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XVIII
DIMENSIONS OF MAGNETIC POLE
and that by using the latter one may avoid the pitfalls which
undoubtedly beset the former. I shall endeavour to show that
such a conception would be incorrect, by comparing with the
assumptions from which Maxwell and Clausius start two
others; theoretically, although not practically, the latter are
as well established as the former, and by using them we can
make the magnetic and electrostatic systems change places.
If these new assumptions had originally been adopted instead
of the old ones, there would have been agreement as to the
electrostatic system, but discussion as to the magnetic system.
This shows clearly a posteriori (and the same can be proved a
priori) that neither of the two systems is in general preferable
to the other or more reliable than it; only one of the two may
be preferable in a given department of electromagnetics, or
more reliable in its application to a given electromagnetic
calculation. In a sense it is simply a matter of chance that
the discussion arose in connection with the electrostatic and
not the magnetic system. I shall compare, as thesis and
antithesis, the old and the new assumptions, together with
the deductions from them.
The thesis then is :-
(a) The work which must be done in order to move a
magnetic pole m in a closed path once around a constant
electric current, which in the time t conveys the quantity e, is
proportional to the strength m of the pole and the strength
e/t of the current: it is independent of geometrical relations.
If then we put A=k,me/t, k, is a constant whose magnitude
and dimensions depend only upon the system of units chosen.
Maxwell considers it best to connect electrical and magnetic
quantities in such a way that this constant becomes a number
of no dimensions. Thus, using the usual notation
[m][e] = ML2T-¹
(M).
(b) The moment md of a magnetic doublet, which for
purposes of calculation can be completely replaced by a small
circular current, is proportional to the strength e/t of the current
and the area ƒ enclosed by it. Hence md = keft, where again
ką is a constant which depends only upon the units chosen.
If k, is a pure number, k, in general will not be so; and con-