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.

396 MR LARMOR, ON THE DYNAMICS OF A SYSTEM OF ELECTRONS OR IONS:
the effect persisting if the field is gently removed: that the field can then act afresh on
the molecules thus newly aggregated: and so on by a sort of regenerative process,
the inducing field and the retentiveness mutually reinforcing each other, until large
polarizations are reached before it comes to a limit. For hard iron these accommodations
take place more rapidly than for soft iron, when the field is weak, and thus are of sensibly
elastic character over a wider range: cf. Ewing, Magnetic Induction, 1892, ch. vi.
ON THE ORIGIN OF MAGNETO-OPTIC ROTATION.
7. The Faraday magneto-optic rotation is obviously connected, through the theory
of dispersion, with the different alterations of the free periods of right-handed and
left-handed vibrational modes of the molecules, that are produced by the impressed
magnetic field. The ascertained law (infra) that the mean of the velocities of the
two kinds of wave-trains is equal to that of the unaltered radiation, shows that the
phenomenon in fact arises wholly from this difference, and is not accompanied by
temporary structural change in the molecule such as would involve alteration of the
physical constants of the medium.
The general relation connecting the refractive index,/ of a transparent medium
with the frequencies (pi, p2,... p^)/27r of the principal free vibrations of its molecules,
which are so great that radiation travels over 103 molecular diameters in one period,
is of type
2-1 = Ar
= 5,~2 + 2 p2 _. pr2
in which A, is a constant which is a measure of the importance, as regards dispersion,
of the free principal period 27r/Pr. The quantity on the right-hand side of this equation,
of form f(p2), is a function of the averaged configuration of the molecule relative to the
aethereal wave-train that is passing over it. Now consider a circular wave-train, say
a right-handed one, passing along the direction of the magnetic field: on the hypothesis
that the spectrum consists of a single series of lines for all of which /c is the same,
the influence of this train on the corresponding right-handed vibrations that it excites
in the molecule will be to superadd a rotation of the molecule as a whole with angular
velocity 2Ic. This will modify the configuration of the vibrating system relative to the
circular wave-train passing over it in the saine way as if an equal and opposite angular
velocity were instead imparted to the wave-train. Thus the actual effect of the magnetic
field on the light will be the same as would be that of a change in the frequency
of the light from pl/2rr to p/27r+ c/47r, the latter terni arising from this imposed angular
velocity: the value of the magneto-optic effect may therefore in such a case be derived
from inspection of a table of the ordinary dispersion of the medium.
The velocity of propagation of the train of circular waves will, on this hypothesis,
be derived by writing p- K or p + c for p according as the train is right-handed
or left-handed, thus giving when K2 is neglected,
/_2 12 _ 2 Ar
2 + 2 -p p - 2.