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XII.—On the Foundations of the Kinetic Theory of Gases. II

Published online by Cambridge University Press:  06 July 2012

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In the present communication I have applied the results of my first paper to the question of the transference of momentum, of energy, and of matter, in a gas or gaseous mixture; still, however, on the hypothesis of hard spherical particles, exerting no mutual forces except those of impact. The conclusions of §§ 23, 24 of that paper form the indispensable preliminary to the majority of the following investigations. For, except in extreme cases, in which the causes tending to disturb the “special” state are at least nearly as rapid and persistent in their action as is the process of recovery, we are entitled to assume, from the result of § 24, that in every part of a gas or gaseous mixture a local special state is maintained.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 33 , Issue 2 , April 1888 , pp. 251 - 277
Copyright
Copyright © Royal Society of Edinburgh 1888

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References

page 252 note * In the Phil. Mag., for April 1887, the same objection is raised by Prof. Boltzmann; who has appended it to the English translation of his paper presently to be referred to. But he goes farther than the other objectors, and accuses me of reasoning in a circle.

page 253 note * The Foundations of the Kinetic Theory of Gases. Phil Mag. 1886, I, p. 481Google Scholar.

page 253 note † Über die zum theoretischen Beweise des Avogadro'-schen Gesetzes erforderlichen Voraussetzungen. Sitzb. der kais. Akad, XCIV, 1886,Google Scholar Oct. 7. In this article Prof. Boltzmann states that I have nowhere expressly pointed out that my results are applicable only to the case of hard spheres. I might plead that the article he refers to is a brief Abstract only of my paper; but it contains the following statements, which are surely explicit enough as to the object I had in view:—

“This is specially the case with his [Maxwell's] investigation of the law of ultimate partition of energy in a mixture of smooth spherical particles of two different kinds.”

“It has since been extended by Boltzmann and others to cases in which the particles are no longer supposed to be hard smooth spheres.”

“Hence it is desirable that Maxwell's proof of his fundamental Theorem should be critically examined.” Then I proceed to examine it, not Professor Boltzmann's extension of it. In my paper itself this limitation is most expressly insisted on.

page 254 note * Théorie Analytique des Probabilités. Livre II, chap. ii, 4. [In using this formula, we must make sure that the ratio m/n is sufficiently large to justify the approximation on which it is founded. It is found to be so in the present case. At my request Professor Cayley has kindly investigated the correct formula for the case in which m and n are of the same order of large quantities. His paper will be found in Proc. R. S. E., April 4, 1887.]

page 255 note * Encyc. Metropolitana. Art. Theory of Probabilities.

page 261 note * Cf., however, Stokes, , Phil. Trans., 1886, vol. clxxvii. p. 786Google Scholar.

page 265 note * Pogg. Ann., cxv, 1862;Google ScholarPhil. Mag., 1862, IGoogle Scholar.

page 265 note † Trans. R. S. E., 1878, p. 717Google Scholar.