SYSTEMS COMPOSED OF MOLECULES. 201 



If we compare the statistical equations (529) and (532) 

 with (114) and (112), which are given in Chapter IV, and 

 discussed in Chapter XIV, as analogues of thermody- 

 namic equations, we find considerable difference. Beside the 

 terms corresponding to the additional terms in the thermo- 

 dynamic equations of this chapter, and beside the fact that 

 the averages are taken in a grand ensemble in one case 

 and in a petit in the other, the analogues of entropy, H 

 and ?/, are quite different in definition and value. We shall 

 return to this point after we have determined the order 

 of magnitude of the usual anomalies of v v ... v h . 



If we differentiate equation (518) with respect to /ii, and 

 multiply by <H), we get 



"0* h b. " = 0? (536) 



whence dtl/d^ = v v which agrees with (527). Differen- 

 tiating again with respect to t a v and to /* 2 , and setting 



we get 



- _, _ to. . ^ rf^% 



| vi 



= 0) (537) 



The first members of these equations represent the average 

 values of the quantities in the principal parentheses. We 

 have therefore 



, = ^ , (539) 



= ^r = lr- ( 54 ) 



