J. W. Gihhs — Eqidllhriiua of Iltterogeneous /Substances. 2 I 7 



H-i—Cj—a., c^ l^i—E.2 )■ 



etc. 



(275) 



Equations (275) indicate that the relation between the temperature, 

 the density of any compcfnent, and the potential for that component, is 

 not aifected by the presence of the other components. They may 

 also be written 



etc. ) 



Eliminating yu,, /<2, etc. from (273) and (274) by means of (275) 

 and (276), we obtain 





(277) 



7= ^lyn^ir^ +M,c,log «+m,«ilog ^j. 



(278) 



E({uation (277) expresses the familiar principle that the pressure in a 

 gas-mixture is equal to the sum of the pressures which the component 

 gases would possess if existing separately with the same volume at 

 the same temperature. Equation (278) expresses a similar principle 

 in regard to the entropy of the gas-mixture. 



From (276) and (277) we may easily obtain the fundamental equa- 

 tion between //', t, v, m^^ ni^, etc. For by substituting in (94) the 

 values of jo, ji^, /.i^, etc. taken from these equations, we obtain 



'p=2^(^£.\m,-\-m^t | c, -^, -c.log « + «,log "^j). (279) 



If we regard the proportion of the various components as constant, 

 this equation may be simplified by writing 



m for ^j wZj, 

 c m for ^ J (c , m J ), 

 am for 2^ (a^m^), 

 Em for ^j (£', mj), 

 and Hm-am log m for ^j (H^ m^—a^ m^ log rn^). 



The values of c, a, -E, and JT, will then be constant and m will denote 

 the total quantity of gas. As the equation Avill thus be reduced to the 

 Trans. Conn. Acad., Vol. III. 28 April, 1876. 



