74 EXPERIMENTAL OBSERVATIONS ON 



it is easy to understand why they found the action of invertase 

 to follow the logarithmic law, whilst subsequent observers using 

 relatively small quantities of enzyme have noted departures from 

 this law. 



" Case III. When the amount of enzyme does not remain constant 

 but for some reason decreases, the magnitude of the active system 

 will not only be a function of the amount of sugar but also of that of 

 the enzyme ; it will therefore be represented by an equation of the 

 second order, in which both of two interacting substances decrease 

 as, for example, is the case in the interaction of an alkali and 

 methylic acetate. Such an expression corresponds to a curve falling 

 off from a logarithmic curve and therefore giving a series of de- 

 creasing values for K when this is calculated for the simple loga- 

 rithmic law. In such a case, the change in its early stages will 

 still be a linear function of the time, as the diminution in the 

 amount of enzyme will not at first materially influence the magnitude 

 of the active system. 



dx 



" Stated shortly, the ordinary equation of mass action -^ = K (S - x), 



cut 



where S is the total sugar and x the amount changed in time if, is 

 applicable only to the period during which a constant relatively large 

 proportion of enzyme is present together with a continually decreas- 

 ing amount of sugar but uninfluenced by the products of change. 



" During the final period, when the products of change exercise an 

 influence by withdrawing enzyme from the sphere of action, 



where E is the total enzyme, y the amount withdrawn in com- 

 bination with the products in time t. 



" During the period when the proportion of sugar present is very 



dx 

 large, x becomes negligible compared with S, so that ~r = KS = &, 



where k is a constant. 



" The apparent duration of the linear period must be affected not 

 only by x becoming no longer negligible compared with S, but also 

 by the extent to which the products of change make their influence 

 felt. 



" It may here be pointed out that Henri's formula combines in a 

 single expression the linear and logarithmic periods, but does not 

 take into account the last period during which the products of 

 change exercise a retarding influence. 



" The action of invertase appears to be much less affected by 

 invert sugar and that of diastase by maltose than is that of lactase, 



