370 MR, R. T. GLAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL. 
We have, therefore, to discuss the effect of these changes in the theoretical values 
of /m, fXo. 
We will further suppose that the angle y is so altered that the section still passes 
through the former position of P— -i.e., so that the only error made in the previous 
determination of its position has been in the position of IP. 
This is probable, for C IP is small and A IP, B It', nearly right angles. 
The new value of y will be 
y=59° 32' 
These changes will produce variations in the values of O L, O'L, X X', for P IP, and 
O I/, O' L', X / X/, for P Q (we assume that L L' is unaltered). 
The complexity of the changes rendered it very difficult to discuss the effects on 
[i 1 , [x. 2 from general considerations. I have therefore calculated the new values in five 
different positions taken from the previous tables. 
The table following gives the general results. 
Table XI. 
Whence taken. 
Difference. 
Mi 
Modified Theory. 
Mi 
Experiment. 
Mi 
Former Theory. 
Difference. 
Table V., 
line 28 
36 
1-66386 
1-66300 
1-66352 
52 
1 
„ VI., 
„ 11 
49 
1-64652 
1'64603 
1-64674 
71 
2 
„ VI., 
„ 21 
65 
1-62872 
1-62807 
1-62897 
90 
3 
„ VII., 
„ 21 
41 
1 "58406 
1-58365 
1-58432 
67 
4 
., VIII. 
„ 11 
43 
1-55200 
1-55157 
1-55216 
59 
5 
Whence taken. 
Difference. 
M2 
Modified Theory. 
Ms 
Experiment. 
Ms 
Former Theory. 
Difference. 
Table V., 
line 28 
-1 
1-68447 
1-68448 
1-68437 
-11 
1 
„ VI, 
„ 11 
-6 
1-68446 
1-68452 
1-68437 
-15 
2 
„ VI, 
„ 21 
+ 1 
1-68448 
1-68447 
1-68437 
-10 
3 
„ VII, 
21 
— 7 
1-68450 
1-68457 
1-68439 
-18 
4 
„ VIII, 
„ ii 
0 
1-68452 
1-68452 
1-68440 
-12 
5 
The difference table on the left is between the modified theory and experiment, that 
on the right between the former theory and experiment. 
The upper table refers to the inner, the lower to the outer sheet. 
It will be seen that the differences for /x l5 /x.-, are both decreased, though still 
remaining of the same sign. 
The differences for /x 1 are about two-thirds of them former value. 
If we then increase C L still further by twice as much as previously, so that the 
total increase is 30', we shall get still closer agreement for /x^ 
