THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 





[FIFTH SERIES.] 



MARCH 1893. 



XXL On the Equilibrium of Vis Viva. — Part III. 

 By Prof. Ludwig Boltzmann*. 



I think that a problem of such primary importance in 

 molecular science ought to be scrutinized and examined on every 

 side, so that as many persons as possible may be enabled to follow 

 the demonstration. — Maxwell, Scientific Papers, ii. p. 713. 



§ 1. On the Variables which reduce the expression for the 

 Vis Viva to a Sum of Squares. 



MAXWELLj was the first to establish the formula for 

 the distribution of vis viva among monatomic gas 

 molecules, which he regarded as perfectly hard spheres of 

 similar or dissimilar form (mass and radius) . He also worked 

 out the case in which the molecules are considered as rigid 

 bodies with three different moments of inertia, and he found 

 that for such a gas the ratio of specific heats must be 1J. 

 Since, however, this ratio has the value 1*4 for the best 

 known simple gases, he concluded that the mechanical analogy 

 is at variance with known facts on this subject J. It is 

 remarkable that Maxwell, who was successful in presenting 

 the solution of the problem with such almost inconceivable 



* Communicated by the Author, from the Sitzungsberichte dor mathe- 

 matisch-jjhysikalischen Classe der honiglich-bayeriscJieu Akademie der 

 Wissenschaften (Munich), vol. xxii. part 3. Translated by James 1,. 

 Howard, D.Sc. 



t "Illustrations of the Dynamical Theory of Gases/' Phil. Mag. 

 January and June 1860, Sci. Pap. i. p. 377. 



\ Maxwell, Sci. Pap. i. p. 409. 



Phil. Mag. S. 5. Vol. 35. No. 214. March 1893. M 



