MR. F. W. DrSOX OX THE POTENTIAL OF AN ANCHOR RING. 
1051 
1 111Y dm 
— \. 277 V (c — K COS x) R c/x 
• 0- u 
2.5(7“ R6 
. " 0 rn . R^ , , /(7 , 9(7'^ R“\ , , /‘So-^ R“ , 
477^6-0 jo j 1 2«3 + ^3 (4 ^^3 + 128 ay + ^3 32 ^4 + 512 af ^} 
= 2n'^ay 
— 277Y<.®| |Aj 
{-i + A,- 
R 3^ R3 
Cl 16 
R3 
E* 
R=cffi 
^4 8- +4 
Ft , , L-l , 3(L-if) 
L + T - — o-- 
(T 
m- 
If we may judge from these few terms this series is very convergent. When 
(T = 1, i.e., in the case of a ring so thick that it touches itself cit the origin, we have 
L = logv8 = 2-080. 
The exhaustion of energy 
1\P 
, . [2-330 
'Ittc 
-177 - -003] 
^ M2 
= 2-150 . — . 
'Ittc 
The first three figures would seem to be correct. 
[Let the same mass be collected into rings of different mean radii, and consequently 
different thicknesses ; let the final mean radius of the ring, that is, the mean radius 
when the ring is so thick that it touches itself at its centre, he taken as unity ; let 
the exhaustion of energy in this position be also taken as unity. Then the exhaustion 
of energy for different mean radii of the ring is given by the following Table ;— 
Mean radius. 
1--25 
1-5 
1-75 
2 
3 j 4 
5 
Exhaustion of potential energy 
•9488 
•8874 
•8284 
•7749 
•C144 i •5162 
■3506 
July 22, 1892.]* 
* This Table was given at the suggestion of one of the Referees, replacing a Table given in the paper 
as read. 
6 .S 2 
