of Edinburgh, Session 1876-77. 
403 
7. Preliminary Note on a New Method of Investigating the 
Properties of Knots. By Professor Tait. 
As we cannot have knots in two dimensions, and as Prof. Klein 
has proved that they cannot exist in space of four dimensions, it 
would appear that the investigation of their properties belongs to 
that class of problems for which the methods of quaternions were 
specially devised. The equation 
p = «K s ) » 
where is a periodic function, of course represents any endless 
curve whatever. Now the only condition to which variations of 
this function (looked on as corresponding to deformations of the 
knot) is subject, is that no two values of p shall ever be equal even at 
a stage of the deformation. Subject to this proviso, <£ may suffer 
any changes whatever-— retaining of course its periodicity. Some 
of the simpler results of a study of this novel problem in the 
theory of equations were given, — among others the complete repre- 
sentation of any knot whatever by three closed plane curves, non- 
autotom ic and (if required) non-intersecting. 
The following Gentlemen were elected Ordinary Fellows 
of the Society : — 
XIobebt A. Macfie, Dreghorn, Colinton. 
William Stirling, Sc.D., M.D. 
Monday, 21 st May 1877. 
Professor KELLAND, Vice-President, in the Chair. 
The following Communications were read : — 
1. On the Cranial Osteology of Rhizodopsis, and on some 
points in the Structure of Ehizodus. By Dr E. H. Traquair. 
2. Notice of Eecent Earthquake Shocks in Argyleshire 
in 1877. By David Stevenson, Civil Engineer. 
Two earthquake shocks have lately occurred in Argyleshire of 
so decided a character that a description of their effects, as observed 
