XV. Supplement to the Memoir on the Transmission of Light in Crystallized 

 Media. By Philip Kelland, B.A. Fellow and Tutor of Queens" 

 College. 



[Read May 1, 1837-] 



(BIOT's LAW.) 



1. In the latter part of this Memoir, I make an application of 

 the formula which I had before deduced, viz. "that the difference of 

 the squares of the velocities of two waves having a common normal, in 

 the direction of that normal, is proportional to the product of the 

 sines of the angles made by it with the two optic axes of the 

 crystal." 



As my object was merely to shew that it was a Theorem wanted 

 for such considerations, I adopted all the approximations which I 

 found in common use. On examining the subject more attentively, 

 I find that some of them if allowable are superfluous, and that the 

 same result is attained, by proceeding to work in a direct manner. 

 I am not, it is true, quite sure that the authors of the investigations 

 considered them as approximations ; they make no remark to that 

 effect, but assume at once that the ray and wave coincide. 



2. In order to find the appearance presented on the transmission 

 of polarized light through a plate of biaxal crystal, the most impor- 

 tant point to be determined is, the difference of retardation of the two 

 waves. 



The want of a proposition, such as that which appears in (23), 

 seems to have driven writers to adopt an approximative process of 

 the following nature. 



First, a ray is supposed nearly to coincide with a wave, and the 

 theorem that the difference of the squares of the reciprocals of the 

 velocities of the two rays is proportional to the product of the sines 



