J. W. Gihbs — Eqxiilihrium of Heterogeneous Substances. 133 



value of (57). for u body consisting of masses like O' and 0" sepa- 

 rated by a lamina i\^. This value may be decreased by^increasing 

 the extent of this lamina, which may be done within a given volume 

 by giving it a convoluted form ; and it will be evident, as before, 

 that the least possible value of (57) will be for a homogeneous mass, 

 and that the value will be negative. And such a mass will be not 

 merely an ideal combination, but a body capable of existing, for as the 

 expression (57) has for this mass in the state considered its least pos- 

 sible value per unit of volume, the energy of the mass included in a 

 unit of volume is the least possible for the same matter with the 

 same entropy and volume, — hence, if confined in a non-conducting 

 vessel, it will be in a state of not unstable equilibrium. Therefore 

 when (50), (51), and (43) are satisfied, if the condition (52) is not sat- 

 isfied in regard to all possible new parts, there will be some homo- 

 geneous body which can be formed out of the substances aS'^, ^Sg, . . . 

 S„ which will not satisfy condition (53). 



Therefore, if the initially existing masses satisfy the conditions 

 (50), (51), and (43), and condition (53) is satisfied by every homoge- 

 neous body which can be formed out of the given matter, there will 

 be equilibrium. 



On the other hand, (53) is not a necessary condition of equilibrium. 

 For we may easily conceive that the condition (52) shall hold true 

 (for any very small formations within or between any of the given 

 masses), while the condition (53) is not satisfied (for all large masses 

 formed of the given matter), and experience shows that this is very 

 often the case. Supersaturated solutions, superheated water, etc., 

 are familiar examples. Such an equilibrium will, however, be practi- 

 cally unstalde. By this is meant that, although, strictly speaking, 

 an infinitely small disturbance or change may not be suflicient to 

 destroy the equilibrium, yet a very small change in the initial state, 

 perhaps a circumstance which entirely escapes our powers of percep- 

 tion, will be sufficient to do so. The presence of a small portion of 

 the substance for which tlie condition (53) does not hold true, is suffi- 

 cient to produce this result, when this substance forms a variable 

 component of the original homogeneous masses. In other cases, 

 when, if the new substances are formed at all, different kinds must be 

 formed simultaneously, the initial presence of the different kinds, 

 and that in immediate proximity, may be necessary. 



It will be observed, that from (56) and (53) we can at once obtain 

 (50) and (51), viz., by applying (53) to bodies differing infinitely 

 little from the various homogeneous ])arts of the given mass. There- 



