Electric Waves round a Large Sphere. 521 



finite at infinity, of the form 



n r 



D„ is determined by the surface condition that when r = a, 



d/Mw+72P)=0, (8) 



and therefore with (5, 7), since the portions not in the series 

 satisfy the condition at once, it follows that 



or Bn = -^(rj ^ . aiJ m (ka) j ^ . a*K m (ka), . (9) 



and this gives a series in y 2 p which is finite everywhere. 

 Finally, all conditions are satisfied by a total magnetic force 

 given by 



_ _B 1 a 3 ~d 1 a rfju—ri 

 1P ~ p -bp R " r~f P Wp'W-r7 2 '~~W~ 



+ sin^r(!L± 1 ^ + D^KKM^, . . (9a) 



where r is equal to or greater than r x , m = n + ^, and D„ is 

 given by (9). The expression for <y x p appropriate to a 

 diverging wave has been used. The series are convergent 

 at all points. 



If the oscillator is on the surface, so that r 1 = a, 



a — r/j, . oo / 2me imir T // \ rk \ hjr /j \d± n 



+ sin 2 6 % 



)-D n )r*& m (kr) d 



*>2n+l a»- 1 dF n 



1 n r' 1 dfi ' 



the summations together vanishing with k. But the second 

 is at all points equal to the first term of jp, and finally, as a 

 series appropriate to all external points, representing divergent 



