92 On the Laws of Crystalline 



which he chiefly employs are relations among certain quanti- 

 ties called pressures ; and it was such a relation that I adopted 

 instead of the law of vis viva. I supposed that, at the confines 

 of two media, the pressure on the separating surface, in a direc- 

 tion perpendicular to the plane of incidence, ought to be the 

 same, whether it be considered as resulting from the vibrations 

 in the first medium or in the second. This hypothesis I con- 

 ceived to be true in general, because I found it to be true for 

 ordinary media ; but I could never assign any better reason for 

 it. Combining it, however, with the principle of equivalent 

 vibrations, I deduced several expressions for uniaxal crystals, 

 and among others a formula for the polarizing angles in diffe- 

 rent azimuths of the plane of reflexion. When this formula was 

 compared with the experiments of Sir David Brewster* on the 

 polarizing angles of Iceland spar, the accordance was so satis- 

 factory as to leave no doubt upon my mind that I had arrived 

 at the true formula for these angles ; and though the truth of 

 the conclusion did not allow me to argue that the premises 



hypothesis of Fresnel. M. Cauchy supposed too, in the above Paper, that the 

 ethereal density is the same in different media ; hut he has found cause to abandon 

 this hypothesis also. See his notes addressed to M. Libri, in the Comptes rendus 

 des Stances de V Academic des Sciences, Seance du 4 Avril, 1836, where he gives the 

 reasons for his present opinions. He says, "Ainsi Fresnel a eu raison de dire, 

 non-seulement que les vibrations des molecules e'therees sont generalement com- 

 prises dans les plans des ondes, mais encore que les plans de polarisation sont 

 perpendiculaires aux directions des vitesses ou des displacements moleculaires. 

 J'arrive au reste a cette derniere conclusion d'une autre maniere, en etablissant 

 les lois de la reflexion et de la refraction a 1'aide d'une nouvelle methode qui 



sera developpee dans mon memorie [cette methode] ne m' oblige plus a 



supposer, comme je 1'avais fait dans un article du Bulletin des Sciences, que la 

 densite de 1'ether est la meme dans tous les milieux. Mes nouvelles recherches 

 donnent lieu de croire que cette densite varie en general quand on passe d'un 

 milieu a un autre." More lately, in his Nouveaux Exercir.es de Mathematiques, 

 7 e Livraison, M. Cauchy states positively that his principles do not permit him 

 to adopt the hypothesis that the density of the ether is the same in all media. He 

 also gives the differential equations which, as he has found by his new method, 

 ought to subsist at the separating surface of two media, and from which he has 

 obtained the formulae of Fresnel for ordinary reflexion. But these equations do 

 not include the laws of crystalline reflexion. 

 * Phil. Trans., 1819, p. 150. 



