6l8 ADAMS AND WILLIAMSON: BIREFRINGENCE AND STRESS 



The change n,^ is the same as that of n^ (for a thrust along 

 OY) so that no birefringence is observed for a ray of hght pass- 

 ing through the block in the direction OY, but the velocity of 

 a ray in the direction of the triple arrow {i. e., along OX) de- 

 pends on the direction of vibration, that is, rix is different from 

 H:, and fly — n^, by definition, is the birefringence.^^ 



Since ordinarily n^ and Uy do not differ from n by more than 

 one part in looo, we may put with a maximum error of a small 

 fraction of one per cent , 



riy — n Wz — n Uy - n,^ 



Uy yir, n 



refore by subtracting Equations (33) and (3c) we obtain 

 fly — n, P (q p^ 



= ^c + .)(? - n (4) 



n 



This equation may be put in slightly different form by making 

 use of the identity 



E 



^ ^ 2(1 + ^) 

 R being the modulus of rigidity. Substituting this value of R 



in Equation (4), we have 



Uy — W- 



5^G - f)- (5) 



n 



From Equations (4) and (5) it is evident that the birefringence 

 is proportional to the difference of the two coefficients p and q. 

 Conversely, p and q can not be determined by measurements of 

 birefringence alone, but if in addition to the birefringence we 

 measure the absolute retardation of a ray of Hght vibrating, 

 say, in the direction OY, both p and q will be uniquely deter- 

 mined. 



Suppose now that instead of a thrust we apply to the block 

 of glass a hydrostatic pressure, P' . In order to obtain a rela- 

 tion connecting the coefficients p and q with the hydrostatic 

 pressure P' , it is obvious from considerations of symmetry that 



" In the case^of a uniaxial crystal, birefringence is usually expressed as w^ — n^, 

 which is identical with ny — its, the direction Y being the direction of the optic 

 axis. 



