206 SYSTEMS COMPOSED OF MOLECULES. 



This is evidently a negligible quantity, since K is of the same 

 order of magnitude as the number of molecules in ordinary 

 bodies. It is to be observed that ?7 gen is here the average in 

 the grand ensemble, whereas the quantity which we wish to 

 compare with H is the average in a petit ensemble. But as we 

 have seen that in the case considered the grand ensemble would 

 appear to human observation as a petit ensemble, this dis- 

 tinction may be neglected. 



The differences therefore, in the case considered, between the 

 quantities which may be represented by the notations * 



H * en [grand ^* en (grand ' ^^ Ipetit 



are not sensible to human faculties. The difference 



and is therefore constant, so long as the numbers z> 1? . . . v h 

 are constant. For constant values of these numbers, therefore, 

 it is immaterial whether we use the average of rj gen or of 77 for 

 entropy, since this only affects the arbitrary constant of in- 

 tegration which is added to entropy. But when the numbers 

 v v . . . v h are varied, it is no longer possible to use the index 

 for specific phases. For the principle that the entropy of any 

 body has an arbitrary additive constant is subject to limi- 

 tation, when different quantities of the same substance are 

 concerned. In this case, the constant being determined for 

 one quantity of a substance, is thereby determined for all 

 quantities of the same substance. 



To fix our ideas, let us suppose that we have two identical 

 fluid masses in contiguous chambers. The entropy of the 

 whole is equal to the sum of the entropies of the parts, and 

 double that of one part. Suppose a valve is now opened, 

 making a communication between the chambers. We do not 

 regard this as making any change in the entropy, although 

 the masses of gas or liquid diffuse into one another, and al- 

 though the same process of diffusion would increase the 



* In this paragraph, for greater distinctness, H gen | grand and %p^l petit have 

 been written for the quantities which elsewhere are denoted by H and rf. 



