76 On tlie Laws of Reflexion 



through the crystal. The section will be an ellipse, and the 

 wave will be polarized by the crystal in a plane parallel to either 

 semiaxis of this ellipse, the index of refraction for the wave 

 being equal to the other semiaxis. This is Fresnel's law of 

 double refraction ; and the theory which led him to it makes it 

 necessary to admit that the vibrations of the wave are perpendi- 

 cular to its plane of polarization; whereas, according to the 

 views which I have adopted, the vibrations of the wave are pa- 

 rallel to its plane of polarization, and to one semiaxis of the 

 elliptic section, while its index of refraction is equal to the other 

 semiaxis. These views nearly agree with the theory of M. Cauchy, 

 according to whom the vibrations of polarized light are parallel 

 to its plane of polarization, but inclined at small angles to the 

 plane of the wave in crystallized media, instead of being exactly 

 parallel to the latter plane, as I have supposed them to be. Be- 

 sides, the theory of M. Cauchy, founded on the six equations of 

 pressure in a crystallized medium, implies the existence of a 

 third ray of feeble intensity, and for the other two rays gives a 

 law somewhat different from that of Fresnel. Being obliged, in 

 order to account for your experiments, to abandon the physical 

 ideas of Fresnel, and to approximate towards those of M. Cauchy, 

 I was embarrassed by this third ray ; and wishing to get rid of 

 it, as well as of the slight deviations from the symmetrical law 

 of Fresnel, I adopted the expedient of altering the equations of 

 pressure, in such a way as to make them afford only two rays, 

 and give a law of refraction exactly the same as Fresnel's. The 

 equations which I found to answer this purpose are the follow- 

 ing : 



