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every other atom. The time-integral of the kinetic energy of any one atom will be equal to the time-integral of the kinetic energy of any other atom. This truism is simply and solely all that the Boltzmann-Maxwell doctrine asserts for a vertical column of a homogeneous monatomic gas. It is,
I believe, a general impression that the Boltzmann-Maxwell doctrine, asserting a law of partition of the kinetic part of the whole energy, includes obviously a theorem that the average kinetic energy of the atoms in the upper parts of a vertical column of gas, is equal to that of the atoms in the lower parts of the column. Indeed, with the wording of Maxwell's statement, § 18, before us, we might suppose it to assert that two parts of our vertical column of gas, if they contain the same number of atoms, must have the same kinetic energy, though they be situated, one of them near the bottom of the column, and the other near the top. Maxwell himself, in his 18(H) paper (u The Dynamical Theory of Grases'*) *, gave an independent synthetical demonstration of this proposition, and did not subsequently, so far as I know, regard it as immediately deducible from the partitional doctrine generalized by Boltzmann and himself several years after the date of that paper.
§ 56. Both Boltzmann and Maxwell recognized the experimental contradiction of their doctrine presented by the kinetic theory of gases, and felt that an explanation of this incompatibility was imperatively called for. For instance, Maxwell, in a lecture on the dynamical evidence of the molecular constitution of bodies, given to the Chemical ►Society, Feb. 18, 1875. said : “I have put before you what “ I consider to be the greatest difficulty yet encountered by u the molecular theory. Boltzmann has suggested that we u are to look for the explanation in the mutual action between
the molecules and the ethereal medium which surrounds “ them. I am afraid, however, that if we call in the help of “ this medium we shall only increase the calculated specific “ heat, which is already too great." Rayleigh, who has for the last twenty years been an unwavering supporter of the Boltzmann-Maxwell doctrine, concludes a paper “ On the Law of Partition of Energy," published a year ago in the Phil. Mag., Jan. 1900, with the following words : “ The difficulties u connected with the application of the law of equal partition
of energy to actual gases have long been felt. In the case of “ argon and helium and mercury vapour, the ratio of specific “ heats (1*67) limits the degrees of freedoms of each molecule
* Addition, of date December 17,1866. Collected works, vol. ii. p. 76.
40 Prof. C. Barus on the Absorption of the
“to the three required for translatory motion. The value “ (1*4) applicable to the principal diatomic gases, gives room “for the three kinds of translation and for two kinds of “ rotation. Nothing is left for rotation round the line joining “ the atoms, nor for relative motion of the atoms in this line. 6 Even if we regard the atoms as mere points, whose rotation u means nothing, there must still exist energy of the last-“ mentioned kind, and its amount (according to law) should “ not be inferior.
“We are here brought face to face with a fundamental “ difficulty, relating not to the theory of gases merely, hut “ rather to general dynamics. In most questions of dynamics, “ a condition whose violation involves a large amount of “ potential energy may be treated as a constraint. It is on “ this principle that solids are regarded as rigid, strings as “ inextensible, and so on. And it is upon the recognition “of such constraints that Lagrange’s method is founded. “ But the law of equal partition disregards potential energy. “ However great may be the energy required to alter the “ distance of the two atoms in a diatomic molecule, practical “ rigidity is never secured, and the kinetic energy of the “ relative motion in the line of junction is the same as if the “ tie were of the feeblest. The two atoms, however related, “ remain two atoms, and the degrees of freedom remain six “ in number.
“ What would appear to be wanted is some escape from “ the destructive simplicity of the general conclusion/’
The simplest way of arriving at this desired result is to deny the conclusion; and so, in the beginning of the twentieth century, to lose sight of a cloud which has obscured the brilliance of the molecular theory of heat and light during the last quarter of the nineteenth century.
II. The Absorption of the Ionized* Phosphorus Emanation in Tubes.—II. By C. Barus f.
1, T?OR reasons of both theoretical and practical import it JO is next necessary to ascertain the precise conditions under which the phosphorus nucleus vanishes on passing
* Whoever writes on subjects relating, like the present, to certain features of ionization is obliged to make free use of tne admirable work (Thomson, C. T. ft. Wilson, Townsend, Rutherford, Zeleny, and others), which has been sent out by the Cavendish Laboratory under the direction of Prof. J. J. Thomson. These researches, like those of Chattock, Elster and Geitel, and others (cf. H. Becquerel in ‘ Nature/ Feb. 21st, p. 396, 1901), are so recent and well known that detailed reference would be cumbersome; but I desire to make my acknowledgments here, f Communicated by the Author.