726 



SUMMARY. 



1. We determined llie progressive change of (he acid formation 

 from some aliphatic saturated acid anhydrides in presence 

 of an excess of water at 0° and 25°. 



2. In the case of the lower acid anhydrides including the butyric 

 acids this proved to be a unimolecular reaction with a relative 

 small temperature coefficient. 



3. As from previous investigations it had appeared that the 

 reaction constant is closely connected with the dissociation 

 constant of the acids forming, it could be deduced, by elimi- 

 nating this intluence, that the hydratation constant decreases 

 as the mass of the saturated group increases, and that the 

 branching of the saturated carbon chain has little influence 

 on this constant. 



4. From the fall of the "constant" for the acid formation from 

 /.sovaleric anhydride it was deduced tliat the formation of acid 

 usually takes place in two |)hases : a. Absor[)iion of water, 

 h. splitting of the hydrate; that with t lie lower acid anhydrides 

 the first reaction occm-s very i-apidly so that only the last 

 unimolecular reaction gets measured ; that in the case of the 

 /.s'ovaleric anhydride the first reaction no longer takes place 

 infinitely in regard to the second so that we must get the 

 image of a follow-reactioii witii unequal reaction constants. 



Delft, December 1913. 



Lab. Org. Chem. Techn. Univ., Delft. 



Mathematics. — "Bilinear congruences and complexes oj plane 

 algebraic curves.'' By Prof. Jan ue Vries. 



1. We shall consider a doubly infinite system of plane curves 

 of order n, consequently a congruence [y"]. We suppose that through 

 an arbitrary point o\\\y one qwvxq passes, and that an arbitrary 

 straight line is cut in n points by only one cur\'e. The congruence 

 is in that case of the first order, and of the first class ; we shall 

 call it for the sake of brevity a Inlinear congruence. 



As a y" of the congruence is determined by a straight line r of 

 its plane (f, all planes (f must pass through a fixed point F, which 

 we shall call the pole. 



A ra}^ ƒ passing through F {polar ray) bears co^ planes (f; the 

 curves y" lying in it form a surface ^ of order {n-\-V), for any 

 point of ƒ lies on only one curve y". 



