J. IK Gihha — Equilibrium of TTelerogeneous Substances. 247 



(In the particular case when a, = 2 «„ tliis equation will he e(iuiva- 

 lent to (333)). By (347) and (348) we may easily eliminate i^i from 

 (346). 



The reader will observe that the relations thus deduced from the 

 fundamental equation (342) without any reference to the different 

 components of the gaseous mass are equivalent to those which relate 

 to the phases of dissipated energy of a binary gas-mixture with com- 

 ponents which are equivalent in substance but not convertible, except 

 that the equations derived from (342) do not give the quantities of 

 the proximate components, but relate solely to those properties which 

 are capable of direct experimental verification without the aid of any 

 theory of the constitution of the gaseous mass. 



The practical apj^lication of these equations is rendered more simple 

 by the fact that the ratio a^'.a^ will always bear a simple relation to 

 unity. When a, and «2 are equal, if we write a for their common 

 value, we shall have by (342) and (345) 



2? V =1 a m t, (3.50) 



and by (345) and (346) 



m C2~C| E. —E2 



at 



(.351) 



ij -j- 2^2^ ^ 



By this equation we may calculate directly the amount of heat 

 required to raise a given quantity of the gas from one given tempera- 

 ture to another at constant volume. The equation shows that the 

 amount of heat will be independent of the volume of the gas. The 

 heat necessary to produce a given change of temperature in the gas 

 at constant pressure, may be found by taking the difference of the 

 values of J, as defined by equation (89), for the initial and final states 

 of the gas. From (89), (350), and (351) we obtain 



Cj—Cj, El— Est 

 Z _ Z^{cit-\-at+B^) + L2{c2t + at+E^)t "" e "^ ^ .g^^) 



L^+L„t e 

 By differentiation of the two last equations we may obtain directly 

 the specific heats of the gas at constant volume and at constant pres- 

 sure. 



The fundamental equation of an ideal ternary gas-mixture with a 

 single relation of convertibility between its components is 



