I. ON THE DOUBLE REFRACTION OF LIGHT IN A CRYS- 

 TALLIZED MEDIUM, ACCORDING TO THE PRINCIPLES 

 OF FRESNEL. 



[Transactions of the Royal Irish Academy, VOL. xvi. Eead June 21, 1830.] 



THE mathematical difficulties under which the beautiful and 

 interesting theory of Fresnel has hitherto laboured are well 

 known, and have been regarded as almost insuperable. He tells 

 us, in his Memoir (see the Memoirs of the Royal Academy of 

 Sciences of Paris, torn. vii. p. 136), that the calculations, by 

 which he assured himself of the truth of his construction for 

 finding the surface of the wave, were so tedious and embarrass- 

 ing, that he was obliged to omit them altogether. A direct de- 

 monstration has since been supplied by M. Ampere (Annales de 

 Chimie et de Physique, torn, xxxix. p. 113) ; but his solution is 

 excessively complicated and difficult. 



Judging from the simplicity and elegance of the results that 

 there must be some simple method of arriving at them, I have 

 been led to consider the subject with the attention which it 

 merits, and have succeeded in discovering a method by which 

 the whole may be explained with that simplicity which is cha- 

 racteristic of every theory that is founded in nature. 



In the following Paper I shall give a brief view of this 

 method, sufficient to enable those who are acquainted with the 

 mechanical principles laid down in the original memoir of 

 Fresnel, to trace, at a glance, the connexion between the several 



B 



