Transparent Inactive Crystal Plates. Ill 



(a) E cos €j(2 cos i sin i) = ~D l cos 8 t sin (i + r x ) 



(b) E sin ej(2 cos i sin i) = 



D^sin 8^ sin i cos i + sin a r^cot r t sin 8 i — tgs l ) 



On division of (J) by (a) 



sin ^(sin i cos i + sin r x cos r^— sin 2 r l tg s l 



ty e i = 



cos 8 i sin^ + rj 



or to e, = tg 8. cos (i— r.) sin r g s 1 



y l J ' v i; cos S, sin (* + r,) v ' 



o- -, , * /. sinV, tg s. . 7 s 



Similarly, tg e Q = tg d cos(2— r.) 5 — ." /. " . (35&) 



J ' ^ 2 y 2 v 2 ; cos 5 a sin(i+r 2 ) v 



By means of these formulas the uniradial azimuths for the 

 refracted waves W, and W 2 can be calculated. At the second 

 boundary surface of the crystal plate, the refracted wave W 1 

 produces two reflected waves W ia , W lb and one emergent wave 

 ¥',, (fig. 2). To calculate the azimuth of the plane of polari- 

 zation of this emergent wave, the relations of Potier are 

 important. The general boundary conditions for this surface 

 and wave W, are defined by equations (20), which, after the 

 manner of (18a) can be written in the abbreviated form : 



D A + R'A + R'/i = D\ cos 8' cos i 



D 1 m 1 + R'.m^-f R\m" i = T>\ sin 8\ 



D 1?il + R>' a + H" l n" i = T>\ cos *', sin i (20a) 



D 1 ^t) 1 + R'jP\ + B l " 1 p" 1 = D\ sin d\ sin i cos i 



On multiplying the first of these equations by n 2 , the second 

 by^? 2 , the third by &,, the fourth by to 2 , and adding, we find 



D 1 (n^ + m x p 2 + 1^ + m 2 pj + B,\(nJ\ +p % m' l + l i n' 1 + mjy'J + 

 w/ . U\(l"n+m 1 p\ + l i ml+my i ) = 



D j(n 2 cos o s cos i+Pi sin 8\ + l 2 cos d' 1 sin i + m 2 sin 8^ sin i cos i) 



In this equation the coefficients of D, B/, K", are = by 

 virtue of the Potier relation (33a), and as the amplitude W is 

 not in general zero, the equation reduces to 



v , «„ cos i + 1, sin i 



tg 8' — ? : — \ . 



p 2 + m 2 sm i cos i 



On replacing n„ l»jp» m 2 in this expression by their respective 

 values from (19), we obtain 



tg d\ = - 



cos 8^ sin r 2 cos i + cos <? 2 cos r 2 sin i (36) 



sin r 



~~T% — L sln d A a u cosr 2 — -a 13 sin r 2 ) + <7 12 cos <? 2 ] + sin£ 2 sin i cos i 



