1102 
MR. R. W. DYSON ON THE POTENTIAL OP AN ANCHOR RING. 
777 
log 8 « - J + i log =} - 2 F [' = c„ (log 8 » - f). 
Therefore 
7 {logSn - I + Ilog^l - 2^ ^ (F - E) - (log 8 ^ - I) = 0, 
c 0 L ^0 J ^0 
where the modulus of the elliptic function is 
Therefore 
P-E 
\/ sin 
; = i (log 8 n - I + I log^ - i (log 8/1 - |) 
• ( 119 ). 
where sin a = I? jzsr. 
Let Co/^o or n = 100. 
Then 
F-E 
\/ sin « 
2*467 
+ |logio^ 
‘'0 
It is easy to construct the following table :• — 
a. 
Cq. 
h. 
o 
20 
1 
•98 
•58 
30 
1 
•90 
•71 
4.5 
1 
•82 
•84 
60 
1 
•70 
•93 
From which, taking Cq the value of the radius at infinity as the unit, we see that 
when h (radius of sphere) = * 6 , * 8 , 1, 1*3; zs, the radius of the ring when passing the 
middle of the sphere, = 1*02, 1*1, 1*3, 1*4. 
§ 46. I'wo coaxal rings of equal strength and volume moving in the same direction. 
Let the radii of the rings be Cj and Cg, and the radii of their cross-sections aj and rtg. 
Then 
= ahc .2 = constant.( 120 ). 
The equation of momentum is 
-\-cf = 2K~ .( 121 ), 
and the equation of energy is 
* This and the next paragraph ha^e been altered since the pa23er was read, in consequence of a very 
valuable suggestion of one of the Referees.—Jirly, 1893. 
