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. 389
As regards the electron el, the first of these terms is the same as that due to
an impressed magnetic field given by
( = - 2m\
(a,', p, 7o)=- e (yx, y, z).
el
The others give rise to terms in the electric forces which are small compared with
the internal electrodynamic forces of the system itself when the angular velocity is
small: and in. our applications these latter will be themselves negligible compared
with the electrostatic forces.
MUTUAL FORCES OF ELECTRONS.
When a system of electrons or ions is moving in any manner, with velocities of
an order lower than that of radiation, the surrounding aether-strain may be taken as
at each instant in an equilibrium conformation: thus the positional forces between the
electrons are simply their mutual electrostatic attractions. As regards kinetic effects, the
disturbance in the aether can be considered as determined by the motion of the electrons
at the time considered, so that the kinetic energy can be expressed entirely in terms of
the motions of the electrons; and the motional forces between two of them are derived in
the Lagrangian manner from the term in this total kinetic energy
ele2r~2-l ( 1&~ + yY1 + l02) + elve,2v2d2r1l2/ds, ds2,
where ds1, ds2 are elements of their paths described with velocities vL, v2. The Weberian
theory of moving electric particles involves on the other hand a kinetic energy term
ele2r2-1 (drl2/dt)2: in the field of the electrodynamics of ordinary currents it however
yields equivalent results as regards mechanical force, and the electromotive force induced
round a circuit, though not as regards the electric force at a point.
THE ZEEMAN EFFECT.
4. On the hypothesis that a molecule is constituted of a system of revolving ions,
a magnetic field H impressed in a direction (1, m, n) adds to the force acting on an
ion of effective mass m and charge e, situated at the point (x, y, z), the term
eH (ny - mz, 1 - nx, mx - ly),
so that its dynamical equations are modified by change of Y, y, z into
x - (ny - nz), y - c (l - nx), z- E (nx - ly),
where K = eH/m, e being in electromagnetic units.
If the ratio e/m is the same for all the ions concerned in the motion, so is K,
and this alteration of the dynamical equations of the molecule will be, to the first
order of K, the saine as would arise from a rotation of the axes of coordinates to
which the system is referred, with angular velocity -K around the axis of the impressed
magnetic field. Hence the alteration produced in the orbital motions is simply equivalent to a rotation, equal and opposite to this, imposed on the whole system. Each
line in the spectrum would thus split up into two lines consisting of radiations circularly
polarized around the direction of the magnetic field, and with difference of frequencies
constant all along the spectrum, namely Kc/27r, together with a third line polarized so that