MR. R. T. GLAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL. 343 
Section IV .—General Theory. 
To apply these results to the theoretical calculation. 
Taking the same figure 
Fig. 7. 
Let the optic axes cut the sphere in O O'; consider a plane cutting the plane A O C 
between C and O' in L say; let N be any point on it; let NLA=y, NO = 9, NO' = 0'. 
Then we know that if v x , are the velocities along the wave normal through N, 
a, b, c the principal velocities, a being the greatest 
v x —v 3 3 =(« 3 —c 3 ) sin 9 sin 9' 
'yi 3 -h'y« i 3 =(tt 3 d-c 3 ) —(a 3 — c~) cos 9 cos 9' 
2v 1 2 =(a 2 -\-c 2 ) — (cr—c 2 ) cos (9-\-9') 
2'y 3 2 =(a 3 +c 2 ) — (a? —c 3 ) cos (9 — 9')> 
We require, therefore, the values of 9 and 9'. 
Now 
cos 9= cos OL cos LN — sin OL sin LN cos y 
= cos OL(cos LN — tan OL sin LN cos y) 
cos OL 
cos X 
cos (LN + A.) 
if 
Similarly 
where 
tan X— tan OL cos y 
COS 0 L /T XT x ,\ 
cos 9 =-cos (LN—X 1 
cos X v ' 
tan X — tan O L cos y. 
( 1 ) 
( 2 ) 
(3) 
(4) 
Thus to use the formulae for i\, v. 2 we require to know accurately the position of the 
optic axes. 
