288
XVII
FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS
Now the system of forces given by the equations (12) and
(13) is just that given by Maxwell. Maxwell found it by
considering the ether to be a dielectric in which a changing
polarisation produces the same effect as an electric current.
We have reached it by means of other premises, generally
accepted even by opponents of the Faraday-Maxwell view.
The equations (12) and (13) appear to us to be a necessary
complement of the equations (1), (2), (3), which are usually
regarded as exact. From our point of view, the Faraday-
Maxwell view does not furnish the basis of the system of
equations (12) and (13), although it affords the simplest
interpretation of them. In Maxwell's theory the equations
(12) and (13) apply not merely to empty space but also to
any other dielectric. Starting from our premises we can also
show these laws to hold in every homogeneous medium. We
must assume the fact as experimentally demonstrated that the
magnetic forces which surround a current-system placed in a
homogeneous medium are distributed according to the equations
(1) in the same way as in empty space. Hence we need only
imagine the conductors and masses of iron which we have con-
sidered to be completely immersed in the given medium. In
this medium we must define the units of electricity and
magnetism in the same terms as in empty space. We must
then determine the constant A, which gives the absolute value
of the magnetic force produced by unit current in the new
electrostatic measure. All further forces follow from the
assumed experimental fact and the general premises; and
since all the propositions are the same as those for empty
space, the final result is the same. It is true that the value
of the constant A will not be the same as in empty space, and
that it will have different values in different media.
Its recip-
rocal is always the velocity of propagation of electric and
magnetic changes. It is an internal constant, but the only
internal electromagnetic constant of the medium. The two
constants of which it is generally built up, viz. the specific
inductive capacity and the magnetic permeability, should in
contrast to it be termed external constants. Not only the
measurement, but even the definition of these latter constants,
requires the specification of at least two media (one of which
may be empty space).