AND OF THE SECOND LAW 57 



Step a 



Determination of the Number of Complexions of a given Physical 

 Configuration of a Known Macrostate 



We will, for simplicity's sake, consider here an ideal gas in a 

 given macrostate and consisting of A7"-like, monatomic, molecules. 

 By generalizing the meaning of our co-ordinates, the following 

 presentation could be made equally applicable to the more general 

 case of Physics contemplated under this heading. 



Of course we must here have clearly in mind what is meant 

 by the state of a gas. For this we may refer to p. 10 (lines 13 to 24) 

 and to p. 19 (lines 8 to 24). The conditions there imposed 

 are all fulfilled if we suppose the state given in such a way that 

 we know: (i) The number of molecules in any macroscopically 

 small space (volume element); and (2) the number of molecules 

 which lie in a certain macroscopically small velocity region (soon 

 to be more fully described). To have the Calculus of Probabilities 

 applicable, each of the tiny regions contemplated under (i) and (2) 

 must still contain a large number of molecules and their motions 

 must besides have all the features of haphazard detailed on pp. 

 25, 26; all this is necessary in order that the contemplated 

 motions may possess all the characteristics of " elementary chaos." 



Before proceeding further on our main line, we will define 

 more fully what is meant by the two elementary regions in which 

 lie respectively the molecules and their velocity ends. After 

 this has been done we will, for convenience, combine these two 

 regions into a fictitious elementary region, say, a six-dimensional 

 one. 



First there is the volume element dx-dy-dz^dV, in which 



(x and x + dx 1 

 y and y + dy \ 

 z and z-\-dz J 

 is located; this element can be conceived as a parallelopipedon 



