42 



which indicates the relation between the number of molecules of 

 glycerine and fatty acid split off after the time Lt^. 



Let us now imagine that after the time Lt^ has elapsed, the con- 

 stant of velocity k changes into k', and let us now consider a 

 following period Lt^. At the beginning of this period the following 

 equation holds : 



^ =f{k X A«,) 

 s = (f{k X A^) 



The same values z and s could, however, have been obtained 

 with the constant of velocity k' in a certain period Lt\, so that: 



^t\=-.Lt, (6) 



At the beginning of this period we have, therefore, also : 



z=f{k'x^t\) 



s = <p{k' X A^\), 



but then is after the lapse of the time t, : 



z=f{k'x{^t\ + AOI 

 and 



s =3 (p\k' X (A«', + At,)\ . 



B'rom these last equations k' X (Aif\ -\- LQ can be eliminated in 

 the same way as k X A/^ from (3) and (4), which proves, there- 

 fore, that (5) also holds after A;, has passed. 



Since the same reasoning may be extended over the whole sapo- 

 nification, it appears that when the number of molecules of split off 

 fatty acid in the saponification of fat can be represented by : 



z =f{k X 



and the number of molecules of split off glycerine by : 



S = (f{k X t), 



in which equations k varies with the time, we must be able to 

 derive a function : 



by elimination of k X t, the form of which does not change during 

 the saponification, and which is independent of the change of k. 



Since in the saponification of fat both split off glycerine and free 

 fatty acid can be determined separately, we have a means in this 

 to examine the mechanism of the reaction. 



It may still be pointed out here that in the change of k with 

 the time must also be included the decrease of concentration of the 

 lye taking place in the saponification in alcalic surroundings. We 

 shall, therefore, have to arrive at analogous equations for acid and 

 alcalic saponification. 



