328 Proceedings of the Royal Society 
definite orders. First, let the orders be to allow no molecules to 
pass from either side. The effect will be the same as if the inter- 
face were stopped by a barrier impermeable to matter and to heat. 
The pressure of the gas being, by hypothesis, equal in the hot and 
cold parts, the resultant momentum taken by each demon from any 
considerable number of molecules will be zero ; and therefore he 
may so time his strokes that he shall never move to any consider- 
able distance from his station. Now, instead of stopping and turn- 
ing all the molecules from crossing his allotted area, let each demon 
permit a hundred molecules chosen arbitrarily to cross it from the 
hot side; and the same number of molecules, chosen so as to have 
the same entire amount of energy and the same resultant momen- 
tum, to cross the other way from the cold side. Let this be done 
over and over again within certain small equal consecutive inter- 
vals of time, with care that if the specified balance of energy and 
momentum is not exactly fulfilled in respect to each successive 
hundred molecules crossing each way, the error will be carried 
forward, and as nearly as may be corrected, in respect to the next 
hundred. Thus, a certain perfectly regular diffusion of the gas 
both ways across the interface goes on, while the original different 
temperatures on the two sides of the interface are maintained with- 
out change. 
Suppose, now, that in the original condition the temperature and 
pressure of the gas are each equal throughout the vessel, and let it 
be required to disequalise the temperature, but to leave the pressure 
the same in any two portions A and B of the whole space. Station 
the army on the interface as previously described. Let the orders 
now be that each demon is to stop all molecules from crossing his 
area in either direction except 100 coming from A, arbitrarily 
chosen to be let pass into B, and a greater number, having among 
them less energy but equal momentum, to cross from B to A. Let 
this be repeated over and over again. The temperature in A will 
be continually diminished and the number of molecules in it con- 
tinually increased, until there are not in B enough of molecules 
with small enough velocities to fulfil the condition with reference 
to permission to pass from B to A. If after that no molecule be 
allowed to pass the interface in either direction, the final con- 
dition will be very great condensation and very low temperature in 
