4i8 



NA TURE 



{August 28, 1884 



oxygen, or nitrogen, or carbonic acid, the temperature is a little 



higher in the denser than in the rarer condition when the ener- 

 the same. By the hypothesis, equality of temperature 



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 prov- 

 ing the temperature to be higher, it therefore 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 ] irove 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 re- 

 pulsive, as generally supposed hitherto, and yet attraction might 

 predominate in the whole reckoning of difference between tlu 

 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 " Repul ive 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 im- 

 pact and the effects of the mutual impacts, however rare, cannot 

 beevaded in any attempt to realise a conception 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, 



ad, according to Boscovich, endowed with forces of mutual 

 positive and negative attraction, varying according to some 

 definite function of the distance, we cannot avoid the question of 

 impacts, and of vibrations and rotations of the molecules result- 

 ing from impacts, and we must look distinctly on each molecule 

 as being either a little elastic solid or a configuration of motion 

 in a continuous all-pervading liquid. I do not myself see how 

 we can ever permanently rest anywhere short of this last view ; 

 but it would be a very pleasant temporary resting-place on the 

 way to it if we could, as it were, make a mechanical model of 

 a gas out of little pieces of round perfectly elastic solid matter, 

 flying about through the space occupied by the gas, and colliding 

 with one another and against the sides of the containing vessel. 

 This is, in fict, all we have of the kinetic theory of gases up to 

 the present time, and this has done for us, in the hands of 

 Clausius and Maxwell, the great things which constitute our first 

 step towards a molecular theory of matter. Of course from it 

 we should have to go on to find an explanation of the elasticity 

 and all the other properties of the molecules themselves, a sub- 

 ject vastly more complex and difficult than the gaseous proper- 

 tics, lur the explanation of which we assume the elastic molecule ; 

 but without any explanation of the properties of the molecule 

 itself, with merely the assumption that the molecule has the 

 requisite properties, we might rest happy for a while in the con- 

 templation of the kinetic theory of gases, and its explanation of 

 the gaseous properties, which is not only stupendously important 

 as a step towards a more thoroughgoing theory of matter, but 

 is undoubtedly the expression of a perfectly intelligible and defi- 

 nite set of facts in Nature. But alas for our mechanical model 

 consisting of the cloud of little elastic solids flying about 

 amongst one another. Though each particle have absolutely 

 perfect elasticity, the end must be pretty much the same as if it 

 were but imperfectly elastic. The average effect of repeated 

 and repeated mutual collisions must be to gradually convert all 

 the translational energy into energy of shriller and shriller vibra- 

 tions of the molecule. It seems certain that each collision must 

 have something more of energy in vibrations of very finely divided 

 nodal parts than there was of energy in such vibrations before 

 the impact. The more minule this nodal subdivision, the less 

 must be the tendency to give up part of the vibrational energy 

 into the shape of translational energy in the course of a col- 

 lision, and 1 think it is rigorously demonstrable that the whole 

 translational energy must ultimately become transformed into 



vibrational energy of higher and higher nodal subdivisions if 

 each molecule is a continuous elastic solid. Let us, then, leave 

 the kinetic theory of gases for a time with this difficulty unsolved, 

 in the hope that we or others after us may return to it, armed 

 with more knowledge of the properties of matter, and with 

 sharper mathematical weapons to cut through the barrier which 

 at present hides from us any view of the molecule itself, and of 

 the effects other than mere change of translational motion which 

 it experiences in collision. 



To explain the elasticity of a gas was the primary object of 

 the kinetic theory of gases. This object is only attainable by 

 the assumption of an elasticity more complex in character, and 

 more difficult of explanation, than the elasticity of gases — the 

 elasticity of a solid. Thus, even if the fatal fault in the theory, 

 to which I have alluded, did not exist, and if we could be per- 

 fectly satisfied with the kinetic theory of gases founded on the 

 collisions of elastic solid molecules, there would still be beyond 

 it a grander theory which need not be considered a chimerical 

 object of scientific ambition — to explain the elasticity of solids. 

 But we may be stopped when we commence to look in the 

 direction of such a theory with the cynical question : What do 

 you mean by explaining a property of matter? As to being 

 stopped by any such question, all I can say is that if engineering 

 were to be all and to end all physical science, we should perforce 

 be content with merely finding properties of matter by observa- 

 tion, and using them for practical purposes. But I am sure very 

 few, if any, engineers are practically satisfied with so narrow a 

 view of their noble profession. They must and do patiently 

 observe, and discover by observation, properties of matter, and 

 results of material combinations. But deeper questions are 

 always present, and always fraught with interest to the true 

 engineer, and he will be the last to give weight to any other 

 objection to any attempt to see below the surface of things than 

 the practical question : Is it likely to prove wholly futile ? But 

 now, instead of imagining the question : What do you mean by 

 explaining a property of matter? to be put cynically, and letting 

 ourselves be irritated by it, suppose we give to the questioner 

 credit for being sympathetic, and condescend to try and answer 

 his question. We find it not very easy to do so. All the pro- 

 perties of matter are so connected that we can scarcely imagine 

 one thoroughly explained without our seeing its relation to all the 

 others, without in fact hiving the explanation of all, and till we 

 have this we cannot tell what we mean by "explaining a pro- 

 perty," or "explaining the properties" of matter. But though 

 this consummation may never be reached by man, the progress 

 of science may be, I believe will be, step by step towards it, on 

 many different roads converging towards it from all sides. The 

 kinetic theory of gases is, as I have said, a true step on one of 

 the roads. On the very distinct road of chemical science, St. 

 Clair Deville arrived at his grand theory of dissociation without 

 the slightest aid from the kinetic theory of gases. The fact that 

 he worked it out solely from chemical observation and experi- 

 ment, and expounded it to the world without any hypothesis 

 whatever, and seemingly even without consciousness of the 

 beautiful explanation it has in the kinetic theory of gases, secured 

 for it immediately an independent solidity and importance as a 

 chemical theory when he first promulgated it, to which it might 

 even by this time scarcely have attained if it had first been 

 suggested as a probability indicated by the kinetic theory of 

 gases, and been only afterwards confirmed by observation. Now, 

 however, guided by the views which Clausius and Williamson 

 have given us of the continuous interchange of partners between 

 the compound molecules constituting chemical compounds in the 

 gaseous state, we see in Deville's theory of dissociation a point 

 of contact of the most transcendent interest between the chemical 

 and physical lines of scientific progress. 



To return to elasticity : if we could make out of matter devoid 

 of elasticity a combined system of relatively moving parts which, 

 in virtue of motion, has the essential characteristics of an elastic 

 body, this would surely be, if not positively a step in the kinetic 

 theory of matter, at least a finger-post pointing a way which we 

 may hope will lead to a kinetic theory of matter. Now this, as 

 I have already shown, 1 we can do in several ways. In the case 

 of the last of the communications referred to, of which only the 

 title has hitherto been published, I showed that, from the 



1 Paper on " Vortex Atoms," Proc. R. S. E. February 1867 ; abstract 01 

 a lecture before the Royat Institution of Great Britain, March 4. iSSi, on 

 "Elasticity Viewed as possibly a Mode of Motion " ; Thomson and Tait's 

 " Natural Philosophy," second edition, part 1, §§ 345 viii. 10345 xxvii. ; " On 

 Oscillation and Waves in an Adynamic Gyrostatic System" (title only), 

 Proc. R. S. E. March 1883. 



