THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
821 
124. The analogy just mentioned suggests a fresh search for a purely dynamical 
explanation of Fresnel’s formula for the influence of motion of the medium on the 
velocity of light, of which we had previously to be content with an indirect demon¬ 
stration on the basis of the law of entropy. In the first place, we shall con¬ 
sider the usually received proof,"" on the theory of a loaded mechanical aether. Let 
p be the density of the aether and p that of the load, and let .9- be the dis¬ 
placement of the medium ; the equation of propagation for the medium at rest is 
(P + P') d^S-jdt^ = K cPS-ldx^; the equation for a medium in which the load p' is 
moving on with velocity v in the direction of propagation is 
cn , .fd , d 
3^ = K 
cm 
dd? 
We have clearly Kjp = V^, /c/(p p) — Y^jpd, where V is the velocity of propa¬ 
gation in free aether ; and on substituting .9 = A exp 27r/\ . i{x — we find for 
the velocity of propagation in the moving medium the value +n(l — p~^), 
which is Fresnel’s expression. This explanation precisely fits in with our previous 
conclusion, that on a mechanical theory the matter must affect the inertia but 
not at all the elasticity of the medium, except as regards the dispersion; and con¬ 
versely, it may be used as independent evidence for that assumption. 
The treatment of the same problem on the theory of a rotational aether follows a 
rather different course. By the hypothesis, the electric displacement or strain .9^ due 
to orientation of the molecules may be treated as derived, by an equilibrium theory, 
from the inducing displacement which belongs to the waves and provides the stress 
by which they are propagated. That part 3,^ of the electric displacement is in 
internal equilibrium at each instant with the displaced position of the molecules, and 
so furnishes no stress for the wave-propagation. The relation between 9-1 and the 
total displacement .9]^ -f is that of electi’ostatics, -91 + -9^ = K9-j^, where K is the 
effective specific inductive capacity of the medium. The equation of propagation 
when the medium is at rest is p cP {3i-\-3d)ldt^ Kd'^3jdx‘’~', showing that the 
relation of tlie average disturbance of the molecule to the distui’bance of the aether is there inti’odnced 
simply by means of an experimental number, the specific inductive capacity of the medium. The 
correlative mechanical hypothesis would require us, not to anchor a massive core of the molecule in space, 
but to introduce a coefficient to express the ratio of the displacement of the molecule to the displacement 
of the medium on some appropriate kind of equilibrium theory,—thus in fact to directly load the aethei’, 
and refer only the variable part of dispersion to the free periods of the molecule; but such an idea would 
introduce all kinds of difficulties with respect to the kinetic theory of gases and material motions in 
general. In the electric theory these difficulties are evaded by the principle that the inertia of matter 
is different in kind from the inertia of aether; the one is subject to electromagnetic forcive, the other 
to electromotive forcive. 
The recent discovery of an upper limit beyond which radiations that can travel in a vacuum do not 
travel across air, has an important bearing on the present subject. 
* Gf. Glazebrook, “ On Optical Theories,” ‘Brit. Assoc. Report,’ 1882. 
