V. A SHORT ACCOUNT OF SOME RECENT INVESTIGA- 

 TIONS CONCERNING THE LAWS OF REFLEXION AND 

 REFRACTION AT THE SURFACE OF CRYSTALS. 



[Fifth Report of the British Association, 1835.] 



To understand the nature of the general problem which a com- 

 plete theory of double refraction requires to be solved, let it be 

 supposed that a ray of light is reflected and refracted at the 

 separating surface of an ordinary medium and a doubly refract- 

 ing crystal, the light passing out of the former medium into the 

 latter. This limited view of the subject is taken merely for the 

 sake of clearness of conception ; since we might suppose that both 

 media are crystallized, without increasing the difficulty of the 

 problem. The question, it is obvious, naturally divides into 

 two distinct heads. The first relates to the laws of the propa- 

 gation of light in the interior of either of the two media, before 

 or after it has passed their separating surface ; and this part of 

 the subject has been fully treated, according to their different 

 methods, by MM. Fresnel and Cauchy. The second division of 

 the subject had been left completely untouched. It relates to 

 the more complex consideration of what takes place at the sepa- 

 rating surface of the media, the laws according to which the 

 light is there divided between the reflected and refracted rays, 

 including a determination of the attendant circumstances indi- 

 cated by the wave theory, with regard to the vibrations in the 

 reflected and refracted rays. In the case above mentioned, when 

 the incident light is polarized, there are four things to be deter- 



