ON OPTICAL THEORIES. 249 
It is another question, and one which we shall discuss shortly, whether 
the double refraction thus produced will give rise to Fresnel’s wave surface. 
There seem, then, to be reasons why we should expect terms such as 
Ketteler has suggested in our equations—terms which will make the mutual 
reaction of the ether and the first matter shell depend rather upon their 
relative accelerations than upon their relative displacements. It is not so 
easy to suggest a mechanical connection between the ether and matter 
which would give rise to this force, but at the same time there is, I 
think, no mechanical reason to be urged against it. 
Voigt’s theory of wave propagation is in one way more comprehensive 
than those we have considered, while in another it is less so. It is more 
comprehensive in that it includes both sets of terms with some others in 
the expression for the mutual reaction; it is less so in that it treats the 
ratio U/w as a small quantity which may be neglected. This same 
remark applies to Boussinesq, whose work in one sense is more general 
that Voigt’s, in that he considers the effect of the attached molecules on 
the condensational or pressural wave. 
The presence of these molecules has been shown in Boussinesq’s 
paper to alter the effective compressibility of the medium as well as its 
density and its rigidity. In the ether we assume that the compressibility 
is small compared with the rigidity, so small that the ratio of the two 
may be neglected, and this must still be the case, even when the ether is 
loaded. But when dealing with the problem of reflexion we are concerned 
with the refractive index of the medium for the condensational wave. 
This will depend on the ratio of the two effective compressibilities, as 
well as on that of the two effective densities, and though either of the 
two compressibilities may vanish when compared with the rigidities, in 
considering their ratio it becomes necessary to take into account any 
change due to the loading of the ether. 
It may not be unreasonable, then, to suppose that the effective density 
of the ether for the condensational wave is different from the effective 
density for the transverse wave. This supposition would account easily 
for the variation from Green’s formula observed when plane polarised 
light polarised at right angles to the plane of incidence is reflected from 
a transparent surface, in that it would allow us to introduce the second 
constant po, as suggested by Haughton and Lord Rayleigh." 
Let us now consider Voigt’s theory. With regard to the problem of 
reflexion his surface conditions appear to be unsound. The ether is the 
continuous medium, and the surface conditions must apply to it simply. 
The conditions of continuity demand that the actual displacements of the 
ether and the actual stresses over the interface, arising, of course, in part 
from the action of the matter, should be the same in the two media. 
The validity of Kirchhoff’s principle has already been considered, and it 
has been shown that it does not lead to results in accordance with experi- 
ment, for it does not give the change of phase which in some cases 
accompanies reflexion. 
But, while this is so, Voigt’s theory shows us that the effects of the 
attached molecules may show themselves either in the rigidity or the 
density of the ether. Now, the work of Lord Rayleigh and Lorenz has 
proved that the effects of reflexion are due mainly, if not entirely, to 
differences of effective density; and so we must look to the terms in 
1 See p. 192. 
