62 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



the digit row will have a particular number of places (io = N). 

 Besides, since the number of molecules belonging to each elemen- 

 tary space is given, each digit will occur equally often in the row 

 in all permissible complexions. Moreover every change in digit 

 arrangement effects a new complexion. The number of the 

 possible complexions or the probability W of the given state is 

 therefore equal, under the conditions specified, to the possible 

 "permutations with repetition." 1 In the simple example chosen 

 we have for such permutation, according to a known formula, 



10! 



3 ! 4 !o! i!o! 

 Consequently in the general case, we have 



where the sign n signifies the product extended over all the P 

 elementary regions. 



Result contained in (16) is equally true for any other physical 

 system, say, one involving radiant energy. For the conditions 

 and the variables are similar to those of the molecular system 

 just employed. The chosen model, the dice system, which served 

 as an easily conceived parallel case, would be equally serviceable 

 in dealing with the elements of radiation. 



1 Compare with pp. 27 and 28 where this permutation process is discussed some- 

 what fully. 



