POLARIZED LIGHT AT THE SURFACE OF A UNIAXAL CRYSTAL. 
611 
Turning now to the extraordinary wave, and again considering the first term only, 
we find 
SO— —K cos 3 0 cos (<£—<£") sin 
Now as the angle of incidence decreases, cos 3 0 and sin both decrease, but 
cos (<£--<£") increases, and we must have recourse to numerical values most easily to 
consider the changes in the product. 
Putting in the values for <^=82° 55' and <f>=l7° 45' we find S0/S\ is numerically 
the greatest in the first case. Hence by decreasing X we increase 6, and that most 
for the high angles of incidence. 
Thus the decrease in X increases the first value of 0 in each of the experiments in 
Table III. by a greater quantity than the second. It therefore decreases the differ¬ 
ences throughout, and does not tend to bring theory and experiment into agreement. 
Hence taking both rays into account an alteration in X will not produce the effect 
required. 
Thus it is not possible to change the constants /B and X so as to produce greater 
agreement between theory and experiment. 
But (3 and A are both measured from the intersection of the incident wave and the 
face of incidence. In treating them as constants we have supposed that as the prism 
was turned this line of intersection remained parallel to itself, thus assuming that the 
prism was accurately levelled, so that the incident and refracted wave normals lie 
always exactly in a principal plane. 
If this be not the case, /3 and X become functions of the angle of incidence, and have 
not strictly the same values in the consecutive lines of Tables I. and II. 
To test the effect of this error experimentally I set the spar prism so that the 
incident wave normal instead of lying in the principal plane was inclined to it at 
about HP, and made a short series of measurements. 
The results agreed very closely with those tabulated in Tables I. and II., and 
proved conclusively that the level error which I feel sure never amounted to as much 
as 2' could not account for the difference between theory and experiment. 
The same is fairly clear from the formula), for in Table It. we could reconcile theory 
and experiment by supposing that at high angles of incidence [3 is somewhat greater 
than 63° 44' 30", and that it decreases continually as the angle of incidence increases, 
but this assumption would just tend to increase the differences given in Table III. 
Thus a small variable error in the value of [3 will not account for the observed 
facts. 
One point, however, needs further investigation. An error has been confessedly 
committed in the value of [3. Can we assign a limit to its value ? 
The fact that the four poles P, Q, R, la R 3 are nearly but not quite in the same zone 
renders it impossible to determine accurately the position of P and Q. The prism 
was levelled by placing a mark across the slit, which when viewed directly appeared 
