52 The Law of Distribution [CH. ra 



in Chapter II. It is however very doubtful whether this proof can claim 

 any superiority on grounds of logical consistency or completeness over 

 Maxwell's original proof. The later proof finds it necessary to assume that 

 there is no correlation between the velocity and space coordinates, while the 

 earlier proof merely assumed that there was no correlation between the 

 separate velocity components inter se. In each case the dynamical conditions 

 equally suggest correlation, until the contrary has been proved, and it would 

 be hard to give reasons why one assumption of no correlation is more 

 justifiable than the other. It should be mentioned that Burbury* has 

 always been of opinion that the later proof of Maxwell is not only logically 

 unsound, but leads to an inaccurate result. He maintains that correlation 

 actually takes place, except in the limiting case of an infinitely rare gas. 

 This view, however, is not borne out by the analysis of the present and of 

 the succeeding chapter. (Cf. 66, infra.) 



A second class of proof of the law is represented by the proof which has 

 been given in this chapter. In this class of proof the aim is to deduce a law 

 from general dynamical considerations. As important examples of this class 

 of proof may be mentioned a proof due to Kirchhoff, given in his lectures*!*, 

 and one due to Meyer and Pirogoff, given in Meyer's Kinetic Theory of 

 Gases\. Both these proofs depend upon a use of the calculus of probabilities 

 which cannot be justified. The proof given in this chapter is my own: 

 it also has been criticised by Burbury^I, but I cannot persuade myself that 

 his criticisms as to the validity of the proof are well founded ||. 



* S. H. Burbury, The Kinetic Theory of Gases, Cambridge, 1899. 



t Kirchhoff, Vorlesungen iiber die Theorie der Wdrme, p. 142. 



J Meyer, Kinetic Theory of Gases, Eng. Trans, by Baynes, p. 370. 



Phil. Mag. v. p. 597. 



H Phil. Mag. vi. p. 529, vn. p. 467. 



|| Phil. Mag. vi. p. 720, vn. p. 468. 





