310 
MR. J. C. McCONNEL ON AN EXPERIMENTAL INVESTIGATION 
passes obliquely through the plate. We have to determine the relation between R 
and D. If we were free to assume that the two wave-fronts in the crystal might be 
treated as parallel this would be very simple, and in my former paper I made this 
assumption; but further consideration has convinced me that the assumption is 
inadmissible, at any rate without a good deal more explanation. It is true that the 
two wave-fronts are very nearly parallel, but it is also true that the retardation to be 
measured depends on the small difference between two nearly equal velocities. I 
therefore give the following more rigorous investigation, which leads, as will be seen, 
to the same result as the questionable assumption. 
Fig. 2. 
Let FGC in fig. 2 represent a plate of quartz. Let ABCD be a wave-front ; of 
which the part AB has not reached the quartz, and the part BC is an “ ordinary ” 
wave-front in the crystal. Let i be the angle of incidence, i i" the two angles of 
refraction. 
Then the retardation of the ordinary wave in passing through the plate is the 
perpendicular distance between CD and ABE 
rp (t 1 ) m/ • i / \ 
= I -: - 7 — = I (Sin i cot L — COS l). 
sin c v ' 
Similarly the retardation of the extraordinary wave is 
T(sin i cot i "— cos i). 
So the relative retardation is 
T sin i (cot cot l) .(l) 
This is a well-known result, the above proof being due to Dr. Routh. I have 
inserted it for the sake of completeness, and to show that so far no approximations 
have been made. 
Let s' s" be the two wave-velocities in the quartz, then 
