Motion of an Electrified Sphere. (U3 



along the axis of z, so that if m be the Newtonian mass, 



mi+l~x'(ct-a)=eF, (5) 



with initial conditions 



£=£=0 aU=0 (6) 



the sphere being initially at rest with f vanishing. 



Oilier conditions may be deduced from the consideration 

 that the undisturbed portion of the external medium com- 

 mences where r = ct + a, so that %(ct — r) == x(d - r) = 

 when r=zct+a, or 



X(~«)=%'(-«)-0 (7) 



The solution of these equations and conditions is, so far as 

 f is concerned, 



„ 2 eA .,, . f / , 4m V ri ") 



S=- a — e- c ^ a sin 4(3 + — hr- + 6 r 



3 mac L \ m /2a J 



1 *F 



2 ?n + m 

 where 



, 2 e 

 m = 



, e¥m' at 1 (2m > + W-w /i ) a^ 



' (m + m') 2 <3 3 * * (m + m') 2 ' c 2 ' 



2 / 4w?V 



- 2 , Asine=-D', (3+^~j Acos6=-(D' + 2aB') 



3 ' ac 



n> _ m (2m 2 + 4mm'-m /2 ) a 3 F R ,_ 3 am' a 2 F 



2(m + ra') 3 ~ c' 2 ' (m + m 7 ) 2 c * ' (8) 



An error of sign has crept into one of the terms as given 

 by Walker, and continues in some of the later analysis, 

 though not interfering with the general conclusions. The 

 value given above has been corrected in this respect. 



The corresponding value of ■% becomes 



/ n 4 i^ , wo • f/o ±.m f \ht — r-\-a 1 



+ A / (c'*-r + a) 2 + B'(d-r + a) + D / 

 where 



A , = 3 ^__ aj 



4 m+m c v 



In Walker's formula (17), p. 264, fcr the value of % after 

 the vibrations have subsided, there is an incorrect sign in the 

 second term. 



We proceed to an examination of the case in which m is 



