Theory of the Dissipation of Energy. 295 



their energy in the gross, we could not discover that in the 

 very special case we have just considered the progress was 

 towards a succession of states, in which the distribution of 

 energy deviates more and more from uniformity up to a 

 certain time. The number of molecules being finite, it is 

 clear that small finite deviations from absolute precision in 

 the reversal we have supposed would not obviate the resulting 

 disequalization of the distribution of energy. But the greater 

 the number of molecules, the shorter will be the time during 

 which the disequalizing will continue ; and it is only when 

 we regard the number of molecules as practically infinite 

 that we can regard spontaneous disequalization as practically 

 impossible. 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) some- 

 thing more than ^ths °^' ^ ne wn °l e energy shall be in one- 

 half of the vessel, and less than ^th 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 

 something more than -^ths shall be in one-half, and some- 

 thing less than ^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 ot 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 per- 

 centage. It is a strange but nevertheless a true conception of 

 the old well-known law of the conduction 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 

 impossible 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 dissipation 6f energy rests. 



