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.

XXI. On the Dynctmics of a Systemn of Electrons or Ions: ctnd on the Influence
of a Magnetic Fielcl on optical Phenomena. By J. LARMOR, M.A., F.R.S.,
Fellow of St John's College.
[Received 24 January 1900.]
THE DYNAMICS OF A SYSTEM OF INTERACTING ELECTRONS OR IONS.
1. IN the usual electrodynamic units the kinetic and potential energies of a region
of aether are given by
=T (87)-lfa2 + / + 2) d,
W= 27r2(f2 +g2 + h2) d,
wherein &r represents an element of volume, (a, /3, 7) is the magnetic force which
specifies the kinetic disturbance, and (f, g, h) is the aethereal 'displacement' which
is of the nature of elastic strain. These two vector quantities cannot of course be
independent of each other: the constitutive relation between them is, with the present
-nits,
fdy di3 da dy d/3 da\ d
\dy dz' dz~ dx' dx -dy) =4 dt(f> g h),
or say curi (a, /, ry)= 47r (f, g, h),
which restricts (f, g, h) to be a stream vector satisfying the equation of continuity:
it also confirms the view that (a, /, y) is of the nature of a time-fluxion or velocity.
It is assumed that (a, /3, y) is itself a stream vector, which must be the case if
electric waves are of wholly transverse type. On substituting in these expressions
(:, v, ), the independent variable or coordinate of position, of which (a, /3, y) is the
velocity, so that (a, e, y)= d/dt (I, r, ^), the dynamical equations of the free aether can
be directly deduced from the Action formula
(T- W) dt = 0.
It is well known that they are identical with MacCullagh's equations for the optical
aether, and represent vibratory disturbance propagated by transverse waves.