MR. R. T. GLAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL. 
361 
Therefore (— - — —J cos (6-\-6') is increased so long as 0 J r O' is less than 90°. 
\H» Ha 
And the increase in 
1_1 
-) cos (0-\-9') is greatest when 9-\-9' is least. 
He /v 
Also the increase in —„--] cos (0+0') is less than the increase in ( ,+ - ). 
1 . 1 
/v h * 
Therefore— 2 + — 2 — (— 2 - 2 ]cos (0+0') is increased, and this increase is greatest 
when 0+0' is greatest. 
Therefore, as 9+9' increases up to 90° j u. 1 decreases. 
When 9-\-9' is greater than 90°, cos (0+0') is negative. 
As 9 + 9' increases, cos (0+0') increases numerically. 
Therefore 
He" Ha 
,,) cos (0+0') increases numerically and is negative. 
Therefore ~ + — 
H^ Ha 
1 A 
o e 
\Ho Ha 
2 ) cos (9-\-9') increases a fortiori. 
Therefore /r 1 decreases. 
Thus the effect of decreasing is to produce a decrease in the value of Hd and this 
decrease continually increases as we go from L to Q. 
Now if we compare the differences between the theoretical and experimental values 
of Hi, given in Tables V. and VI., we see that they increase with 0 the theoretical 
value being in excess of the experimental. 
The effect of the assumed alteration in the value of /x, ; would be to decrease the 
theoretical value of Hi by an amount which constantly increases, that is, to bring it 
more nearly into agreement with experiment. 
But the effect in Tables VII. and VIII. would be contrary. 
On referring to them we see that the differences between theory and experiment 
continually decrease. 
The effect of the proposed alteration would be to subtract from the theoretical value 
of Hi given in those tables : a quantity which increases rapidly as we get further 
from L. 
The result would be that the theoretical value would soon become less than the 
experimental, and the difference between the two would continually increase. 
We might, it is true, choose the decrement of/x t . so as to make the extremities of the 
arcs considered coincide, and then the differences would be diminished throughout. 
The effect of this would be to make the theoretical section lie outside of the experi¬ 
mental for about 75°, then cut it and he inside it. 
Whether the two could again be made to coincide when cutting the plane A O B 
experiment alone could settle. 
Let us now consider the effect of the supposed change on Hi- 
We have 
3 A 
MDCCC LX XIX. 
