from Crystallized Surfaces. 77 



dr\ 



+ 

 dz 



p. 



In these equations, the axes of co-ordinates are perpendicular 

 to each other, and parallel to the principal directions of the crys- 

 tal ; x, y, z are the co-ordinates of a vibrating molecule at the 

 time t ; , rj, are the components of the displacement of the 

 same molecule at the same time ; a, b, c are the three principal 

 indices of refraction out of the crystal into an ordinary medium 

 in which the velocity of light is equal to F"; and p is the density 

 of the ether, which density I suppose to be the same in all media. 

 The quantities A, F, E are the components, parallel to the axes 

 of x, y, z, respectively, of the pressure upon a plane perpendi- 

 cular to the axis of x ; F, B, D are the components of the pres- 

 sure upon a plane perpendicular to the axis of y ; and E, D, C 

 the components of the pressure upon a plane perpendicular to 

 the axis of z. The values of Z), E, Fare the same as those given 

 by M. Cauchy ; but the values of A, B, C are different from 

 his, and much simpler. By introducing into the equations of 

 M. Cauchy the condition that the vibrations shall be performed 

 without any change of density, the resulting values of A, B, C 

 might be shown to agree nearly with those given above. The 

 six pressures, A, J3, C, D, E, F, being known, it is easy to find 

 the pressure upon a plane making any given angles with the 

 axes of co-ordinates. 



These things being premised, it is time to mention the laws, 

 or rather hypotheses, which I have imagined for discovering the 

 relations that exist, as to direction and magnitude, among the 

 vibrations in each ray, when reflexion and refraction take place at 

 the separating surface of two media, whether crystallized or not. 

 In stating the two very simple laws that have occurred to me 



