204 SYSTEMS COMPOSED OF MOLECULES. 



-^ = >7gen> (549) 



which corresponds to the equation 



we have i/^ = $ + log [v, 



and H-^^ n + ^ yi -- @ + . (551) 



This will have a maximum when * 



Distinguishing values corresponding to this maximum by 

 accents, we have approximately, when v l , . . . v h are of the 

 same order of magnitude as the numbers of molecules in ordi- 

 nary bodies, 



Q + /*iVi . . + ^ftVft Igen 



- -- 







2 \d vi d v 



(553) 



2 Vc?!'!^/ \</ 20 



'(554) 

 where (7 = Q + ^^" ^+ W " ^ (555) 



and A 1/1 = vi v/, A 1/2 = v 2 v 2 ', etc. (556) 



This is the probability of the system (^ . . . v h ). The prob- 

 abilty that the values of v 1 , . . . v h lie within given limits is 

 given by the multiple integral 



* Strictly speaking, rj/ gen is not determined as function of v 1} . . . v h , except 

 for integral values of these variables. Yet we may suppose it to be deter- 

 mined as a continuous function by any suitable process of interpolation. 



