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.

402 MR LARMOR, ON THE DYNAMICS OF A SYSTEM OF ELECTRONS OR IONS:
GENERAL VIBRATING SYSTEM IN WHICH THE PRINCIPAL MODES ARE CIRCULAR.
9. We are entitled to assert, on the basis of Fourier's theorem, that any orbital
motion which exactly repeats itself with a definite period can be resolved into constituent
simple elliptic oscillations whose periods are equal to its own and submultiples thereof.
Such a motion would therefore correspond to a fundamental spectral line and its system
of harmonics. The ascertained absence of harmonics in actual spectra shows either that the
period corresponding to the steady orbit is outside the optical range, or else that the steady
motion emits very little radiation as in fact its steadiness demands. The radiation would
then arise from the various independent modes of disturbance, each of elliptic type on
account of the absence of harmonies, that are superposed on the steady orbital motion.
To ascertain the nature of the polarization of the vibrations when in a magnetic field,
we have first to decompose each orbital motion into its harmonic constituents, which are
elliptic oscillations: each of the latter can be resolved into a linear oscillation parallel to
the axis of the magnetic field, another at right angles to it, and a circular oscillation
around it; and of these the second linear oscillation can be resolved into two equal circular
oscillations in different senses around it. Now when the uniform rotation around the axis
is superposed on the components they all continue to be of the requisite simple harmonic
type, but the periods of the two circillar species,-which as has been seen are of amplitudes
different as regards the various molecules but equal in the aggregate,-become different:
they are the three Zeeman components.
Nothing short of complete circular polarization of the constituent vibrations of permanent
type in each molecule will account for the corriplete circular polarization of each of the
flanking Zeeman lines. If these vibrations were only elliptical, but propagated with different
velocities according to the sense in which the orbit is described, each would be equivalent
to a circular vibration together with a linear one: and as the total illumination is the sum
of the contributions from the independent molecules, the circularly polarized light would
then be accompanied by unpolarized light of the same order of intensity. This restriction
of type of vibration suggests the employment in the analysis of variables each of which
corresponds to a circular vibration, as do the:, Vî variables in what follows.
For simplicity let us take the axis of z parallel to the impressed magnetic field, and
let (X, Y, Z) represent the statical forces transmitted by aether-strain from the other ions
in the molecule to a specified one. The equations of motion of that ion are
m (x -y) = X, m(y + K) = Y, m = Z.
We now make no assumption with regard to the magnitude of the electric charges and
effective masses of the various ions, which may differ in any manner. In this ion let us
change the variables to
I:= x + Y, rY]= x- ty,