182 REPORT—1885. 
of light through a medium consisting of a series of small spheres im- 
bedded in the ether. The velocity of light in the interspaces is the same 
as in free space, and the wave length is supposed to be great compared 
with the intermolecular distances. It is assumed, then, that the disturb- 
ance u at any point may be written u = (vp+u.)C+u,S, where the 
average values of u, and w, over the space containing some considerable 
number of molecules are zero, and C and S are written for the sine and 
cosine of kt—lz—my—nz—6. From this it follows that,if » be the refrac- 
tive index and d the density, 9 
The paper is followed by one by Lorenz and K. Prytz, giving the 
results of an elaborate series of observations which show a close agree- 
ment between this expression and experiment. 
is proportional to d.* 
Chapter IIJ.—ABeRRATION AND PHENOMENA CONNECTED WITH THE Motion 
or THE Mrpium THROUGH WHICH LiGHT IS BEING PROPAGATED. 
§ 1. The aberration of light on the undulatory theory was accounted 
for by Fresnel! on the supposition that a moving body of refractive 
index p carries with it a quantity of ether of density »?—1, the density in 
a vacuum being unity, while light is propagated through this ether, part 
of which is at rest and part moving with a velocity v (that of the body), 
as if the whole were moving with the velocity (l—p~*)v. 
The experiments of Fizean? on the displacement of the fringes of 
interference by a moving medium led to a result in close accordance with 
this theory, 
§ 2. A more general and simpler proof than the one published by 
Fresnel of the fact that this leads to the ordinary laws of reflexion and 
refraction was given by Professor Stokes in 1846.3 
In this paper Professor Stokes points out that the same result as to 
the velocity of light in the medium will be arrived at if we suppose the 
ether on entering the medium to be condensed, and on leaving it to be 
rarified, while the whole ether in the body travels with the velocity given 
above ; for, if we take two planes, one outside the other inside themedium, 
each moving with the velocity v normal to itself, the quantity of ether 
which crosses the two planes per unit time will be the same, and hence, 
if V be the velocity of the ether in the medium, then we have, since the 
densities are 1 and p? respectively, 
= we (v—V), 
and hence _ pel 
a. 
Moreover, this comes to the same thing as supposing the medium to be at 
rest, while the ether outside moves with a velocity v, and that inside 
with a velocity v/p?. The direction of a ray is shown to be that in which 
the same portion of a wave moves, moving relatively to the medium, and is 
found by drawing from a given point a line of length V/» in a direction 
* Compare this with a similar paper by H. A. Lorenz, p. 255. 
1 Fresnel, Annales de Chimie, t. ix. p. 57. 
2 Fizeau, Annales de Chimie (3), t. lvii. p. 385. 
8 Stokes, ‘On Fresnel’s Theory of the Aberration of Light,’ Phil, Mag. vol. xxviii. 
p. 76; Mathematical Papers, vol. i. p. 141. 
