J. W. Glbbs — J^fjiulibriuiti of Ileteroyeneous ISubstaiices. 231 



Moreover, as by (277) 



pv = {(fi hi ^ + a.^ »*3 + rtg iii^) f, (;508) 



we have on eliminating v 



/:?, ii.2 fi, + /3.^ — 1 



loff ^1 '"2 P . 



»i3 («! m, -{- «3 Wig -f «3 ?>?.3) 



^ ^' C 



3 3 ^^ 3 ^ 



where 



^' == A J Cj -f- ^ 2 <^2 - *'3 + '^ 1 ^' I + '^ 2 ^i! — «3- ("^ 1 ") 



It will be observed that the quantities /ij, /J.^ will always be posi- 

 tive and have a simple relation to unity, and that the value of 

 /i, -f /!^2 ~ 1 will be positive or zero, according as gas G^ is formed 

 of (tj and G2 with or without condensation. If we should assume, 

 according to the rule often given for the specific heat of compound 

 gases, that the thermal capacity at constant volume of any quantity 

 of the gas 6^3 is equal to the sum of the thermal capacities of the 

 quantities which it contains of the gases G^ and G.^, the value of B 

 would be zero. The heat evolved in the formation of a miit of the gas 

 6^3 out of the gases G ^ and G2, without mechanical action, is by 

 (283) and (257) 



A , (c, « + ^1) + A2 (c'2 t-^KJ - (C3 t+U^), 

 or Bt -\- a, 



which will reduce to C when the above relation in regard to the 

 specific heats is satisfied. In any case the quantity of heat thus 

 evolved divided by ^3 t^ will be equal to the differential coefficient of 

 the second member of equation (307) with respect to t. Moreover, 

 the heat evolved in the formation of a unit of the gas G.^ out of the 

 gases 6r, and G2 imder constant pressure is 



Bt + C+A,«i t 4- A..a2t-a,,t=zB't-\-C, 

 which is equal to the differential coefficient of the second member of 

 (309) with respect to t, multiplied by a^ t'^ . 



It appears by (307) that, except in the case when ji ^ + f-j^ = 1, 

 for any given finite values oi' iii ^, in.,, ni^, and t (infinitesimal values 

 being excluded as well as infinite), it will always be possible to 

 assign such a finite value to v that the mixture shall be in a state of 

 dissipated energy. Thus, if Ave regard a mixture of hydrogen, oxy- 

 gen, and vapor of water as an ideal gas-mixture, for a mixture con- 

 taining any given quantities of these three gases at any given tem- 



