q.* G„-, - - f*q* = [0.+0.+C.(0.+0.)]* G + 2i(C a ) 



*j 2D TT 



J J J J J 2D 



J J 



(57) 



Equating the factors of G„_^ gives a relation for the source strength 



q.* = [a.+a.+C. (o .+0 .) ]■■ 

 J J J 3 J J 



for j = 3 and 5 (58) 



Equating the remaining terms in Equation (57) gives 



f*q.* = -2TTi [CO.]- 

 2 J J 



(59) 



The inverse Fourier transforms of Equations (58) and (59) can be expressed as 



q. = [a.+a.+C. (o .+o .)] 

 J J J J J J 



(60) 



2ui [C.a^] = - J q.a) f(x-C)d? 

 L 



(61) 



The kernel f(x) is the inverse Fourier transform of Equation (42). Elimination of 

 C. gives an integral equation for the outer source strength 



,.(x) 



taj«^ 



2Tra. 



J -I 



I 



q.iK) f(x-?)dC = (o.+a.) 



(62) 



INNER SOLUTION 



By substitution of Equation (61) for C. (x) into Equation (46), the inner so- 

 lution is given by 



•P. = Vf^^ - ^- ((}).+?.) q.(?) f(x-5)d5 

 J 1 2TO. J J J J 



(63) 



14 



