FOUNDATIONS OF THE KINETIC THEORY OF GASES. 267 



out direct loss or gain of heat, and belong rather to a species of Adiabatic than 

 to an Isothermal. Neither Van der Waals nor Clausius, so far as I can see, calls 

 attention to the fact that when there are molecular forces the mean-square speed of 

 the particles necessarily increases with diminution of volume, even when the mean- 

 square speed of a free particle is maintained unaltered ; and this simply because the 

 time during which each particle is free is a smaller fraction of the whole time. 

 But when the whole kinetic energy is treated as a constant (as it must be in an 

 Isothermal, when that energy is taken as measuring the absolute temperature), it is 

 clear that isothermal compression must reduce the value of E. It further follows that 

 the temperature of a gas might be enormously raised if its volume were sufficiently 

 reduced by the process (capable of being carried out by Clerk- Maxwell's Demons) of 

 advancing, at every instant, those infinitesimal portions of the containing walls on which 

 no impact is impending. This is certainly not probable. If, on the other hand, we were 

 to look at the matter from the point of view of intense inter-molecular repulsion (such as, 

 for instance, Clerk-Maxwell's well-known hypothesis of repulsion inversely as the fifth 

 power of the distance, which was so enthusiastically lauded by Boltzmann), we should be 

 led to the very singular conclusion that such an assemblage of particles might possibly 

 be cooled even by ordinary compression ; certainly that the Demons could immensely 

 cool it by diminishing its volume without doing work upon it. 



If this mode of reasoning be deemed unsatisfactory, we may at once fall back on 

 thermodynamic principles ; for these show that a gas could not be in equilibrium if 

 either external, or molecular, potential could establish a difference of temperature from 

 one region of it to another. For it must be carefully remembered (though it is very often 

 forgotten) that temperature-differences essentially involve the transference of heat, on the 

 whole, in one direction or the other between bodies in contact : — so that if there be a 

 cause which can produce these temperature-differences, it is to be regarded as a source of 

 at least restoration of energy. Let the contents of equal volumes at different parts of a 

 tall column of gas under constant gravity be compared. In each the pressure may be 

 regarded, so far as it is due to the external potential, as being applied by bounding* 

 walls. But the temperature is the same in each, and the only other quantity which is 

 the same in each is E. For, as the particles are free to travel from point to point 

 throughout the whole extent of the group, the average value of E must be the same for 

 all ; and, therefore, in regions where the density is small, it must be that of free particles : 

 — i.e., absolute temperature. 



71. For the isothermal formation of liquid, heat must in all cases be taken from the 

 group. This must have the effect of diminishing the value of E. Hence, in a liquid, the 

 temperature is no longer measured by E, but by E + c, where c is a quantity whose value 

 increases steadily, as the temperature is lowered, from the value zero at the critical point. 

 Thus, since of course we must take the physical fact of the existence of liquids as a new 

 datum in our calculations, and with it the agglomeration into doublets, triplets, &c. 

 (whose share of the average energy differs in general from that of their components when 



