IV. 



ON THE EQUILIBRIUM OF HETEROGENEOUS 



SUBSTANCES. 



ABSTRACT OF THE PRECEDING PAPER BY THE AUTHOR. 

 [American Journal of Science, 3 ser., vol. xvi., pp. 441-458, Dec., 1878.] 



IT is an inference naturally suggested by the general increase of 

 entropy which accompanies the changes occurring in any isolated 

 material system that when the entropy of the system has reached a 

 maximum, the system will be in a state of equilibrium. Although 

 this principle has by no means escaped the attention of physicists, 

 its importance does not appear to have been duly appreciated. Little 

 has been done to develop the principle as a foundation for the general 

 theory of thermodynamic equilibrium. 



The principle may be formulated as follows, constituting a criterion 

 of equilibrium : 



I. Far the equilibrium of any isolated system it is necessary and 

 sufficient that in all possible variations of the state of the system 

 which do not alter its energy, the variation of its entropy shall 

 either vanish or be negative. - 



The following form, which is easily shown to be equivalent to the 

 preceding, is often more convenient in application : 



II. For the equilibrium of any isolated system it is necessary and 

 sufficient that in all possible variations of the state of the system 

 which do not alter its entropy, the variation of its energy shall 

 either vanish or be positive. 



If we denote the energy and entropy of the system by e and r\ 

 respectively, the criterion of equilibrium may be expressed by either 

 of the formulae 



W.^o, (i) 



(*e),0. (2) 



Again, if we assume that the temperature of the system is uniform, 

 and denote its absolute temperature by t, and set 



^ = -fy, (3) 



the remaining conditions of equilibrium may be expressed by the 

 formula 



O, (4) 



