202 



On substituting these values, the right-hand side of the equation for 

 determining a 3 contains the constant terms 



C"^T[ C ° Sl " i sm Ml + 3 cos 0 j j Wl ^— r 

 This latter factor may be more conveniently put into the form 



A , -t — 7 -^1 ^2 , — - ^2 



a?iyi«i rt • + \ - y? - — — + n -\x 2 - y? - — 



* l '2n-n x 2 v 2n-n x w 2n-n x 21 * 2n-n l 

 Let us first find the value of the first pair of these terms. Now, 



and 



n 1 Un-n' C-B 



where 



fx (15 



M y = — i — (a 3 + 2/3 2 a) a?^ + 3 (a 3 + 2/3 2 a) - sin 2 c 4a - 2/3 y, 8 * 



+ sin 2 1 2 a - (3 - — ar x 2 Ei 

 Zi 



15 ^ 



i\T = I_ (« 3 + 2a/3 2 - 2a - ft sm 2 t) 3^ 



then 



A + i Oi 2 - yi 2 ) Bi 



becomes, considering first the term multiplied by n - n 1 , 



~ |y ^(a 3 + 2^)"^ + (3(a 3 + 2/3 2 a) - sin 2 1 4a - 2/3) ^ 



+ sin 2 < 2a - jS^ 3 ] - ^ ar/^ 0^2, + — {-^ (a 3 + 2/3 2 a 

 12 r* I 8 



-2a-(3 sin 2 t) (^V - y, 2 ^) 



or 



^-^y|(2(a 3 + 2/3 2 a) - 2a - (3 sin 2 0 (a?,^ + + sin 2 * 2a - j 



3 — \ »-»■' 



