35 



where q (r .) is the velocity at r^. due to the undisturbed stream. Also 

 F/z; =-4;.p[a°(r.x«o)+r.-^] 



For the doublet 





a" — - + a, ■■ + o| 



^ dx^ 1 dx dy ^ dx dz_ 



' + o, — r-+o; — 



_ ^ aa? (92/ ^ <9y2 ^ (9z/ <93_ 



,920 ^2 , ^2 ; 



1 ^a; (92 ^ ay (93 ^ ^a^ 



which can be conveniently written in vector form 



Also 



dk 



r/z) = -4.p— 



[89] 



[90] 



[91a] 



[91b] 



[91c] 



[911 



[92] 



i 



i 



M.(i)={t.x?.(i). V) +^np[a° -^-^ — ^ 

 ^ ' ^ \ ' (9y ^ (9a; /i 



[93a] 



[93b] 



[93c] 



M/iJ = r. xF/iJ +4;rp(q^xA). 



[931 



