29 
Ordinary Meeting, November 2nd, 1880. 
Edward Schunck, Ph.D., F.R.S., V.P., in the Chair. 
“On the Conditions of the Motion of a portion of Fluid 
in the manner of a Rigid Body,” by R. F. Gwyther, M.A. 
The condition that a portion of fluid may comport itself 
as a rigid body, or that fluid may remain in a state of rela- 
tive rest upon or within a moving solid, has not, as far as I 
am aware, been mathematically investigated. We know, 
however, that in certain cases, as on the surface of the earth, 
the condition can be realised, or that any deviation has not 
been discovered by undirected investigation. 
In the case considered, the velocity at points in the fluid 
must consist of a common linear velocity, and a common 
angular velocity about some axis, moving or fixed. There- 
fore, using the quaternion notation, the velocity must be of 
the form 
a = 2 + Yer, 
where S is the common linear velocity, e the vector axis 
of instantaneous rotation, and r the vector of any point in 
the fluid. 
The equation of motion is 
Bto- + i vp = a (1) 
P 
a denoting the force acting on the element of the fluid, p 
and p having the usual meanings. Under the condition 
stipulated no viscosity is called into action. 
If p be a function of p only, we may write 
— vp = v P. 
p 
Substituting the required form of <r we get 
S + Ver + 2Ve(2 + Ver) = a — VP (2) 
Proceedings — Lit. & Phil. Soc. — Vol. XX. — No. 3 . — Session 1880-1. 
