THE ELECTEfC AHD LUMINIFEROUS MEDIILM. 
811 
or rotationally elastic, or it may combine these two properties ; there is no^’" other 
alternative. 
As to the intrinsic nature of the rotational elasticity of the free aether, although it 
is an important corroboration of our faith in the possibility of such a medium to have 
Lord Kelvin’s gyrostatic scheme by which it might be theoretically built up out of 
ordinary matter, yet we ought not to infer that a rotational free aether is necessarily 
discrete or structural in its ultimate parts, instead of being a continuum. As a 
matter of history, the precisely similar argument has been applied to ordinary solids ; 
the fact that deformation induces stress has been taken, apparently with equal force, 
as evidence of molecular structure in any medium which exhibits ordinary elasticity. 
It is necessary to put some limit to these successive refinements; there must be a 
final type of medium which we accept as fundamental without further analysis of its 
properties of elasticity or inertia : and there seems to be no adequate reason why we 
should prefer for this medium the constitution of an elastic solid rather than a consti¬ 
tution which distortion does not affect,—perhaps there is just the reverse. 
117. The fluidity of the medium allows us to apply the methods of the dynamics 
of particles to the discussion of the motions through it of these electrons or strain- 
configurations, and their mutual influences. The potential energy of a system of 
moving electrons will be the energy of the strain in the medium ; unless their 
velocities are appreciable compared with the velocity of radiation, this will be a 
function of their relative positions alone. The kinetic energy is that of the fluid 
circulation of the medium, which will under the same circumstances be a quadratic 
function of the velocity-components of the electrons, with coefficients which are 
functions of their relative positions. When however their velocities approach that of 
radiation the problem must be treated by the methods appropriate to a continuum, 
and cannot be formulated merely in terms of the positions of the electrons at the 
instant. It will suffice for the present to avoid the difficulties of the general case by 
supposing the velocities to be small, and the strain-configuration of each electron 
therefore carried on unaltered by it; as the correction required depends on {cjaf it 
will possibly be negligible for any actual problem. 
Let us then consider a single electron represented by a charge e moving along the 
direction of the axis of x with velocity v. The components of rotation in the medium 
due to its presence are at any instant — e [djdx, djdy, djdz) and those of the 
displacement current are derived from them by o])erating with the factor — v djclx. 
This displacement current is the curl of the velocity of the medium, whence it may 
be easily verified that this velocity is ev (0, — djdz, djdy) being a circulation round 
the line of motion of the electron.t The kinetic energy is thus ^ (ev^Ky^ + z^) dr ; 
* Professor FitzGerald remarks that it might, conceivably, resist absolute linear displacement. A 
hypothesis of this sort, which is on a lower plane than those mentioned above, is in fact involved in the 
usual expositions of Fresnel’s dynamics of double refraction. 
t It is to he observed that we cannot expect to obtain an expression for the displacement in the 
5 T. 2 
