82 Mr. J. Walker. Relative Retardation between Components 



(1) Let the plate, be cut from a uniaxal crystal, then writing 

 6 = 0, equation (i) gives the two equations 



_p 2 = a- and 



(p 2 c 2 ) {(I cos x + n sin %) 2 + m 2 } + (p- a?) (I sin x n cos x) 2 = 0, 

 and the values of n are given by 



2 + <) -1+ (a 2 -c 2 ) (I sin x w cos x) 2 = 0, 

 whence 



1 /_ sin 2 1 



a 



2 sin 2 x) (l c 2 sinH'/V-) c 2 (a 2 c 2 ) sin 2 x c 

 + (a 2 c 2 ) sin x cos x cos ?0 sin i/v} (a 2 cos 2 x + c 2 sin 2 x) 

 and 



A _ ^/v~ a 2 sin 2 i (a. 2 - G 2 )sin x cos x cos w sinz 

 T ~ a a 2 cos 2 x + c 2 sin 2 x 



v/fVr cos 2 x + c3 s ^ n2 x) (^' 2 c 2 sin z i) c 2 (a 2 c 2 ) sin 2 x cos 2 w sin 8 * 

 a 3 cos 2 x 4- c 2 sin 2 x 



(2) Let the plate be cut from a biaxal crystal perpendicularly to 

 the mean line ; then taking the axes of elasticity as the co-ordinate 

 axes, the biquadratic in n becomes 



(7rcT~ -f cVm 2 + aW) (P + m 2 + w 2 ) 



-{(fc s + c 8 ) Z 2 + (c 3 + a 2 )m 3 +(a 3 + & 2 ) 2 } + l = 0, 



or 



2 )} {l-6 2 / 2 - 2 m 2 } = 0, 

 and %i, n 2 being the positive roots of this equation 

 (i -O 2 a a fc 3 = ( 2 4- 6 s ) - 6 2 (c 2 + a 2 ) Z 3 - a 2 (6 s + c 2 ) m 2 



and 



" 'V 4- c 2 ) sin 2 w\ sin 2 i 





T 2 



2ab \/(v z c 2 sin'- i) { v~ (6 2 cos 2 w + a 2 sin 2 t?) niir t} 



: 



