AN INTERRUPTED MEDIUM. 513 



2 ILL 8 x 8 .?/ 8 /3 = 2 ^ (-t*+p 2 ) sintf>cos 2 | -2 I sin 2 ** 

 r 



9 Ar 1 ?I 1 e?R 1 



+ 2 R sm 2 -TT + - -T sin * i -- -7 an f > 

 2 e ax e ax ) 



the sum of which is 



( k i 



I -2 Isin 2 y + 2Rsin 2 -+ - sin 





c* . M . , /rfl rfR\ 



= TJ- sin d) ( I + R) + sm rf> I - -- -j ) 



2 e r \dx dx ) 



where M = 2 f 0r + ^5> + ^ S*S y 



r r ' sin 



= 2 (0r + 5 a: 2 ) sin e8x cosf8y+ C . ^ 2 y cos 



/ Sill *JJ r 



for both the incident and the reflected wave. 

 D = 2 r+ * 2 l-< 



Again, 2(^)r'+ 5a^ 2 ) 5a y =2 (^)/ + f 2 cos 2 $"+^ 2 sin 2 "$) 



{/fee yfc o 



- 2 T sin <, cos ^ sin 2 y + 2 T sin 0' sin & sin 2 -g- 



1 *-/ T 1 1 ^V TH' 



- -j sin ( 7 cos 6 sin k, e ~j~j~ sul 0' sin 6' sin 



2 



where stands for either e or o, as the case may be ; and <p for $, or <' : 

 and 2 -*p- 5 x" 8y' 8/3, = 2 ^- sin 0, cos 0, ( e 2 +j 2 ) (2 T cos 0, cos 6 sin 2 -~- 



