284 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



When a surface of discontinuity has more components than one 

 which do not occur in the contiguous masses, the adjustment of the 

 potentials for these components in accordance with equations (617) 

 may take place very slowly, or not at all, for want of sufficient 

 mobility in the components of the surface. But when this surface 

 has only one component which does not occur in the contiguous 

 masses, and the temperature and potentials in these masses satisfy 

 the conditions of equilibrium, the potential for the component peculiar 

 to the surface will very quickly conform to the law expressed in (617), 

 since this is a necessary consequence of the condition of mechanical 

 equilibrium (614) in connection with the conditions relating to tem- 

 perature and the potentials which we have supposed to be satisfied. 

 The necessary distribution of the substance peculiar to the surface 

 will be brought about by expansions and contractions of the surface. 

 If the surface meets a third mass containing this component and no 

 other which is foreign to the masses divided by the surface, the 

 potential for this component in the surface will of course be deter- 

 mined by that in the mass which it meets. 



The particular conditions of mechanical equilibrium (612)-(615), 

 which may be regarded as expressing the relations which must subsist 

 between contiguous portions of a fluid system in a state of mechanical 

 equilibrium, are serviceable in determining whether a given system 

 is or is not in such a state. But the mechanical theorems which 

 relate to finite parts of the system, although they may be deduced 

 from these conditions by integration, may generally be more easily 

 obtained by a suitable application of the general condition of 

 mechanical equilibrium (606), or by the application of ordinary 

 mechanical principles to the system regarded as subject to the forces 

 indicated by this equation. 



It will be observed that the conditions of equilibrium relating to 

 temperature and the potentials are not affected by the surfaces of 

 discontinuity. {Compare (228) and (234). }* Since a phase cannot 

 vary continuously without variations 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 

 completely determined by the phase at any given point and the 

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



* If the fluid system is divided into 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 84.) The propositions which follow in the above paragraph may be 

 extended to this case. 





