562 Proceedings of the Poyal Society 
But, when the polygon is gauche, the second of the above con- 
ditions becomes 
and the solution is somewhat more difficult. Its interest consists in 
its leading to a new and curious question in quaternions. 
5. On Vortex Motion. By Professor Tait. 
{Ahstrcict.) 
This paper contained a discussion of the consequences of the 
assumption of continuity of motion throughout a perfect fluid ; one 
of the bases of von Helmholtz’s grand investigation, on which 
W. Thomson founded his theory of vortex-atoms. It is entirely on 
the assumed absence of finite slip that von Helmholtz deduces the 
action of a rotating element on any other element of the fluid, and 
that Thomson calculates the action of one vortex-atom or part of 
such an atom on another atom, or on the remainder of itself. The 
creation of a single vortex-atom, in the sense in which it is defined 
by Thomson, involves action applied simultaneously to all parts of 
the fluid mass, not to the rotating portion alone. 
Monday, Zrd March 1884. 
Sir william THOMSON, F.E.S., Vice-President, in 
the Chair. 
The Council having awarded the Keith Prize for the Biennial 
Period 1881-83 to Mr Thomas Muir, for his Researches into the 
Theory of Determinants and Continued Fractions, the most recent 
instalment of results obtained by him being in a Paper on “ Per- 
manent Symmetric Functions,” the Chairman presented the prize. 
Professor Chrystal, in explaining the grounds of the award, said 
— While it would be easy to give you an idea of the manner of 
man whom the Society has delighted to honour, I feel that the 
task imposed upon me by your Council of giving the members at 
large some idea of the actual work for which the Keith Prize has 
in this instance been awarded is a difficult one. 
Were the subject of my discourse a physicist, a geologist, or 
even a biologist, I might tell you of the mills that would be turned 
by means of his discoveries, of the kinds of coal or of diamond to 
