KINETICS OF HYDROLYSIS 



379 



certain limiting conditions. The possibility was thus 'indicated 

 that a combination of the two formulae might be found to ade- 

 quately represent all of the phenomena. Obviously the process 

 represented by equation (i) plays a predominant part when the 

 ferment-concentration is high; that represented by equation 

 (ii) plays a predominant part when the ferment-concentration 

 is low. We must therefore introduce into the combined equation 

 some factor e which will denote the proportionality between 

 the two processes, and which will be dependent upon the mass 

 of ferment. We thus obtain the equation: 



log 



a 



nat. 



a — X 



-\- ex = k4', 



(ill) 



introducing the modulus of the natural logarithms (0.4343) we 



obtain 



a 



log 



10' 



a — X 



+ 0.4343 ex = 0.4343 k^t, 



which may be written 

 logio 



a 



a 



X 



+ 0.4343 ex = kzt. 



(iv) 



The following are the values of kz calculated by Abderhalden 

 and Michaelis from equation (iv) for the four series of deter- 

 minations cited above: 



With the exception of the two values enclosed in brackets, 

 which are obviously influenced by experimental errors, the value 

 of kz for each set of determinations is evidently, within the ex- 



