64 REPORT — 1894 



Report on the Present State of our Knowledge of Thermodynamics. 



By G. H. Bryan. 



Part II. — The Laws op Distribution of Energy and their Limitations. 

 ( With an Aj)petulix by Prof. Ludwig Boltzjiann.) 



Introduction. 



L This Report deals primarily with the Boltzmann-Maxwell Law and 

 Maxwell's Law of Partition of Kinetic Energy, which form the basis of 

 the Kinetic Theory of Gases. One of the main points kept in view has 

 been to show where to draw the line between dynamical systems which 

 do and dynamical systems which do not satisfy the laws in question. 



Since the appearance of the first Report ' several papers have appeai-ed 

 which have thrown a somewhat different light on certain aspects of the 

 subject, and have thus materially assisted in crystallising our knowledge 

 of this branch of Thermodynamics into a definite form. In order to pre- 

 vent unnecessary controversy, I have, as far as possible, avoided drawing 

 conclusions from arguments of a vague and theoretical nature. Where, 

 however, results are based on purely mathematical calculations they must 

 be understood to be liable to modification should further examination 

 show the calculations to be faulty or inaccurate. It is necessary to 

 mention this, as one of the investigations cited in Part I. has subse- 

 quently been found to be incorrect, with the result of very materially 

 altering our \'iews on the question at issue.^ 



A great advance in the present subject is due to tlie extension of the 

 use of generalised co-ordinates, by which greater generality has been given 

 to results and the analysis much simplified, as a comparison of Boltzmann's 

 early papers with modern writings abundantly testifies. A further sim- 

 plification has been effected by the use of the Jacobian notation. 



For convenience I have in places written exp — 7iEforexp( — AE) or e~''^. 



The present Report is divided into three sections. In Section I. 

 Maxwell's Law of Partition of Energy is regarded in the aspect of a general 

 dynamical theorem, without reference to any particular applications, and 

 without taking into account the effect of collisions. Section II. treats of 

 the Boltzmann-Maxwell Law for a system of bodies colliding with one 

 another indiscriminately, and partaking of the nature of gas molecules. 

 Section III. deals briefly with certain researches connecting the Boltzmann- 

 Maxwell Law with the Theory of Probability, the Virial Equation, and the 

 Second Law of Thermodynamics. 



Section I. — Non-coli-iding Systems. 

 Clerk Maxwell's Investigations. 



2. Clerk Maxwell's investigations^ have played such a prominent part 

 in the literature of the Kinetic Theory that I think it desirable to 

 recapitulate his paper briefly, so as to show more clearly what assump- 

 tions he made and how much he actually proved. 



' Cardiff Beport, 1891, pp. 85-122. 



'^ The results stated in the first tAvelve lines of Part I. Section III. § 44 are now 

 known to be erroneous. See also §§ 36, 37 below. 



' ' On Boltzmann's Theorem of the Avernge Distribution of Energy in a System 

 of Material Poin's,' Tran\ Canih. ritil. Soc, xii. 1879. 



