56 Laws of Reflexion and Refraction 



mined, namely, the magnitude and direction of the reflected vi- 

 bration, with the magnitudes of the two refracted vibrations. The 

 four conditions necessary for this determination are furnished 

 by two new laws, which could not be easily stated without en- 

 tering too much into detail. The results applied to determine 

 the polarizing angle of a crystal, in different azimuths of the 

 plane of reflexion, agree very closely with the admirable experi- 

 ments of Sir David Brewster on Iceland spar. In the course of 

 these experiments it was observed that the polarizing angle re- 

 mained the same when the crystal was turned half round (through 

 an angle of 180) ; although the inclination of the refracted 

 rays to the axis of the crystal was thereby greatly changed. 

 This remarkable fact is a consequence of theory. After some 

 complicated substitutions in the primary equations, the value of 

 the polarizing angle is found to contain only even powers of the 

 sine or cosine of the azimuth of the plane of reflexion, and there- 

 fore a change of 180 in the azimuth produces no change in the 

 polarizing angle. 



The two new laws above mentioned, on which the theory 

 depends, occurred to the author in the beginning of last Decem- 

 ber ; but, owing to an oversight in forming one of the equations, 

 they were not fully verified until the beginning of June. 



In this theory it is supposed that the vibrations are parallel 

 to the plane of polarization, according to the opinion of M. Cau- 

 chy. This is contrary to the views of Fresnel, whose theory 

 of double refraction obliged him to adopt the hypothesis that 

 the vibrations are perpendicular to the plane of polarization. It 

 is further supposed that the density of the vibrating ether is 

 the same in both media ; and the hypothesis of a constant den- 

 sity in different media, which was found necessary for the 

 theory, seems to accord, better than the supposition of a varying 

 density, with the phenomena of astronomical aberration. 



If we conceive the three principal indices of refraction for 

 the crystal to become equal, we shall obtain the solution of a 

 very simple case of the general problem with which we have 

 been occupied the case of an ordinary refracting medium such 



