237 
of Edinburgh, Session 1876-77. 
Brought forward, 373 
Deduct Deceased — Dr James Warburton Begbie ; David 
Bryce; G. Stirling Home Drummond; Lewis D. B. 
Gordon, C.E. ; Sir George Harvey ; Dr Laycock ; Thomas 
Login, C.E. ; Alexander Russel ; The Marquis of Tweed- 
dale, ......... 9 
Resigned — Hon. Charles Baillie (Lord Jerviswoode) . 1 
_ io 
Total number of Ordinary Fellows at November 1876, . 363 
Add Honorary and Non-Resident Fellows, . . 56 
Total Honorary and Ordinary Fellows at commencement 
of Session 1876-77, ....... 419 
Monday , ltith December 1876. 
Sir WILLIAM THOMSON, President, in the Chair. 
The following Communications were read : — 
1. On the Hoots of the Equation Y pcf>p = 0. By Gustav 
Plarr. Communicated by Professor Tait. 
2. Applications of the Theorem that Two Closed Plane Curves 
intersect an even number of times. By Prof. Tait. 
( A bstract . ) 
The theorem itself may be considered obvious, and is easily 
applied, as I showed at the late meeting of the British Association , 
to prove that in passing from any one double point of a plane closed 
curve continuously along the curve to the same point again, an even 
number of intersections must be passed through. Hence, if we sup- 
pose the curve to be constructed of cord or wire, and restrict the 
crossings to double points, we may arrange them throughout so that, 
in following the wire continuously, it goes alternately over and under 
each branch it meets. When this is done it is obviously as com- 
pletely knotted as its scheme (defined below) will admit of, and 
except in a special class of cases cannot have the number of crossings 
reduced by any possible deformation. The excepted class is that in 
