194 
Proceedings of the Royal Society of Edinburgh. [Sess. 
In this case all phases occur, and that with equal frequency, yet there 
is not equipartition of the radial and transverse components. In the 
previous example all phases occurred, but not apparently with equal 
frequency. 
When collisions occur amongst the particles, equipartition becomes more 
and more nearly satisfied as the mean free path becomes smaller and 
smaller relatively to the diameter of the sphere, unless some cause other 
than a boundary condition intervenes to prevent equipartition, or to prevent 
that condition of “ molecular chaos,” the postulation of which seems 
to be equivalent to the postulation of equipartition. Such a cause is 
that co-ordination of velocities which Burbury contemplates as due to the 
tendency to release local variations of pressure, on a molecular scale, along 
paths of least resistance. It does not appear that, either in rare gases 
whose mean free path is comparable to the linear dimensions of the 
enclosing vessel, or in dense gases where it is not comparable to these 
dimensions, there is necessary equipartition of energy amongst all the 
freedoms. 
(. Issued separately August 28 , 1907 .) 
