80 BELL SYSTEM TECHNICAL JOURNAL 



(determined by a compression) is up, the values of I, m, and n are 



/ = 0; m = cos d\ n = — sm d. (4) 



In this definition, a right handed crystal is taken as one which causes 

 the plane of polarization of light traveling along the Z or optic axis to 



-U-2200 



6^2000 





1600 



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



ROTATION ON X AXIS - -• »- + ROTATION ABOUT X AXIS 



IN DEGREES IN DEGREES 



. Fig. 4 — Frequency constant for thin plates plotted against angle of cut. 



rotate in the sense of a right handed screw. Substituting the values 

 of (3) and (4) in (2) we find 



Xii = ^66 cos^ Q + C41 sin^ Q — 2cu sin 6 cos 6 = Ces', 



X23 = — Ci4 cos^ 6 — (cii + C23) sin 6 cos 6, 



X22 = C22 cios^ 6 + C44 sin^ 9 -f Icn sin 6 cos 6, (5) 



X33 = C44 cos^ 6 + ^33 sin^ d, 



X12 = Xl3 = 0. 



With these values of X, the three solutions of equation (1) are 



C\ — \ — , 



\ p 



\( 1 r X22 I x,-?3 / / X22 XssX^ ^ TT^o X22 X23 

 ZIP p \ \ P P / P p 



where K^ = X23VX22X33. 



The frequency of any plate with its edges free to move will be 



(6) 



f = -(2n+l) n = 0, 1,2, 



(7) 



