Crystalline Reflexion and Refraction. 1 93 



In what precedes, it has been supposed that the reflexion and 

 refraction take place at the first surface of the crystal, because 

 this is the more difficult and complicated of the two cases into 

 which the question resolves itself. But it will usually happen 

 in practice that a ray which has entered the crystal will suffer 

 total reflexion at the second surface, while the new kind of vibra- 

 tion is propagated into the air without. The refracted wave will 

 then be always perpendicular to the axis of x' ; the two reflected 

 rays, within the crystal, will be plane-polarized, according to the 

 common law, but they will each undergo a change of phase ; 

 and the vis viva of the two rays together will be equal to that of 

 the incident ray, the vis viva being measured by the square of 

 the amplitude multiplied by the proportional mass. 



In conclusion, the author states a mathematical hypothesis 

 by which both the laws of dispersion, and those of the elliptic 

 polarization of rock crystal, may be connected with the laws 

 already developed. 



