MR. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
The constants are to be chosen so that 
1053 
and 
V, - Vo = 0 1 
I 
dV. dVi , , „ „ I" 
rfit - rfR + "X = ° J 
at the surface of the ring. 
Thus 
1 + 
(;i + 1) + — 1) 
Ao = 1 -{- 
{)i + 1 ) A .2 = — {71 — 1 ) — {n + 1 ) B 3 J 
and 
f + Ai + Ag = Bg 
I (w + 2 ) + nAi + 0 ^ — 2 ) Ag = — (a — 2 ) Bg 
'"+^+A, + A, = ^+B,+ B, 
n -\- 1 
y" d“ 2) A {71 + 2) A^ + nAj. — — 
r • 
n + 
y<B, 
These equations give 
Ai = 
rt 
71-1' 
Ao = 
1 
11 1 
A5 — f + + Bg 
{71 + 2) Ag = — f {n — 2) — ?iBo — {n + 2) Bg 
B.,= 
H — 1 
11 
71 
2 (71 - 2 ) ■ 
A, = — 2. 
A. = 
2?!, + 3 
(11 + 1 ) {n + 2 ) ■ 
Thus we find that to the second power of cr, 
Bg = 
B.= 
B. = - 
71 + 1 ’ 
(2?^ - 3) 
{11 — 1 ) ( 7 i 
2 . 
11 
2 (n + 2) • 
- 2 ) 
Vi j'Kv> cos nx 
27r«/S„ \aj 11 
1 /R\« + i 
+ i 
+ i 
11 \aj 71 — 1 \ a 
2 (271 + 3) /E\« + 3 
1 /T>\«-1-1 1 
cos {n — 1) X + 
R\« + i 
11 (n + 1) \a 
cos {71 + i)x 
4 r /PA"+ 2 
/ IN/ \ I COS {)l + 2) X + ~ i ( “ ' 
ji (n + 1) (ih + 2) \aJ ' ' ^ 71 \«y 
. ct 
COS nx 
+ 
3 /PA"+ 3 
/PA“ 
PA" 
71 — 1 V 6f , 
_ O 
COS {n — 2) X 
• ( 11 ), 
