POLARIZED LIGHT AT THE SURFACE OF A UNIAXAL CRYSTAL. 
613 
Thus in reality the principal plane of the prism is inclined at a small angle to the 
plane E x E 3 , the intersection of the two being the exterior bisector of the angle 
E x O Eg. Let H Eh, fig. 6, be the line of intersection. If, M' the new position of B 
and M respectively, X the optic axis. 
Fig. 6. 
Then M, M', X, B, B', lie on a great circle, and BB'^MM/^MHM' 
whence 
B 3 H=90°—37° 28' 
E 3 X=6' 
sin MM'— sin B 3 N cosec a?B 3 H 
MM=8' 
And if 8 (3 be the change thus produced in /3 
S£=XB'-XB=BB , = 8 / 
and if A' is the new position of A 
but 
MA=X M'A^X+SX 
MA^M'A' .\8X=0 
The value of /3 then, if these observations be true, is some 8' too small. This would 
alter somewhat all the values of 6 in Tables II. and III., but would produce little or 
no effect on the differences. The observations themselves, however, are only approxi¬ 
mate, and can be used to give some idea of the limit of error made in giving to /3 
the value 63° 44/ 30", though hardly to determine its value more accurately. It is 
certain that /3 is rather too small; it is also fairly certain that it is not 10" too small, 
and for our purpose at present, between these limits one value is as good as another. 
It therefore seemed that no real advantage would be gained by recalculating the 
theoretical values of 9 for a value of f3 somewhat greater than 63° 44/ 30". 
The observations recorded above were made during the autumn of 1880, and at 
that time I was enabled by Lord Eayleigh’s kindness to order, for the Cavendish 
Laboratory, two graduated circles, mounted so as to revolve about an axis at right 
angles to their planes, with tubes through their centres to carry a X icoi/s prism or 
other such apparatus. The verniers attached read to 15", and by means of various 
