VELOCITY OF REACTION 79 



the concentration of the substratum, the effect of the enzyme is 

 the same upon each molecule of the substratum. Now this need 

 not necessarily be the case experimentally, and probably is not 

 so ; for as the number of substratum molecules decreases, there 

 will be continually a larger number of enzyme molecules relatively, 

 and there may be in consequence a greater amount of action upon 

 each substratum molecule, that is, the value of k on this account 

 will increase throughout the reaction. Thus indirectly k becomes 

 a function of x, the quantity inverted, but not (as Henri's formula 

 would indicate by its derivation) on account of a directly favour- 

 ing action upon the enzyme of the products of the reaction. There 

 is no experimental basis for the assumption that the effect of the 

 enzyme upon each molecule of substratum (if the expression may 

 be allowed) is the same, no matter what the concentration in sub- 

 stratum ; and when the concentration of the substratum falls in 

 the course of the reaction, then the available substratum upon 

 which the enzyme acts being lessened, the effect upon each mole- 

 cule must be increased. Therefore although the velocity of change 

 diminishes as the mass action law indicates, on account of the 

 diminution in unchanged material, there is a factor of increase 

 on account of greater activity being exercised by the constant 

 number of enzyme molecules upon each of the now smaller number 

 of substratum molecules. 1 A second assumption which is made 



dx 

 in applying the law j~ k (a x) to enzymic action has already 



(it 



been alluded to in the derivation of the equation (ses p. 52), 

 viz. that the action is taken to be irreversible, or that the tendency 

 to reversion may be neglected. 



This assumption is in all probability not experimentally justi- 

 fiable, especially at the later stages of the reaction. For it does 

 not follow that because a reaction runs practically to completion, 

 as, for example, that induced by invertase upon cane-sugar, that 



1 A kinetic analogy may make the contention clearer. Suppose the enzyme 

 molecules are a fleet of battleships, firing at a number of targets which are 

 gradually sunk as a result. Then as the targets sink, the rate of disappearance 

 will decrease, and provided the number of targets is large enough the rate will 



be proportional to the number at any instant, that is, the law =k (a-x) will 



dt 



hold. As the firing goes on, however, there will come in a factor of increase 

 in the rate of sinking, because each target will be attacked by an increased 

 number of ships. 



