52 



equations for g and T, from which k . t are more or less easj to 

 eliminate in accordance with the values assumed for p and q. 



§ 10. Before proceeding to substitute for p and q numerical 

 values, we point out that the equations (22) and (23) do not 

 allow us to substitute the following values : 



P = 7s ' ^ = 3 and q = 2p. 



It is easy to see that in the derivation of (22) and (23) operations 

 have been performed, which it is not allowed to execute with the 

 above mentioned values of /; and q. If we yet wish to introduce 

 these values, we must proceed as in § 9, and substitute the assumed 

 values for p and q from the very first. We then get transcendental 

 equations for the function : 



^{T,g) = 0. 



§ 11. Let us now first define the limits between which all the 

 curves represented by the functions \p {7\g) = 0, for different values 

 of p and q, must lie. It is clear that the extreme values, which 



p and q can have, are oo and — . 

 ^ ^ 00 



Let us first put p = cc and q z=: co. The physical meaning of 



this is, that the increase of concentration of the lower glycerides 



at the surface of contact in consequence of the adsorption is so 



great that their velocity of saponfication compared with that of the 



triglyceride, is oo. 



The equations (22) and (23) pass in this case into: 



^ = 1 — e-3^' (24) 



T=l — e-^kt ........ (25) 



from which 



g=T (26) 



This result can of course at once be understood. In fig. 2, where 



g and T are both given in percentages, A represents this limit. 



The equation g ^^ T will be more fully discussed in § 19. 



Let us now put q = — . The physical meaning of this would be 



oo 



i 



that the monoglyceride reaches only a concentration of — in conse- 

 quence of negative adsorption in the boundary layer. This limit 

 has only mathematical signification. (See Fig. 2 p. 53.) 



The equations (22) and (23) pass in this case after finite time, 

 into : 



^ = : . (27) 



