﻿On the Partition of Eneryy. 451 



new ; it is the point of view and the method which, we 

 think, differ from previous treatments 



No discussion of the question of' partition would be com- 

 plete without consideration of its relation to thermodynamic 

 principles. We shall leave this view of the subject to a 

 future paper ; for the iucreased light thrown on the statistical 

 nature of entropy raises many interesting points which could 

 not be discussed here properly without making the present 

 work run to inordinate length. 



§ 2. Statistical Principles and Weiyht. 



Before proceeding to the problem it will be well to review, 

 in general outline, the principles of the theory of the 

 partition of energy, though we have nothing new to say in 

 this connexiou. We shall be concerned with collections of 

 molecules, Planck vibrators, etc. — each individual unit will 

 be called a system, and we shall call the whole collection an 

 ■assembly. We shall be dealing mainly with assemblies com- 

 posed of groups of systems, the individuals in each group 

 being identical in nature. In order to make the problem 

 definite it is necessary to assume that each system has 

 a definite assignable energy, and yet can interact with the 

 others. This requires that the time of interactions, during 

 which there will be energy which cannot be assigned to a 

 definite single system, is negligibly small compared with 

 the time during which each system describes its own 

 motion. 



For such an assembly we are to calculate various average 

 properties of its state, when it describes its natural motion 

 according to whatever laws it may obey. There will at any 

 rate be an energy integral, and we have therefore to calcu- 

 late these averages subject to the condition of constant 

 energy. To determine the basis on which these averages 

 are to be calculated we are to apply the principles of proba- 

 bility ; and the calculation of itself falls into two stages, the 

 prior and the statistical. The prior stage aims at establishing 

 what are the states which are to be taken as of equal 

 probability. In the statistical stage we have simply to 

 enumerate the states specified in the prior stage, allow for 

 the fact that the systems are macroscopically indistin- 

 guishable, and evaluate the averages taken over these 

 states. 



It is not here our purpose to enter into a full discussion 

 of the fundamental questions that arise in connexion with 

 the determination of what states ought to be taken as equally 



2 G2 



