140 Proceedings of Royal Society of Edinburgh. 
considered present analogies to the molecular systems of luminous 
gases. We at least see, therefore, how it may he possible for 
gaseous systems to he free from subjection to the law of equi- 
partition of energy within their vibratory freedoms. 
But it seems also that the possible conclusions reach further. 
Rayleigh [Scientific Papers, vol. iv., no. 253), in verifying Maxwell’s 
conclusions, points out the severely restrictive character of 
Maxwell’s assumption. It implies that the system, between two 
successive attainments of any given phase, must have passed 
through all phases consistent with the equation of energy. 
Maxwell’s own words are: “The material points may act on 
each other at all distances, and according to any law which is 
consistent with the conservation of energy, and they may also 
be acted on by any forces external to the system, provided these 
also are consistent with that law. The only assumption which 
is necessary for the direct proof is that the system, if left to itself 
in its actual state of motion, will, sooner or later, pass through 
every phase which is consistent with the equation of energy. 
“Now it is manifest that there are cases in which this does not 
take place. The motion of a system not acted on by external force 
satisfies six equations besides the equation of energy, so that the 
system cannot pass through those phases, which, though they satisfy 
the equation of energy, do not also satisfy these six equations. 
“ Again, there may he particular laws of force, as, for instance, 
that according to which the stress between two particles is 
proportional to the distance between them, for which the motion 
repeats itself after a finite time. In such cases a particular value 
of one variable corresponds to a particular value of each of the 
other variables, so that phases formed by sets of values of the 
variables which do not correspond cannot occur, though they 
may satisfy the seven general equations. 
“But, if we suppose that the material particles, or some of them, 
occasionally encounter a fixed obstacle such as the sides of a vessel 
containing the particles, then, except for special forms of the sur- 
face of this obstacle, each encounter will introduce a disturbance 
into the motion of the system, so that it will pass from one un- 
disturbed path into another. The two paths must both satisfy the 
equation of energy, and they must intersect each other in the 
