EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 151 



appearing in any other form or combination, but solely as constituting 

 the gas in question (in a state of purity), we may without loss of 

 generality give to E and H the value zero, or any other arbitrary 

 values. But when the scope of our investigations is not thus limited 

 we may have determined the states of the substance of the gas for 

 which e = and ij = Q with reference to some other form in which the 

 substance appears, or, if the substance is compound, the states of its 

 components for which e = and r\ = may be already determined ; so 

 that the constants E and H cannot in general be treated as arbitrary. 

 We obtain from (255) by differentiation 



c j 1 j a j , / C E , c+a H\j 

 --de = dr] dv + ( & + - --- -Jdm, (256) 

 e Em m v \e-Em m m 2 / 



whence, in virtue of the general relation expressed by (86), 



( 258 > 



T}). (259) 



We may obtain the fundamental equation between \fs } t, v, and m 

 from equations (87), (255), and (257). Eliminating e we have 



\fs = Em + cmt tq, 



and clog = H+alog ; 



m ' v ' 



and eliminating rj, we have the fundamental equation 



. (260) 



Differentiating this equation, we obtain 



= m(.Z/+clog+alo )dt -- dv 

 \ 5 ra/ v 



(261) 

 whence, by the general equation (88), 



r+clog+alog ), (262) 



f rfii/ 



amt 



p= 



V ' 



\ (264) 



v / 



