SYSTEMS COMPOSED OF MOLECULES. 



205 



20 dvi ...dv h . 

 (557) 



Tliis shows that the distribution of the grand ensemble with 

 respect to the values of v v . . . v h follows the " law of errors " 

 when i/j', . . . v h ' are very great. The value of this integral 

 for the limits oo should be unity. This gives 



or 



6 cMI = i, 



ilogi>-|log(2 ff ), 



where D = 



V 



/ dVn.V 

 Wviflfow 



that is, D = 



(558) 



(559) 



'(560) 



(561) 



Now, by (553), we have for the first approximation 



H - ^ gen = C = 1 log D - | log (2ir0), (562) 



and if we divide by the constant JT,* to reduce these quanti- 

 ties to the usual unit of entropy, 



H - ^gen = ^g J> ~ h log (27T@) 



.ST 2 JL 



* See page 184-186. 



