AN INTERRUPTED MEDIUM. 51 5 



d*a. d 2 (3 d 2 y d 2 a d* 8 d 2 y , . -. 



Moreover, ^y, ^', -jf respectively differ from -^, -jf, -^ only in hav- 



ing Q, x (a - a,) in place of Q*, (a, - a), Q y (8 - /3,) in place of Qy, (/?,- 8), and 



Q* (7-7/) n 



But -2 = c 2 a, &c. = &c. 



a i* 



Hence the following equations result : 



c2 ^f-t -o\ M ^/ rfl ^ R \ c2 r ^ 



-sm w (1 K)+ smffl I - --- I 1 sin (b cos 

 2 e Vdz dx ) 2 



c 2 rrv />, M, rfT . a M' . 



-- 1 sin q) sin an -- : - sin (p. cos a -- - sin a> sin f 

 2 e, dx e' dx 



, . . . . (1.) 



'sine'-c 2 T a . +<&,,+ Q^ (,-) (2.) 

 By subtracting these equations, we get 



or (c 2 -Q,, - Q,) (a, - a) = 



wherefore a, - a = ......... (1.) 



Similarly (3, - p = ......... (2.) 



7,-7 = ......... (3.) 



And by adding the above equations, and striking out the parts which are com- 

 mon to both sides, we obtain 



M/rfl dR\ . , M, dT . a M' rfT . 



( - --- -IsinrfM -- '- smro. cose sin (b sin u 

 e \dx dx I e, dx e' dx 



= 0. . . . (4.) 

 dy f dy 



M/dl dE\ , M, dT , fi M' dT ' ,, . & 



[ -- 1 -- I COS04 -- - COS0.COSC7 -- - COS 0) Sin U 



e \dx dx) e, dx e' dx 



FrfR, F, rfT, /c 2 \ /c 2 \ 



+ 7 77 + 7 ^7 U~ D J Ry+ U" D ') Ty - 



M/dP rfR'\ M, rfT . ,3 M' dT' .,, 



- ( _ -_ ) + ' sm 6 + -- cos 6' 

 e \d x dx) e, dx e dx 



These equations differ from those which I gave in my Memoir on light reflected 

 at the surface of a crystal, in having the terms Ry, R-, T y , T* additional. Thus it 

 VOL. xv. PART iv. 6 Z 



