Effects of Dissociation on the Physical Properties of Gases. 175 

 |=2v/^I...] 



§=2v/^^[...].. 



2x -\-z-\- x' — number of A present = Ni say, 



2i/ + ^+/ ,, B ,, =^2 say. 



For the sake of simplicity we will write the above equations 

 thus : — 



1 dv 



-^ =az2x''^ — x{2aiiX + ai2y + aiQZ-Vai^x'-\-auy'], 



2^176 dt 



Z V ITU "f 



1 cl^ 



^-^ -^ =«34'^Y— ^{«01^'P + «02y + 2«00^ + «03'^' + ^04y}j 



2^' + 2; + .'C^ = Ni, 



(1) 



where 



a =,^ ./>». + "', Exp (- "'■ + '"^ gJV 



«^^=.;V'K±% Exp (-!^.±!!!!.|), 

 v/' t'i V ?^i„??i„ \ 4:7n„ma (7/ 



(2) 



except for a^^, ^44, ^34. 



When the gas is in its stable state, 



dx __dy _dz _^ 

 dt ^dt~dt ~ ' 



and we get five equations to determine the five unknowns, 



We can at once reduce these to three equations of the 

 second degree in x^ y, z by eliminating y' , z' by means of the 

 last two. As we shall chiefly have to do with gases mixed in 

 their chemical proportions, we will suppose for the future that 

 N;,^ = ]Sr2 = N (say). Then dividing equations (1) by N^, and 

 (2) by N, we may regard x^ y, z as the proportions of AA, 

 BB, AB to the whole number of A or B present. 



23. In general, from three equations of the second degree 

 between three unknowns we shall get eight sets of solutions. 

 But all the solutions of equations (1) may not suit our pur- 

 pose. We must reject as unsuitable all imaginary roots, all 

 negative roots, and all positive roots in which x or y>\^ and 



