86 
where 
MR. F. W. DYSON ON THE POTENTIAL OP AN ANCHOR RING. 
P 
K 
A 
M 12A + 1 p , 144\2 + 24A + 57 
2 -612- ‘^6 + M. 
T\T /t , 4A + 1 0 , 16a® + 8a — 23 
M(1 + -^o- + 
»"-/ 12X+7 
P-liT + 
512 
ISA® - 3A + 5 
64 
+ M', 
cr^) + M'^(i+|cr^), 
C = M'c2(l + fo-2), 
„ / 4A® + 8A +1 0 
= - 16 - 
2a3 + 9a® + 6A - 
64 
cr^ I ; 
Also the linear momentum of the cyclic motion is given by 
r? 0 [-1 /\ii\o 4A® + 5A 2 
Z = TTC-^Kp^l — (X+ l)o-"- ^ -O-^j- 
§ 1 9. The motion of a ring in an infinite fluid is discussed in Basset’s ‘ Hydro¬ 
dynamics,’ vol. 1, pp. 196-208. 
It is there shown that if a ring be set rotating with angular velocity co about a 
diameter of its circular axis, it will make complete revolutions if 
but will oscillate if 
OJ 
>Za/ 
AP (E - P) 
(O 
-S- 
V AP (R - P) 
Putting in the values of the constants, a very fine ring will make complete 
revolutions if 
" > “o a/- 
Tra" V I 
and will oscillate if 
av: 
P T y 
CO < 
P + 
A possible steady motion of the ring occurs when it moves with velocity w parallel 
to the axis, and has also an angular velocity 12 round its axis. It is shown that this 
motion will be staide if 
(Rjo + Z) [(R _ P) + Z] + ^ P 
is positive. 
