256 Proceedings of the Royal Physical Society. 
the theories of Fresnel, Cauchy, Neumann, &c., in which 
the motion of the ether within a crystal is determined as 
if it were a single vibrating medium unacted on by the 
molecules which interpenetrate it, and possessing special 
properties different from what it is supposed to possess in 
vacuo, without at the same time attempting to give any ex- 
planation of the manner in which the ether might be sup- 
posed to have derived these properties. These theories, even 
with the arbitrary hypotheses made, are unsatisfactory in 
other respects. 
The idea that the action of the material molecules must 
be taken into account, in any satisfactory theory of crystal- 
line refraction, appears to have suggested itself many years 
ago to several physicists. Even Cauchy latterly felt the 
necessity of doing so, as appears from some investigations 
in one of the volumes of the " NouveauxExercices,"and from 
his papers in the twenty- second volume of the " Memoires 
de ITnstitut." Lame has also made investigations in this 
direction (see a memoir in the "Journal de TEcole Poly- 
technique," tom. xiv.) Dr Lloyd, in the first number of the 
" Proceedings of the Eoyal Irish Academy," describes in 
words some researches he had made with the same object; 
and, finally, Professor Stokes, in his " Eeport on Double 
Eefraction" to the Cambridge meeting of the British Asso- 
ciation in 1862, in expressing his " belief that the true dyna- 
mical theory of double refraction has yet to be found," 
indicates his opinion very decidedly, that " the ponderable 
molecules must be taken into account in a far more direct 
manner" than has been done in previous theories. 
We now proceed to investigate the general equations of 
motion of the etherial medium, when acted upon by the 
material molecules, supposing the ether to be disco7itinuous,' 
and to be incompressible by the forces exerted upon it by 
the material molecules.* 
Let X y z, y^ z^, be the co-ordinates of particles of 
* It is desirable to investigate the consequences of this supposition in the 
first place, on account of the simplification which is thereby introduced into 
tlje equations of motion. 
