576 Proceedings of the Royal Society 
the yielding is not necessarily in the direction of the pressure. 
There is, however, always one direction of coincidence, and there 
may be three. When there are three, if two of these form a right 
angle, the third is also perpendicular to both of them. 
2. On Vortex Motion. By Professor Sir William Thomson. 
(Abstract .) 
This paper is a sequel to several communications which have 
already appeared in the Proceedings and Transactions of the Royal 
Society of Edinburgh.* It commences with an investigation of 
the circumstances under which a portion of an incompressible fric- 
tionless liquid, supposed to extend through all space, or through 
space wholly or partially bounded by a rigid solid, can be projected 
so as to continue to move through the surrounding liquid with- 
out change of shape ; and goes on to investigate vibrations exe- 
cuted by a portion of liquid so projected, and slightly disturbed 
from the condition that gives uniformity. The greatest and least 
quantities of energy which a finite liquid mass of any given initial 
shape and any given initial motion can possess, after any varia- 
tions of its bounding surface ending in the initial shape, are next 
investigated ; and the theory of the dissipation of energy in a 
finite or infinite frictionless liquid is deduced. A finite space, filled 
with incompressible liquid, traversed by a great multitude of parts 
of itself, each very small in comparison with the average distance 
of any one of the parts from its nearest neighbour, is next con- 
sidered, and thus a kinetic theory of gases, without the assump- 
tion of elastic atoms, is sketched; also a realisation by vortex 
atoms of Le Sage’s “ gravific ” fluid consisting of an innumerable 
multitude of “ ultramundane corpuscles.” 
Towards the vortex theory of the elasticity of liquids and solids, 
the propagation of waves along a row of vortex columns alternately 
positive and negative, in a liquid contained between two rigid 
parallel planes, close enough to give stability to the row of columns, 
is next investigated. 
In conclusion, it is pointed out that the difficulties of forming a 
complete theory of the elasticity of gases, liquids, and solids, with 
* Vortex Atoms. Proceedings, February 1867 ; Transactions, 1868-1869. 
