52 Dr. Meyer Wilderman on the Velocity of 



each part of the heterogeneous system maybe either increased 

 or diminished). If we distinguish the letters referring to the 

 different parts by accents, the variation in the energy of the 

 system may be expressed by 8e ! + Be" +.'.., and the general 

 condition of equilibrium requires that 



Se' + Se" + . . . Ac. >0 



for all variations which do not conflict with the equations of 

 condition. These equations must express that the entropy of 

 the whole given mass does not vary, nor its volume, nor the 

 total quantities of any of the substances S 1? S 2 . • . S«. We 

 will suppose that there are no other equations of condition. 

 It will then be necessary for equilibrium that 



t'drf —p'dv' + Pi'dmi + fi2 / dm 2 / . . . +fM n 'dm n ! 

 + t»d V ,/ -p"dv // + iJL l "dm 1 // +fjL 2 "dm 2 " . . . + Mn n d?7i / ' n 



+ &c. >0 . . , . (15) 



for any values of the variations for which 



<V + <V' + di/"+ &c. =0, ... (16) 



dv' + dv" + dvP'+ &c. =0, ... (17) 



dm 1 , + dm^ + dmj u + &c. = 0, \ 



dmj + dm 2 + dm 2 w + &c. = 0, l 



(18) 



dm n ' + dmn" + dmj" + &c = 0. 



For this it is evidently necessary that 



t'=t"=t f " =&c (19) 



p>=p"=p"> =& c (20) 



^'=^'=^ =&c. \ 



/* 2 '=/V'=/V" =*o. ( 



fJLn' = fin" = ft,/" = &C. 



(21) 



Equations (19) and (20) express the conditions of thermal and 

 mechanical equilibrium, viz. that the temperature and the pressure 

 must be constant throughout the whole mass. In equations (21) 

 we have the conditions characteristic of chemical equilibrium. 

 If we call a quantity /x, as defined by such an equation as 

 (12), the potential for the substance m in the homogeneous 

 mass considered, these conditions may be expressed as 



