ON OUK KNOWLEDGE OF THERMODYNAMICS. 119 



(ii.) Sacli a tendency cannot be independent of the law of force 

 between the molecules, for if we take the case of a system of particles 

 attracting one another with forces varying directly as the distance, the 

 motion will be strictly periodic, and there will be no tendency towards 

 equalisation of energy. 



(iii.) The tendency cannot be independent of initial circumstances, for 

 if the motion of every point were I'eversed we should have a configura- 

 tion which would tend further and further away from the ' special state.' 



(iv.) It therefore appears probable that in estimating the tendency to 

 equalisation of energy among the molecules, account must be taken of 

 the effects of the luminiferous a3ther. The molecules cannot be considered 

 as forming a complete dynamical system in themselves. It seems, then, 

 impossible to overcome the difficulties of the kinetic theory ; all that can 

 be done is to shift these difficulties from the molecules on to the aether, 

 and they then reappear in another form. 



We will now examine how far these difficulties have been met by the 

 researches of those who take a less gloomy view of the question. 



It is no doubt impossible, from the inherent difficulty of the problem, 

 to investigate any general property of non-reversible processes in a body 

 composed of an infinitely large number of molecules ; for, when even the 

 ' Problem of Three Bodies ' has not been fully solved, how can we expect 

 to fully solve the problem of an infinite number of bodies ? 



But without doing this it is jjossible to investigate certain irreversible 

 phenomena by the methods of the kinetic theory, and thus to account 

 for the degradation of available energy under circumstances in which the 

 problem is soluble. 



49. Thus Tait ' has worked out the rate of equalisation of average 

 energy in a mixture of two kinds of spheres. He has, moreover, applied 

 his formula to the case of a mixture of equal parts of oxygen and nitrogen 

 on the supposition that the aggregate masses are equal, that the number 

 of molecules per cubic inch^o xlO-", and that the sum of the radii of 

 the molecules=3 xlO"* of an inch. He finds that the dificrence of the 

 average energies of the two systems of molecules will fall to '01 of its 

 original value in ^ X lO"'-* of a second. This result surely affords very 

 strong evidence in favour of a gener.al tendency towards the ' special 

 state.' 



Moreover, the kinetic theory has been applied to explain the phe- 

 nomena of heat-conduction, viscosity, diffusion of a mixture of gases, 

 and other irreversible processes. These have all been worked out by 

 Tait in the same series of papei's. One very great merit of his work is 

 that he has in every instance clearly set forth the assumptions on which 

 his proofs are based. The investigations are, therefore, not liable to 

 objection, as is so often the case with the work of writers who have 

 implicitly made similar assumptions without explicitly stating them. 



With regard to the second 'point, Sir W. Thomson has pointed out ^ 

 that the law of the direct distance possesses unique properties distinct 

 from those of any other law. It is, in fact, the only law of force under 

 which the whole motion is strictly periodic and the equations of motion 

 are completely integrable — a fact sufficiently vvell known to manufac- 

 turers of Senate House problems. But as there is still some uncertainty 



' ' On the Foundations of the Kinetic Tbeoiy of Gases,' Trans. R.S.E. 1886, 

 Section V. 



» On Some Test Cases, Sec. § 10. 



