1064 
MR. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
^3 = 1 -h 
a 
3 a® 
= S (‘°g ? - i) - 8o= ! - a), by (26), 
= 1-j6°gr-R 
agreeing with the result given supra, p. 94.—July 22, 1893.]* 
An interesting oscillation of the ring is that in which the mean radius increases 
and diminishes, necessitating a decrease and increase of the cross-section. 
We have 
= const. 
8c 
Me — Mc(^^ — y : 
i«g- 
277 dc 
0 
J 
Eemembering that aA is constant, 
Therefore, 
cl_ 
dc 
, 8c 
log — -t- I 
° a ' 
1 A 8c , , 1 /I , 1 a\ 
+ -c{c+a2c) 
Mc-Mo,^= + :^(loKf-f) = 0. 
Thus the angular velocity in the position of relative equilibrium is given by 
7]\H a 8 c - 
= log 
8c, 
a 
■ ( 26 ), 
agreeing with the results found, a7ite, p. 94, 
For the small oscillation, write c = Cq x, a = (Iq + y, in the above equation. 
Then, 
apx -j- 2 ap^y — 0, oi' y — 
_ i A 
* See note, p, 1060. 
