55 



case, then the saponification of triacetine in stages can be directly 

 proved by this way. 



When the equations (25) and (33) are compared it appears ') that 

 measurement of the velocity of fatty acid separation can never be 

 conclusive with respect to the question whether or no the saponi- 

 fication of triacetine in acid solution takes place in stages^). 



In column 2 of table 3 (see p. 54) we find the values of 

 100 T corresponding to the given values of 100^ for the case that 



§ 13. Let us now put p ^=1, q=z ^, i.e. in consequence of the adsorp- 

 tion the concentration of the monoglyceride in the boundary layer 

 is 4 times as great as it would be if no adsorption had taken place. 



For this case equations (22) and (23) become : 



g=z\ + 8g - 3A;< — 6é-2^f — 3e -'»^-' (35) 



7'= I -f 3e -3^-< — 3e-2^-' — e-^^i = 1 — e-^t|l — (l-^-^')';. (36) 

 Fi-om these two equations é~^^ can be eliminated by solving the 

 fourth power equation (35) and substituting the found value in (36). 

 From (35) we find : 



e-f^i='/^ (4-V"l6-92-f )/92 - 4- 8Kl6-92-f 181-^(2-^)^ + 7,(1-^)1 



in which ; ' (37) 



3 3 1 



z = V,. |2-)/^(l-l^r^) - ]/g{l+l^üJ)l ^ 



In column 4 of table 3 are found the values of 100 T calculated 

 by the aid of these equations. 



These equations will be more fully discussed in § 22. The curve 

 D of fig. 2 represents the corresponding values of 100 T and 100^^/ 

 graphically. It touches the boundary line B at y = T=:0. 



§ 14. If we put p = 2, q ^2, then : 



^— 1 _|_ 8g-3A:<_3,.-4i<_G^-2^-< ..... (35) 



7'=l+e 3kt_2e-'ifct — i_g-2U^2-e-k') . . . (38) 

 It appears that the split off quantity of glycerine is a same func- 

 tion of the time as in the case that ^^ = 1, 5-1=4. This is a general 

 property. If p = %n and q == 2m, or p = m and q = 4/)i, in both 

 cases we have : 



^m- ,3 , 6 ^ ,, 



(ƒ — - I g—Slct g -4mkt\ ^~'2inkl 



^ (4m-3)(2m-3) 4m-3 2rn-3 



1) In the acid saponification in solution k is invariable. 



2'^ Gf. § 1. The fatty acid splitting off likewise becomes seemingly monomolecular 

 for p = Yg» q = oc and for p = <», ^ = 2, 



