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. 391
uniform rotation in the case of the massive positive ions are small compared with the
magnetic part of the forces acting on the negative ions. If these maintaining forces
are absent, the system can still be regarded as a molecule in its undisturbed motional
configuration rotating with uniform angular velocity, but subject to disturbing forces equal
and opposite to those required to thus maintain it. Now this undisturbed motional configuration is a stable one: thus the effect of these slight disturbing forces is to modify it,
but to an extent much smaller than the uniform rotation induced by the magnetic field.
Our proposition is thus extended to a molecule consisting of an interacting system,
constituted of equal negative ions together with much more massive positive ions, and also
if so demanded of other massive sources of attraction. It would however be wrong to
consider each negative electron as describing an independent elliptic orbit of its own,
unaffected by the mutual attractions exerted between it and the other moving negative
electrons: for the attractions between ions constitute the main part, if not the whole, of
the forces of chemical affinity. But without requiring any knowledge of the constitution of
the molecular orbital system, the Zeeman triplication of the lines, with equal intervals
of frequencies for each line, will hold good wherever the conditions here stated obtain.
It appears from the observations that the difference of frequencies of the components
magnetically separated is not constant for all lines of the spectrum: so that this simple
state of affairs does not hold in the molecule. The difference of frequencies seems however
to be sensibly constant for those lines of any element which belong to the same series, as
well as for those lines of homologous elements which belong to corresponding series; a result
which cannot fail to be fundamental as regards the dynamical structure of molecules, and
which supports the suggestion that inr a general way the lines of the same series arise
from the motions of the same ion or ionic group in the molecule, executed under similar
conditions. The directions of the circular polarizations of the constituent lines were shown
by Zeeman to be in general such as would correspond in this kind of way to the motions
of a system of negative ions in a steady field of force.
It remains to be considered whether we are right in thus taking the stresses
transmitted between the electrons, through the aether, as those arising from the configuration of the electrons alone, and in neglecting altogether the motional forces between
them. The former assumption is equivalent to taking the strain in the surrounding
aether to be at each instant in an equilibrium state: this will be legitimate, because
an aethereal disturbance will travel over about 103 diameters of the molecule in one
of the periods concerned, —the error is in fact of order 10-6. The motional forces between
two electrons are of type, as regards one of them,
( d d\ -x- + Y,2 + Jz2+ d$ -v 12
(dt dx, dlxj el2 ( ri2 2 v1v2 dseds2)
To obtain a notion of orders of magnitude, let us consider the special case of two electrons
+ e, -e describing circular orbits round each other with radius r. Then qmv2/r=c e2/r2,
* Preston, Phil. Mag., Feb. 1899.