948 Problem* connected with the Motion of Charged Spheres, 

 which satisfy all the conditions if \c=\'e' and also 



A(\ + l) =B[(V4.1')«" A ' + (V-1)/'], 



A\ 2 = BV 2 [e~ K '-e k 'l 

 which leads to a period equation for X of the form 



tanh K a A, = 



KXfK-1 



This equation has only one real root, a negative one whose 

 numerical value is less than K~* and which therefore becomes 

 very small if K is large. All the other roots are complex; 

 and represent oscillations in the Held. 



The problem has therefore been completely determined as 

 far as we are able to go. If: we assume that the damped 

 oscillations represented by the complementary integral of the 

 conditions become evanescent before the solution here given 

 ceases to hold, we can go one step farther. 



Neglecting these oscillations, the couple necessary to keep 

 the sphere going is 



2 ec 1 ca-M 



O 2 * ■ 



~ " 9 ~T" 



and this determines the effective inertia to the motion which 

 arises from the electric charge. 



This paper concludes my immediate object of interpreting 

 the principal results of Walker's paper without any of the 

 complications caused by introducing the material mass of 

 the sphere. The results are all capable of a reasonable 

 interpretation without this complication and they then lend 

 their support to the idea of a purely electromagnetic 

 constitution of the electron. 



Sheffield, May 1911. 



