9 
General Meeting, October 18th, 1881. 
E. W. Binney, F.R.S., F.G.S., President, in the Chair. 
Mr. Thomas Gair Ashton, B.A., of Manchester, and Mr. 
Ludwig Mond, of Winnington Hall, Northwich, were elected 
Ordinary Members of the Society. 
Ordinary Meeting, October 18th, 1881. 
E. W. Binney, F.R.S., F.G.S., President, in the Chair. 
“On the Failure of certain Mathematical Solutions of the 
Problem of the Motion of a Solid through a Perfect Fluid,” 
by R F. Gwytheb, M.A. 
Of the solutions with which I intend to deal, we may 
take that by Stokes for the motion of a sphere as the type. 
In his paper (Camb. Trans., vol. viii. and Reprint) Stokes 
considers to what degree his solution differs from the re- 
sults of experience, and discusses the origin of this diver- 
gence. I propose to show that the origin is possibly of a 
different nature to any there discussed. Stokes’ solution 
may be stated thus : If A be the centre of the sphere, of 
radius a, AX its direction of motion at time t, (r,0) the 
zonal coordinates of any point in the fluid referred to AX 
as axis, and if 0 be the velocity potential of the motion, 
Va 3 
( p = const - J-^-cos0 
and 
~ = i ~2 C ^osd + ~ |(3oos 2 0 - 1) - £; 3 (3 cos 2 0 + l)j (1) 
giving the fluid pressure. 
Proceedings— -Lit. & Phil, Soc,— Vol. XXI. — No. 2.— Session 1881-2* 
