MR. F. W. DYSON ON THE POTENTIAL OF AN ANCHOR RING. 
1105 
n. 
9- 
^\! 
k^Ik. 
8 
18= 
■437 
1'345 
11 
19° 
•460 
1-337 
20 
20° 
•484 
1-329 
100 
22° 20' 
•537 
1-308 
.3300 
26" 
•620 
1-271 
Roughly speaking, when n is between 8 and 100, the ratio of for this limiting 
case is between ^ and f. 
The following diagram calculated from the equations (12 l)and (122) gives, forn= 100, 
simultaneous values of the radii of the rings and their distance apart in the limiting 
case in which the inner ring just goes to an infinite distance in front of the outer one. 
The radius of the front ring is given by an abscissa of the circle in the diagram, the 
radius of the back ring by the corresponding ordinate, and the distance apart by the 
abscissa of the curve. Thus NQ is the distance apart when the ratio of the radii is 
tan 30°, or when the rings have the radii OM and MP. 
§ 47. When 9q is greater than the limiting value the greatest distance apart to 
which the vortices can go is given by the equation (124). When Oq is less than the 
MDCCCXCIII.—A. 7 B 
