G(P,Q) in the interior domain of this closed surface. If the point P is 

 outside S, we have 



411 Jj i 

 J J S+Z, 



GCP.Q) ^ -**(Q> ^i 21 



3n, 



3n, 



dS Q = 



where n is the normal drawn inwards to the domain under consideration. 



* 

 Integrating by parts over Z , as before, we find 



o-fcJJ 



G(P.Q) ^-ffll _**<Q> MffjSi 



3n, 



9n, 



d S, 



4tty. 



GCP.Q) ^ V(Q) ^g^ 



dy» (18) 



z'=0 



Subtraction of Equation (18) from Equation (15) yields 



*< P > = " 4¥ 



G( P, Q) |M21 + iligl _ L (Q) M.S) + ^ (Q) iM 



Q % ) | % 3n Q 



d S, 



47TY ol 



GCP.Q) \W - Kg*] ~ ^%^ {♦(Q)V(Q)} 



3x' ( 3x' 



dy* 



z' = 



4tty, 



>(x',y') G(P,Q) I dx'dy' 



l Z '=0 



(19) 



Now we assume that the fictitious velocity potential is chosen in such a 

 way that it has a value identical with <p on S. Then, the relations on S 

 are 



12 



