202 SYSTEMS COMPOSED OF MOLECULES. 



From equation (539) we may get an idea of the order of 

 magnitude of the divergences of v l from its average value 

 in the ensemble, when that average value is great. The 

 equation may be written 





(541) 



The second member of this equation will in general be small 

 when j/j is great. Large values are not necessarily excluded, 

 but they must be confined within very small limits with re- 

 spect to /JL. For if 



(542) 



for all values of ^i between the limits /*/ and /-tj", we shall 

 have between the same limits 



dvi > cZ/xi , (543) 



and therefore 



/I 1 \ 



> m" - Hi'- (544) 



The difference /*/' ^ is therefore numerically a very small 

 quantity. To form an idea of the importance of such a 

 difference, we should observe that in formula (498) ^ is 

 multiplied by v 1 and the product subtracted from the energy. 

 A very small difference in the value of /^ may therefore be im- 

 portant. But since v <B) is always less than the kinetic energy 

 of the system, our formula shows that ^' //,/, even when 

 multiplied by vj or i^", may still be regarded as an insensible 

 quantity. 



We can now perceive the leading characteristics with re- 

 spect to properties sensible to human faculties of such an en- 

 semble as we are considering (a grand ensemble canonically 

 distributed), when the average numbers of particles of the vari- 

 ous kinds are of the same order of magnitude as the number 

 of molecules in the bodies which are the subject of physical 



