30 LOTKA. 



forming part of that enclosure. Here it is not enough, for complete 

 equilibrium, that (1) be satisfied, but (38) also must hold. 



Furthermore, the conditions (1) and (38) define equilibrium, but 

 are insufficient to determine its stability, since they give us no in- 

 formation regarding the behavior of the system when H A" H e, i.e. 

 when not in equilibrium with the external parameter H e- 

 \ In order to settle this point we must have some further data. We 



are here interested in systems in which such additional data are 

 furnished in the following manner: 



In the case of these systems it is found that, in relation to the 

 parameter G a certain parameter H having certain peculiar properties, 

 can be defined by a relation. 



ip (^1, ^2, G, H) = constant (39) 



or its equivalent 



^ (x, Ai, Ai,. . . G, H) = constant (40) 



The peculiar property of G referred to above is as follows 



— =0 according as // — //« =0 (41) 



It will perhaps be well, before proceeding any farther, to illustrate 

 this by a concrete example. Consider the system 



2 //2O ^2/^2+02 (42) 



If ^1 is the mass of //2O expressed in mols, ^'1 the mass of H2 and ^'2 

 the mass of O2 similarly expressed; if V is the volume (parameter 6') 

 and if P is the pressure (parameter H) exerted upon the enclosure, 

 then the equation (39) here takes the form 



PV = (6+ ^'1+ ^2) Re (43) 



where 6 is the absolute temperature and R the general gas constant. 

 Or, if Ai, A'l, A' 2 are the initial masses of i/oO, Ih and O2 respectively, 

 (expressed in mols), and x measures the progress of the reaction, as, 

 for example, by the number of O2 mols formed, then evidently 



^1-^1-20- (44) 



^\=A\-\-2x (45) 



^',= A',-\-x (46) 



