95 
of Edinburgh, Session 1866 - 67 . 
seen to bound obliquely from one another, shaking violently from 
the effects of the shock. The result was very similar to that ob- 
servable in two large india-rubber rings striking one another in the 
air. The elasticity of each smoke-ring seemed no further from 
perfection than might be expected in a solid india-rubber ring of 
the same shape from what we know of the viscosity of india-rubber. 
Of course this kinetic elasticity of form is perfect elasticity for 
vortex rings in a perfect liquid. It is at least as good a beginning 
as the “clash of atoms” to account for the elasticity of gases. 
Probably the beautiful investigations of D. Bernoulli, Herapath, 
Joule, Kronig, Clausius, and Maxwell, on the various thermo- 
dynamic properties of gases, may have all the positive assumptions 
they have been obliged to make as to mutual forces between two 
atoms and kinetic energy acquired by individual atoms or mole- 
cules, satisfied by vortex rings, without requiring any other property 
in the matter whose motion composes them than inertia and in- 
compressible occupation of space. A full mathematical investiga- 
tion of the mutual action between two vortex rings of any given 
magnitudes and velocities, passing one another in any two lines, 
so directed that they never come nearer one another than a large 
multiple of the diameter of either, is a perfectly solvable mathe- 
matical problem; and the novelty of the circumstances contem- 
plated presents difficulties of an exciting character. Its solution 
will become the foundation of the proposed new kinetic theory of 
gases. The possibility of founding a theory of elastic solids and 
liquids on the dynamics of more closely-packed vortex atoms may 
be reasonably anticipated. It may be remarked, in connection 
with this anticipation, that the mere title of Rankine’s paper on 
“ Molecular Vortices,” communicated to the Royal Society of Edin- 
burgh in 1849 and 1850, was a most suggestive step in physical 
theory. 
Diagrams and wire models were shown to the Society, to illus- 
trate knotted or knitted vortex atoms, the endless variety of 
which is infinitely more than sufficient to explain the varieties 
and allotropies of known simple bodies and their mutual affinities. 
It is to be remarked that two ring atoms linked together, or one 
knotted in any manner with its ends meeting, constitute a system 
which, however it may be altered in shape, can never deviate from 
