452 



BELL SYSTEM TECHNICAL JOURNAL 



Ssi = 5i4(sin^ 6 — 2> sin^ 6 cos^ 6) + (2^11 — 2sn — ^44) sin^ d cos d 



+ (2^13 — 2^33 + 544) cos^ 6 sin d, 

 544' = (4533 + 45ii — 8^13 — 2^44) sin^ 6 cos^ 6 + 4^14 



X (sin^ cos ^ - sin 6 cos^ d) + 544(sin'' 6 + cos" d) 



and 



dii = dn, 



du = - i[^u(l + cos 26) + (/i4 sin 2^], 



f^is' = - |[c?ii(l - cos 2d) - dii sin 2dJ, 



dii = ^14 cos 26 — dn sin 26. 



The curves representing the 5' values for varying angles of orienta- 

 tion are plotted on Fig. 30 while the values of d' are plotted on Fig. 35. 



-90 -80 -70 -60 -50 -40 -30 -20 -10 10 20 30 40 



ANGLE OF ROTATION IN DEGREES 



60 70 80 90 



Fig. 35 — Piezo-electric constants of a perpendicularly cut crystal as a function of the 



angle of rotation. 



