MU. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
1095 
= 277 X m 
,«i9 
J I 
{(^ - 
sec- 6 (10 
sec'^ 9 
3 a ’ 
where tan 9 = 
T!5 
= 277 S m^Ci 
( 101 ). 
§ 42. The kinetic energy is given by 
T = 
JJ 
77 1 1- 
C7 
rfcT ) i ^ 
c/ct dz 
, id~'¥ . (d'^ 1 , , 
dm 
( 102 ). 
Now, outside the ring 
and inside the ring 
At the surface of the ring 
(1^ cl^ i _ 
dz^ dm^ m dm ’ 
nuc 
1^1 
TTiTf, 
4^ = 
TT 
iog^-2) + 2’yr, 
77 
(103). 
Therefore, inside the ring 
'F = 
7/il6-i 
77 
i>'g!'-h + s?o+“9(i-S)- 
(104). 
Integrating throughout this ring, the part of the kinetic energy arising from 
this is 
S (log + Wi + aiglia + •■•)} • • ■ (105). 
Adding the integiuls arising from the other rings, the kinetic energy 
= i7r\X (log ^‘1 - i) + 2 2 7«,m,Ji3 
(106). 
The equations of motion may be written in the interesting forms, 
1 0T1 
- 8'^ 0,^ I 
1 0T I 
. (107). 
