146 BUTLER ART. D 



can be expressed by the conditions that it shall be possible to 

 give to T, P, Mi,...Mn in 



6 - Tr? + Py - MiWi - MiTTh ... - MrMn (199) 



such values that the value of this expression shall be zero for 

 every homogeneous part of the system. The equilibrium is 

 practically stable if 



^ ^ Tt) -\- Pv - Mimi - M^m^i ... - M„m„ ^ (200) 



for any other body which may be formed from the same com- 

 ponents, and this condition may be united with the former one 

 in the statement that it shall be possible to give T, P, Mi,. .. 

 Mn such values that the value of (200) for each homogeneous 

 part of the system shall be as small as for any body whatever 

 made of the same components. 



IX. The Internal Stability of Homogeneous Fluids* 



26. General Tests of Stahility. Consider a homogeneous 

 fluid, the ultimate components *Si, S2, . . . *S„ of which are pres- 

 ent in the amounts mi, TO2, . . . m„. The conditions imposed 

 in deducing the conditions of equilibrium are fulfilled if we 

 suppose that the fluid is contained in a rigid envelop which 

 is a non-conductor of heat and impervious to all its com- 

 ponents. The conditions (199) and (200) might be employed 

 to determine the stabflity of the fluid, but it is desirable to 

 formulate them in a somewhat more general manner, since 

 for the stability of the fluid it is necessary that it shall be in 

 equilibrium both with respect to the formation of new parts as 

 defined in the last section, and also with respect to the forma- 

 tion of phases which may only differ infinitesimally from the 

 original phase of the body. Gibbs states the condition of 

 stability as follows: 



"7/ it is possible to assign such values to the constants T, P, 

 Ml, Ml, . . .Mn that the value of the expression 



^ - T-n + Pv - MiWi - M^nh ... - Mnrrin (201) [133] 



* Gibbs, I, 100-105. 



