J. W. Gibhs — Equilibrium of Heteroyentous /Substances. 1)37 



We have supposed the solid to be homogeneous. But it is evident 

 that in any case the above conditions must hold for every separate 

 point where the solid meets the fluid. Hence, the temperature and 

 pressure and the potentials for all the actual components of the solid 

 must have a constant value in the solid at the surface where it meets 

 the fluid. Now, these quantities are determined by the nature and 

 state of the solid, and exceed in number the independent variations 

 of which its nature and state ai'e capable. Hence, if we reject as 

 improbable the supposition that the nature or state of a body can 

 vary Avithout affecting the value of any of these quantities, we may 

 conclude that a solid which varies (continuously) in nature or state 

 at its surface cannot be in equilibrium with a stable fluid which con- 

 tains, as independently variable components, the variable components 

 of the solid. (There may be, however, in equilibrium with the same 

 stable fluid, a finite number of different solid bodies, composed of the 

 variable components of the fluid, and having their nature and state 

 completely determined by the fluid.)* 



Effect of Additional Equations of Condition. 



As the equations of condition, of which we have made use, are 

 such as always apply to matter enclosed in a rigid, impermeable, and 

 non-conducting envelop, the particular conditions of equilibrium 

 which we have found will always be sufficient tor equilibrium. But 

 the number of conditions necessary for equilibrium, will be dimin- 

 ished, in a case otherwise the same, as the number of equations 

 of condition is increased. Yet the problem of equilibrium which has 

 been treated will sufficiently indicate the method to be pursued in all 

 cases and the general nature of the results. 



It will be observed that the position of the various homogeneous 

 parts of the given mass, which is otherwise immaterial, may deter- 

 mine the existence of certain equations of condition. Thus, when 

 difterent parts of the system in which a certain substance is a vari- 

 able component are entirely separated from one another by parts of 

 which this substance is not a component, the quantity of this sub- 

 stance will be invariable for each of the parts of the system which are 

 thus separated, which will be easily expressed by equations of condi- 

 tion. Other equations of condition may arise from the passive forces 

 .(or resistances to change) inherent in the given masses. In the prob- 



* The solid has been considered as subject only to isotropic stresses. The effect of 

 other stresses will be considered hereafter. 



Trans. Conn. Acad., Vol. III. 18 November, 1875. 



