402 CHEMICAL DYNAMICS 



water will not be appreciably affected by the inclusion of a 

 minute proportion of the water in the products of hydrolysis. 

 Only one molecular species is appreciably changing in concen- 

 tration, therefore, namely the protein. The number of molec- 

 ular collisions per second between the water and the protein 

 molecules will therefore be proportionate, at any instant, to the 

 concentration of unaltered protein at that instant. If the initial 

 concentration is a and the amount hydrolysed after time t 



is x, the velocity of hydrolysis f-^-J is given by -r = k (a x), 



in which k is the velocity-constant (specific velocity, or velocity 

 per unit concentration) of the reaction. Integrating this, and 

 recollecting that when t = 0, x = we obtain equation (i) . 



The simplifying assumptions which we have been compelled 

 to make in deriving this formula are very numerous and very 

 many of them devoid of either theoretical or experimental justi- 

 fication. Hence it is not surprising that it has not often been 

 found to hold good by those who have followed the time-relations 

 of protein hydrolysis. 



Victor Henri and Larguier des Bancels (54) studied the di- 

 gestion of gelatin and casein by trypsin, following the hydrolysis 

 by observing the increase in the conductivity of the digest, under 

 the assumption that each molecule of hydrolysed protein con- 

 tributes equally to the observed increase in conductivity. They 

 found that the values of 



7 1 i a 



k = - log 



t 6 a x 



were tolerably constant for brief periods of digestion and for 

 varying values of a ( initial substrate-concentration), in none 

 of their experiments, however, did they approach the stage of 

 complete digestion, and Arrhenius (3) has shown that their 

 results are equally well expressed by the formula: 



x = kiVt (ii) 



which is the well-known "rule of Schutz" to the effect that the 

 quantity of protein which is digested by a given quantity of 

 proteolytic ferment is proportional to the square root of the 

 period occupied in digestion. 



Bayliss, also employing the conductivity method (5), studied 

 the hydrolysis of casein by trypsin. He found that the constant, 



