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Proceedings of the Royal Society 
obviate the resulting disequalisation of the distribution of energy. 
But the greater the number of molecules, the shorter will be the 
time during which the disequalising will continue ; and it is only 
when we regard the number of molecules as practically infinite 
that we can regard spontaneous disequalisation as practically im- 
possible. And, in point of fact, if any finite number of perfectly 
elastic molecules, however great, be given in motion in the interior 
of a perfectly rigid vessel, and be left for a sufficiently long time 
undisturbed except by mutual impact and collisions against the 
sides of the containing vessel, it must happen over and over again 
that (for example) something more than x 9 x ths of the whole energy 
shall be in one-half of the vessel, and less than x Vth of the whole 
energy in the other half. But if the number of molecules be very 
great, this will happen enormously less frequently than that some- 
thing more than x 6 oths shall be in one-half, and something less 
than x 4 x ths in the other. Taking as unit of time -the average 
interval of free motion between consecutive collisions, it is easily 
seen that the probability of there being something more than any 
stated percentage of excess above the half of the energy in 
one-half of the vessel during the unit of time, from a stated 
instant, is smaller the greater the dimensions of the vessel and 
the greater the stated percentage. It is a strange but never- 
theless a true conception of the old well-known law of the con- 
duction of heat, to say that it is very improbable that in the course 
of 1000 years one-half of the bar of iron shall of itself become 
warmer by a degree than the other half; and that the probability 
of this happening before 1,000,000 years pass is 1000 times as 
great as that it will happen in the course of 1000 years, and that 
it certainly will happen in the course of some very long time. 
But let it be remembered that we have supposed the bar to be 
covered with an impermeable varnish. Do away with this impos- 
sible ideal, and believe the number of molecules in the universe 
to be infinite; then we may say one-half of the bar will never 
become warmer than the other, except by the agency of external 
sources of heat or cold. This one instance suffices to explain the 
philosophy of the foundation on which the theory of the dissipa- 
tion of energy rests. 
Take however another case, in which the probability may be 
