4 Proceedings of ihe Roijal IrisJi Academi/. 



It may be observed that on the sphere t" = t = t, and 'r{t) = r„. Also 



8/ 



Mn(yjr{r'r-^ 



doc 



di 



so that if T = t" -■= t, 



dx dx \ dr 



dt \ dr" ) ' 



at \ dr J 



dx) dx \ \dt ' ' • 



l')-(l')— ^X--(W- 



All the quantities r satisfy two relations which will be made use of. 



2(|Y-F-'(|Y.o. 



df^ r(T) dx dx 

 On inverting the order of integration, we get 



^ = 



pr^^dr, 



du 



du,V\Tri)-' 



V-{t - n)' - (x - a'o - X, («))- -{y-y^- yii^'))' -{z-z^-Zy {u)y j 'K 



Eeforming the integration with respect to f?w 



'lirpv^^dr,, 



2r,r(n) ^ V'(t - tof- {r(tc) + r.f 



Changing from complex to real integration, we get 



rrt) 



4^ = 'I-n-f) V^i\d'}\ 



""" d.u 



- / ['' du 



2TrpV r^dr —-■ 

 •(0 J r r(n) 



