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 : 



lognat. 



a x 



ex 



k z t; 



(iii) 



introducing the modulus of the natural logarithms (0.4343) we 

 obtain 



a 



logic 



a x 



which may be written 

 logi 



+ 0.4343 ex = 0.4343 fcrf, 



+ 0.4343 ex = 



a x 



(iv) 



The following are the values of k z 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 & 3 for each set of determinations is evidently, within the ex- 



