51 



1 . (19) 



(2p-3)(^-3) {2p-d){q-2p)^ {q-S){q-2p)\ 



At last the number of molecules of split off glycerine (s) can be 



calculated from: 



ds 



- = 3gk. y, 



at 



or from 



r—^x^ y). 



We then find : 



(2p-3)(g-3) ^(2p-3)(g-2^) (r%-2p) i 



The number of molecules of split off fatty acid is, as appears 

 from the scheme at the beginning of this § : 



^ =r 3.t' -|- 3 . 2y -f 3s. 



When we substitute in this the equations (16), (19), and (20), we get : 



e=.3aJl-l±(^^^^-:^.-3.+ ^(^)_,-.,. ^^^..'(21) 



I (2p-3)(^-3) ^ (2p-3)(^-2p) {?-3)(5-2p) 



Now we can eliminate k.t from the formulae (20) and (21) for 

 definite values of p and q, which gives us a relation between 5 and £:. 

 It. is however, more practicable to substitute two other quantities 

 for s and z. 



The total number of molecules of glycerine is a. If we now call 

 that part of the total quantity of molecules of glycerine that is 

 split off g, then 



s 

 a 



The total number of molecules of fatty acid is 3a. If we now call 

 that part of the total quantity of molecules of fatty acid that is 

 split off T, then: 



Z 



T =—. 

 3a 



Now follows from the equations (20) and (21): 



^ — 1 ^ g-3A:< J 1 ^ g-2M-« ^ g-9A:« (22) 



(2p-3)(^-3) ^ (2p-3)(^-2p) (9-3)(9-2/>) ^ 



^ 1 _ l+(2p-l)(,^^_3,^ _^(^)__,-.M. ^„ ,- ,.. (23) 



(2p-3)(^-3) ^ {2p-^){q-2p) iq-S){q-2p) 



If now p and q are successively given different values, we obtain 



4* 



and 



