Open AccessX. On the collision of elastic bodies
Author(s) -
S. H. Burbury
Publication year - 1892
Publication title -
philosophical transactions of the royal society of london. a
Language(s) - English
Resource type - Journals
eISSN - 2053-9231
pISSN - 0264-3820
DOI - 10.1098/rsta.1892.0010
Subject(s) - spheres , inertia , physics , moment of inertia , elastic collision , distribution (mathematics) , maxwell–boltzmann distribution , relative velocity , classical mechanics , mathematical physics , quantum mechanics , mathematical analysis , mathematics , electron , astronomy
In a paper read before the Society on June 11, Sir William Thomson expressed a doubt as to the general truth of the Maxwell-Boltzmann doctrine concerning the distribution of energy among a great number of mutually acting bodies, and suggested that certain test cases should be investigated. The test that he proposed on that occasion was a number of hollow elastic spheres, each of mass M, and each containing a smaller elastic sphere of massm , free to move within a larger one. This pair he calls a doublet. This case is within the general proof of the doctrine given below. It is, however, I think amenable to a simpler treatment, which has been applied to the case of elastic spheres external to one another. 1. Every doublet has a centre of inertia of the sphere M and its imprisonedm . Let V be the velocity of that centre of inertia, R the relative velocity of M andm . If V and R be given in magnitude, R given in direction, V may have any direction, and in Maxwell’s distribution, for given direction of R, all directions of V are equally probable. Conversely, if, whatever be the values of V and R, for given direction of R all directions of V are equally probable, Maxwell’s law prevails. Now consider a very great number of doublets, all having their relative velocity and the velocity of centre of inertia within limits R, R +d R, and V, V +d V. Consider them before and after collisions between M andm . Nothing is changed by collision except the direction of R, and that change of direction is independent of the direction of V. Therefore after collision for given direction of R all directions of V are equally probable, and therefore Maxwell’s distribution prevails after as well as before collision, and is therefore not affected by collisions.