ELECTRIC WAVES ROUND A PERFECTLY REFLECTING OBSTACLE. 115 



Similarly, when /> i\, 



-^)= . . (3). 



The solution of equation (l) that is required is that solution i// which becomes 

 infinite in the same way as ^ at the point (r lt 0) and for which ty/dr vanishes when 

 r = a ; the real part of Ctye'" will be the required magnetic force at any point, for 

 9 (yp)/9r will vanish when r = a, that is, the electric force tangential to the sphere 

 will vanish. From the expression (2) for i//] it follows that the required solution is of 

 the form 



where ri>r>or, and the constants are determined so that t)i///3r = when r a, hence 

 $ = -rr'V/' I *+'.. (2n+ 1) K n+ , 2 (t/cr,) 



when 



',>?> a 



and 



when 



r>* (5). 



Writing 



KT = Z, Kl\ Zi, Ktt = Z , Z-J^u^z) = 2 1; --7T~' J , 



u = R' /J sin <f>, v = R 1 ' 8 cos <f>, HI = RI'" sin t^, rj = Rj 1 '- cos (f> 1 , 



MO = RO' /J sin <f> , v = R ' ; - cos (^) , 

 it follows that 



that is 

 Again 



Q 2 



