J. ^V. Glbbs — Equllihriioti of Ileievogeneous SuhsUtvces. 229 



but which sliouhl differ in respect to the attractions between tlieir 

 atoms antl the atoms of some other substances, and therefore in tlieir 

 tendency to combine Mith such sul)stances. In tlie mixture of such 

 gases by diffusion an increase of entropy wouhl take ))hice, although 

 the process of mixture, dynamically considered, might be absolutely 

 identical in its minutest details (e\ en with i-espect to the i)recise path 

 of each atom) with processes which might take ]>lace without any 

 increase of entropy. In sucli respects, entropy stands strongly con- 

 trasted with energy. Again, when such gases have been mixed, there 

 is no more irapossil)ility of the separation of the two kinds of molecules 

 in virtue of their ordinary motions in the gaseous mass without any 

 especial external influence, than there is of the separation of a lumio- 

 geneous gas into the same two parts into which it has once been 

 divided, after tliese have once been mixed. In other words, the 

 impossibility of an uncompensated decrease of entropy seems to be 

 reduced to improbability. 



There is perhaps no fact in tlie molecular theory of gases so well 

 established as that the number of molecules in a given volume at a 

 given temperature and .pressure is the same for every kind of gas 

 when in a state to which the laws of ideal gases apply. Hence the 



quantity — — in (297) must be entirely determined by the number of 



molecules which are mixed. And the increase of entropy is therefore 

 determined by the number of these molecules and is independent of 

 their dynamical condition and of the degree of difference between 

 them. 



The result is of the same nature when the volumes of the gases 

 which are mixed are not equal, and when more than two kinds of gas 

 are mixed. If we denote by v^, v^? etc., the initial volumes of the 

 different kinds of gas, and by V as before the total volume, the 

 increase of entropy may be written in the form 



:E^ {m^ a^) log V- :S^ {m, a, logy J. 

 And if we denote by r,, rg, etc., the numbers of the molecules of the 

 several different kinds of gas, we shall have 



r^ = (Jm^ «!, ?'2 = Cm^ a.^, etc., 

 where (J denotes a constant. Hence 



V ^:V:: m^a^ : 2 ^{m^a.^) ::1\ : ^, r^ ; 

 and the increase of entropy may be written 



^^^ilog^i^i -^i(^ilog^i) ^ (298) 



C 



