ACTION OF ENZYMES AND CELLS 175 



of formation of C and D is the difference of these two expressions, or 

 &! c A .c i; -& 2 C C .C D . But the velocity of reaction is the limit of the 

 change in concentration divided by the change in time when both 

 change in concentration and in time are infinitely small that is, 



dc 

 velocity = >. A , the negative sign being used because C A is decreasing. 



Accordingly, the equation for the velocity of reaction is 



This equation holds, under the conditions as to constancy of resist- 

 ance laid down above, throughout the course of the reaction, and hence 

 if a, b, c, and d be the initial molecular concentrations of the four 

 substances, and at the end of a time t the molecular concentrations of 

 A and B have changed by an amount - x, and become a - x and 

 b - x respectively, while C and D have changed also by an equal amount 

 + x, and become c + x and d + x respectively, then the equation be- 

 comes 



dr 



^ = k 1 (a-x) (b-x)-k 2 (c + x) (d + x). (2) 



If the initial concentrations and the values of k and k 2 are known, 

 the course of the reaction can accordingly be determined, and the 

 amount of x after any given time be determined by integration of 

 the above equation, remembering that when t = Q, x = 0. The values 

 of kj_ and k 2 can be determined by making measurements at suffi- 

 ciently close intervals of the value of x at different times during the 

 reaction , the initial concentrations being known and substituting in 

 the equation. 



The ratio of the two constants k and k 2 in the equation for 

 velocity of reaction is equal to the value of the constant K of the 



equation of equilibrium, for at equilibrium- -T. A is zero, because 



no change is occurring in the substance, therefore from the equation 



dc 

 - - 1 "* = k C A . C B k> 2 c c . C D , we have at equilibrium k^ C A . C R - k. 2 C C .C D = 0, 





C A .C B 



but in the equation of equilibrium 



C..C. 

 CA-C- 



therefore K=. 11 . 



