1906-7.] Partition of Heat Energy in Molecules of Gases. 195 
XX. — On the Partition of Heat Energy in the Molecules of Gases. 
By Dr Paul Ehrenfest. ( Communicated by Dr W. Peddie.) 
(Read January 7, 1907. MS. received March 7, 1907.) 
In a paper published some time since,* Mr Peddie takes up the following 
question : Given a gas whose molecules contain atoms which are held 
together by purely elastic forces, do there exist, even in this simplest type 
of multiply-atomic molecules, cases in which, when there is equilibrium 
of heat, the average equipartition of kinetic energy demanded by the 
Boltzmann-Maxwell Law does not exist ? 
Mr Peddie’s formulation of the question possesses, above all, the merit of 
having directed the discussion of the Boltzmann-Maxwell Law of energy 
partition to a case which adapts itself readily to calculation. This dis- 
cussion of elastically oscillating systems assumes a special interest in regard 
to the difficult problem of the partition of energy between ether and 
matter. 
Having in view the great importance which, in this way, this 
formulation of the question possesses, I propose to show — 
1. There actually exist, in the sense of the general question, a class of 
cases in which elastically oscillating systems certainly exhibit non- 
equipartition. These cases are obtained by means of special simultaneous 
assumptions : (a) regarding the mechanical structure of the oscillating 
molecule ; ( b ) regarding the character of the collisions amongst the molecules. 
But this class of non-equipartition cases does not contradict Boltzmann’s 
line of thought. It verifies, rather, certain restricting remarks which, 
without developing them farther, Boltzmann made in his first work on the 
H-theorem. 
2. Mr Peddie seeks, in the special development of his work, to construct 
an essentially different class of non-equipartition cases. Their existence 
would in fact be irreconcilable with Boltzmann’s results. Yet, as I shall 
show farther on, this special presentment, at least in its present form, does 
not suffice to prove the existence of the second class of non-equipartition 
cases. 
It would thus appear that the construction, postulated by Mr Peddie 
for elastically oscillating molecules which do not exhibit equipartition , 
* W. Peddie, “ On Vibrating Systems which are not subject to the Boltzmann-Maxwell 
Law,” Proc. Roy. Soc. Edin., vol. xxvi. 1906 (pp. 130-141). 
