Conway — On the Motion of an Electrified Sphei-e. 

 If, for instance, ?t = 1, in (A), 



whilst (E) gives 



1 / 9 \"' 1 



p,„ = /;„(V)- =/;„(,,) (^-|^j -, 





Hence we see that if the centre of the sphere is at rest, the harmonicoid 

 solutions degenerate into the known solutions of harmonic or Ikssel- 

 harmonic type which are employed in fixed sphere problem. We shall 

 speak of a harmonicoid solution as a continuation of the corresponding 

 solution for the fixed sphere. 



IV.— Method of General Solution and Examples. 



The sphere being placed in any field of force, solve the problem as if the 

 centre of the sphere were at rest. We thus get an electric force oo and a 

 magnetic force c"°3o expressed as sums of functions of harmonic type. 

 Continue this function, and we get an electric force 



£ = On + c"'ai + Coo + c"'a3 + . . . 



and a magnetic force 



r, = c--j3„ + c-% + c-% + . . . 



The electromotive intensity 



Oo + C'n, + c"-(a2 + Fir/jj) . . . 



(where a is the velocity of a point on the boundary) is, however, not normal 

 to the sphere, with the exception of the first term «„. Suppose again that the 

 centre of the sphere is at rest, and find an electric force c"'yo, such that 



c''("> + 7a) 



is normal, and let c"'8o be the magnetic force. On forming the continuation 

 and adding, we have 



e' = Oo + C-' (ai + 7„) + C-' (a, + yO + . . . 



„'= c-'|3o + c-^/S, + 8„) + . . . 



The electromotive intensity is now normal for the first two terms, but the 

 third term c"^ [m + 71 + Va^^) is not normal ; we can, however, determine 



