bo 
Ot 
Oo 
Structure of the Atom. 
hae. ees ve? ve? 
or me 
D4 kao Bos ik 
ma? > 

This value of w? is greater than that required to make the 
equilibrium of the ring stable for displacements at right 
angles to its plane; if the central corpuscle, instead of being 
in the plane of the ring, was one side of the centre of the 
sphere of positive electrification while the ring was on the 
other side, the rotation required to make the equilibrium of 
the detached corpuscle stable would be less than when it was 
in the plane of the ring; for equilibrium the distance of the 
detached corpuscle from the centre of the sphere must be six 
times the distance of the plane of the ring from that point. 
Conditions for the stability of rings containing more than 
six corpuscles. 
I find that a single corpuscle in the centre is sufficient to 
make rings of 7 and 8 corpuscles stable ; in the latter case, 
however, one of the values of g? though positive is exceedingly 
small. When the number of corpuscles exceeds 8 the number 
of central corpuscles required to ensure stability increases 
very rapidly with the number of corpuscles in the ring. 
The frequency equation is 
eee, OP 
Ae @ 

(L)—L,) — mg? )( No—Na—mg?) = (M,—2mwg)’. 
Now N,— N; is always positive and M is small compared with 
L and N; hence this equation will have real roots if 
3 eS) . dpe? 
a ee 

WF (Ly a L,) 
is positive. The greatest value of Lo>—L, is got by putting 
k=n/2 whenn is even, and =(z—1)/2 when z is odd: hence 
the condition that the values of g should be real, 7. e. that the 
equilibrium of the ring should be stable, is 


dpe 3 eS, 
> >(L,—Ila) ——~—* when n is even 
Fi a ( 0 4 “ 4 Gi = | 
and 
3 pe? 38 
aE >> (Lage Ding, Wag when, © is, odd: 
a a ae 
From this equation we can calculate the least value of p 
which will make a ring of n corpuscles stable. The values of 
Phil. Mag. 8. 6. Vol. 7. No. 39. March 1904, sh 

