1242 
been repeatedly made to get a kinetie interpretation that was as 
lucid as possible. With regard to its contents the following discussion 
is closely connected with the well-known work of lL. Bo.rzmann’), 
H. A. Lorentz?), O. Stern*), G. Jäcer *), and particularly that of 
P: Lancevin*)*). By making use of the virial thesis and of the 
remarkable property which is further on formulated by equation 
(1), it is, however, possible to simplify the derivation. 
Let in an infinitely extended mass of water through a closed 
surface 2 a region G of the volume V be distinguished by the 
following definition: let inside 2 besides the water molecules (IV ) 
also n sugar molecules (S,....S,...-.S,) be present, outside it 
only watermolecules. The surface 2 may possess the following 
properties (of a “semi-permeable membrane’): whenever the centre 
of gravity of a molecule S is about to pass through &, the molecule 
is perfectly elastically reflected by 2; 2 does not exert any forces 
on the molecules HW’, bowever. We want to know the pressure 
(osmotic pressure), which @ experiences per cm* through the collisions 
of the sugar molecules. 
Crausius’ virial thesis, applied only to the sugar molecules, requires 
that: 
OD + Srl Kmer Yay eee =O ee ee 
Here 
Ths Yhy 2h are the coordinates of the centre of gravity of the th 
sugar molecule at an arbitrary moment 4; 
X,, Yr, Zn are the resultants*) of all forces acting at the moment 
ton the At sugar molecule; 
L the kinetic energy of the translation of all the molecules S 
added together at the moment 7. 
The horizontal line expresses: taking a mean of a very long time @. 
Let us now follow the A‘ molecule S during the time 4. The 
force Ny, Yr. Z, on the Ath molecule is owing to three causes: 
1. to the collisions on the surface 2— N;’, YM’, Zi’: 
2. to the attraction and repulsion by all the other molecules 
> Mae yt als 
1) L. Botrzmann, Z. f. ph. Ch. 6 (1890) 474 ; 7 (1891) SS. [Wiss. Abh. N°. 93, 94]. 
2) H. A. Lorentz, Z, f. ph. Ch. 7 (1891) 36. |Abbandl. I, p. 175]. 
3) O. Stern, Z. f. ph. Ch. 81 (1912) 441. 
4) G. Jäcer, Ann. de Phys. 41 (1913) 854. 
5) P. Langevin, Journ. Ch. phys. 10 (1912) 524; 527. 
6) Cf. also Pu. Konnsramm, These Proc. 7, 729. 
7) We suppose for the sake of simplicity that the molecules are centres of force 
of one dimension, 
