274
XVII
FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS
later stage the principle was hardly mentioned, but was taken
for granted as self-evident. After the discovery of the electric
forces exerted by variable currents or moving magnets, a similar
principle was added relative to these electric forces, and this,
too, was not definitely expressed. It has perhaps nowhere
been explicitly stated that the electric forces, which have their
origin in inductive actions, are in every way equivalent to
equal and equally directed electric forces of electrostatic origin;
but this principle is the necessary presupposition and conclusion
of the chief notions which we have formed of electromagnetic
phenomena generally. According to Faraday's idea the electric
field exists in space independently of and without reference to
the method of its production; whatever therefore be the cause
which has produced an electric field, the actions which the
field produces are always the same. On the other hand, by
those physicists who favour Weber's and similar views, electro-
static and electromagnetic actions are represented as special
cases of one and the same action-at-a-distance emanating from
electric particles. The statement that these forces are special
cases of a more general force would be without meaning if we
admitted that they could differ otherwise than in direction
and magnitude, that is, according to nature and method of
action. But, apart from all theory, the assumption we are
speaking of is implicitly made in most electric calculations;
it has never been directly rejected, and may thus be regarded
as one of the fundamental ideas of all existing electromagnetics.
Nevertheless, to my knowledge no one has yet drawn attention
to certain consequences to which it leads, and which will be
developed in what follows. As premises we in the first place
employ the two principles referred to, which we might desig-
nate as the principle of the unity of electric force and that
of the unity of magnetic force. These may be regarded as
generally accepted, even if not as self-evident. In the second
place, we use the principle of the conservation of energy; that
of action and reaction as applied to systems of closed currents;
that of the superposition of electric and magnetic actions;
and lastly, the well-known laws of the magnetic and electro-
motive actions of closed currents and of magnets. The in-
vestigation throughout refers to closed currents, even where
this is not specially stated.