378 



CHEMICAL DYNAMICS 



off so rapidly as it should were it a simple monomolecular re- 

 action of which the velocity constant is simply enhanced in 

 magnitude by the presence of the ferment. 



In the derivation of equation (i) it is assumed that the velocity 

 of transformation at any moment is proportional to the mass of 

 substrate which is at that moment undergoing change. The 

 theoretical velocity therefore falls off in direct proportion as the 

 substrate is used up. The next simplest assumption, taking 

 cognizance of the fact that the velocity of transformation does 

 not decrease with the rapidity demanded by the monomolecular 

 formula, is that the velocity of transformation is independent 

 of the mass of the substrate, and is therefore expressed by the 

 equation : 



dx 



which, when integrated, yields 



x = kit. (ii) 



Calculating the values of ki from this formula, for the above 

 four series of experimental data Abderhalden and Michaelis 

 obtained the following results : 



It is evident that k 1} calculated from formula (ii), tends to 

 approximate constancy for the lower ferment concentrations (2 cc. 

 and 3 cc.), while it altogether fails to do so for the higher ferment- 

 concentrations. To the latter solutions, as we have seen, equa- 

 tion (i) applies tolerably well. Neither equation, therefore, 

 taken by itself, represents the entire process; each applies under 



