MR, R, T. GLAZEBROOK OR PLANE WAVES IN A BIAXAL CRYSTAL. 353 
X =5° 19' 45".(16) 
X/=4° O' 50".(17) 
I/N=L'P-|-PN (N being now on the side of P remote from L') =35° 3' l4"+<£'. 
L'N+X =40° 22'59"+f.(18) 
L'N —X/=31° 2' 24 " + $ .(19) 
poo OT f — 
log=1*9947864 .(20) 
° cos X, v ' 
, cos O'L' — , 
log - =1*99/0226 .(21) 
& cos X/ v ’ 
and as before, we can calculate from these data the values of 0, O' and hence of /x, p ., 
Tables YII. and VIII give the results of this. 
The fifth column gives the values of L N + X for the inner sheet, the next L N —X', 
the next 0-\-0', the eighth the value of the reciprocal of the velocity calculated on 
Fresnel’s theory [by means of Section IV. (1 and 2)], 
— 0 =<x 3 +c 2 — (cft—c 2 ) cos (6-{-O') 
/V 
= ci 2 -fic 3 — (ct 2 —c 2 ) cos (0—0') 
the ninth, the same quantity from experiment, and the last, the excess of the 
theoretical over the experimental value. 
The values of 9—6' given in the fourth column are calculated for the inner sheet. 
Now as the values of <f>' corresponding to the same incident wave are different for 
the two sheets, the values of 9 and 9' will be different; but on referring to the values 
it will be seen that after the first twenty observations, 0—6' is very nearly constant 
throughout the arc considered ; so that /x, varies very slowly, and except just at first, 
we may, to the degree of approximation required, use the value of 0 and 0' for the 
inner sheet in calculating the theoretical value of the reciprocal of the velocity for the 
outer sheet. 
In the case of the first twenty observations for which 0—0' varies appreciably with 
(j)', the experimental values of p 3 are obtained by interpolation from those values in 
Table I., to which they correspond. 
Table V. contains the theory for I. 
„ VI. „ „ II. 
„ VII. „ „ III. 
„ VIII. „ „ IV. 
2 z 
MDCCCLXXIX. 
