J. W. (ribbs — Eqiiilibriiim of Heterogeneous ^<ubstances. 2;j3 



suppositions otherwise tlie same), we shall have for infinitesimal 

 values of ^ an infinitesimal value either of w/ , or Wig, and for infinite 

 values of t finite or infinitesimal values of rit^ according as /j, -|- /i^ 

 is equal to or greater than unity. 



The case which we have considered is that of a ternary gas-mix- 

 ture, but our results may easily be generalized in this respect. In 

 fact, whatever the number of component gases in a gas-mixture, if 

 there are relations of equivalence in ultimate analysis l)etween these 

 components, such relatioTis may be expressed by one or more equa- 

 tions of the form 



A , (S^ , + A2 C'^io + A 3 (SV^ + etc. in 0, (31 1) 



where @j, (S^g? ^^c. denote the units of the various component gases, 

 and A,, A 2, etc. denote positive or negative constants such that 

 2^ A , =: 0. From (311) with (R6) we may derive for phases of dis- 

 sipated energy, 



Aj //j + A2 11-2 + ^^3 /'3 + ^tc. =0, 



or ^^j (A,//,) = 0. (312) 



Hence, by (276), 



^,[^,a,\og~^) = A + B\o^t ^ J, (313) 



where A, B and (' are constants determined by the equations 



A = 2, {X,II, - A,c, - X,a,), (314) 



B=^,{\,c,\ (315) 



C=2,{X,E,). (316) 



Also, since 2^ ^^ — ^1 ('"'^ 1 "' 1 ) ^ 



^' J (A , «j log «? , ) — ^ (A ^ a , ) log JS" J (« J m , ) 



-f ^^(A,«,)log/> = .4 + ^'log<--^, (317) 



where 



B' = 2, (A,c,-f A,«J. (318) 



If there is more than one equation of the form (311), we shall have 

 more than one of each of the forms (313) and (317), which will hold 

 true simultaneously for phases of dissipated energy. 



It will be observed that the relations necessary for a phase of dis- 

 sipated energy between the volume and temperature of an ideal gas- 

 mixture, and the quantities of the components which take part in 

 the chemical processes, and the pressure due to these components, are 

 not affected by the presence of neutral gases in the gas-mixture. 



Trans. Conn. Acad., Vol. III. ::0 May, 187(3. 



