J. ir. Gihhs — Equilibrium of Heterogeneous Substances. 115 



quantity which is not infinitely small relatiA^ely to the variations 

 of the quantities which determine tlie state of the system, without 

 altering its entropy,— or, if the system has thermally isolated parts, 

 without altering the entropy of any such part, — this variation 

 involves changes in the system which are prevented by its passive 

 forces or analogous resistances to change. Now, as the described 

 variation in the state of the system diminishes its energy without 

 altering its entropy, it must be regarded as theoretically possible to 

 produce that variation by some process, perhaps a very indirect one, 

 so as to gain a certain amount of work (above all expended on the 

 system). Hence we may conclude that the active forces or tenden- 

 cies of the system favor the variation in question, and that equi- 

 librium cannot subsist unless the variation is prevented by passive 

 forces. 



The preceding considerations will suffice, it is believed, to establish 

 the validity of the criterion of equilibrium which has been given. 

 The criteria of stability may readily be deduced from that of equi- 

 librium. We will now proceed to apjily these principles to systems 

 consisting of heterogeneous substances and deduce the special laws 

 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 EQUILIBRIUiNt FOR HETEROGENEOUS MASSES IN 



CONTACT WHEN UNIXFLtTENCED BY GRAVITY, ELECTRICITY, DISTORTION 



OF THE SOLID MASSES, OR CAPILLARY TENSIONS. 



In order to arrive as directly as })ossible 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. 



