Yim 



!5Sx(x.y-z) = Q(x,y,z) 



+ Fe 



^1 a„dx, j sec^d^l 



^k(i^-lz-f I) 



dkde 



Q k - kg sec^ 6 - ijjL sec 



Kn Qfi r 



where 



= Q+ Re-^ r sec^^d^ r 



'^=-i^rf h'"-"* 



k( iw- I z-f I ) 



k - kg sec^ 6 - i^ sec 



z I ) _ k( iw- i f-z I ) 



dkde* 



(19) 



dkde* 



A uniform doublet distribution of the strength b^ on a vertical line x= 0, y = 0, 

 f < Zj < CO produces 



^OxC^'-y.O = Fo(x,y,z) + Re j dz ^ ^ j J 



k(ia.-|z-Zi|) 



k^ e |_^ 



Q k - kg sects'- i/i, sec 



dkd^ 



knb. 



k( i^Q- I z-f I ) 



F„+ Re 



dkde , 



where 



F = — 



77 a 



1 



k cos ^ 



kCicg-l f + z| ) k(ia,o-| f-z| ) 



dkd^ 



and 



Putting 



Wq = X cos 6' + y sin c' . 



t>o = ao/l^o 



(20) 



(21) 



and considering another similar doublet line as given by Eq. (20) but with the 

 negative strength on the line x=l, y=0, f < Zj <co^ whose x component of ve- 

 locity is 01^, we combine all three cases. Then we obtain 



-'Sx^^Ox 



>ix = Q+Fo + Fi-Re 



^r/ 



k(ic.-lz-f I) 



dkdt^ 



(22) 



688 



