Equation (63) is the unified inner solution which is valid for all wave numbers K. 

 The details of the derivation and error estimations are given in Reference 3, 



In Equations (62) and (63), when j is 5 for pitch motion, the two-dimensional 

 source strengths, a- and o^, can be expressed as a function of a„ and a„, respec- 

 tively. The two-dimensional potential for pitch motion is 



(64) 



(65) 



From these equations, a and a are given by 



(66) 



iU 



(67) 



By substitution of Equations (66) and (67) into Equation (62), the integral equation 

 for the outer pitch source strength is given by 



^^M - 



ia^+o^) 



2-no 



3 J 



I 



q^(0 f (x-S)dC = ^(O^+O^) + ^ ^3 



(68) 



The inner solution for pitch motion becomes 



,(s) ix 



5 ^5 



27TO, 



/• 



3+cl)3) q3(?) f(x-C)d5 



(69) 



The derivation of the kernel function, f(x), from f*(k,K,K) will be given later. 



15 



