Dynamical Theory of Heat and Light. 39 



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 o£ 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 

 MaxwelPs 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 parti tional 

 doctrine generalized by Boltzmann and himself several years 

 after the date of that paper. 



§ 56. Both Boltzmann and Maxwell recognized the ex- 

 perimental 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." 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 

 u 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. 



