290 MR. R. T. GLAZEBROOK OR PLARE WAVES IR A BIAXAL CRYSTAL. 
b*=a~ / —/3= 1—/3 
c~ — a z —y = l—y 
Then 
(3 =0-00338 
y =0-01222 
y -/3=0-00884 
In the second set of observations the plates are inclined to the incident light, so that 
the light when in the crystal passes along an optic axis. 
To calculate the displacement of the fringes on Fresnel’s theory, it becomes neces¬ 
sary to know the velocity of the light in the crystal; this is given by 
v 1 °= 1 —y sin 2 y 
y being the angle between the direction of vibration and the normal to that circular 
section of the w*ave surface whose radius is a or unity. 
Hence 
v i~ 1 “ay s i n2 X 
neglecting y~ sin 4 y, &c. 
Theory gives for the displacement measured in wave lengths 
N= 12-73 
Experiment gives 
N= 11-87 
For the other two waves theory gives 
N=46'03 
Experiment gives 
N=45-49 
In the third experiment the light was incident at about 60°. 
In this case, <£ being the angle between the direction of vibration and the normal to 
the circular section radius b 
v x ~= 1 — /3 cos 2 (j)—y sin 2 <f) 
and to the same approximation 
v x = 1 — h(/3 cos 2 </>+y sin 3 </>) 
Whence theory gives 
N=19-57 
Experiment gives 
N=20-63 
Thus in each case the agreement between theory and experiment is fairly close; but 
we must remember that the quantities to be measured are very small, and that in 
obtaining the theoretical results, small quantities have been neglected, without showing 
