28 



LOTKA. 



SO that we must have, for stability, 



>0 



(28) 



In consequence, given stability of equilibrium, the sign of 



dxi 

 dG 



will be the same as that of the numerator in (23), i.e., that of the 

 expression 



dG dy dG dy 



(29) 



Example. Consecutive Reactions. By the way of example we may 

 apply these results to the case of a pair of consecutive reversible 

 reactions. 



-Si+ S2+ . . . + 8rZ S'i+'S'2+ . . . + S'C -5"!+ S"2+ . . . + S"t (30) 



Let X denote the progress of the first reaction from left to right (so 

 that, for example, a quantity, 'piX of the substance S» has been trans- 

 formed at time t); and let y similarly denote the progress of the 

 second reaction, from left to right. 



Let us consider the effect upon .Ti, the equilibrium value of x, of an 

 increment bA" k in the initial amount of substance S" k appearing as 

 product of the second reaction. 



We have, according to (23) ■ 



(31) 



We shall assume stability, so that the denominator is positive. 

 In the numerator, evidently ^ 



8 If we exclude any possible catalytic influence. 



