ADAMS AND WILLIAMSON! BIR^IfRINGENCE; AND STRESS 617 



in which x^, jy, and z~_ are dilatations in the three directions 



parallel to the three principal axes, v is the velocity of light in 



the unstressed material, and Vx> Vy, and v. are the velocities of 



light waves whose vibrations are parallel to the three axes. 



p and q are coefficients which are to be determined by experiment. 



If n is the refractive index of the unstressed medium and Ux, 



fly, and n^ are the refractive indices for light vibrating in the three 



principal directions, then nv = n^Vx = nyVy = n-v^ and from 



Equation (ia) 



Vx - V n - fix q p 



= - Xx +- iyy + 2,). (2) 



V ■ fix V V 



Referring again to Fig. 3, it is obvious that a thrust, P, acting 

 on the block in the direction OY will produce the three prin- 

 cipal dilatations : 



X, = aP/E 



yy= - P/E 



Z, = aP/E 



E being Young's modulus and a Poisson's ratio. Substituting 

 in Equation (2) we have 



fix - n P p /Pa\q P r p ^1 r \ 



= -(i - a) - -(-E^r = ^ (i - 0-)" ~ ^~ ]■ (3a) 



^ V \E /v E {_ V vJ 



E 

 Similarly it can be shown that 



fly — n P ( p 



2(T 



fly E 



'- + 2) (3.) 



V v/ 



and 



= fc^.)^-4 (3.) 



EL V VJ 



^3 



When the coefficients p and q have once been determined, 



these three equations may be used for calculating the effect of 



a thrust, P, in the direction OY (Fig. 3) on the three indices of 



refraction fix, fiy, and n^ corresponding to light vibrating in the 



directions OX, OY, and OZ. The changes in refractive index 



for a given thrust, P, depend on the elasticity constants E and 



p q 



a, and the coefficients — and - which are characteristic of the 



V V 



given material and can be determined experimentally. 



