62 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



which apply to different classes of phenomena. For this purpose we 

 shall use the second form of the criterion of equilibrium, both because 

 it admits more readily the introduction of the condition that there 

 shall be no thermal communication between the different parts of the 

 system, and because it is more convenient, as respects the form of 

 the general equations relating to equilibrium, to make the entropy 

 one of the independent variables which determine the state of the 

 system, than to make the energy one of these variables. 



The Conditions of Equilibrium for Heterogeneous Masses in 

 Contact when Uninfluenced by Gravity, Electricity, Distortion 

 of the Solid Masses, or Capillary Tensions. 



In order to arrive as directly as possible at the most characteristic 

 and essential laws of chemical equilibrium, we will first give our 

 attention to a case of the simplest kind. We will examine the con- 

 ditions of equilibrium of a mass of matter of various kinds enclosed 

 in a rigid and fixed envelop, which is impermeable to and unalter- 

 able by any of the substances enclosed, and perfectly non-conducting 

 to heat. We will suppose that the case is not complicated by the 

 action of gravity, or by any electrical influences, and that in the 

 solid portions of the mass the pressure is the same in every direction. 

 We will farther simplify the problem by supposing that the varia- 

 tions of the parts of the energy and entropy which depend upon the 

 surfaces separating heterogeneous masses are so small in comparison 

 with the variations of the parts of the energy and entropy which 

 depend upon the quantities of these masses, that the former may be 

 neglected by the side of the latter ; in other words, we will exclude 

 the considerations which belong to the theory of capillarity. 



It will be observed that the supposition of a rigid and non- 

 conducting envelop enclosing the mass under discussion involves no 

 real loss of generality, for if any mass of matter is in equilibrium, it 

 would also be so, if the whole or any part of it were enclosed in an 

 envelop as supposed; therefore the conditions of equilibrium for a 

 mass thus enclosed are the general conditions which must always 

 be satisfied in case of equilibrium. As for the other suppositions 

 which have been made, all the circumstances and considerations 

 which are here excluded will afterward be made the subject of 

 special discussion. 



Conditions relating to the Equilibrium between the initially existing 

 Homogeneous Parts of the given Mass. 



Let us first consider the energy of any homogeneous part of the 

 given mass, and its variation for any possible variation in the com- 



