Having generalised in Section 4.4 Maxwell's Equations to take into account the effects of
polarisation and magnetisation within media, we find we are left with too few equations
in the number of unknowns now involved, to obtain a solution. The number of equations
in the expanded set of variables is madę sufficient when we provide a specification of the relationship between the polarisation and magnetisation vectors P and M and the
internal electric and magnetic fields E andHwhich may be regarded as their direct cause.
In our physical experience there is a wide variety of media which we might encounter,
and hence a variety in the behaviour to be described. There is also a variation in the degree
of precision with which it might be convenient to describe that behaviour. The subject
we have identified is therefore a wide one, and we will provide here only an elementary
and incompletetreatment.