277/i I ( - I CO du> - 27TH 







since r' - (h^+7o^). Hence, if the positive axis for the dipole moment is chosen also as the 

 positive axis in defining the axisynimetric stream function i/f, 



iA = -fi [119k] 



Here a> denotes distance from the axis of the dipole. If x denotes distance along the 

 axis, measured from the dipole, 



9 '~On'/2 X _ CO 



r=[x'^ + co'^\ , cos 6 = — , sin = — 

 r r 



The variables x and To n ay also be regarded as two out of a set of cylindrical coordinates 

 x,'co,ci), and in terms of them the potential and the corresponding components of velocity are 



ax a x'^ \ x7o 



<^=-; <7,=— 3— -1 , 7~=3^— - [119l,m,n] 



and q^^ = Q. 



CO 



Or, if Cartesian coordinates are used, with the a;-axis drawn in the direction of the 

 dipole moment for positive n, and if the dipole is at (x^,y^,z^), as in Figure 198, 



1/2 i/j 



and the potential and the three velocity components m.ay be written, from [119g] and [118b, c,d], 



= fi [119o] 



^,^ iHx-x^Y \ ?,(x-x^)(y-y^) ?,(x-x^) (z- z^) 



U = I ~ 1 I ! V = yi. , 1£ = {l 



,3 \ ,2 / ,5 ,5 



[119p,q,r] 



If the a;-axis is otherwise drawn, let the direction of the dipole axis for positive ji have 

 direction cosines l,m,n. Then, by rotation of axes it is seen that 



302 



