24 LOTKA. 



Si which disappears in the transformation when x increases, and let 

 A'j be the initial value of some component S'j which appears in the 

 same transformation. 



We have, according to (4), 



^ ^ _ dl /df 



dAi dAil dx ^ ' 



If we are dealing with a system of constant mass, we have an equa- 

 tion of constraint 



mi^i+ m2^2+ . • . = miAi+ m2/l2+ ... (8) 



where mi, m2, . . . are the molecular weights of the substances Si, S2,... 

 From (8) we find by differentiation 



'*•■ =1 (9) 



dAi 

 so that we may write, instead of (7), 



8Ai, d^i/ dx 



(10) 



From (10) it is seen that -— - and — are always of the same sign 



oAi d^i 



df . . . . 



provided — is negative, i.e., provided that the system is stable in the 

 dx 



equilibrium defined by/ = 0. That is to say, if the system is stable, 

 and if adding a quantity of a component disappearing in the trans- 

 formation increases the velocity of the transformation (at the previous 

 equilibrium), then such addition will shift the equilibrium in the 

 direction of increased transformation. In this case, then, the principle 

 of Le Chatelier holds good. 



On the contrary, by similar reasoning, it is found that if the addition 

 of a quantity of a particular substance disappearing in the transforma- 

 tion retards the transformation, the principle does not hold as regards 

 that substance. 



Again, by similar reasoning, it is found that the principle holds or 

 does not hold, according as the addition of a substance *S'j appearing 

 in the transformation retards or hastens the transformation. We 

 may therefore summarize the facts as follows : 



