Crystalline Reflexion and Refraction. 35 



riments as I was aware of at the time. This other hypothesis I took up 

 from reading an article by M. Cauchy in the Bulletin des Sciences Mathema- 

 tiques,* in which he arrives, by a peculiar process, at the formulae of Fresnel for 

 the case of ordinary reflexion. The hypotheses which he chiefly employs are 

 relations among certain quantities 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 direction 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 conceived 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 ^nnaxaLcrystals, and among others a formula for the pola- 

 rising angles iit^ different azimuths of the plane of reflexion. When this 



* Sur la Refraction et la Reflexion de la Lumiere, Bulletin des Sci. Math. Juillet, 1830. In 

 this paper the vibrations of polarised light must be supposed perpendicular to the plane of polarisa- 

 tion, though the paper was published immediately after the author had promulged the contrary opinion. 

 The latter opinion, which I adopted from him because it harmonized with my analogy before 

 mentioned, he has formally renounced of late, and has returned to the hypothesis of Fresnel. 

 M. Cauchy supposed too, in the above paper, that the ethereal density is the same in different media ; 

 but he has found cause to abandon this hypothesis also. See his notes addressed to M. Libri, in the 

 Comptes rendus des Seances de 1' 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 etherees sont generalement comprises dans les plans des ondes, 

 mais encore que les plans de polarisation sont perpendiculaires aux directions des vitesses ou des 

 d^placements moleculaires. J'arrive au reste a cette derniere conclusion d'une autre maniere, en 

 itablissant les lois de la reflexion et de la refraction a I'aide d'une nouvelle methode qui sera 



developpee dans mon memoire [cette methode] ne m'oblige plus a supposer, comme je I'avais 



fait dans un article du Bulletin des Sciences, que la densite de I'^ther est la meme dans tous les 

 miUeux. Mes nouvelles recherches donnent heu de croire que cette densite varie en general, quand 

 on passe d'un milieu a un autre." More lately, in his Nouveaux Exercices de Mathgmatiques, 

 7' 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 formulse of Fresnel for ordinary reflexion. But 

 these equations do not include the laws of crystalUne reflexion. 



F 2 



