1245 
the indications given by LANGrvIN. ©) For the experimental investi- 
J | 
gation we may refer to Finpray ‘Der osmotische Druck” (Dres- 
den 1914). 
Remarks. 
For the pressure on a semi-permeable membrane in the case of 
very dilute solutions it is, as we see immaterial whether or no 
there is interaction between the molecules S and the molecules JW. 
Certain other effects of the osmotic pressure, can, however, only 
be brought about in consequence of such interaction: e.g. the dif- 
ference of level that comes about between the solution and the pure 
water, when they are in tubes open at the top, and are in com- 
munication through a semi-permeable membrane. Let us consider 
the following imaginary case: The “sugar” molecules have no in- 
teraction at all with the water molecules. It is clear that there 
cannot ensue a difference of level -— the sugar simply evaporates 
from the solution. When a glass bell-jar is put over the two commu- 
nicating tubes, the following state of equilibrium is obtained: two 
solutions of the same concentration on either side with an equally 
high level. If the two tubes are placed each under a bell-jar of its 
own, sugar-vapour is formed over the solution with a pressure of 
the same value as the osmotic pressure of the solution and no diffe- 
rence of level appears then either. 
If the difference in level in question is to make its appearance, 
none of the three following factors can, indeed, be omitted : first 
the tendency of the sugar to spread (its kinetic pressure), secondly 
the cohesion of the water, thirdly the interaction of the molecules 
S and W, without which it would not be possible for the sugar 
to lift up the water. 
Mathematics. — “On Nörner’s theorem’. By Dr. W. van DER 
Woupe. (Communicated by Prof. JAN bE Vries). 
(Communicated in the meeting of March 27, 1915). 
$ 1. Britt and Nörner’s well-known paper on algebraic functions *) 
has as starting-point a theorem*) shortly before pronounced by 
Nörner. Its meaning may principally be indicated as follows: 
“A curve I, may be represented by the form 
F,=AF, + BF, 
2?) Mata. Annalen, 7 (p. 271.) 
5) Math. Annalen, 6 (p. 351): “Ueber einen Satz aus der Theorie der algebrai- 
schen Funktionen.” 
