Abstract
(1)Maxwell, in his article (Phill. 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 enunciation 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 the Kinetic Theory of Gases ” (Trans. R. S. E. for May 1866).
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References
Scientific Papers, ii., p. 724.
Ibid., 714, 715.
Ibid., 726–726.
Ibid., 722.
Or of Maxwell 's "b", in 723.
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On Some Test Cases for the Maxwell-Boltzmann Doctrine regarding Distribution of Energy. Nature 44, 355–358 (1891). https://doi.org/10.1038/044355b0
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DOI: https://doi.org/10.1038/044355b0