404 CHEMICAL DYNAMICS 



ferment in a given time is directly proportional to the initial 

 concentration of the substrate, i.e., the true form of equation (ii) is 



a result which had previously been established by Schiitz and 

 Huppert (loc. cit.) 



Arrhenius (loc. cit., p. 64) has pointed out that the Schiitz 

 rule may be derived from the monomolecular formula provided 

 we assume that the catalysor in the system enters into combi- 

 nation with and so is inactivated by the products of the reaction. 

 This derivation is, however, only valid for the early stages of 

 hydrolysis, during which x is small in comparison with a. 



Regarding the dependence of the velocity of hydrolysis upon 

 the ferment-concentration, Taylor (loc. cit.) finds that the time 

 required to hydrolyse a given quantity of protamin sulphate to 

 a given degree is inversely proportional to the quantity of fer- 

 ment present. I have found (107) that the velocity-constant 

 of the hydrolysis of calcium and barium caseinate in dilute 

 solutions, also calculated from the monomolecular formula, is 

 directly proportional to the concentration of trypsin, but at 

 higher substrate concentrations (A^/400 Ca(OH) 2 neutralized by 

 casein) the ratio k/F increases with increasing ferment-concen- 

 tration. Hedin (47) (48) (49) has studied the hydrolysis of 

 casein by trypsin very carefully from this standpoint and finds 

 that the relation 



Ft = constant, (iv) 



where F is the mass of ferment and t the time required to attain 

 a certain degree of hydrolysis, holds good over a wide range of 

 ferment-concentrations. 



Employing the method of observing the rate of solution of 

 coagulated protein enclosed in capillary tubes Schiitz found 

 that the rate of digestion is proportional to the square root 

 of the ferment (pepsin) -concentration. Taylor (loc. cit.) and 

 Arrhenius (loc. cit.) have, however, pointed out that if this 

 method of measurement be employed, processes of diffusion and 

 solution are liable to be confused with the process of hydrolysis. 

 From the results of Hedin, however, which are cited above, 

 since Ft = constant and the rule of Schiitz (x = k V7) holds 

 good in a large number of instances of protein hydrolysis, it 



