THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
775 
Again, such a view would disturb the explanation, as above, of the tact that the 
forcive on a charged conductor in an electric field is a surface-traction equal at each 
point of the surface to the energy in the medium per unit volume. There is in any 
case nothing contradictory in the hypothesis of a stationary tether ; if the fluid is not 
allowed to stream through the circuits of the atoms, we have only to make the 
ordinary supposition that the molecules are at distances from each other considerable 
compared with their linear dimensions, and it can stream past between them. 
77. Let us test a simple case of motion of a body through the Eether, with respect 
to the theory of radiation. Consider a horizontal slab of transparent non-radiating 
material, down through which light passes in a vertical direction ; the equilibrium of 
exchanges of radiation would be vitiated if the amount of light transmitted by the 
slab when in motion downwards with velocity v were ditferent from the amount 
transmitted when it is at rest. Let V be the velocity of the light outside the slab, 
and V/p -h — v' the velocity in the moving slab. For an incident beam, of ampli¬ 
tude of vibration which we may take as unity, let r be the amplitude of the reflected 
beam, and It of the transmitted beam. The conditions governing the reflexion are 
continuity of displacement at the surface, and continuity of energy, estimated in 
MacCullagh’s manner as proportional to the square of the amplitude ; thus the con¬ 
ditions at the first incidence are 
1 R 
V - f - (V -f v) = (V/p - v') RL 
On neglecting squares of v/V and v'/V, these equations lead to 
1-1 
V \p + 1 
+ 
p - t'^i I d fj. ] 
2p / V p -f 1J 
The ratio R', in which the amplitude is changed by transmission at the lower 
surface of the slab, is derived from the above by replacing V by V/p, and p by 1/p, 
and interchanging v and v '; thus 
Hence 
R' = 
P -f- 1 
1 
Y 'xp + 1 
ni 'l _i_ ttf _1_1 
2 ; V p + 1J‘ 
RR' = 
4a 
(P + 1)~ 
pr' p - 1 ] 
V 2 J' 
That the amount of the light transmitted should not be altered by the motion of 
the slab requires that v' = r/p^, which is Fresnel’s law ; it has been assumed in the 
analysis that the light is propagated down to the slab as if the mther were at rest, 
in accordance with Fresnel’s hypothesis. It will be observed that the amplitudes of 
the refracted and reflected light, at either surface separately, are disturbed by the 
