VALIDITY OF THE PRINCIPLE OF LE CHATELIER. 29 



so that this numerator reduces to 



= . (32) 



Stability demands 



dA"k dy 



f > .(34) 



On the other hand the principle of Le Chatelier would make 



This, by (31), in view of (32), (33), (34), will be true or not according as 



S^ > (36) 



Hence the principle of Le Chatelier holds good or not, as applied to 

 the effect of A"k upon xi, according as 



af-J" (3^) 



From this point on the discussion would follow essentially similar 

 lines as in the case of a single dependent variable; it is therefore un- 

 necessary to carry this out in further detail. 



Influence of External Factors. We have hitherto tacitly assumed 

 that (1), or (18), (19) are the only conditions for equilibrium, or, that, 

 if there are any other conditions to be satisfied, these are in some way 

 automatically taken care of. 



In point of fact, in general, in addition to a condition of the form 



Jt = ^^'' ^^ ^^^ 



there will be further conditions of the form 



H= H, (38) 



where H is a, parameter entering into the function /, while //« is a 

 parameter defining certain "external conditions." For example, H 

 may be the pressure exerted by a gaseous mixture against an enclosure, 

 and He may be the external pressure applied to a movable piston 



