POLARIZED LIGHT AT THE SURFACE OF A UNIAXAL CRYSTAL. 
609 
where 
tan 9"= tan /3 cos 
«=F662 6=1*488 
J3=63° 44' 30" X=53° 22' 
The observations recorded were made on November 16, 1880. 
For the rotation of the sugar cell, measured by Fizeau’s method, the value 4° 4' 20" 
was obtained as the mean of seven measures, the two extremes of which differed by 5'. 
If our theory then were correct, each of the differences given in Table III., 
column 5, should be 4° 4' 20". 
We see at once that this is very far from being the case. The values of the 
rotation commence by being much less than 4° 4' 20" and, with the exception of 
Experiment 4, increase fairly regularly as the angle of incidence decreases. 
As was the case with the ordinary ray, the rotations agree with experiment for an 
angle of incidence of about 50°; from that point onwards the theoretical rotation is 
too great. 
Thus the theoretical rate of change in the position of the plane of polarization is 
too small for high angles of incidence, but increases as the angle of incidence 
decreases, and finally becomes too great. 
Several other series of experiments lead to the same conclusions. 
It remains then to discuss the effect of an error in the values of X or (3, and this 
is all the more necessary, for we know that the values taken are only closely 
approximate. 
Let us take the ordinary wave first for which we have 
cot (9= tan j3 cos (X-\-<j)') sec (<£—<£') 
and consider the effect of decreasing /3 by a given amount. 
The logarithm of cot 9 is thus decreased throughout by the same quantity. 
Now the change produced in 9 by a given change in log cot 9 is greatest when 9 is 
nearest to 45°, thus by any change in f3 the values of 9 will be more altered in 
Experiment 14 than in Experiment 1. 
But we have to consider the change in the difference between two consecutive 
values of 9. 
When 6 is near 90° log cot 6 changes more rapidly for a given change in 9 than 
when it is near 45°. 
If then in Experiment 1 we subtract from each of the values of log cot 9 a certain 
quantity, it will alter the value of 9 in the second line by an amount considerably 
greater than the alteration it produces in the first line, and thus the difference 
between the two values of 9 will be reduced. 
If on the other hand we consider Experiment 14, each of the values of 9 there will 
4 i 2 
