KINETIC THEORY OF GASES m 



There is no record what reply Thomson made to this very clear 

 statement. 



Having established the fundamental propositions in the first paper Tait 

 proceeded in his later papers to develop the subject in its application to 

 viscosity, thermal conduction, diffusion, the virial, and the isothermal equations. 

 Certain strictures which Tait in his fourth paper applied to Van der Waals' 

 method of evolving his well-known isothermal equation led to a discussion 

 with Lord Rayleigh and Professor Korteweg (see Nature, Vols. XLIV, XLV, 

 1891-92). While accepting their explanations of Van der Waals' process 

 he was not convinced that the process was valid in the sense of being a 

 logical following out of the virial equation. 



On November 23, 1893, Tait reviewed in Nature (Vol. XLIX) the second 

 edition of Dr Watson's Treatise on the Kinetic Theory of Gases : and the 

 following paragraphs give very clearly his own view of the significance and 

 aim of his papers on the subject : 



"I believe that I gave, in 1886 (Trans. /?. 6". E. Vol. XXXIII), the first (and 

 possibly even now the sole) thoroughly legitimate, and at least approximately 

 complete, demonstration of what is known as Clerk-Maxwell's Theorem, relating to 

 the ultimate partition of energy between or among two or more sets of hard, smooth, 

 and perfectly elastic spherical particles. And I then pointed out, in considerable 

 detail, the logical deficiencies or contradictions which vitiated Maxwell's own proof 

 of 1859, as well as those involved in the mode of demonstration which he subse- 

 quently adopted from Boltzmann. Dr Boltzmann entered, at the time, on an elaborate 

 defence of his position ; but he did not, in my opinion, satisfactorily dispose of the 

 objections I had raised. Of course I am fully aware how very much easier it is for 

 one to discover flaws in another man's logic than in his own, and how unprepared 

 he usually is to acknowledge his own defects of logic even when they are pointed 

 out to him. But the only attacks which, so far as I know, have been made on my 

 investigation, were easily shown to be due to misconception of some of the terms 

 or processes employed 



" From the experimental point of view, the first great objection to Boltzmann's 

 Theorem is furnished by the measured specific heats of gases ; and Dr Watson's 

 concluding paragraphs are devoted to an attempt to explain away the formidable 

 apparent inconsistency between theory and experiment. In particular he refers to a 

 little calculation, which I made in 1886 to show the grounds for our confidence in 

 the elementary principles of the theory. This was subsequently verified by Natanson 

 (Wied. Ann. 1888) and Burbury (Phil. Trans. 1892). Its main feature is its pointing 

 out the absolutely astounding rapidity with which the average amounts of energy 

 per particle in each of two sets of spheres in a uniform mixture approach to equality 

 in consequence of mutual impacts. Thus it placed in a very clear light the difficulty 

 of accepting Boltzmann's Theorem, if the degrees of freedom of a complex molecule 

 at all resemble those of an ordinary dynamical system." 



