XVII
289
FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS
In what precedes I have attempted to demonstrate the
truth of Maxwell's equations by starting from premises which
are generally admitted in the opposing system of electro-
magnetics, and by using propositions which are familiar in it.
Consequently I have made use of the conceptions of the latter
system; but, excepting in this connection, the deduction given
is in no sense to be regarded as a rigid proof that Maxwell's
system is the only possible one. It does not seem possible to
deduce such a proof from our premises. The exact may be
deduced from the inexact as the most fitting from a given
point of view, but never as the necessary.¹ I think, however,
that from the preceding we may infer without error that if
the choice rests only between the usual system of electro-
magnetics and Maxwell's, the latter is certainly to be preferred;
and that for the following reasons :—
1. The system of the electromagnetic action of closed
currents founded on direct action-at-a-distance is in its present
state certainly incomplete. Either it must introduce different
kinds of electric force, which it has never done, or it must
admit the existence of actions which hitherto it has not taken
into account. Maxwell's system does not in the same way
contain within itself the proof of its incompleteness.
2. When we attempt to complete the usual system of
electromagnetics, we always arrive at laws which are very com-
plicated and very difficult to handle. And either we refuse
to admit the accumulated results of paragraph 2, in which
case we end with an unfruitful declaration of incompetence;
or, as from the standpoint of the system seems more reasonable,
we accept them as being valid, and so arrive at forces which
in fact are the same as those demanded by Maxwell's system.
But then the latter offers by far the simplest exposition of the
results.
1 The mode in which we have deduced conclusions from the principle of
the conservation of energy clearly marks at each stage the point at which
our deductions are only the most fitting, and not the necessary ones. This
mode is the most fitting from the standpoint of the usual system of electro-
magnetics, for it corresponds exactly to the accepted proposition in which
Helmholtz in 1847 and Sir W. Thomson in 1848 deduced induction from
electromagnetic action. But perhaps it may not be the only possible method;
for just as in that proposition, so we have in ours made tacit assumptions besides
the principle of the conservation of energy. That proposition also is not valid
if we admit the possibility that the motion of metals in the magnetic field may
of itself generate heat; that the resistance of conductors may depend on that
motion; and other such possibilities.
M. P.
U