value as found from the first term, namely, eE/(κ2 – mn2). The equation thus becomes
.
If P denote[1] the electric moment per unit volume, we have
P = er × the number of such systems in unit volume of the medium;
so P must be of the form
,
where ε evidently represents the dielectric constant of the medium, and σ is the coefficient which measures the magnetic rotatory power. In the magneto-optic term we may replace H by K, the external magnetic force, since this is large compared with the magnetic force of the luminous vibrations. Thus if D denote the electric induction, we have
.
Combining this with the usual electromagnetic equations,
we have
.
When a plane wave of light is propagated through the medium in the direction of the lines of magnetic force, and the axis of x is taken parallel to this direction, the equation gives
and these equations, as we have seen,[2] are competent to explain the rotation of the plane of polarization.