-260 Mr L. C. Jackson on a Mathematical Investigate 

 Attraction due to positive corpuscles : 



attraction of positive corpuscle E on electron ( 1 



EC 2 * 



radial component : 



a 2 + v 2 — 2a r cos ( ~ -f 6 J 



a — r cos I ^ - + J 



a 2 + 7 i2 — 2ar cos 



2tt 



s a t /" — -av cus I -^- + 6 I r* 



total attraction due to positive corpuscles 



( a - rGos xw+ d )) 



= + 



-I a 2 + r 2 -2ar cos (^ + d) j* 1 



e 2 / a — r cos ( -^ 4- 6 ) J 

 |a 2 + r 2 -2a^cos^ + ^VV 



, 2 (a-rcos(27r4-^)) m 



r {«* + ,.*_ 2^cos(2tt + 0)}*' " " W 



where 6 is written for 6 Q -\-{(o l — (o)t. 

 Hence 



< '(a-,-co g ( J g r +g)) 



-waro 2 = (5) 



This determines a state of possible equilibrium for the 

 inner ring. It is now necessary to find whether the equi- 

 librium is stable or not. To do this, it is necessarv to find 



