentheorie, in Enzyklop. d. math. Wissensch., Leipzig, 1994.

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