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§10. – INDUCTIVE CIRCUITS AND OPEN SECONDARIES
Translated from Recherches
critiques sur l'Ėlectrodynamique Générale,
Annales de Chimie et de Physique, Vol. 13, p. 145, 1908.
When a condenser discharges through a wire, one obtains, as we know, a
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<![if !vml]><![endif]>, 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
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.