﻿838 Messrs. C.-Gr. Darwin and R. H. Fowler on 

 The characteristic function has the properties 



E = T 2 |J ( 8 ' 2 ) 



S =V + T0, ..... (8-21) 



x r T fei' (8 ' 22) 



an 



Definition. — The characteristic function for any part of 

 assembly is k times the sum of the logarithms of the partition 

 functions of all the component systems of the fart when the 

 argument of the partition functions is S = £~ 1///cT . 



With this definition we can show at once that the thermo- 

 dynamic processes are mathematically equivalent to those 

 we have been carrying out from the statistic. 1 point of view. 

 There is no need to repeat the work, as the mere change 

 from T to S exactly transforms (8'2), (8*21), (8'22) into 

 .(7-11), (7-6), (7 3) if ^ = ^MJog/ r (^,^,^;.. ). 



The characteristic function contains two arbitrary con- 

 stants, which occur in the form S — E /T. Of these, E is 

 seen to correspond to the arbitrary zero of the energy of the 

 systems, which appears in each exponent of the partition 

 function. The constant S depends on the absolute values 

 adopted for the weight factors. We have made the con- 

 vention of taking this as unity for simple quantized systems; 

 but it is only a convention, and quite without effect on the 

 various average values, which are all that ( an ever be 

 observed. Indeed, the only conditions attaching to the 

 weight factors are precisely analogous to those attaching to 

 entropy in classical thermodynamics — a definite ratio is 

 required between the weights of states of systems which 

 can pass from one to the other (as in the dissociation of 

 molecules); — but as long as two systems are mutually not 

 convertible into one another, it makes absolutely no difference 

 what choice is made tor their relative weights. 



Many writers have attempted to give reality to the con- 

 vention that weight has an absolute value, and from it have 

 defined absolute entropy. Such a definition cannot possibly 

 make any difference in any thermodynamic results ; but the 

 object was mainly to deal with the Nernst Heat Theorem, 

 and there it has been successful. It is, however, much more 

 rational to do without this somewhat mystical idea, and to 

 suppose that the theorem is a consequence of the equality of 

 weights of any allotropic forms in the states of lowest energy 



