160 MR. GEORGE W. WALKER ON THE INITIAL ACCELERATED 



Hence the total components of electric force at r = a are 



e 



(X + X, Y + Y, 



= jjifa y, z), 



The surface density of electricity is given by a- where 



ea ka \ , 3x 2 1 , /nA , ax \ 3a? } , n ., 



= (T^r^v^^ 



It may be verified that the terms in x'(Ci) and x"(0) contribute zero to the total 

 electric charge as is required. 



Since there is a surface current in addition to the, convection current due to 

 transference of the sphere, the mechanical reaction on the sphere is 



= f { a- ( X + X) - w (fl, + ft) + r (y,, + y) } c7S, 



where 11, v, iv are the components of current determined by the surface discontinuity 

 of magnetic force and the integration is taken over the sphere. 

 Neglecting squares of small quantities the value is 



J? 2 T 2 \ S 



K,x \ 



I L I - .-. I 



1 



T=f \ <-*>(i+r3 



+ ^ 



1 + 



1-P 



dx. 



The evaluation of the integral, which is somewhat tedious, gives for the reaction 

 the value 





_ 

 6 C 2 F(l-F) k* (l-F) 3 / 2 



The equation of motion of the sphere under a force F is thus 



We thus prove that, to the given order of approximation, a uniformly accelerated 

 motion is possible as soon as the vibrations subside, and conclude that the initial 

 electric inertia for longitudinal acceleration is 





