XVIII
293
DIMENSIONS OF MAGNETIC POLE
versely. Now Clausius holds that according to Ampère's theory
it is necessary to connect magnetic and electrical quantities in
such a way that he shall be a number of no dimensions; from
which it follows that
[m] = [e] LT-¹
(C).
The consequences of the assumptions (M) and (C) are as
follows:-
1. In the magnetic system we start with the dimensions
[m] = M¹LT-¹. From this we deduce, as the dimensions of
electric pole,
MIL', according to (M); M'L, according to (C).
Hence there is agreement.
2. In the electrostatic system we start with the dimensions
of electric pole [e] = M¹L'T-¹. From this we deduce, as the
dimensions of magnetic pole,
M'L', according to (M);
MLT-2, according to (C).
The two expressions are different, and this is the objection
urged against the electrostatic system.
» 1
In setting forth the antithesis I shall make use of the
expression "magnetic current." A constant magnetic
current is represented by a wire-shaped ring-magnet which
gains or loses equal quantities of magnetism in equal times.
For sufficiently short periods we can produce such currents of
any desired strength, and for periods of any length if we make
them sufficiently weak. The electrical forces exerted by such
a current are known, and every system of electromagnetics
contains the following propositions, although they may be
differently expressed :--
(a) The work which must be done in order to move an
electric pole e in a closed path once around a constant magnetic
current, which in the time t conveys the quantity m, is pro-
portional to the strength e of the pole and the strength m/t
of the current; it is independent of geometrical relations. If
then we put A = k'e.m/t, what has been stated for k₁ and ką
1 See XVII. p. 276.