and 



f ; . V. ^ dT - f ^ dT - f ^ dS - f ^ dS (58) 

 J. ^'PQ i'PQ J^-^PQ J.^'PQ 



The convention on the positive sense of n requires that it be directed 

 inwards on the sphere S.. For the term in (57), we have 



V X r f^dS= f V /^\x (n-xv)dS = - f ^^r/d. 

 J ^PQ J \ PQ/ J r 



^0 ^0 " 



. • " ■«? - I n n • v 



dfi + AiTVp , (59) 



^0 



2 

 where dS = r_ dfi; and in (58), 



if.'''-[''"- 



Also we have 



V ^^-^ dS = - I n n • vdS7 (60) 



^0 ^0 



lim V r ^ dx = Vp r ^ dT (61) 



r^-O J^, PQ Jj^ PQ 



since the velocity field of a volume distribution of sources is continuous. 

 Collecting the results in Equations (56) to (61) now yields (53) for P in D. 



23 



