Manchester Moiiairs, Vol. /Hi. (1908), ^V^. JJ. 



III. A Method of Calculating the Number of Degrees 

 of Freedom of a Molecule among which the 

 Partition of Energy is governed by the Principal 

 Temperature. 



By H. Bateman, M.A. 



Head October 20th, igo8. Received for Publication October 2jrd, i§o8. 



I. In the statistical mechanics of a system of 

 molecules each of which has a definite number of 

 degrees of freedom, there is a remarkable theorem due to 

 Boltzmann* which establishes a law of equipartition in 

 the average distribution of energy among the degrees of 

 freedom. 



The principal embodied in this law is apparently of 

 very wide application, for it is easy to recall many in- 

 stances in which there is equipartition in the distribution 

 of different types of energy. For instance in a plane or 

 spherical wave of light the magnetic energy is equal to 

 the electric energy, and in many types of wave motion 

 studied in the subjects of Hydrodynamics and Sound the 

 Kinetic energy in a wave length is equal to the Potential 

 energy. 



In the case of a perfect gas Boltzmann's theorem 

 leads to an equation expressing the ratio of the specific 

 heats in terms of the number of degrees of freedom for 



* It was enunciated by Waterston in a less general form in 1821 and 

 rediscovered by Maxwell in 1859. Boltzmann's investigation was given in 

 1868 in the Sitztingsb. der K. Akad. Wiss. Wieii, vol. 58, pp. 517-560. 

 The subject was again taken up by Maxwell in 1879. Camb. Phil. Trans., 

 vol. 12, pp. 547-570 ; " Collected Works," vol. 2, p. 713. 



December 3rd, igo8. 



