610 
MR. R, T. GLAZEBROOK ON THE REFRACTION OF PLANE 
be more affected by tbis change than in Experiment 1, but the effect produced on the 
value of 9 in the first line will be nearly the same as that produced on the value of 9 
in the second, and thus the difference between the two values will not be so much 
altered. 
Thus a decrease in (3 will decrease everywhere the theoretical value of the rotations, 
but it will affect the high angles of incidence considerably more than the low. It 
will thus tend to bring the theory more into accordance with experiments. 
Let us see how it will affect the extraordinary ray. 
• 
The term in the formula with ■ ^ for a factor is practically a small and slowly 
varying correction except for the very highest angles of incidence; let us consider it 
as constant with regard to (3 and see how a decrease in /3 affects the values of 9 
supposed to depend only on the term 
tan /3 cos (X+<£") cos (</>— <f>") 
Exactly the same reasoning applies to this as in the case of the extraordinary wave. 
The values of 6 in Experiment 14 will be most decreased, but the alteration in the 
value of 6 in the second line of Experiment 1 will be much greater than the alteration 
of the value of 9 in the first line, while the change in the values of 9 in Experiment 14 
will be much the same for the two. Thus, by decreasing (3 the differences will be 
decreased throughout, but the changes will be greatest when the angles of incidence 
are large. 
Thus a decrease in (3 will increase the differences between the theory and 
experiment. 
Hence considering the ordinary and extraordinary rays together, a change in f3 will 
not reconcile the facts observed. 
Calculation shows that decreasing [3 by 30' decreases the differences in Experiments 
4, 11, and 14 by 6', 4', and 1' 20" respectively for the extraordinary ray, and the 
amounts are about the same for the ordinary. 
We must now consider alterations in X; putting tan {3= R we have for the ordinary 
ray 
cot 9— K sec cos (X-j-^') 
therefore 
S(9=K sin 3 9 sin (X-j-<//) sec (<£—<£')SX. 
Now when <£ is large 9 is nearly 90° and <£— <f> is large. 
Thus sin 9 sin (X-j-^ 7 ) and sec (</>—<£') all increase with <//, and therefore S9/SX is 
greatest when cf> is large. 
Thus the alteration produced in 9 is greater the greater the angle of incidence. 
If then we decrease X we shall reduce in every case the differences between the 
corresponding values of 9, but we shall reduce them most for high angles of incidence 
and thus tend to bring the theory more into accordance with experiment. 
