250 REPORT—1885. 
Voigt’s theory which affect the density as the most important. These 
terms are 
d? 
-( r apt n) (u—U). 
The other terms, 
(oF +058) @- 0) 
dz” dzdt? ° 
show themselves as a variation of the effective rigidity. In order to 
obtain a consistent theory of reflexion we must treat these as of secondary 
importance compared with the first terms. Now, this is inconsistent with 
both theories of double refraction as advanced by Voigt, for the first 
condition for either is that 7 and 7 must be independent of the direction. 
It would seem from this that they should be the same in all media. 
Boussinesq adopts the opposite view. He makes his double refraction 
depend on the terms which correspond to r and n, and neglects the 
variations of the others with the direction. If we do this—and we seem 
to be forced into it by the further requirements of our theory—the funda- 
mental equations in a crystal become those given by Lord Rayleigh. 
These, we have seen, if we assume the strict transversality of the 
vibrations, do not lead to Fresnel’s wave surface. On the other hand, if 
we suppose that the vibrations in a crystal are at right angles to the 
ray, not to the wave normal, the result agrees with all the consequences 
of experiment, for we obtain Fresnel’s surface as the wave surface, but 
we are left in a difficulty as to the normal wave. 
With regard to metallic reflexion, the theory as given by Sir W. 
Thomson explains completely the difficulty raised by Lord Rayleigh as to 
a negative value for »?. It does not, however, enable us to decide how 
much of the effect is due to the fact that the highest possible free period of 
the ether in the metallic medium is below that of the incident light, and 
how much is due to opacity arising from terms such as du/dt, as supposed 
by Lord Rayleigh. The correct equations to which such a theory would 
give rise are yet unsolved, but the principles required by the solution are 
well known. 
It seems, then, that this theory promises to afford us the solution of 
the difficulties which still surround theoretical optics, and to account at 
once for the phenomena of reflexion and refraction, dispersion and double 
refraction. Of course, in all cases of transparency the matter motion is 
infinitesimally small compared with that of the ether. The ether is to 
be looked upon as moving through a sort of network of fixed matter 
particles. Terms depending on the reaction between the ether and 
these fixed portions of matter will be introduced into the equations, 
and these terms will be expressible as functions of wu, v, w and their 
differential coefficients. The matter particles will not move appreciably, 
and their movement is not necessary for the explanation of refraction and 
ordinary dispersion; for on Ketteler’s modified theory we have, if we 
omit the viscous terms, 
2 Bin? 
atte Digi es ce 
= is a mp (v*—n*)? 
and the ratio of the amplitudes is ; 
§?n? 
G2 =n*)’ 
