1098 MH. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
Then 
c (^log ^ — ■j'j — 2c cosec ^ (F — E) + c sin ^ . F Cq (log ^ ~ • (112). 
In addition to this a^c = Cfo^- 
When the ring is so near the plane that 2 is much smaller than Cj though greater 
than a, 
F = log ^ -- log ~ . approximately. 
E = 1. 
Therefore, 
o(log| + i) = o„(log|”-i) .(113). 
When the ring is near the plane, the equations of motion are 
(114), 
m 
cz= - - i log 
a 
+ i 
(115). 
From these, or more simply from the equation of energy 
Therefore 
Let 
and 
Then 
on i ^ / G 
= — e" V - 
TTftn ^ Cn 
Co/c [log (Sc'oA'o) - i] 
IIIG\ 
(^3 — ^l) = [ \/- • ''^dc. 
J Cj V Cq 
c/Cq — X", 
h = log —“ 
CL, 
7 
!• 
•me* 
'O^'O 
(h 
(116). 
