SURFACES OF DISCONTINUITY 619 



is also one of less energy — using the word "quasi-equilibrium" 

 to designate a state in which the equilibrium conditions for the 

 temperature and potentials are satisfied, but not the mechanical 

 condition which connects the difference of pressures in the two 

 phases with the tension and curvature. More than that, if 

 there is no quasi-equilibrium varied state which has less energy 

 than the unvaried state there is no non-equilibrium varied 

 state which has less energy; for as we have just seen if there 

 were one such non-equilibrium state there must be at least one 

 such quasi-equilibrium state. Thus if there is no equilibrium 

 state, or quasi-equilibrium state, infinitesimally near to the 

 given state which has a less energy than that state, it is one of 

 stable equilibrium. Now all such states, equilibrium or quasi- 

 equilibrium, are states for which e is given by the fundamental 

 expression in terms of the variables 77', 77", 77^, v', v", s, w/, 

 rrii', . . . , and so we can apply the analytical method of maxima 

 and mimima outlined above to the solution of the problem of the 

 stability of a given state, without concerning ourselves about the 

 mechanical equilibrium of the dividing surface in any adjacent 

 state. 



44- Illustration of Gibbs' Method by a Special Problem 



The problem with which Gibbs illustrates this method on 

 pages 249, 250 concerns the system which we have used, for 

 simplicity, to expound the method, with the limitation that the 

 edge of the surface of discontinuity is constrained not to move, 

 so that the two fluid phases are, as it were, separated by an orifice 

 to the edge of which the film adheres. The whole is enclosed 

 in a rigid, non-conducting envelop. Suppose a small variation 

 takes place from this condition of equilibrium, so that the 

 volumes change from v' and v" to u' + 8v' and v" + 8v''' where, 

 of course, 8v' + 8v" = 0. This will entail a change in the 

 position and size of the surface, its area becoming s + 8s. The 

 total quantity of any component remains unchanged, but the 

 potentials in the masses and at the surface change. Since the 

 first component has a given amount for the whole system 



liv' + 7i"v" + TiS = constant, 



