EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 285 



throughout the fluid system satisfy the general condition of practical 

 stability for phases existing in large masses (viz., that the pressure 

 shall be the least consistent with the temperature and potentials), 

 they will be entirely determined by the phase at any given point and 

 the differences of level. (Compare page 149, where the subject is 

 treated without regard to the influence of the surfaces of discon- 

 tinuity.) 



Conditions of equilibrium relating to irreversible changes. The 

 conditions of equilibrium relating to the absorption, by any part of 

 the system, of substances which are not actual components of that part 

 have been given on page 282. Those relating to the formation of 

 new masses and surfaces are included in the conditions of stability 

 relating to such changes, and are not always distinguishable from 

 them. They are evidently independent of the action of gravity. We 

 have already discussed the conditions of stability with respect to 

 the formation of new fluid masses within a homogeneous fluid and at 

 the surface when two such masses meet (see pages 252-264), as well 

 as the condition relating to the possibility of a change in the nature 

 of a surface of discontinuity. (See pages 237-240, where the surface 

 considered is plane, but the result may easily be extended to curved 

 surfaces.) We shall hereafter consider, in some of the more import- 

 ant cases, the conditions of stability with respect to the formation 

 of new masses and surfaces which are peculiar to lines in which 

 several surfaces of discontinuity meet, and points in which several 

 such lines meet. 



Conditions of stability relating to the whole system. Besides the 

 conditions of stability relating to very small parts of a system, 

 which are substantially independent of the action of gravity, and 

 are discussed elsewhere, there are other conditions, which relate to 

 the whole system or to considerable parts of it. To determine the 

 question of the stability of a given fluid system under the influence 

 of gravity, when all the conditions of equilibrium are satisfied as 

 well as those conditions of stability which relate to small parts of 

 the system taken separately, we may use the method described on 

 page 249, the demonstration of which (pages 247, 248) will not 

 require any essential modification on account of gravity. 



When the variations of temperature and of the quantities M lt M 2 , 

 etc. {see (617)} involved in the changes considered are so small that 

 they may be neglected, the condition of stability takes a very simple 

 form, as we have already seen to be the case with respect to a 

 system uninfluenced by gravity. (See page 251.) 



We have to consider a varied state of the system in which the 

 total entropy and the total quantities of the various components are 

 unchanged, and all variations vanish at the exterior of the system, 



