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.

MR LARMOR, ON THE DYNAMICS OF A SYSTEM OF ELECTRONS OR IONS: ETC. 381
It will now be postulated that the origin of all such aethereal disturbances consists
in the motion of electrons, an electron being defined as a singular point or nucleus
of converging intrinsic strain in the aether, such for example as the regions of intrinsic
strain in unannealed glass whose existence is revealed by polarized light, but differing
in that the electron will be taken to be freely mobile throughout the medium. For
all existing problems it suffices to consider the nucleus of the electron as occupying so
small a space that it may be taken to be a point, having an electric charge e
associated with it whose value is the divergence of (f, g, h), that is, the aggregate
normal displacement f(lf+~mgg+nh) dS through any surface S enclosing the electron: over
any surface not enclosing electrons this integral of course vanishes, by the stream
character of the vector involved in it. Faraday's laws of electrolysis give a substantial
basis for the view that the value of e is numerically the same for all electrons, but may
be positive or negative.
As our main dynamical problem is not the propagation of disturbances in the
aether, but is the interactions of the electrons which originate these disturbances, it will
be necessary to express the kinetic and potential energies of the aether as far as
possible in terms of the motions and positions of the electrons. The reduction of T
may be effected by introducing the auxiliary variable (F, G, H) defined by
curl (F, G, H) =(a,, y).
dH dG\ dF dH dG dF }
Thus T (7)-l (d(d dH 13+ ( G _ 'Y dT
Jdy Cy dz d dx \dx dy
f( ' d/7 da dy d/i dus
= (87r)-ij, w, Z dS-+ G -Z dx + H Ydx - d _
a, /3, y
Now it follows from the definition of (F, G, H) that
d (dF dG dHI d 3 d
dV2F — + -+ j - - =r I - ~- -
dx (dx dy dz dy dz)
(df
dt'
with two similar equations. Solutions of these equations can be at once obtained by
taking dF/dx + dG/dy + dl/dz to be null: this makes F, G, H the potentials of volume
distributions throughout the medium of densities f h g, h, together with contributions as
yet undetermined from the singular points or electrons. The most general possible
solution adds to this one a part (F0, Go, H0) which is the gradient of an arbitrary