t 397 ] 
yill. The Distribution of Molecular Energy. 
By J. H. Jeans, B.A., Scholar of Trinity College, and Isaac Newton Student in 
the University of Cambridge. 
Commwiicated by Professor J. J. Thomson, F.R.S. 
Received June 14,—Read June 21, 1900. 
Introduction. 
§ 1. This paper is primarily an attempt to deal with certain points connected with 
the apjilication to the Kinetic Theory of Gases of Boltzmann’s Theorem on the 
partition of energy in a dynamical system. 
It is found by experiment that the ratio of the two specific heats of certain 
monatomic gases {e.g., mercury, argon) is If. If we admit that the energy of these 
gases is distributed in The manner indicated by Boltzmann’s Theorem, then this 
theorem leaves no escape from the conclusion that the molecules of these gases must 
he ligid and geometrically perfect sjfiieres. A similar diJficulty arises in connection 
with other gases : the number of degrees of freedom which a consideration of the 
ratio in question leads us to expect a molecule of a gas to possess, is always less than 
the number which the spectrum of tlie glowing gas shows to actually exist. 
Further, Boltzmann’s Theorem excludes the possiljility of the ratio of the two 
specific heats having any values except one of a certain series of values, whereas 
exjieriment shows that the ratio is not always equal to one of this series, although 
it is generally very near to such a value. Finally Boltzmann’s Theorem leaves no 
room for a variation of this ratio with the temperature, although such a variation is 
known to exist. 
In the present paper I have tried to suggest a way by which it is possible to 
escape from this dilemma. As there is not snificient known aliont tlie constitution 
of a molecule to enable it to be completely specified as a dynamical system, the 
paper is limited to the consideration of two imaginary types of molecules. 
The conclusions arrived at are the same in each case. In the first place the 
distribution of energy which is given by Boltzmann’s Theorem is the only distri¬ 
bution which is permanent under the conditions 'postidated by this theorem. And in 
the second place, this law of distribution may break down entirely as soon as we 
22.5.1901 
