INTENSITY OF EELECTED AND REFRACTED LIGHT. 411 



(p'r 



where M = 2 (0r + — 8f\ sinK of 



1^ 8x8^8^=2^^(8 1/^-8 a/^) sin (peos^(f)X j-2Isin2-^ + - sinK.r'j 

 - 2 ^ • i8f'--8a;"') sin cos^^ x j -2R sin^ ^' + J ^ sin K x"\ 



= -"2- sm cos 2<^ (I_R) + 3 y sin (p cos ^0 (^^-^ j 



By adding this term to that which we have just found, the sum is 



<^ • ^/T Dx M . , /^I <^R\ ^^ 

 -2sm0(I-R) + -^ sm0(^--^) - D I. ■ 



^(4>^+^^8af^\(a'-a) = 



2{<P^+^8af^) JTsin(^'+T.^^,^^^^,^-l3Rsin<^-l4 

 = 2 (</)/+ ^5a7'2^ j^Tsin0' + 5T,+ Tsin0' + T,-rrRsin0-I,j 



0/+ -^ (5 ;r; cos (^'+5^2 sin 20') j sin0'x | -2Tsin2-^' + - ^sinKa7,j 

 + 2(0/+^a^) j-T,(l-.-'»'^^cos/ay) + ^^'.-'»'^%in/cfyj 

 = Q,(a-a)-^T sin 0' (sin ^0' _ 2 cos ^0') + — ;^ sin 0' (sin ^0' - 2 cos 20') - D, T, 



