74 
MR. P. W, DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
Therefore, the equations giving A^, Ag, &c., are 
A. (- 1 + A,cr=(- i + 
(\-2 . 99\-.30 
V 2 
K i I ~ ^ \ \ s 1 1 4X, + 17 0, , 54X, — 15 4 
( A ’ +- ^ — O' ) + ^2 ( - ^-55— 0 -- H-— cr^ 
32 
+ Agcr^ -I- 
25G 
20X + 107 
, /6X - 11 , 240X - 83 „ , , , 
A1 ( + -755-o-' ) + A^cr- 
192 
3- \ 4 64 
12X + 13\ 
o-M-^A,cr^ = 
— c^w. 
-- J _ 2 A 3 - lOor^A, = 0. 
. loX — 28 A / t + 61 0 1 . , 1 1 21 
A,--+ A2(+3%-— <T-)+ A 3 (-i +AVo--) 
A, 
64 
420\ - 809 
3072 
+ A,(-6-fic.‘2)-if^cx^A3 
+ A3 — A4, ~ 24 Ag = 0, 
2¥4^8 A3 + tIs A3 - A, - I Ag - 120 Ag = 0 . 
= 0 . 
These equations give 
A,= -|(l- 
r 2 \ 
. I , 12X + 1 „ , 48X2 + 344X + 159 , > , 
-+ -1024- 
. 18X + 7 o 
As =-o-- c-u. 
A,= 
64 
24X + 25 
384 
cr" ) cht. 
384 
0 
C-'U. 
. 0 .. 
= Tii 
The kinetic energy is given by the equation 
>T= - Ik'^r/S 
an 
n 2rT 
(A^Ji + AsOA'J 4 -.. ,} cos (f) u cos y cos (f> {c — a cos y) a 7y d(() 
n 
'0 •'0 
TTCICU 
{AiJi + . . .}|cosy - f - 2 cos 2yj% 
