XI. ON THE LAWS OF CRYSTALLINE REFLEXION AND 

 REFRACTION. 



[Transactions of the Royal Irish Academy, VOL. xvm. Read Jan. 9, 1837.] 



WHEN a ray of light, which has been polarized in a given plane, 

 suffers reflexion and refraction at the surface of a transparent 

 medium, the rays into which it is divided are found to be po- 

 larized in certain other planes ; and it becomes a question to 

 determine the positions of these planes, as well as the relative 

 intensities of the different rays ; or, in theoretical language, to 

 find the direction and magnitude of the reflected and refracted 

 vibrations, supposing those of the incident vibration to be given. 

 The transparent medium may be either a singly-refracting sub- 

 stance, such as glass, or a doubly-refracting crystal, like Iceland 

 spar. When the medium is of the first kind, the problem is 

 comparatively simple, being, in fact, nothing more than a par- 

 ticular case of the problem which we have to consider when the 

 medium is supposed to be of the second kind. In the progress 

 of knowledge it was natural that the simpler question should be 

 first attended to ; and accordingly Fresnel, during his brief and 

 brilliant career, found time to solve it. But the general problem, 

 relative to doubly-refracting media, had not been attempted by 

 anyone, when, in the year 1834, my thoughts were turned to 

 the subject. I then recollected a conclusion to which I had 

 been led some years before, and which, on this occasion, proved 

 of essential service to me. Being fond of geometrical construe- 



