174 REPORT—1885. 
We may conclude, then, that Fresnel’s laws as to double refraction 
would hold in a medium stramed in the manner Boussinesq considers, 
but the theory as a whole is liable to the same criticisms as have been 
made to Green’s. Boussinesq is the author of another and different 
theory, which we shall consider later, and which gives a better explana- 
tion of the phenomena. 
§ 7. This same problem has been dealt with by Professor C. Niven,' who 
has arrived at similar results without introducing considerations based 
on molecular reactions. 
§ 8. The problem of donble refraction has been treated in a different 
manner by M. Sarrau, following up the suggestions of Cauchy as to the 
nature of the ether in a crystal, and his theory is developed in two papers 
in ‘Liouville’s Journal.’ In these papers” the density of the ether in a 
transparent medium is supposed to vary in a periodic manner from point 
to point. The ether is arranged in concentric shells of variable den- 
sity round each matter molecule, and its density, variable round each 
matter molecule, is the same at any one of a series of points situated 
similarly with regard to the matter molecules. The ether is periodically 
homogeneous, and the coefficients which occur in the elasticity equations 
are no longer constant, but are periodic functions of the co-ordinates of 
the point whose displacement is being considered ; from these equations 
are deduced a series of others with constant coefficients, containing the 
average displacements of the ether in an element of volume. It is to 
these average displacements that optical effects are supposed to be due. 
Cauchy * has indicated the path to be followed in deducing these 
auxiliary equations from the fundamental forms, and M. Sarrau arrives 
at the following conclusion. 
If the fundamental equations be represented by 
2 } 
mH F(S a. Oo yey) 
dt? “da! dy! dz! 
dv 
=e. m9) 2 4 ») a A e ey 
2 
du Al ) 
dt? d i J 
Where F, G, H are functions with periodic coefficients of w, v, w and 
their differential coefficients, then the auxiliary equations will be— 
du 
i= BV, iG ea! 
dt? 4 33 
pF A 
a nit ee a 
| 
J 
1 CO. Ntven, Quarterly Journal of Pure and Applied Mathematics, No. 55, 1876. 
2 Sarrau, C. A. vol. lx. p.1174. ‘Sur la propagation et la polarisation de Ja lumiére 
dans les cristaux,’ Liouville’s Journal, S. ii. t. xii. p. 13; t. xiii. p. 59. 
3 Cauchy, Comptes Rendus, t. xxx. p. 17. 
(9) 
== 4 Gl + H’””’ 
{ 
