92 BUTLER ART. D 



IV. The Conditions of Equilibrium between Initially Existent 

 Parts of a Heterogenous System* 



9. General Remarks. Gibbs first considers the equilibrium of 

 heterogeneous systems when uninfluenced by gravity, by 

 external electric forces, by distortion of the solid bodies, or by 

 the effects of surface tension. A mass of matter of various 

 kinds, the conditions of equilibrium of which are to be deter- 

 mined, is supposed to be "enclosed in a rigid and fixed envelop, 

 which is impermeable to and unalterable by any of the sub- 

 stances enclosed, and perfectly non-conducting to heat." It is 

 supposed that there are no non-isotropic strains in the solid 

 bodies, and that the variations of energy and entropy which 

 depend on the surfaces separating the heterogeneous mass are 

 so small in comparison with those which depend on the masses 

 themselves that they may be neglected. The effects excluded 

 here are examined in detail in later parts of the Memoir. 



Gibbs points out that "the supposition of a rigid and non- 

 conducting envelop enclosing the mass under discussion involves 

 no real loss of generality, for if any mass of matter is in equilib- 

 rium, it would also be so, if the whole or any part of it were 

 enclosed in an envelop as supposed; therefore the conditions of 

 equilibrium for a mass thus enclosed are the general conditions 

 which must always be satisfied in case of equilibrium." The use 

 of such an envelop ensures that the volume of the system remains 

 constant and that no heat is received from or given up to any 

 outside bodies. Since a system which is in equilibrium cannot 

 undergo any irreversible change, its entropy must, under these 

 conditions, remain constant. 



In the first place, the conditions relating to the equilibrium 

 between initially existing homogeneous parts of the mass are 

 examined; the conditions for the formation of masses unlike 

 any previously existing are discussed in a later section. 



10. Conditions of Equilibrium When the Component Substances 

 Are Independent of Each Other. ■\ Let the energies of the 

 separate homogeneous parts of the system be e', e" etc. 



♦Gibbs, I, 62-70. 

 t Gibbs, I, 62^67. 



