a I 4 



NA TURE 



[February 28, 1895 



revealed in every respect. No one hypothesis has hitherto 

 attained this last end, the Theory of Gases not excoplel. Bjt 

 this ihi. srj- agrees in so many respects with the facts, that we can 

 hardly doubi that in gases certain entities, the number and siz: 

 of which can roughly be determined, fly about pell-mell. Can 

 it be seriously expected that they will behave ex.icily as aggre- 

 gates of Newtonian centres of force, or as the rigid bodies of 

 our .Mechanics ? And how awkward is the human mind in 

 divining the nature of things, when forsaken by the analogy of 

 what wc see and touch directly? 



The following assumptions, while not profes.sing tn explain the 

 mysteries to which Lord Salisbury alluded, nevertheless show- 

 that it is possible to explain the spectra of gases while ascribing 

 5 degrees of freedom to the molecules, and without departing 

 from Boscovich's standpoint. 



Let the molecules of certain gases behave as rigid bodies. 

 The molecules of the gas and of the enclosing vessel move 

 through the ether without loss of energy as rigid bodies, or as 

 Lord Kelvin's vortex rings move through a frictionless liquid in 

 ordinary hydrodynamics. If wc were to take a vessel filled with 

 one gram of g.as kept during an intinitely long time always at 

 o C. and containing always the same portion of ether, every 

 atom of ether and every atom of our g.ts molecules would reach 

 the same average vis viva. If then wc were to raise the 

 tempcriture to l' C and to wait till every ponderable and every 

 ether atom was in thermal equilibrium, the total energy would be 

 augmented by what we may call the ideal specific heat. But in 

 actually heating one gram of gas, the ether ahv.ays flows freely 

 through the walls of the ve-sel. It comes from the universe, 

 and is not at all in thermal equilibrium with the molecules of 

 the gas. It is true that it always carries off energy, if the out- 

 side space is colder than the gas ; but this energy may be so 

 small as to be quite negligible in comparison with the energy 

 which the gas loses by heat-conduction, and which must be ex- 

 perimentally determined and suhtr.acted in measuring the 

 specific h(.at. Only certain transverse vibrations of the ether can 

 transfer sensible energy from one ponder.ible holy to another, 

 and therefore a correction for ladiant heat mu-t be applied to 

 observations of specific heats. These transverse vibrations are 

 not produced (as in the older theories of light) by simple atomic 

 vibrations, but their pitch depends on the shape of the hollow 

 space which the molecule forms in the ether, just as Hertzian 

 waves are not caused by vibrations of the ponderable m.itter of 

 the brass halls, the form of which only determines the pitch. 

 The unknown electric action accompanying a chemical process 

 augments these transverse vibraliins enormously. The geneial- 

 ised coordinate; of the ether, on which these vibrations depend, 

 have not the same vis viva as the coordinates which de- 

 termine the position of a molecule, because the entire ether has 

 not had time to come into thermal equilibrium with the gas 

 molecules, and has in no respect ati.iined the stale which it 

 would have if it were enclosed for an infinitely long lime in the 

 same vessel with the molecules of the gas. 



But how can the molecules of a gas behave as rigid bodies? 

 Arc they not composed of smaller atoms? Probably they are ; 

 but the vis viva of their internal vibrations is transformed 

 into progressive and rotatory motion so slowly, that when a gas 

 is brought to a lower temperature the molecules may retain fur 

 days, or even fur years, the higher 77/ viva of their internal 

 %'ibration5 corresponding to the original temperature. This 

 transference of energy, in fact, takes place so slowly that it can- 

 not be perceived amid the fluctuations of temperature of the 

 surrounding bodies. The possibility of the transference of 

 energy being so gradual cannot be denied, if we also attribute 

 to the ether so little friction that the Eirth is not sensibly 

 reta'iled by moving through it for many hundreds of years. 



If the ether bean external medium which flows freely through 

 the gas, we might find a difficulty in explaining how it is that 

 the source of radiant heat seems to he in the energy of ihe gas 

 itsel'. But I still think it possible that the source of energy of 

 iht electric vibralioni caujed by the impact of two g.is mole- 

 cules in the surrounding ether, may be in the progressive and 

 rotatory energy of the molecule. If the electric stales of two 

 molecules differ in their motions of approach and separation, 

 the energy of progressive motion may be transformed into 

 electric energy. 



