396 Lord Kelvin [April 27, 



each atom will be in every part of the tube as often as is 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, are equal to those 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 

 1866 paper (' The Dynamical Theory of Gases '),* 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 generalised by Boltzmann and himself several 

 years after the date of that paper. 



§ 56. Both Boltzmann and Maxwell recognised 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 the 

 " molecular theory. Boltzmann has suggested that we 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." Bay lei gh, 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 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 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. Even if we regard the atoms as 

 " mere points, whose rotation means Dothing, there must still exist 



* Addition, of date December 17, 1866. Collected works, vol. ii. p. 76. 



