VELOCITY OF REACTION 199 



case of enzymes, that a maximum is soon reached beyond which 

 further addition of enzyme produces no noticeable effect whatever, 

 and it is hardly necessary to add that for concentrations somewhat 

 short of the maximum, the linear law does not hold, as the linear 

 portion of the curve gradually rounds off to the asymptotic line 

 which marks the maximum velocity with increasing concentration. 

 Having regard to the high molecular weight which enzymes possess 

 and correspondingly low molecular concentration, and also the low 

 percentage amount present when the maximum amount of increased 

 effect with concentration is obtained, we have here incontrovertible 

 evidence of a difference in mode of action of enzymes and inorganic 

 catalysts such, for example, as sucroclastic enzymes and the 

 hydrogen ion of acids. Here the sucroclastic enzyme is already in 

 possession of its maximum effect at a molecular concentration, at 

 which the action of the hydrogen ion is practically imperceptible, 

 and the hydrogen ion goes on increasing in effect, as the concen- 

 tration is increased, at a rate considerably greater than corresponds 

 to the increased ionic concentration, while the action of the enzyme 

 remains at a constant level. 



The enzymes which within the limits indicated above obey the 

 law of direct proportionality between concentration and activity 

 are: Invertase (O'Sullivan and Tompson, Henri, E. R. Armstrong), 

 Rennin (Segelcke u. Storch, Soxhlet, Lorcher, Duclaux, Fuld), 

 Lipase (Kastle u. Loewenhart), Trypsin (Bayliss). 



In the case of other ferments, however, although the same 

 falling off to a maximum value at an upper limit, at which the 

 percentage of ferment is still very low, is observed in all cases, 

 it is found that even well below this limit of maximum effect the 

 linear law is not obeyed of direct proportionality between concen- 

 tration of enzyme and intensity of action. 



In most such cases, the majority of experimenters have arrived 

 at the conclusion that the law first empirically deduced from 

 experiments upon pepsin by E. Schiitz, and known as " Schiitz's 

 law," is that which best expresses the effects of concentration upon 

 intensity of action within a certain range. The law is that the 

 intensity is directly proportional to the square root of the concen- 

 tration, or put conversely, that the relative concentrations of 

 enzyme are directly proportional to the squares of the intensities 

 (that is, the amounts changed in equal times). Expressed in an 

 equation, if t and & 2 are the velocity constants (or quantities 



