SYSTEMS COMPOSED OF MOLECULES. 193 



The value of e p is of course zero in this case. But the 

 value of e q contains an arbitrary constant, which is generally 

 determined by considerations of convenience, so that e g and e 

 do not necessarily vanish with v^ , . . . v h . 



Unless II has a finite value, our formulae become illusory. 

 We have already, in considering petit ensembles canonically 

 distributed, found it necessary to exclude cases in which ty 

 has not a finite value.* The same exclusion would here 

 make ^r finite for any finite values of v l . . . v h . This does 

 not necessarily make a multiple series of the form (506) finite. 

 We may observe, however, that if for all values of v l . . . v h 



\l/ ^. CQ + ^1 Vl) 4" C h V ht (507) 



where , c v . . . c h are constants or functions of , 



Co-MMl+CjK . . . -K/*A+C A V A 



e 



^ 



_n p 

 & e 



O. c_ 

 0^0 



. . . e 



-+ e .-. + e (508) 



The value of II will therefore be finite, when the condition 

 (507) is satisfied. If therefore we assume that fl is finite, 

 we do not appear to exclude any cases which are analogous to 

 those of nature.f 



The interest of the ensemble which has been described lies 

 in the fact that it may be in statistical equilbrium, both in 



* See Chapter IV, page 35. 



t If the external coordinates determine a certain volume within which the 

 system is" confined, the contrary of (507) would imply that we could obtain 

 an infinite amount of work by crowding an infinite quantity of matter into a 

 finite volume. 



13 



