U06 
MR. F. W. DYSOJT OX THE POTENTIAL OP AN ANCHOR RING. 
limiting value /3, the inner ring goes to an infinite distance from the outer one, 
increasing in radius towards the limiting value K:v/2sind^, the radius of the outer 
ring diminishing towards the limiting value k\/2 sin 6^. 
The equation determining is 
sin 0Q [log 8n —1 + f log (\/2 sin 6q)] + cos Oq [log Sn — | + f log (\/ 2 cos ^q)} 
r sill 2^0 cos (f) dcf) 
-h \/ (1 — shi 2^0 cos (/)) 
= sin 6^ [log 8« —l-f f log(v/2 sin 6^)] + cos 6^ [log 8n — |log(^2 cos 6^)} (12G). 
The table in § 46 gives 22^ 20' as the value for ^ for rings in which n = 100. 
The tables below give the greatest distance the rings will separate for values of 
0Q > 22° 20'; and the radii at infinity of the rings for values of Oq < 22° 20'. and 
Ko are the radii of the rings when they are in the same plane ; are their radii 
when at an infinite distance apart, if they separate; and 2 : is their greatest distance 
apart if they remain together. 
^0* 
t 
A'l . 
/ 
0 
0 1 
5 • 
•123 
1-408 
5-50 
•144 
1-407 
10 
•246 
1-392 
12-49 
•309 
1-379 
15 
•366 
1-366 
22-20 
•537 
1-308 
20 
•484 
1-329 
38-30 
•880 
1-056 
(\, 
^2 
0 
25 
•598 
1-282 
1-044 
30 
•707 
1-225 
•500 
35 
•811 
1-159 
•245 
40 
•909 
1-083 
•084 
