368 MATHEMATICAL APPENDICES 9* 



APPENDIX II 



MAXWELL'S LAW 



9*. On Some Older Proofs 



/THE state of_equilibrium of a multitude of molecules of gas, as 



/ has been already shown in 22, does not consist in their all 



moving with equal speed. On the contrary, the velocity of any 



particle changes at every encounter, not only in direction but also 



in magnitude. But the values of the speed fluctuate about a 



mean value. The law of devIaTJiorT of the actual speeds of the 



particles from this mean value was first perceived by Maxwell; 



he found that the components of the molecular velocity are 



distributed among the particles of a gas in equilibrium with the 



same regularity as we find in all apparently fortuitous phenomena 



and processes which are really subject to fixed changes. For the 



^^distribution of the speeds the same law holds good which, accord - 



^ing to Gauss, regulates the distribution of chance errors of 



observation among the several observations. 



Very many proofs have been given of Maxwell's law. One 

 such proof was attempted in the first edition of this book, wherein 

 /the law was put forward as the most probable of all conceivable 

 / laws. Although the mathematical investigation of this idea is 

 closely connected with the proof given by Gauss 1 of the method 

 of least squares, the proof in its first form cannot be admitted as 

 valid, and the doubts thrown upon it byBoltzmann 2 and von 

 Kries 3 must be held to be well founded. 



N. N. Pirogoff, 4 however, showed that my proof can be 



1 Theoria motus corp. ccel. 175-177. 

 8 Wiener Sitzungsber. Ixxvi. 1877, p. 373. 



3 Principien der Wahrscheinlichkeitsrechmtng, Freiburg 1886, Chap. VIII. 

 p. 192. 



4 Journ. d. Euss. pliys.-chem. Ges. xvii. 1885, pp. 114-135, 281-313. Ab- 

 stracted in Fortschr. d. Physik, 1886, pt. 2, p. 237. Exner's Repertorium, 

 xxvii. 1891, p. 540. 



