Muvthy 



so that the surface integral over S ' becomes the line integral 



<> ( € T , ".- « T ) f ( i,n) d v 



= (x + h Q d ) 



f(f,i?) d„ 



which may be re-written as a surface integral by Stokes' theorem 



We have, therefore, generally, 



I 



f ( i,r,) dUv 



I 



i (.€,» .);+ (x + h G fl) 



df U,n) 



dS 



d£di 



°o ^o 



It is obvious that there is no additional correction term required 

 when f ( £, 77 ) is uniform throughout S Q or when it has a zero 

 value at the boundary. 



Applying this result to the integral over S in (V. 13) we may write 



1 / 1 ^ <t. 



^(x, y, z) = 



( G !$. _ *_|2. dS + 



3n dn 



f.// 



So 1 



JL [(Vp - iap )G] dH>! + 

 ^ s £ s J 



(Vp - iarp ) G + (x + h 0) 



S„ S Lr 



+ ■ 



47Tg 



U 



[*]G, -G[^] + -^|>]g] 



d*? 



Lb + L S (V. 14) 



We will now proceed to discuss the integral over the hull surfaces. 

 Considering first 



228 



