﻿the Partition of Energy. 453 



all our results it is immaterial — indeed, until such questions 

 as dissociation are considered it makes no difference to adopt 

 different conventions for different types of system. The 

 convention has the advantage of shortening a oood manv 

 formula? and freeing them from factors which are without 

 effect on the final results. 



An exception to the above rule for assigning- weights to 

 quantized motions occurs in the case of degenerate si/stems, 

 where there are two degrees of freedom possessing the same 

 or commensurable frequencies. In this case there is only 

 one quantum number, and the state of the system is partly 

 arbitrary. Bohr * shows that the rational generalization is 

 to assign to such a state a weight factor which can be 

 evaluated by treating the system as the limit of a non- 

 degenerate system, and quantizing it according to any pair 

 of variables in which it is possible to do so. The number of 

 the permissible states which possess the same total quantum 

 number will give the weight of the state. A corresponding- 

 rule holds for systems degenerate in three or more degrees 

 of freedom. 



The meaning of weight can perhaps be made clearer by 

 considering its introduction the other way round — beginning 

 with an assembly of simple quantized systems of various 

 frequencies. Griven the energy, there is a definite number 

 of possible states, which are fully specified by the energy 

 assigned to each system. We then make the hypothesis that 

 it is right to assign an equal probability to each such state 

 in the calculation of averages. This is now the fundamental 

 postulate. The generalization to degenerate systems goes as 

 before, by introducing weight factors. Finally, passing 

 over to mechanical systems, such as free molecules, we are 

 led by an appeal to the converse of the Correspondence 

 Principle to attach weight dq x . . . dp^/h 3 to each 6-dimen- 

 sional cell which specifies completely the state of a single 

 molecule. 



The second, statistical, half of the problem consists in 

 enumerating the various complexions possible to the assembly. 

 By a complexion we mean every arrangement of the assembly, 

 in which we are supposed to be able to distinguish the in- 

 dividuality of the separate systems. We count up the total 

 number of complexions which conform to any specified 

 statistical state of the assembly, and attach to each the 

 appropriate weight factor. Thus the probability of this state 

 is the ratio of the number of its weighted complexions to the 



* Bohr, loc. cit. p. 26. 



