1903.] Electric Waves round a Conducting Obstacle. 



253 



Now 



8 n ixL 8 8 1 



(2» + l)P M = %±i-^-\ 



(2b + 1), 1 _ = „-^_ + („ + 1) 1 - ; 

 making these substitutions and rearranging the series, it becomes 



00 ^ 



^ = ?- 1 -^42^-i)?K H _i(6Kr 1 ) jr^r-*J n _i(Kf) 



+ ( ft + 2)r-^ +| (Kr)}](l-/^)^ 



that is 



where 



8P, 



h = f*S^(n)Jw+i(Kr)(l -/-) V , ? '<?i (2), 



i d/x 



If, then, a solution ^ of equation (1) can be found, which is such 



that \p becomes infinite as at the point (r v 0) and ^ vanishes when 



Or 



r = ft, the real part of Cxf^e LKYt will be y, the required magnetic force, 



for then — (yp) will vanish when r = a, that is, the electric force 

 dr 



tangential to the sphere vanishes. The solution required will be of 

 the form 



f = r^^(n)[J w+ x(Kr) + A w K w+ ,( fc Kr)](l-/,2)^, 



where i\ > r > ft, and the constants A n are determined by the con- 

 dition that ^ = 0, when r = ft ; hence 



where ?i>r>«. 



^{ft l! J Ji+ ^M} 



Kn' +i (tier) 



(l-/-)-^> 



