Maxwell-Boltzmann Doctrine of Distribution of Energy. 79 



June 11, 1891. 

 Sir WILLIAM THOMSON, D.C.L., LL.D., President, in the Chair. 



The Presents received were laid on the table, and thanks ordered 

 for them. 



Sir John Conroy, Mr. Edwin Bailey Elliott, Mr. Percy C. Gilchrist, 

 Dr. William Dobinson Halliburton, Mr. John Edward Marr, Mr. 

 Ludwig Mond, Professor Silvanus Phillips Thompson, and Captain 

 Thomas Henry Tizard were admitted into the Society. 



The following Papers were read : 



I. " On Some Test Cases for the Maxwell-Boltzraann Doctrine 

 regarding Distribution of Energy." By SIR WILLIAM 

 THOMSON, D.C.L., P.K.S. Received June 11, 1891. 



1. Maxwell, in his article (' Phil. Mag.,' 1860) " On the Collision of 

 Elastic Spheres," enunciates a very remarkable theorem, of primary 

 importance in the kinetic theory of gases, to the effect that, in an 

 assemblage of large numbers of mutually colliding spheres of two or 

 of several different magnitudes, the mean kinetic energy is the same 

 for equal numbers of the spheres irrespectively of their masses and 

 diameters ; or, in other words, the time-averages of the squares of the 

 velocities of individual spheres are inversely as their masses. The 

 mathematical investigation given as a proof of this theorem in that 

 first article on the subject, is quite unsatisfactory ; but the mere enun- 

 ciation of it, even if without proof, was a very valuable contribution 

 to science. In a subsequent paper (" Dynamical Theory of Gases," 

 * Phil. Trans.' for May, 1866) Maxwell finds in his equation (34) 

 (' Collected Works,' p. 47), as a result of a thorough mathematical 

 investigation, the same theorem extended to include collisions between 

 Boscovich points with mutual forces according to any law of distance, 

 provided only that not more than two points are in collision (that is 

 to say, within the distances of their mutual influence) simultaneously. 

 Tait confirms Maxwell's original theorem for colliding spheres of 

 different magnitudes in an interesting and important examination of 

 the subject in 19, 20, 21 of his paper " On the Foundations of ihe 

 Kinetic Theory of Gases " (' Trans. R.S.E.' for May, 1866). 



2. Boltzmann, in his " Studien iiber das Gleichgewicht der leben- 

 digen Kraft zwischen bewegten materiellen Punkten " (' Sitzb. K. 



