356 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



are most simple and most general in their definitions, and which 

 appear most important in the general theory of such systems. The 

 slightly different form in which the subject would develop itself, 

 if condition (4) had been chosen as a point of departure instead of (2), 

 is occasionally indicated. 



Equilibrium of masses in contact. The first problem to which 

 the criterion is applied is the determination of the conditions of 

 equilibrium for different masses in contact, when uninfluenced by 

 gravity, electricity, distortion of the solid masses, or capillary tensions. 

 The statement of the result is facilitated by the following definition. 



If to any homogeneous mass in a state of hydrostatic stress we 

 suppose an infinitesimal quantity of any substance to be added, the 

 mass remaining homogeneous and its entropy and volume remaining 

 unchanged, the increase of the energy of the mass divided by the 

 quantity of the substance added is the potential for that substance in 

 the mass considered. 



In addition to equality of temperature and pressure in the masses 

 in contact, it is necessary for equilibrium that the potential for every 

 substance which is an independently variable component of any of 

 the different masses shall have the same value in all of which it is 

 such a component, so far as they are in contact with one another. 

 But if a substance, without being an actual component of a certain 

 mass in the given state of the system, is capable of being absorbed 

 by it, it is sufficient if the value of the potential for that substance 

 in that mass is not less than in any contiguous mass of which the 

 substance is an actual component. We may regard these conditions 

 as sufficient for equilibrium with respect to infinitesimal variations 

 in the composition and thermodynamic state of the different masses 

 in contact. There are certain other conditions which relate to the 

 possible formation of masses entirely different in composition or state 

 from any initially existing. These conditions are best regarded as 

 determining the stability of the system, and will be mentioned under 

 that head. 



Anything which restricts the free movement of the component 

 substances, or of the masses as such, may diminish the number of 

 conditions which are necessary for equilibrium. 



Equilibrium of osmotic forces. If we suppose two fluid masses 

 to be separated by a diaphragm which is permeable to some of the 

 component substances and not to others, of the conditions of equi- 

 librium which have just been mentioned, those will still subsist which 

 relate to temperature and the potentials for the substances to which 

 the diaphragm is permeable, but those relating to the potentials for 

 the substances to which the diaphragm is impermeable will no longer 

 be necessary. Whether the pressure must be the same in the two 



