
—— - 
— 
, 
,, 
. . ; : 
this is equal to 40 A? sins} AOB™ 
TE 
__ LONDON, EDINBURGH, ann DUBLIN 
PHILOSOPHICAL MAGAZINE 
AND 
JOURNAL OF SCIENCE. 

_ [SIXTH SERIES.]/ “° 
t 
¥ 4 
\ 
A 5 \ 
\ 
MARCH 1904. ye ; 


Stability and Periods of Oscillation of a number of i 
arranged at equal intervals around the Cirewmferencé 
Circle ; with Application of the results to the Theory of Atomic 
Structure. By J.J.THomson, F.2.S., Cavendish Professor 
of Experimental Physics, Cambridge™*. 
HE view that the atoms of the elements consist of a 
number of negatively electrified corpuscles enclosed in 
a sphere of uniform positive electrification, suggests, among 
other interesting mathematical problems, tke one discussed in 
this paper, that of the motion of a ring of n negatively 
electrified particles placed inside a uniformly electrified 
sphere. Suppose when in equilibrium the n corpuscles are 
arranged at equal angular intervals round the circumference 
of a circle of radius a, each corpuscle carrying a charge e of 
negative electricity. Let the charge of positive electricity 
contained within the sphere be vg, then if 6 is the radius of 
this sphere, the radial attraction on a corpuscle due to the 
' positive electrification is equal to ve?a/b*; if the corpuscles are 
at rest this attraction must be balanced by the repulsion 
exerted by the other corpuscles. Now the repulsion along 
OA, O being the centre of the sphere, exerted on a corpuscle 
at A by one at B, is equal to we cos OAB, and, if OA=OB, 

9 
~ 
hence, if we have x cor- 
puseles arranged at equal angular intervals 27/n round the 
circumference of a circle, the radial repulsion on one corpuscle 
* Communicated by the Author. 
Phil. Mog. S. 6. Vol. 7. No. 39, Mareh 1904. Ss 

