49 



k p.k q.k 



(O (x) (y) (s) 



In this x4 represents a molecule of triglyceride, which can be 

 converted into a molecule of digljceride {B, C, or D) in three ways 

 with a constant of velocity k. A molecule of diglyceride, e.g. Z^ can 

 give a molecule of monoglyceride {E or F) in two ways with a 

 constant of velocity p.k, while finally every molecule of monogly- 

 ceride forms glycerine {H) with a velocity constant g'.^. The number 

 of molecules of A present after a time t will be expressed by r, 

 the number of molecules of B, C, and D each by .r, of E, F, and 

 G each by ?/, and of H by .?. 



It is clear, that when there is no difference in saponifiability of 

 the different ester groups, the concentrations of B, C, and D, and 

 of E, F, and G are equal inter se at any moment. 



Let us now suppose a molecules of triglyceride A to be present 

 at the beginning of the reaction. 



The velocity of saponification of ^ is now denoted by the equation: 



dr 



-It = ''-' (^) 



When we integrate- (7) and consider that for ^ =r 0, r =i a, then 

 follows: 



r=:a.e-^^f (8) 



The variation of the number of molecules B (hence also of C 

 and D) is represented by : 



da; 



-~ =k .r—2pk .a; • (9) 



When the value of r from (8) is substituted in (9), then follows: 



dtV 



\- 2pk.a;^a k .e-^kt (10) 



This equation can be solved by putting: 



a; z= m X. fi (11) 



in which, therefore, an arbitrary value can be given e.g. to ni ; n 

 is then fixed. 



4 



Proceedings Royal Acad. Amsterdam. Vol. XX. 



