REFLECTED AT THE SURFACE OF A CRYSTAL. 47 



_ 1 II' sin <' s in & M' (sin 2 </>' - 2 cos 2 </>') - D, T,. (c.) 



f f .1 



The value of D, is 2 (0 / + ^ 5 *">) (1 - *<-' cos/5/) ; 

 and the values of M, and M' respectively 



(b' r' 

 2 (</>/ + !-- e 2 ) sin A; e, and 2 (0 >' + *-^- o 2 ) sin A o. 



d)'/ 

 In the same way we can write down the value of 2 -^7- tf dy' 8/3, from that 



O f 



Thus 2 - 5 a:' 8y' d /9,= 3 sin <, cos 0, | - ~ T cos 0, cos 6 



+ ' -T cos d),cos6 } +3 sin d)' cos (f)' I TJ- T' cos <i' sin 0' -- - sin (b r sin 6' \ 

 e, dx j \2 e' da; } 



= 3 { -sin^cos 2 ^cose(^T-|' g) + sin 0' cos 2 0' sin fr g T' - ^ ^) ] 



1^ Sxfdz'dj^O. Denote 

 then 



The reduction of equation (5), or the value of ~, is consequently obtained by add- 



ing together the quantities of (a), (b), (c), (d), (e). 

 Now the sum of (a) and (b) is 



s'mcp (I-R) - .- si 



ri TJ^ M 

 (I_R)-- 



the sum of (c) and (d) is 



(c 2 AT rf T\ 

 2 T - y-' j (sin 2 */),- 2 cos 2 0, + 3 cos 2 0,) 



(c 2 M' dT'\ 

 2 T'- J (sin 2 <j(>'-2 cos 2 0' + 3 cos 2 <') - D ; T y 



M' dT'\ 

 



-- - 

 and (e) is Q^.^-a). 



