320 MR. R. T. GLAZEBROOK ON PLANE 4VAVES IN A BIAXAL CRYSTAL. 
(1.) The normal to the principal plane of the prism; (2.) The intersection of this 
plane with the plane B C B'; (3.) The intersection of the principal plane with the 
plane A C A'. 
(1.) Rotation about a normal to the principal plane of the prism. 
This cannot produce the required effect, for though we can thus decrease the 
differences on one side of the maximum radius vector of the section, we increase those 
on the other side by about the same amounts. 
(2.) Rotation about the intersection with B C B'. 
This is of no use, for the effects produced on opposite sides of the maximum radius 
vector are again of an opposite kind. 
(3.) There remains, therefore, oidy the rotation about the line of intersection with 
the plane C A C', or a variation in the angle y. This change is to be such that the 
sections of the outer and inner sheets may be brought into closer proximity; y must 
therefore be decreased. 
Now on referring to the tables of the experimental results, it will be seen that none 
of those in Table III., lines 1-11, Table VI., lines 1G-29, and Table IX., lines 1-16, 
differ greatly from 1’68125. 
If it were then permissible to neglect the angle y, this would be the value of \±i, and 
the other section would be on Fresnel’s theory an ellipse of [x a , [x c . 
In the abstract published in the ‘Proceedings of the Royal Society,’ No. 188, 1878, 
this has been done, and a limit assigned to the error thus introduced. 
Professor Stokes has since pointed out that near the optic axes the limit is con¬ 
siderably too small, and thus led me to the accurate calculation of the theoretical 
valties of [x x , /To given above. 
The effect of a decrease in the angle y may, therefore, be estimated by referring to 
the calculations for the case in which we put y=0. 
The accompanying table gives the results. 9 being the angle between the wave 
normal and the major axis of the ellipse, which is given by 
9=<f>''& 0 
where 9 0 is the angle between the normal to the face of the prism and major axis, 
and is 
= 20° O' 40" [Section V. (2)]. 
