MR. R. T. GLAZEBROOK OR PLANE WAVES IN A BIAXAL CRYSTAL. 
329 
Whence 
l 2 (a 2 —tr) (a 3 - b 2 ) = (c<?-v 2 ) {a 2 -v 2 ) 
m 2 (b' 2 — c 2 )(b 2 — a 2 ) = (6 3 — v 2 )(b 2 —v 2 ) 
n 2 (c 2 —a 3 ) (c 3 —5 3 ) = (c 2 -^ 3 )(c 3 -V) 
From the tables for the second prism, we see that for the inner sheet for 
d>'=28° IF 21"- = F53021 
v i 
For the outer sheet, 
<£'= 28° F 21"-=1-68391 
V 2 
Since the value of v 1 changes very slowly, we may reasonably treat these two values 
for <•// as coincident, and substitute in the above formulae. 
We find 
cos -1 ^ = 49° 35' 
cos- 1 m 1 = 40° 27' 
Again, fur inner sheet for 
<F= 38° 2' 41” - = 1-53037 
v i 
For outer sheet 
</>'= 31° 42' 34” 1 = 1-68437 
V 2 
Treating these two as coincident, we find 
For inner sheet for 
For outer sheet 
Whence 
cos 1 7i., = 55° 44' 
cos -1 77^ ; , = 34 0 23' 
<£' = 26° 5' 11” - = 1-53028 
A 
<F= 26° 19' 10” -=1-68378 
v 2 
cos- 1 %=47° 56' 
cos -1 w 3 =42 0 8' 
We may justify the treating of the two values of cf>' as the same, by the considera¬ 
tion that /x 1 varies at the rate of 00001 (about) for 1°, and therefore the difference for 
20' is inappreciable. 
Now the angle between the radii vectores in the first and second case cannot be 
less than 
2 u 
MDCCCLXXIX. 
