Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

AND THE INFLUENCE OF A MAGNETIC FIELD ON OPTICAL PHENOMENA. 397
For the case when there is only a single free period this result coincides with FitzGerald's
formula (Roy. Soc. Proc. 1898), which has been shown by him to give the actual order
of magnitude for a Faraday effect as thus deduced from the Zeeman effect.
If we were to consider that each system, of lines in the spectrum arises from an
independently vibrating group of ions in the molecule, as (supra) there may be some
temptation to do, then the value of (2 - 1)/(/2 + 2) in this formula would be obtained
by addition of the effects of these independent groups: thus if the value of the Zeeman
effect were known for each line of the spectrum of any substance, and the law of
dispersion of the substance were known, the Faraday effect could be deduced by calculation. To our order of approximation we should have
_ _- 1 ~ E + K4rArP
2 + ) (p2-p2)2*
the circumstance that the mean of the velocities of propagation is unaltered points to the
A coefficients being unaffected by the magnetism, thus suggesting absence of change in
the mean conformation, as already remarked.
For the case in which the free periods that effectively control the dispersion all
belong to the same series of spectral lines, so that K is the same for all of them, the
formula for the dispersion need not come into the argument. The influence of the
impressed magnetic field on the index of refraction of circularly polarized light is then the
same as the change of p to p + 'KC according as the polarization is left-handed or righthanded. Because that influence is equivalent to rotation of the optically vibrating molecule
with angular velocity Kc, the molecule will now be related in the same way to a wavetrain with angular velocity p ~ i/c as it was previously to one with angular velocity p.
dV
Thus light corresponding to angular velocity p is now propagated with velocity V + -
dp
instead of V. Now if X be the wave-length in a vacuum and /u the refractive index,
we have V= c//p, p = 27re/X: and the rotation of a plane of polarization for a length
I of the medium, being ~p multiplied by the difference of times of transit, is
(l/YI,-l/V,). 27ro/X, which is 7rlc. 6V/V2X,
where SV= /cdV/dp = 2 d-l/dx~-, so that the result is 2-X dx'
This expression, - X d-, for the coefficient of magnetic rotation as a function of the
wave-length, has been given by H. Becquerel* and shown by him to be in good
agreement with actual values as regards order of magnitude, and also with Verdet's
detailed observations along the spectrum in the cases of carbon disulphide and creosote.
The restriction on which it is here based, namely that the dispersion is controlled by free
periods for all of which the Zeeman constant is the same, can be neglected for the case
of the anomalous dispersion close to an absorption band, because there the dispersion
* Comptes Rendus, Nov. 1897: it was based on the assumption that the magnetic field involves rotation of the
aether with velocity tK.