380 CHEMICAL DYNAMICS 



perimental error, constant. The value of e, it is evident, rises 

 with decreasing ferment-concentration, but not in direct pro- 

 portion. 



It is of great interest to observe that equation (iii) and (iv) 

 is of the same form as that which Henri (13) (6) has found to 

 hold good for the inversion of cane sugar by invertase. The 

 theoretical foundation of Henri's equation, therefore, calls for 

 consideration in this connection.* 



Henri started from the point of view that the ferment, in the 

 presence of a substrate which is undergoing digestion, may con- 

 ceivably exist in three modifications, namely, in combination 

 with the substrate (concentration = Fs), in combination with 

 the products (concentration = Fp), and in the free condition 

 (concentration = F/), Calling the total concentration of ferment 

 F, we obviously have : 



F = F, + Fp + Ff. (v) 



Assuming that in the formation of the ferment-substrate 

 compound one molecule of ferment unites with one molecule 

 of substrate we have, from the mass-law: 



Ff{a-x)=^F,, (vi) 



/ft 



in which — is the equilibrium-constant of the reaction. 

 m 



Similarly assuming that in the formation of the ferment- 

 products compound one molecule of ferment unites with one 

 molecule of the hydrolysis-products we have: 



FfX = -Fp, (vii) 



n 



in which - is the equilibrium-constant of the reaction. 



n 



Combining equations (v), (vi) and (vii) we obtain: 



F 



^f = r~i — 7 n ' (viii) 



I -j- m [a — X) -f- nx 



and 



= , ^'"^(''-f^ , (ix) 



1 -\- m [a — X) -\- nx 



* The derivation of Henri's equation which follows is, essentially, quoted 

 from Taylor (19). 



