294
XVIII
DIMENSIONS OF MAGNETIC POLE
will hold good for k. Now we may regard it as advantageous,
say with respect to the theory of unipolar induction, to take
this very equation as the fundamental equation for the con-
nection and to make ka pure number. We thus arrive at
the assumption :-
-1
[m][e] = ML2T-¹
which also coincides with (M).
(M'),
(b) For purposes of calculation an electrical doublet
can be completely replaced by a small magnetic circular
current, whose plane is perpendicular to the axis of the
doublet. Thus the moment es of the doublet must be pro-
portional to the strength m/t of the current and the area
which it embraces. Hence we put ed = kfm/t. Theoretically
there would be nothing wrong—although from the standpoint
of present theories and applications it would be unpractical-
if we started from this equation and made kg a pure number.
We should then have :-
:-
[e] = [m]LT-¹
(C').
The consequences of the assumptions (M') and (C') are as
follows:-
1. In the magnetic system we still have
[m] = M¹L¹T-¹.
Hence the dimensions of electric pole would be deduced as
M*L*, according to (M'); MLT-2, according to (C').
Thus there is now the inconvenience that in the magnetic
system different assumptions lead to different results.
2. In the electrostatic system we still have
[e] = M¹L¹T~¹.
Hence in this the dimensions of magnetic pole are
M*L*, according to (M'); ML, according to (C'),
and the electrostatic system has the advantage previously
assigned to the magnetic system.