TRANSACTIONS OF SECTION A. 615 



since I first read Davy's 'Repulsive Motion,' about thirty-five years ago, but I 

 never made anything- of it, at all events nave not done so until to-day (June 16, 

 1884), (if this can be said to be making anything of it), when in endeavouring to 

 prepare the present address I notice that Joule's and my own old experiments 1 on 

 the thermal effect of gases expanding from a high pressure vessel through a porous 

 plug, proves the less dense gas to have greater intrinsic potential energy than the 

 denser gas, if we assume the ordinary hypothesis regarding the temperature of a gas, 

 according to which two gases are of equal temperatures '-' when the kinetic energies 

 of their constituent molecules are of equal average amounts per molecule. 



Think of the thing thus. Imagine a great multitude of particles enclosed by a 

 boundary which may be pushed inwards in any part all round at pleasure. Now 

 station an engineer corps of Maxwell's army of sorting demons all round the 

 enclosure, with orders to push in the boundary diligently everywhere, when 

 none of the besieged troops are near, and to do nothing'when any of them 

 are seen approaching, and until after they have turned again inwards. The 

 result will be that with exactly the same sum of kinetic and potential 

 energies of the .same enclosed multitude of particles, the throng has been 

 caused to be denser. Now Joule's and my own old experiments on the efflux 

 of air prove that if the crowd be common air, or oxygen, or nitrogen, or 

 carbonic acid, the temperature is a little higher in the denser than in the rarer 

 condition when the energies are the same. By the hypothesis, equality of tempera- 

 ture between two different gases or two portions' of the same gas at* different 

 densities means equality of kinetic energies in the same number of molecules of 

 the two. From our observations proving the temperature to be higher, it there- 

 fore follows that the potential energy is smaller in the condensed crowd. This — 

 always, however, under protest as to the temperature hypothesis — proves some 

 degree of attraction among the molecules, but it does not prove ultimate attraction 

 between two molecules in collision, or at distances much less than the average 

 mutual distance of nearest neighbours in the multitude. The collisional force 

 might be repulsive, as generally supposed hitherto, and yet attraction might predo- 

 minate in the whole reckoning of difference between the intrinsic potential energies 

 of the more dense and less dense multitudes. It is, however, remarkable that the 

 explanation of the propagation of sound through gases, and even of the positive 

 fluid pressure of a gas against the sides of the containing vessel, according to the 

 kinetic theory of gases, is quite independent of the question whether the ultimate 

 collisional force is attractive or repulsive. Of course it must be understood that if 

 it is attractive, the particles must be so small that they hardly ever meet — they 

 would have to be infinitely small to never meet — that, in fact, they meet so seldom, 

 in comparison with the number of times their courses are turned through large 

 angles by attraction, that the influence of these purely attractive collisions is 

 preponderant over that of the comparatively very rare impacts from actual contact. 

 Thus, after all, the train of speculation suggested by Davy's ' Repulsive Motion' 

 does not allow us to escape from the idea of true repulsion, does not do more than 

 let us say it is of no consequence, nor even say this with truth, because, if there 

 are impacts at all, the nature of the force during the impact, and the effects of the 

 mutual impacts, however rare, cannot be evaded in anv attempt to realise a con- 

 ception of the kinetic theory of gases. And in fact," unless we are satisfied to 

 imagine the atoms of a gas as mathematical points endowed with inertia, and, 



1 Republished in Sir W. Thomson's Mathematical and Physical Pavers, Vol. I. 

 Article XL1X. p. 381. 



2 That this is a mere hypothesis has been scarcely remarked by the founders 

 themselves, nor by almost any writer on the kinetic theory of gases. No one has 

 yet examined the question : what is the condition as regards average distribution of 

 kinetic energy, which is ultimately fulfilled by two portions of gaseous matter, 

 separated by a thin elastic septum which absolutely prevents interdiff usion of matter, 

 while it allows interchange of kinetic energy by collisions against itself 1 Indeed 

 I do not know but that the present is the very first statement which has ever been 

 published of this condition of the problem of equal temperatures between two 

 gaseous masses. 



