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XVII
FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS
a magnetising force at the instant when the intensity of the
field is reduced to zero; and that the same ring is subject to
an alternating polarisation when we turn it about an axis
which is perpendicular to the direction of the electric force.
It does not appear impossible that such actions may become
capable of experimental detection. Again, a ring-magnet
whose polarisation is continually changing its direction must
by induction call forth alternating polarisations in all neigh-
bouring iron rings; but this action is certainly too small to
reach an observable value.
2. It may at first sight seem as if the actions here
deduced from generally accepted premises permitted of
incorporation without disturbance into the usual system of
electromagnetics; but this is not the case. In fact, suppose
that in place of the ring-magnets so far considered we have
endless electric solenoids, in which the current-intensity is
variable; then the induced electric forces produced by these
solenoids are certainly quite analogous to those exerted by the
variable magnets.
From these latter forces we deduced
magneto-dynamic attractions, and we must therefore infer
corresponding electrodynamic attractions between the variable
solenoids. But as long as the currents in them are constant
no action takes place. Hence in general the electromagnetic
attraction between currents must depend on their variations
and not merely on their momentary intensities. This state-
ment is in opposition to an assumption uniformly accepted in
the usual electromagnetics.¹ The correction which must be
made in the laws of the magnetic actions of constant currents
to make them applicable to variable currents may be
calculated from our premises. But this correction requires,
on account of the principle of the conservation of energy, a
correction in the induced electrical forces as well. This again
requires a second correction in the magnetic forces, and so on;
so that we obtain an infinite series of successive approxima-
tions. We shall now calculate these separate terms.
We
assume that they are simply to be added to the total result,
and that, if only the infinite sums converge to definite limits,
then these limiting values are those corresponding to the
1 Cf. v. Helmholtz, "Über die Theorie der Elektrodynamik," Wissenschaftliche
Abhandlungen, vol. i. p. 729.