AND OF THE SECOND LAW 61 



to the circumstance that each individual molecule is equally 

 likely to belong to any one of the elementary regions. The 

 desired probability W of the given state of the molecules corre- 

 sponds therefore to the number of different kinds of throws (com- 

 plexions), by which the given distribution / can be realized. 

 For example, if we take N=io molecules (dice) and P = 6 

 elementary regions (dice faces), and assume that the state is so 

 given that it is represented by: 



3 molecules in elementary region i 



4 " " " 2 



" 3 



1 " 4 

 o " " " 5 



2 " " " 6 



Then this state can be realized by one throw, in which the 10 

 dice show the following digits: 



ist 2d 3d 4th sth 6th 7th 8th 9th loth die 



the 2621126214 digit (15) 



Under each of the 10 dice stands the digit shown uppermost 

 in the throw. In fact, we see 



3 dice with digit i 



4 " " 2 



" " 3 



1 4 

 o " " 5 



2 " 6 



In like manner the same state can be realized by many other 

 such complexions. The desired number of all possible complex- 

 ions can be found by considering the digit row designated above 

 by (15). For, since the number of molecules (dice) is given, 



