1878.] Propagation of Plane Waves in a Biaxal Crystal. 497 



Then yjr is given by the formula 



^=D-H-0 .... (1). 



" But without making any other supposition as to the law of double 

 refraction, or assuming anything beyond the truth of Huyghen's 

 principle, which, following at once from the superposition of small 

 motions, lies at the base of the whole theory of undulations, we may 

 at once deduce from the directions of incidence and emergence the 

 direction and velocity of propagation in the crystal." 



For we have — 



sin sin 0' 



-y sin0=V sin0' .... (2), 



v sin >/r= V sin if/ .... (3), 



<p'-\-f=i (4). 



Adding and subtracting (2) and (3), 



. 6 + — yfr Tr . 0' + \!/ 0' + \5r' 



v sin — r cos - — i = V sin r cos 



2 2 2 2 



+ ^ • — T7 0' + ^' • 0' — V 



*y cos r sm — T — V COS — — sm — L. . 



2 2 2 2 



Dividing and recollecting (4), 



tan i^L-t tan - — t = tan i. cot ^— t, 

 z z2 Z J> 



tan - = tan - cot ( t^—t tan — — 

 2 2 2 2 



This gives —fr~~' 



Combining with (4) we can get 0' and ^r, and then find the value of 



y 



v from either (2) or (3). In practice the value of /i or — was used. 



v 



In accordance with these suggestions I undertook a series of obser- 

 vations at the Cavendish Laboratory, Cambridge, which I propose to 

 describe in the paper, adding moreover a comparison of the results 

 with the theories of Fresnel and Lord Rayleigh. Fresnel is the only 

 experimenter who has attempted to verify his theory by experiment, 

 and his attempt affords no verification, for in applying it he used 

 approximate results, and to the degree of approximation to which he 

 went the theory developed by Lord Rayleigh (Phil. Mag., vol. xli, 

 Series iv, 1871) leads to exactly the same equations to determine the 

 velocity of propagation as were used by Fresnel, so that his results 

 form equally a verification of Lord Rayleigh's theory. 



