126 Mr A. B. Basset, On the Motion of Solids.  [Oct. 31, 
Here L’ =} (Pw + Ru* + AG’) + Cw — 4K, 
u=a#cos 0 — z sin 0, 
w=a#sin 6 + 2 cos 6. 
Since LZ’ does not contain 2 or z, we have 
rae const. ; = const. ; 
whence Pucos 6+ Rwsin 0+ € sin = E 
— Pusin 6 + Rw cos 0+ €, cos = F. 
Since u=0, w=0 when 0=0; we obtain H=0, F=6,, 
therefore Pu =—€,sin 0 
Rina teats A Ceaades See (22) 
aL’ 
Also ~=(R —P) ww + fu, 
dé 
-- 2 
whence Aé+&? (> — a) sin 6 cos 8 + a sin 6 =0. 
This is the equation which is obtained by eliminating wu and w 
from the equation of energy by means of (22), and differentiating 
the result with respect to the time. 
[7. The expression for Z' in the form obtained in § 3. (18) 
cannot always be employed to determine the two dimensional 
motion of a number of cylinders round which there is circulation, 
owing to the fact that it sometimes happens that in this case some 
of the terms are infinite. The adaptation of the formula to this 
problem, and its application to determine the motion of a cylinder 
moving in a liquid bounded by a fixed plane, will be dealt with in 
a paper shortly to be communicated to the Society. Nov. 18th.] 
Dec. 11th. I take the opportunity of correcting two errors in 
my former paper “On the Motion of a Ring.” 
On p. 55 it is stated that the two values of p” are negative. 
This is necessarily the case if Zy is positive; but it is possible for 
Zy to be negative, either by reason of the ring being prolate, or by 
reason of its velocity being in the opposite direction to that of the 
cyclic motion through its aperture. In either of these cases the 
coefficient of p* will be negative, and the motion will be unstable 
unless © be sufficiently great. 
On p. 60. The statement that both positions of steady motion 
are stable, is incorrect. 
The condition of stability is, that the right-hand side of the 
last equation should be positive. This requires that 
2 ida ipal 2 nD 
e- ¢; 5) +3 cosa) Tie + 2 (a -5) (1 — 3 cos a)}>0, 
If there is no circulation €, = 0, and the condition is that cosa 
should be greater than + or less than —4. 
