248 Prof. J. J. Thomson on the 
When k=0, ths frequency equation is 
Ge al (14-2,/ 2) — mq?) — mq’) =4m’a"q"; 
the solution of which is 
ee dve? 
q=0, q= more tes +4w'=\/ —7g +o". 
When k=1, the frequency equation is 
wy 2 2 yy) 2 
(6/2 +2) os — my?) = (24/2 — 2g : 
the solution of this is 
a DY Dalene ve 
q ota / Wiel ra aes O + mie 


ga ota / W241 Oye, cial PR 1/241 
me Qf2+-1mbPe  2n/2+1 
When £=2, the frequency ee i3 
ye @ ang Nae =a Gail *) = 4Am?o? "GPa 
Regarding this as a quadratic in gq’, we see that the roots are 
positive, so that the values of g are real and the arrangement 
is stable. The roots of the ce are 
pian 3 / > 2 
eee 6 sy (4+ = ; +2@ 
2 1d— WEF « é .. 8(v 244) 6 (ae 
Ey meat t 2/Q mar 
Let us now consider the motion at right angles to the 
plane of the orbit. When 4=0, the frequency equation is 




ve ; 
ae nig —=0, 
or 2 vee 
= Vedas 
When £=1, the frequency equation is 
ve" 
BP 
or g=ro. 
= (8V 242) — mg? = (0, 
