MOTION OF ELECTRIFIED SYSTEMS OF FINITE EXTENT, ETC. 167 



These forms give at r = 



' Y' 7>\ S" , .- - , 



: (a 2 -/tV) ' C 3 a (a 2 -A 3 x 2 ) 2 * C 2 (1 -A- 2 ) (a'-J l ' y ' 



thus securing the condition that (X', Y', Z') should be radial at the surface. 

 Further, at r = a we have 



e (1-P) .r 2fcWt J(l -A: 2 ) ^y _ , y 

 a (a 2 -kV) C 2 1 (a 2 -* 2 * 2 ) 2 2 (a J -k 



V . ,. 



~ a - 2 



C 2 a 



.- 



a 2 - - a2 - 2 2 



- /- a ,r 2 ) ( 1 - F) 2 C 2 a 2Jt (1 - A' 



(] . 

 2 a -- 22 2 2 



a a- 

 Hence the surface density of electricity is given }>y 



- e 



wr 2^(i) 



Thus a redistribution of the charge takes place while the total charge is unaltered. 

 The mechanical reaction in the direction of y is ^-JcrY'f?S since there is no surface 



current. Neglecting squares of/^,, we obtain on reduction the value 



As in former cases, a uniformly accelerated motion is found to be possible, and the 

 initial electric inertia for a transverse acceleration is 



This result differs from ABRAHAM'S formula in so far as it contains the product term. 



The limiting value of the expression for k = is f e 2 /C 2 . 



7. Comparison ivith Experiment. In the preceding sections we have considered 

 the acceleration to be produced by a purely mechanical force. It is perhaps almost 

 directly obvious that if the force is due to a uniform electric field F, no change of 

 electric inertia is produced when F 3 and higher terms are neglected, as we have 

 merely to superpose on the former solutions a uniform field with the appropriate 

 induced electrification on a body moving uniformly. Initially, of course, this 

 state is produced by the aid of a rapidly damped harmonic train. As a matter of 

 fact the problems already solved were first worked out for an electric field which was 

 afterwards annulled with a view to making clear how much of the induced electrifi- 

 cation was due to the accelerated motion itself. 



