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.

382 MR LARMOR, ON THE DYNAMICS OF A SYSTEM OF ELECTRONS OR IONS:
function of position X: but this part does not affect the value of (a, f/, y) through
which (F, G, H) has been introduced into the problem, so that the definite particular
solution is all that is required.
Now the motions of the electrons involve discontinuities, or rather singularities, in
this scheme of functions. One mode of dealing with them would involve cutting each
electron out of the region of our analysis by a surface closely surrounding it. But a
more practicable method can be adopted. The movement of an electron e from A to an
adjacent point B is equivalent to the removal of a nucleus of outward radial displacement from A and the establishment of an equal one at B: in other words it involves
a transfer of displacement in the medium by flow out of the point B into the point
A: now this transfer can be equally produced, on account of the stream character of
the displacement, by a constrained transfer of an equal amount e of displacement
directly from A to B. Hence as regards the dynamics of the surrounding aether, the
motion of such a singular point or electron is equivalent to a constrained flow of
aethereal displacement along its path. The advantage of thus replacing it will be great
on other grounds: instead of an uncompleted flow starting from B and ending at A,
there will now be a continuous stream from B through the surrounding aether to A
and back again along the direct line from A to B: in other words the displacement
will be strictly a stream vector, and in passing on later to the theory of a distribution
of electrons considered as a volume density of electricity, the strictly circuital character
of the electric displacement, when thus supplemented by the flow of the electrons, will
be a feature of the analysis.
For greater precision, let us avoid for the moment the limiting idea of a pointsingularity at which the functions become infinite. An electron will now appear as an
extremely small volume in the aether possessing a proportionately great density p of
electric charge. Its motion will at each instant be represented by an electric flux of
intensity p(&, y, z) distributed throughout this volume, which when added to the aethereal
displacement now produces a continuous circuital aggregate. For present purposes for
which the electron is treated as a point and the translatory velocities of its parts are
very great compared with their rotational velocities, this continuous flow may be condensed
into an aggregate flux of intensity e (x, y, i), concentrated at the point (x, y, z).
At each point in the free aether, outside such nuclei of electrons, the original
specification of magnetic force, namely that its curl is equal to 47rd/dt of the aethereal
displacement, remains strictly valid. It has been seen that the effect of the motion
of any specified electron, as regards the surrounding aether, is identical with the effect
of an impressed change in the stream of aethereal displacement at the place where it is
situated: thus the interactions between this electron and the aether will be correctly
determined by treating its motion as such an impressed change of displacement. This
transformation however considers the nucleus as an aggregate: it will not be available
as regards the interactions between different parts of the nucleus: thus in the energy
function constructed by means of it, all terms involving interaction between the electron
as a whole and the aether which transmits the influence of other electrons will be