492 
Proceedings of the Royal Irish Academy. 
E the coefficient of elasticity. 
/ the moment of inertia. 
I) the deflection of the centre. 
After the publication of Q. 3809, the Rev. K. Townsend, F.T.C.D., 
called my attention to the fact, that there was a discrepancy between 
my result and a similar formula arrived at by Poisson, Mecanique, 
2nd Edition, vol. ii., p. 612. Poisson's formula, translated into the 
present notation, gives 
W 
1 + 
7)^ 
The discrepancy has arisen from the circumstance that Poisson has 
considered as negligible in deducing the differential equation of the 
curve, while in finding the length of the curve, he retains a term of 
the same order. If terms of the magnitude ^ be retained throughout 
the investigation, as manifestly is necessary for a legitimate approxi- 
mation, then the 4 in the denominator of the second term in Poisson's 
result should be replaced by an 8. 
The peculiarity of this expression has been already adverted to, 
namely, that it does not vanish when I) vanishes. 
lY. — Note oisr a Hydeodtnamical Theorem due to Professor Stozes. 
A circular cylinder moves through an indefinitely extended in- 
compressible liquid : determine the movements of the particles of the 
liquid. 
The present note is merely 
to present in a geometrical form 
the solution of this problem given 
by Professor Stokes. 
Let the shaded portion of 
the figure represent the cylinder 
of which 0 is the centre. 
Let A OB be the direction 
in which the cylinder is moving. 
To find the direction in 
which a particle of the liquid P 
is moving, describe a circle POR 
touching AB at 0, then P is 
moving in the direction of the 
tangent to the circle, and all 
points on the circle are moving 
in the directions of the arrows. 
Further, the velocity of P varies 
inversely as the square of the distance OP, so that the circle APC is 
the locus of points moving with the same velocity : the velocity of 
