﻿990 Dr. J. P. Partington on the 



of i is then given, according to these authors, by 



. . (2,rm) 3/2 yfc 6/2 



2 = 10ff« v , . . . . 



CO 



where m is the mass of the atom, k is Boltzmann's constant 

 (R/No, where N is Avogadro's constant), and h is Planck's 

 constant. With numerical values (see § 7 below), and p in 

 atm.j this gives 



C= -1-589 + 1-5 log M, .... (7a) 



where M is the atomic weight, referred to the same standards 

 as N . 



4. The object of the present communication is the extension 

 of this line of investigation to a hypothetical diatomic 

 molecule which, it is believed, represents with some approxi- 

 mation the structure of a particular group of gases *. A 

 general solution would obviously enable us to predict the 

 results of all types of gaseous reactions without recourse to 

 experiment, and would provide a long-sought solution to a 

 fundamental problem of chemical affinity. 



The method of calculation adopted is that of generalized 

 statistical mechanics |. An isolated system, possessing an 

 energy e, and composed of a large number of molecules 

 which exert no forces on one another, is assumed to be 

 definable in terms of a set of generalized coordinates 

 Qi, q 2 , ..., and a corresponding set of generalized momenta 

 Pii P21 • • • related by the first canonical equation of Hamilton, 



Zi^eftpi. ...... (8) 



According to the Quantum Theory, 



H = 1 1 . . . dq 1 dq 2 . . . dpi dp^ 



which is independent of time and of the particular choice of 

 coordinates, has a definite value for each element of the 

 generalized space (Elementargeoiet) . In the case of an ideal 

 gas, the mean energy e coincides with the energy e in any 

 point of the element, and 



Xe~^ = ({ dq 1 dq 2 ...dp 1 dp 2 ... ^-^ 



(9) 



* Partington, Trans. Faraday Soc. 1922. 



"f J. W. Gibbs, ( Elementary Principles of Statistical Mechanics/ 

 Planck, Warmestrahlung, 4 Aufl. 1921. Jeans, l Dynamical Theory of 



