IN CRYSTALLIZED MEDIA. 347 



(cot m sin >/> - sin € cos 0) (cot m sin x\, + sin e cos ■«// ) 



_ t'ns 6 cose 



2 cos -^ sin 6 ^ ■ 



cos 6 



Now if O and R in the figure (18) be the two optic axes, it is evi- 

 dent that 



ssa;, = v/,, a;,20 = ^-e, x,%R = - + e\ 

 2 2 



.• . cot OxiZ = cot tn sin \jxseee — cos >// tan e, 



cot ^a;iS = cot m sin \// sec e + cos \}r tan e ; 



.-. - cot 2m = cot(0^,»; - Ex,%), 



TT — 2fi = OxjS — RxiZ 



= Oxjiji - Rx^t/i + 2%x,yi, 



= Ox,y, - Rx,y, + 2{%x^N-n) 



= Ox^y^ - Rx>y, + tt - 2m ; 



.-. Ox^y, = Rx,y, ; 



therefore the plane which defines one vibration bisects the angle be- 

 tween the planes passing through the normal to the front of the wave 

 and these two optic axes. 



The plane which defines the other is manifestly at right angles 

 to this. 



23. We saw in (21) that the expression for the difference of the 

 squares of the velocities is 



V" -v^ = («= - b^ ^'"^^^"^'^ 

 ^ ^ sin 2m 



-»T . /-, cos e sm m 



Now sm UXi = 



sin .fix, = 



sin Ox,z ' 

 cos f sin m 



sin Rxj z ' 

 Vol. VI. Paet II. Yy 



