346 
MR. R. T. GLAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL. 
XM (=0 4 say) = 123° 32' 
XM'(=6>' 4 , gay)= 59° 52' 
arc YA'M (= 0 5 say) = 117° 17' 
arc YA'M'(=# 5 say) = 181° 3' 
Fig. 8. 
Since Y, M, M', are in one zone with A and B, and B bisects arc M M' 
2BA'Y=M'A'Y+MA'Y 
arc BA'Y= 149° 10' 
A'Y=149° 10' —90° 
= 59° 10' 
Let a 4 /3 4 y 4 be the direction angles of X. 
Then, as before, [Section II. (1)] 
. &,+e. . d'-e. 
sm 4 2 - 4 sm- 4 -- 4 
COS 
&c. 
whence 
a 4 = 3° 28' 50" 
&=91 0 42' 
To test these values let us calculate the angle X Y; the triangle X A B gives 
whence 
cos XAB== 
cos XB 
sin AX 
77-XAB=60° 43' 50" 
In the triangle X A Y we now know AX, AY and the angle X A Y. 
