180 F. E. Wright — Transmission of Light through 



Substituting these values in equation (9), we obtain the 

 usual equations 



a ll —e i + (o > — e a ),8in a 6 cos 5 w 



a »j— e" + (o a — e) sin a sin'' to 



a 83 = e 2 sin a + o 2 cos 2 6 (39) 



« a3 =(o a — e' J ) cos sin 6 sin w 



w 31 r=(o a — e 2 ) cos sin 6 cos to 



a J2 = (o 2 — e' 2 ) sin 2 cos <d sin oj 



and the coefficients of tg r in the second half of (38a) become 

 «,,»„' sin 2 i—l=n * sin a i [e a + (o 2 — e 2 ) sin 2 6 cos 2 w] — 1 

 2o 31 n» 2 sin 2 «=2w a sin 2 £ (o 2 — <? 2 ) cos 6 sin cos cu (40) 

 " 33 "o 2 sin 2 i=n„ a sin 2 t (e 2 sin 2 + o a cos 2 6). 

 From equations (38a) and 40), r„ for the extraordinary wave 

 can be calculated. If n =l, as is practically the case when 

 the crystal plate is surrounded by air, equation (38a) can be 

 written in the following form, which is logarithmically con- 

 venient : 



sin r =o sin i\ (41) 



B COS w ± 4/ B 2 COS 2 to + C( -r-5-n: + A cos 2 m — e 2 ) 

 T \sin i I 



tg K = - 



e 2 — A cos 2 to — 



sin i 

 wherein A = (e 2 — </) sin 2 6 



B = (e 2 -o 2 ) sin 6 cos 6 

 C = e 2 sin 2 6 + o" cos 2 6 . 



To find the azimuths 8 , S e of the planes of polarization of 

 the refracted waves W , W e , fig. 6 is again useful. In the 

 spherical triangle Q z z\ the relation obtains 



sin r cot 6 — cos r cos a , tn . 



cot <5 = = (42a) 



sin to 



while in the spherical triangle Q e s 2' 



. cos r e cos to — sin r. cot ., ,. 



tg S, = '- — — i . (425) 



y ' sin to v ; 



The uniradial azimuths e and e e are calculated from equa- 

 tions (35a). For the ordinary wave the wave normal and ray 

 direction coincide and the angle s o =0. 



Accordingly 



tg i —tg <5 cos (i—r ). (43) 



In the analogous expression for tg e e , 



V /• \ Si"' **• Hi S e /,,\ 



tq c — tg o„ cos (1— r e ) — ^ — -. — —. ; (44) 



w " J ' v ; cos <5 e sni (^ + r e ) v ; 



tg s e occurs but can be expressed in terms of known angles. 1 



1 MacCullagh, Coll. Works, 1880. Trans. Eoy. Irish Acad., xvii. 1833. 

 Poekels, F., Lehrbuch der Kristalloptik, 194-195, 1906. 