Moreover, it is doubtful whether emission of rays of visible 

 light takes place in simple gaaes without chemical .action. 

 Certainly the light of solium and thit of Gassiot's tubes do i 

 not come from gnes who^c m^ilcculet arc in ihirmal equilibrium. I 



It may be objected that the above is nothing more than a 

 series of imperfectly proved hypotheses. But granting its im- 

 probability, it sulfices that this explanation is not impossible. 

 For then I have shown that the problem is not insoluble, and 

 nature will have found a better solution than mine. 



§ 2. Mr. Culverwell's objections ag.iinst my Minimum 

 Theorem bear the closest connection to what I pointed out in 

 the second part of my paper, " Bemerkungen iiber einige 

 Probleme der mechanischen Warmeiheorie," Silz. her. dcr k. 

 IVitn. Acad. vol. Ixxv. 1S77. There I pointed out that my 

 Minimum Theorem, as well as the so-called Second Law of 

 Thermodynamics, are only theorems of probability. The Second 

 Law can never be proved mathematically by means of the 

 equations of dynamics alone. 



Let us compare two motions of a dynamical system. At the 

 beginning of the second motion, let the coordinates specifying 

 the position of every part of the moving system, and the mag. 

 nitudes of all the corresponding velocities, be the same as they 

 were at the end of the first motion, but let the direction of 

 every velocity be exactly reversed. Then in the second motion 

 the system moves exactly in the opposite way to what it does in 

 the first ; hence, if for the first motion we have 



/VQ 

 ] T^°' 



then for the second we must have 



That is, if under certain conditions 



\ T -°- 

 we can always find other initial conditions which give for the 

 same system with the same equations of motion. 



In the same manner, Mr. Culverwell wishes to refute my 

 Minimum Theoiem. ^Ir. Culverwell's reasoning is suspicious, 

 because by the same reasoning we could prove that oxygen and 

 nitrogen do not difluse. Suppose that initially one half of a 

 closed vessel contains pure oxygen, ami in ihe other half pure 

 nitrogen ; when the difl'usion lias advanced for a certain time, 

 reverse the directions of all velocities, then the gases separate 

 again, and, according to Mr. Culverwell's argument, wc could 

 believe that the probability that oxygen and nitrogen separate, 

 is as great as the probability that they mix. 



Though inleresting and striking at the first moment, Mr. 

 Culverwell's arguments rest, as I think, only upon a mistake of 

 my assumptions. It can never be proved from the equati ns of 

 motion alone, that the minimum function II must always de- 

 crease. It can only be deduced from the laws of probability, 

 that if the initial stale is not specially arranged for a certain 

 purpose, but haphazard governs freely, the probability that 

 H decreases is always greater than that it incre.ises. It is well 

 known that the theory of probability is as exact as any other 

 mathematical theory, if properly understood. If wc make 

 6000 throws with dice, we cannot p.-ove that we shall throw 

 any particular number exactly 1000 times ; but we can prove 

 that the ratio of the number of throws in which that number 

 turns up to the whole number of throws, approaches the more 

 to 1/6 the oftener we throw. 



Let us now take a given rigid vessel with perfectly 

 smooth and perfectly elastic walls containing a given number of 

 gas-molecules moving fir an indefinitely long time. All rii^iilar 

 motions (. .^■. one where all the nioleculits move in one plane) shall 

 be excluded. During the greater part of this time II will he 

 very nearly equal to its minimum value II (min.), Let us con- 

 struct the ll-curve, i.t. let us lake the lime ns axis of abscissae 

 and draw the curve, whose ordinalcs are the corresponding 

 values of II. The greater majority of the ordinales of this 

 curve are very nearly cquil to II (min.). Mat because greater 

 values o( II are not malhcmalicaliy impossible, but only very 

 improbable, the curve has certain, though very few, summits 

 or maximum ordinates which rise to a greater height than 

 H(min.). 



Wc will nowconsider a certain ordinate H, ,11 (min.). Two 

 cases are possible. H, may be very near the lop of a summit, 

 so that II decreases if we go either in the p isiiive or negative 

 direction along the nxis ri-|)icsenting time. The second 



NO. 1322, VOL. 51] 



