68 
MR. F. W. DYSOI^ ON THE POTENTIAL OP AN ANCHOR RING. 
1 dY 
The density at any point is 
The charge 
r2n r27r ] 
= -) I, z; ;;r x)«# 
IQ JO 477 dn 
ac dY 
ac d.Y . . j 
- 2 ). &<’ - 
= 77 A 
This value is evidently correct, for the potential at a great distance is or 
Ai 
dcf) 
77 A;^ 
0 \/+ c® — 2cr sin 0 cos cj) 
Putting s = (T in the expression for V, we find 
A,= 
A 3 — 
, /X + I 12X2 4. 23X + 8 o 
-64- 
, /X 12X2 + 21X-1 
Ai --- O- 
Ai 
16 
A - f 
128 
A6 = 
5X - 6 
6144 
256 
Substituting these values we find that 
Ai fx , o 4X2 + 8X + 5 _.3 , 192X3 + 416X2+^48X + 171 ^ 
Vo = ^-^ X + 2 - 
16 
2048 
(T 
, kc. 
and 
477 dll 477 ffC 
, ,2X+1 24x2 + 7 „\/^2 
1—1 —-V.-o-' - + 0 - COS X 
/8X - 1 36X2 + X + 1 ■ 
V "I6 ~ 128 
64 
a ") cr" cos 2x — 
16X - 3 „ „ 11 (8X - 1) , 
-0-3 (jog 3^-fb 24 ~ 
64 
[The capacity (q) 
:= ttAJY 
TTCj\X+^ 
4X2 + 8X + 5 ^ 192X3 + 416X2 + 448X + 171 
— CT' + --rTTZ- CT' 
16 
2048 
