466 Lord Kelvin on the Maxwell- Boltzmann Doctrine 



object was to prove a strong prima facie case by the accumu- 

 lation of numerous instances from independent sources. I 

 am at present engaged in obtaining results which, I trust, 

 may be more suitable for mathematical criticism, and those 

 mentioned in the foregoing paper may be taken as prelimi- 

 nary samples. I have also investigated a large number of 

 instances in which the results are much less complicated than 

 in the case of sulphuric acid, and I have thus accumulated a 

 mass of evidence showing that changes similar to those 

 already found do occur at simple molecular proportions. The 

 accumulation of such evidence, however, is a work of time, 

 but I hope in the end to succeed in dislodging Prof. Rucker 

 from his present neutral position of neither affirming nor 

 denying my conclusions. 

 February 1892. 



LI. On a Decisive Test-case disproving the Maxwell-Boltzmann 

 Doctrine regarding Distribution of Kinetic Energy. By 

 Lord Kelvin *. 



THE doctrine referred to is that stated by Maxwell in his 

 paper " On the Average Distribution of .Energy in a 

 System of Material Points" (' Camb. Phil. Soc. Trans.,' 

 May 6, 1878, republished in vol. 2 of Maxwell's ' Scientific 

 Papers ') in the following words : — 



" In the ultimate state of the system, the average kinetic 

 energy of two given portions of the system must be in the 

 ratio of the number of degrees of freedom of those portions/' 



Let the system consist of three bodies, A, B, C, all movable 

 only in one straight line, KHL: 



B being a simple vibrator controlled by a spring so stiff 

 that when, at any time, it has very nearly the whole energy 

 of the system, its extreme excursions on each side of its 

 position of equilibrium are small : 



C and A, equal masses : 



C, unacted on by force except when it strikes L, a fixed 

 barrier, and when it strikes or is struck by B : 



A, unacted on by force except when it strikes or is struck 

 by B, and when it is at less than a certain distance, H K, 

 from a fixed repellent barrier, K, repelling with a force, F, 

 varying according to any law, or constant, when A is between 

 K and H, but becoming infinitely great when (if at any time) 

 A reaches K, and goes infinitesimally beyond it. 



* Communicated by the Author : from an advance-proof of the Proc. 

 Roy. Sdc for April 28, 1892. 



