13 

 where 



dR do d\ 





and Sg and s^ are the unit vectors in the (R = const., A = const,) and (/? = const., 6 = const.) 

 directions respectively: 



^e = -i sin 6 + j cos cos A + k cos 6 sin X [22b] 



S;i^ = -j sin A. + k cos A [220] 



The components of the force parallel to the i, j, k, directions become: 



/2 77 y« /7 p 

 - (R.-^J^ cos ^ + $2 COS + -^^ (D? 

 J L ' ^ «i"' ^ ^ [26a] 



+ 2/?. <I)„$^ sin sin dddX 



^iy(0=-^ - (ff,$„)^ sin^e cos \ + (1)2 sin2 COS A + (|)2 COS A 



° [26b], 



(f6iG?A 



Fj^(i)=- -(/?.(I)^)2 sin2 (9sinA + $g sin^e sin A + 0)2 sin A 



[26c] 



2/?.$^$^, sine cos ^sinA - 2/?.$^$ cos Alfi^^d^A 



In the region o < R < | f ,• - fj 1, where r. is the position vector of the singularity nearest 

 fj., the potential is analytic, so it can be expressed as an expansion in spherical harmonics 

 which converges throughout this region, 



oo n 



1> = y^ y^/?" P^(f/)(< cos sA+ 6^sin sA) 



n=o s=o |-27] 



y^ y^^ /?-<"+! >P^(,x)(< cos s\-+6^ sinsX) 



n—o s=o 



