246 Prof. J. J. Thomson on the 
For the vibrations perpendicular to the plane of the orbit, 
we have for k=0, 
q= / ~ 
= peta 
mb? 
nd ve” e 
q=4/—,-7G= 
mb? 4ma 
Thus the six frequencies corresponding to the six degrees 
of freedom of the two corpuscles are 
fa, 4) 2 eae 0, 4/8 +8 
mb? mp ae a 
When the corpuscles are not rotating round the circle, 
jor k=, 


2 
two of these roots are zero, three equal to ae and the 
sixth equal to se Thus the effect of rotation on the 
triple frequency ,/ve2/mb* is to separate the roots, one re- 
‘mmaining unaltered, one increasing, and the other dimiuishing. 
Case of three corpuscles. 
Ue a 





=e “eye Uo 
ne = < M,=0, = we “ 
Be= 7p hae Une 
SSSUE T, =T,, U,.=—U,, L,=1,, N,=N,, 
M,=—M,, P.= P,. 
For the vibrations in-the plane of the orbit, when k=0, 
the frequency equation is 
2 
(/ 3 3 ae mg?) (— mg?) =4m’*w"q"; 
the solution of this is 
+4o%}'= i= 3ve? tor} 
na mb? 
g=0 and g= fae 
