INTENSITY OF ORDINARY AND EXTRAORDINARY RAYS. 413 
Br ah aa ae ee ete foe 
r Ly 
ED ies alot peewee fe awe 
v' = A‘cos $ sin — ‘) Qa 
A i ei: 
+ B'cos $ aes set a $_*) 
A 
ese (= reos>+ysing 7¢ 
9 | 
rN 7) or. 
Baie,» | eee See eeieineh Vy 
Qa 
r 
The equations for the incident light remain unaltered; thus 
u =— Asin ¢ sin (ee eee oa £) 2 @ | 
A T/ | 
v= Acos¢sin a oy =) Qa (13.) 
wah « (xeos¢+ysngd ti. 
5 C sin aa q) 27 
The equality of the components of the motion in these three 
systems of waves 11, 12, and 13, xz being = 0, give 
Asin ¢ — A’sin ¢ =— A"sin ¢! ) 
B! sin ¢ = + B" sin g! 
Acoso Alcos¢= B!"W/—I1cos 9! ( Tybalt) 
B! cos¢ = — A" /—1 cos #. J 
CCl 3.0! 
D'=D’, 
and the equation (8.), applied to 11, 12, and 13, gives— 
(C —C’)sin ¢ cos ¢ =—D" / —1sing!cos q! 
D’ sin ¢ cos 6 = —C" / —Ising!cos wt ete) 
Consequently we see, from the equations (a.), that 
A? = A? + B?, 
and from 6 and ec, that 
C? = C? + D2, 
i. e. that all the light is reflected. Moreover, we obtain from a, 
