J. W. Gihhs — Eqii'dihriiitii of Ileterof/e'neoiis Substances. 451 



discontinuity. [Compare (228) and (234).] * Since a phase cannot 

 vary continuously without vai'iations of the temperature or the 

 potentials, it follows from these conditions that the phase at any 

 point in a fluid system which has the same independently variable 

 components throughout, and is in equilibrium under the influence of 

 gravity, must be one of a certain number of phases which are com- 

 pletely determined by the phase at any given point and the difference 

 of level of the two points considered. If the phases throughout the 

 fluid system satisfy the general condition of practical stability for 

 phases existing in large masses (viz., that the ])ressure 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 210, where the subject is treated without 

 regard to the influence of the surfaces of discontinuity.) 



Cofiditions of eqiiilihriuiu 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 448. Those relating to the formation of new 

 masses and surfaces are included in the conditions of stability relat- 

 ing 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 for- 

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

 surface when two such masses meet (see j)ages 416-429), as well as 

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

 a surface of discontinuity. (See pages 400-403, 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 v>hole system. — Beside the 

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

 are substantially independent of the action of gravity, and are dis- 

 cussed elsewhere, there are other conditions, which relate to the 



* If the fluid system is divided iuto separate masses by solid diaphragms which are 

 permeable to all the components of the fluids independently, the conditions of equi- 

 librium of the fluids relating to temperature and the potentials will not be affected. 

 (Compare page 139.) The propositions which follow in the above paragraph may be 

 extended to this case. 



