JOHN H. NORTHROP 489 



centration of substrate. It follows from this that if two solutions 

 are compared, each containing the same quantity of substrate, and 

 allowed to digest the same length of time, but with varying concen- 

 trations of enzyme, the amount of substrate digested will be pro- 

 portional to the square root of the enzyme concentration. This is 

 the usual form of Schiitz's rule. 



It will be remembered that in the derivation of this equation two 

 simplifying assumptions were made: (1) that x, the concentration of 

 peptone, is large compared to Q, the concentration of active pepsin; 

 and (2) that the quantity of substrate present remains relatively 

 constant. The first condition is fulfilled as soon as the digestion has 

 progressed more than a few per cent, provided the original concentra- 

 tion of pepsin is small compared to the concentration of albumin. 

 The second condition, on the other hand, fails to hold after more than 

 30 or 40 per cent of the substrate is digested. It can be predicted then 

 that Schiitz's rule will not hold during the first few minutes of the 

 reaction, or at the end of the reaction, or if the enzyme concentration 

 is too high. As is well known, this is exactly the result obtained by 

 experiment (cf. Arrhenius^^) . 



The failure of the rule to hold during the first part of the digestion 

 is due to the fact that x at this time is not large compared with Q and 

 hence the relative change in Q is not inversely proportional to the 

 change in x (as assumed in the derivation of the equation) but is 

 much slower as demanded by equation (2). In order to express the 

 fact correctly for the first part of the reaction, then, it would be 

 necessary to substitute for Q in equation (4) the value of Q as defined 

 by equation (3). As has been previously stated, this expression is 

 too unwieldy to handle conveniently. The discrepancy due to 

 changes in the substrate concentration, however, may be corrected 

 very simply if the rate of digestion is directly proportional to the 

 concentration of substrate when the concentration of the latter is 

 low. Experiment shows that this is actually the case. (The effect 

 of the substrate concentration is at present under investigation.) 

 The active concentration of substrate at any moment then will be 

 A—x, where A is the original total concentration of substrate and x is 

 the amount transformed. This has already been done in equation (5) 



