On the Maxwell-Boltzmann Doctrine of Kinetic Energy. 397 



April 28, 1892. 



Mr. JOHN EVANS, D.C.L., LL.D., Treasurer and Vice-President, 

 followed by The LORD KELVIN", President, in the Chair. 



A List of the Presents received was laid on the table, and thanks 

 ordered for them. 



The following Papers were read : — 



I. " On a Decisive Test-case disproving the Maxwell- 

 Boltzmann Doctrine regarding Distribution of Kinetic 

 Energy." By The Lord Kelvin, Pres. R.S. Received 

 April 6, 1892. 



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, HK, from a fixed repel- 

 lent barrier, K, repelling with a force, E, 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. 



Suppose now A, B, C to be all moving to and fro. The collisions 

 between B and the equal bodies A and C on its two sides must 

 equalise, and keep equal, the average kinetic energy of A, immediately 

 before and after these collisions, to the average kinetic energy of C. 

 Hence, when the times of A being in the space between H and K are 



VOL. LI. 2 E 



