﻿474 Prof. D. N. Mallik on the 



electrons defined by <— -f ^— + ^— = — p may be replaced 



by a surface distribution I cos 0, per unit area of spherical 

 surface. And thus, as in the corresponding magnetic theory, 



4 A 



this part of the force in the direction of x will be kttj- per 



unit charge [Maxwell, vol. ii. art. 399]. For the second 

 force we. may, obviously, assume an elastic force in the 

 direction of a, due to displacement of electron, and this 

 will be 



-^(.I'-.i-o) (say) = -A~' .... (27) 

 P 



while the frictional force will be of the form \A'. Hence, 

 for equilibrium 



M 



. \ Adr 477- C / A\ C 



(28) 



Putting 



/*= j^r^o, \Adt = A, yfdr — ef\ &c, 



we have 



l^=^(JH^) + ^\fT-ifi), ■ ■ (29) 

 or for simplicity 



^ A=, 2 (/4-iA)+^ r ^(2/7-i^), • • (30) 



all the quantities having their mean values taken over a 

 small sphere, enclosing a charge. 

 For motion, we have p'x = A, 



or S*pdT=A, (31) 



where for A we take its mean value, as before. 



Accordingly, since for a single electron of mass m, self- 

 inductance L, and charge e, 



T = J(^ + L^ 2 )(i 2 + 2/ 2 + i 2 ), . . . (32) 

 we have 



^ fl0 A + (Le'--tm)l='^e"-(/-+ £)+e*(jy-i/3) 



4*7T / A\ 



= / -« 2 (/+ 5 -) + <' 2 (7B-^C).(33) 



