386 
Proceedings of the Royal Society 
necessarily “helicoidal asymmetry,” a ring of this kind is neces- 
sarily enantiomorph to its mirror-image. 
In the plate the lines AB, CD represent a locked cylinder ; AB, 
EF a knotted cylinder ; AQ, Pit the smallest locked cylinder ; CD, 
EF the smallest knotted cylinder ; the parallelogram ABCD an 
anchor-ring of the first kind] AGCH one of the second kind, if 
AC and GH represent the seam about the axis ; one of the third kind 
if these lines represent the seam about the core; AG El one of the 
fourth kind ; AKLC the smallest ring of the first kind, with one 
hole in each sheet ; AOLJ the smallest ring of the second (or of 
the third) kind, with two holes altogether ; MALK the smallest 
ring of the fourth kind, the smallest ring indeed of any, having 
only one hole altogether. 
We have hitherto considered the complex as composed of 'per- 
forated sheets locked together, or of a perforated sheet knotted, but 
there is another way in which it may be imagined. 
We saw that the smallest circular hole had a radius of one-third 
of the distance between the centres of two neighbouring holes in 
the same sheet; but we can make the hole smaller if, instead of 
making it circular, we make it hexagonal. There is then no waste 
space; every part of the complex is composed of two layers, one 
over the other. Flow we may suppose this hexagonal boundary to be, 
not the edge of a hole, but a line of intersection, where the surface, 
instead of ceasing, disappears between the two other sheets. 
The knitted model exhibited illustrates this form of complex. 
4. On the Foundations of the Kinetic Theory of Gases. 
By Professor Tait. 
(< % ) On the ultimate average Distribution of Energy 
among Systems of smooth Colliding Spheres. 
The following note was written at the instance of Sir W. 
Thomson. It is directed mainly to one extremely important point 
connected with the Kinetic Gas Theory ; and is designed to show 
to the ordinary reader the nature of the investigation, and of the 
real evidence for the result, without the imposing array of symbols 
which is usually marshalled in papers on that Theory. 
