180 



BELL SYSTEM TE,CHNICAL JOURNAL 



and hence, by measuring at 45° between the two axes, one can evaluate the 

 As term. 



Similarly, for the YZ plane, ip = 90°, 6 = variable and. 



By 



[-(/3ii - fe) + {8n - 6-n) sin2 d - fe sin 20]^ 



+ [2/3i2 cos d - 2/D,3 sin 6]'. 



(85) 



Hence, when a natural birefringence exists, we have 



3 



A. 



l^vz 



M 



M - ^ + Ai - A.) 



+ (-2 - -2 + A, - Ao) 



2 + A, - A, 

 In the XF plane 6= 90°, ^ = variable and 



B, 



sni 



— A4 si 



n 2^ 



(S6) 



Then, for natural birefringence. 



^12) sin2 if — (/333 - 1S22) — /3i2 sin 2(pY 



+ [2/5i3 sin v? — fe cos (^]2. 



•Dxu 



(A -A 



.Va Mb 



+ Ai - A 



I sin" 



I 2 — 2 

 \Mc M6 



— ( ~ - "^ + A;; — A2 ) — Afi sin 2(p 



'6 



■) 



(87) 



(88) 



Hence, with measurements at 45° between the axes and with suitably ap- 

 plied fields and strains, the three effects A4 , A5 and Ae can be measured. 

 Since the axes of the test specimen are turned with respect to the X, Y and 

 Z axes, suitable transformations of the effects Ai to Ae with respect to the 

 new axes will have to be made. These can be done as shown in reference (4) 

 by means of tensor transformation formulae. 



Another method for measuring the constants in A4 , A5 , Ae is to measure 

 the amount they rotate the axes of the Fresnel ellipsoid. As an example con- 

 sider the 2:41 constant of ADP. For example, if we look along the X axis and 

 apply a field in the same direction, then, in equation (74), 6 = 90°, (p = and 



tan 2\J/ = 



2/32 



/333 - 13-2 



1 



ifJ-b + Mc)(m6 — Mc) 



(89) 



fie Mb 

 According to Car{)enter, the 241 electro-optic constant of ADP is 6.25 X 10"''' 

 in cgs units. Ha = iib = 1.5254; Mc = 1.4798; hence the angle of rotation for 

 a field of 30,000 volts per centimeter = 100 stat volts cm is 



yp = —2.25 X 10^ radians = 7.7 minutes of arc. (90) 



