450 J. TFI Gihhs — EqulUhriuin of Heterogeneous Substances. 



The mechanical conditions of equilibrium, however, have an espe- 

 cial importance, since we may always regard them as satisfied in any 

 liquid (and not decidedly viscous) mass in which no sensible motions 

 are observable. In such a mass, when isolated, the attainment of 

 mechanical equilibrium will take place very soon; thermal and chem- 

 ical equilibrium will follow more slowly. The thermal equ^ilibrium 

 will generally require less time for its approximate attainment than 

 the chemical ; but the processes by which the latter is produced will 

 generally cause certain inequalities of temperature until a state of 

 complete equilibrium is reached. 



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 pecu- 

 liar 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 temperature 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 

 coiirse be determined 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 sub- 

 sist 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 theo- 

 rems 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 condi- 

 tion of mechanical equilibrium (606), or by the application of ordi- 

 nary 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 

 teiMjierature and the potentials are not affected by the surfaces of 



