( 78 ) 



that really has a vortex i.e. a rotation vector everywhere in space. 



We can say namely: 



If of a force field in each point the divergence (a scalar) and the 



rotation (a plant vector) are given, then it is the V of a potential : 



r div. dv r rot. dv , . ^ , , i /. , i 



I 1- I : this formula takes the held as an 



integral of fictitious fields of agens points and of single vortices. 



Crystallography. — "On the fatty esters of Cholesterol and 

 Pliytosterol, and on the anisotropous liquid phases of the 

 Cholesterol-derivatives." By Dr. F. M. Jaeger. (Communicated 

 by Prof. A. P. N. Franchimont.) 



(Communicated in tlie meeting of May 26, 1906). 



§ 1. Several years ago I observed that pliytosterol obtained from 

 rape-seed-oil suffers an elevation of the melting point by a srAall 

 addition of cholesterol. The small quantity of the first named sub- 

 stance at my disposal and other circumstances prevented me from 

 going further into the matter. 



My attention was again called to this subject by some very 

 meritorious publications of Bomer ') on the meltingpoint-elevations 

 of phytoterol by cholesterol and also of cholesterol-acetate by phyto- 

 sterol-acetate. Apart from the fact that the crystallographic data 

 from 0. Mügge led me to the conclusion, that there existed here an 

 uninterrupted miscibility between heterosymmetric components, a 

 further investigation of the binary meltingpoint-line of the two 

 acetates appeared to me very desirable, as the ideas of Bomer on 

 this point are not always clear; this is all the more important, as 

 we know that Bomer based on these melting point elevations a 

 method for detecting the adulteration of animal with vegetable fats. 

 My further object was to ascertain in how far the introduction of 

 fatty acid-residues into the molecule of cholesterol would modify the 

 behaviour of the estei'S in regard to the phenomenon of the optically- 

 anisotropous liquid phases, first noticed with the acetate, propionate 

 and berizoate, with an increasing carbon-content of the acids. Finally 

 I wished to ascertain whether there was question of a similar 

 meltingpoint-elevation as with the acetates in the other terms of the 

 series too. 



1) BöMER, Zeit. Nahr. u. Genussm. (1898), 21, 81; (1901). 865, J070; the last 

 paper s,with Winteu) contains a complete literature reference to which 1 refer. 



