AN INTERRUPTED MEDIUM. 535 



or 



__ __. - - 



cos 9 ' cos 9 [ a i (0 -40 



, z 2 f27-a)('2y-a) ... .sin 2 i 2 -/ 

 - (a + 6) cos (b ' s - -^r - '-+CL\ -- f rra 



' cu - 



J 



-r 

 7 Y 



- a 04) - '-')* = 



or 



or 



_ -- 9 



cos 9 y cos 9 a (5 4) L 2 



cos 9 ' cos 



IV. To two dimensions : 



, ,, 



r (a 2-4/) ---- r cos9 (7 

 9 a + 6 v y a + 6 



a (2 y r a Y) + 6 ( 7 r a 7) . 2 ... 



-i '- - -. - * ' .. ..^ ' . - ^ cos a> fz 2 r- ) 

 (7 - Y) ( + r) 



a }=0 



If a = 6; a = 7 + Y, a = ^ + ^ (by II.) 



TTr . z 2 r 2 ., , sin 2 d) 4* 2 a.. . 4 06 



III. glVeS r (I *) - -r H^C z - r ) Z COSd) (7-7') f a = 



cos 9 y cos 9 a b 2i- + 6 



or H (1 )sin 2 9 4-) ( ) = a cos 2 <|) (7 Y) 



(i - r} 



or 7 Y = 5* -r-r nearly ; 



i a cos * 9 



7 + Y = 



:> - o 



<v = (a 4- 



2 



2 

 VOL. XV. PART IV. 7 K 



