329 
of Edinburgh, Session 1873-74. 
A ; rarefaction and very high temperature in B ; and equal tem- 
perature in A and B. The process of disequalisation of tempera- 
ture and density might be stopped at any time by changing the 
orders to those previously specified (2), and so permitting a certain 
degree of diffusion each way across the interface while maintaining 
a certain uniform difference of temperatures with equality of pres- 
sure on the two sides. 
If no selective influence, such as that of the ideal “ demon,” 
guides individual molecules, the average result of their free 
motions and collisions must be to equalise the distribution of 
energy among them in the gross; and after a sufficiently long 
time, from the supposed initial arrangement, the difference of 
energy in any two equal volumes, each containing a very great 
number of molecules, must bear a very small proportion to the 
whole amount in either; or, more strictly speaking, the probability 
of the difference of energy exceeding any stated finite pro- 
portion of the whole energy in either is very small. Suppose 
now the temperature to have become thus very approximately 
equalised at a certain time from the beginning, and let the motion 
of every particle become instantaneously reversed. Each molecule 
will retrace its former path, and at the end of a second interval of 
time, equal to the former, every molecule will be in the same 
position, and moving with the same velocity, as at the beginning ; 
so that the given initial unequal distribution of temperature will 
again be found, with only the difference that each particle is 
moving in the direction reverse to that of its initial motion. This 
difference will not prevent an instantaneous subsequent commence- 
ment of equalisation, which, with entirely different paths for the 
individual molecules, will go on in the average according to the 
same law as that which took place immediately after the system 
was first left to itself. 
By merely looking on crowds of molecules, and reckoning 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 mole- 
cules being finite, it is clear that small finite deviations from 
absolute precision in the reversal we have supposed would not 
