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+ . . . + SC S'i+S'2+ . . . + S'C «"!+ ^"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 x\, 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. 



