﻿30 Mr. G. F. H. Smith on the General Determination 



In his classical report on double refraction which was 

 presented to the British Association at the Cambridge 

 meeting of 1862, Stokes pointed out* that the velocity of a 

 wave, the normal of which lies in a plane perpendicular to 

 the faces of a prism, and its direction with respect to the 

 faces and, therefore, to the crystallographic axes, can be 

 accurately determined from observations of the angle of 

 incidence and the corresponding angle of deviation, and he 

 gave the formulae required. Cornu f has more thoroughly 

 discussed the same question, especially in regard to the 

 remarkable tilt of the refracted image with respect to the edge 

 of the prism which is observable in such strongly bire- 

 fringent substances as calcite and sodium nitrate. He, indeed, 

 measured this tilt in the case of the image given by the 

 extraordinary ray and made use of it for the determination of 

 the extraordinary indices of these substances. In most 

 substances the tilt is not sufficiently perceptible to be used for 

 purposes of measurement. 



The formulae required in the case of refraction through a 

 prism are as follows : — 



sin i = n sin r, . 



• (i) 



r + »*'= A, . . 



• (3) 



sin i' = n sin r', . 



• (2) 



i + i' = A + D, . 



• W 



where i and i' are the angles which the incident and emer- 

 gent waves make with the faces of incidence and 

 emergence respectively, 



r and r f the angles which the refracted wave makes 

 with the same faces, 



n is the index of refraction of the wave in the 

 crvstalline medium, that of the surrounding medium 

 being assumed to be unity, 



A the angle of the prism, and D the angle of 

 deviation. 

 The above equations reduce to 



v " 2) ==tan % tan v ¥~) cot ~Y~ ' ' ( 5 ) 



tan 

 and we further have 



r — r' A A , ,„ 



^ = ^ r=r ^ J = --r', .... (6) 



* Report, p. 273. 



t " De la refraction a, travers im prisme suivant une loi quelconque," 

 Annates scientifiques de VEcole Normale Supei'ieure, ser. 2, 1872, vol. i. 

 pp. 231-272 ; 1874, vol. iii. pp. 1-46 ; cf. also Liebisch, Physikalische 

 Krystalloyraphie, Leipzig, 1891, pp. 295 8, 376-8, and Walker, ' The 

 Analytical Theory of Light/ Cambridge, 1904, pp. 8-15. 



