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 " Nouveaux Exercices," and from 

 his papers in the twenty- second volume of the " Memoires 

 de rinstitut." Lame has also made investigations in this 

 direction (see a memoir in the " Journal de l'Ecole Poly- 

 technique," torn, 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 " Keport on Double 

 Kefraction" 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 discontinuous, 

 and to be incompressible by the forces exerted upon it by 

 the material molecules.* 



Let x y z, x 1 y Y z r 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 

 the equations of motion. 



