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. 383
involved; but the intrinsic or constitutive energy of the electron itself, that is the
total mutual energy of the constituent parts of the electron exclusive of the energy involved
in its motion as a whole through the aether, will not be included: this latter part is in
fact supposed (on ample grounds) to be unchangeable as regards all the phenomena now
under discussion, the nuclei of the electrons being taken to occupy a volume extremely
small in comparison with that of the surrounding aether*.
This principle leads to an expression for the force acting on each individual moving
electron, which is what is wanted for our present purpose. But the equations of ordinary
electrodynamic theory belong to a dense distribution of ions treated by continuous
analysis, and we have there to employ the averaged equations that will obtain for an
effective element of volume of the aether containing a number of electrons that practically
is indefinitely great.
We derive then the equations of the aether considered as containing electrons from
those of the uniform aether itself by adding to the changing aethereal displacement
(f y, h) the flux of the electrons of type e (, y, i) wherever electrons occur. In the
transformed expression for T we can, as already explained, treat the part of the surface
integral belonging to the surface cutting an electron out of the region of integration
(as well as any energy inside that surface) as intrinsic energy of the electron, of unchanging amount, which is not concerned in the phenomena because it does not involve
the state of any other electron. The contribution from the surface integral over the
infinite sphere we can take to be zero if we assume that all the disturbances of
electrons are in a finite region: the truth of this physical axiom can of course be directly
verified.
We have therefore generally
T= f(Fu + Gv + Hw) dr,
wherein
(F, G, H)= f(, v, w) r- d:
and in these expressions the total electric current (uî, v, w) will consist of a continuous
part (f, g, h) which is not electric flow at all, and a discrete electric flux or true current
of amount e (X, y, Z) for any electron e. When the electrons are considered as forming
a volume density of electrification, this latter will be considered as continuous true electric
flow constituted as an aggregate of all the different types of conduction current, convection
current, polarization current, etc. that can be recognized in the phenomena, each being
connected by an experimental constitutive relation with the electric force which originates
it. The orbital motions of the electrons in the molecule cannot however be thus included
in an electric flux, but must be averaged separately as magnetization. Neither the
true current nor the aethereal displacement current taken separately need satisfy the
* For a treatment on somewhat different lines cf. Pihil. Trans. 1897 A, or 'Aether and Matter,' Ch. vi., Camb.
Univ. Press, 1900.
t It may be formally verified, after the manner of the formula for T in ~ 2, that this amount tends to a
definite limit as the surface surrounds the electron more and more closely.