1092 
MR. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING, 
Due to this ring alone 
Ttt J 
— ^ I 
J I 
Clfdh 
cos d(j) 
rn 
Jo \/ {{d — — 20^7^' cos (f) + Cf} 
cd cos (j) dcf) 
,^y {{z' — %)“ + w'~ — 2CjnT' cos (f) + Cj~} 
(87) 
Take a point on the surface of the first ring. Let its coordinates be 
~ '"h * 20 S X, sin x- 
The part of T due to the ring itself is 
f _ 2 + '”8 8^1/"I - I !!i cos ^ ^ 
( 88 ). 
The part due to the ring is 
^ 77 (Ci-niCOSx) 
]MoC.d 
cos (j) d(j) 
' \/{(h + shi X — + (h — '"9 cos xY — Sc, (c^ 
' 0 
COS COS (f> + c^~] 
Let tlie integral 
p C;^C 2 cos (f) d(f) 
•hv/Kn -- hY + - 2ciCo cos <f) + 
be called Ijg. 
Then the part of due to the ring is 
It I • dI|o 
“ Ij 3 +OiSinx^^-^-%cosx-^“ 
. (89). 
a”ci is constant: write 
TT 
Then at a point Cj — cosx, sin x, on the surface of the ring C^, we find 
??z, r 1 8o _ log 8c-, la^ — t 
'5'= 27 I G°g „ - 2 - -^7<=°SX+--- 
TT 
I ^^*'2 Jt I ■ ^^fl2 dijo I 
+ - I Ii3 + «i Sin X - «i cos X + . . . 
Ill-i 1 T I • dl ];5 dlj 3 
Ii 3 + 0 , sin X-J^- «1 cosx hT + • ■ • 
+ 
+ 
dc, 
(90). 
J 
