12 



singularities and their radii R^ chosen sufficiently small so that no. two spheres overlap. We 

 designate by F.fijthe integral in F. evaluated over the sphere S^-. Then 



Fi =SF/zJ 



[20] 



Since F, is independent of the particular choice of S', ^ ^(i) is independent of 7?^.. 



We refer the region around the singularity at r^. to a system of space polar coordinates 

 with the origin at r • (see Figure 3). 



(a; - x^ 



X - X. = R cos 6 [21a] 



y - y- = R sin 6 cos A [2lb] 



s - 2. = R sin 9 sin A [21c] 



The quantities appearing in Equation [19a] may be written 



n = i cos 6 + j sin 6 cos A + k sin d sin A 



+ ^flS/) + 



q • q 





1 



sin 6 



<I>\ s 



A^A 



1 ^l 



sin^ e 



[22a] 



[23] 

 [24] 



da = ff2 sin OdedX 



[25] 



