1050 
MR. P. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
Comparing this with the value of the potential at the surface of the ring, given 
above, we have equations to determine the constants Aj, An, &c. 
Tliese o'ive 
o 
Ai 
A 3 
A 3 
A 4 
A. 
I \ .'S ^ + T •:> lA + i) 4 
X + I 
cr — 
3 A + 5 
64 
cr 
3 (X + - 5 -) 
_ 1 J- " o-' — 
si- 16 "" 
5 (X + -j^) ^ 
64 ^ 
35 (X + ^ 
: - (T‘ 
1024 
12X + 19 
512 
a 
> 
( 8 ). 
Thus the potential is found at all internal points as far as terms in crh 
Writing L (log Bc/a) instead of X + 2, as far as terms of the second order 
V = 27ra^ 1 L + 4 (1 
EC 
^ 
'L - 1 E 
2 a 
If 
8fd 
cos X 
I 
+ O" 
_ - 1 
16 8 
Pd , 3 (L - Pd 
" m -f-cos 2x 
<5 4 
9 %--cos 2x 
+ 
(9). 
§ G. The value of V is a maximum, when 
and 
x=o, 
— 2ll + cr (L — 1) « — I 
Idl 
= 0 , 
that is, when R=cr.^(L — !)« + terms in a-\ 
This maximum value 
= 2™= |l + i - f (L - IF + j (r - If - .. 
= 277a' |L 4 - 44 -^(r — 1)^ "r - • - j' 
§ 7. The exhaustion of potential energy 
