334 Dr. G. Bakker on the 



If we consider further, for a point of the capillary layer,, 

 the thermic pressure as independent of the direction (Stefan, 

 Fuchs, Rayleigh, van der Waals), and only as a function of 

 the density, the cohesion S x must he in consequence of the 

 equation (1) also a function of the density, because p^ is a 

 constant. By this I mean the following : — 



If one considers at a fixed temperature, firstly, a plane 

 capillary layer which limits a large bulk of liquid, and, 

 secondly, a set of capillary layers which limit very thin 

 liquid films (black spots), the cohesions Si have the same 

 value in the corresponding points of all the considered 

 capillary layers. (Two points are called corresponding- 

 points when, in these points, the value of the density is the 

 same.) 



The same property can also be demonstrated for the 

 cohesion in the direction parallel to the surface of the capil- 

 lary layer. 



When, namely, Y denotes the potential of the forces of 

 cohesion and p the density in a point of the capillary layer, 

 we have 



d0=-pdV (2) 



According to Rayleigh *, we have further : 



\ - -ap 1 ^ 2 dW ± ^ 2 3 4 ({¥ 



and for the cohesion S 3 parallel to the surface of the capillary- 

 layer I have given j : 



o o , Co d' 2 p c 4 d x p 



Therefore 



iV P =~S 2 (3) 



If we thus consider 6 as a function of the density, the 

 relation (2) gives likewise this property for the potential Y, 

 and the relation (3) demands the same for S 2 . Hence it 

 follows that So must have the same value in the corresponding- 

 points of the considered capillary layers, when only for the 

 vapour, icliich touches these capillary layers, 6, p, and Y Imve 

 the same values. 



If p 2 denotes the pressure for a point of the capillary 



* Phil. Ma<2-. Feb. 1892, p. 210. 



t Zeitschr. f. phys. Chem. xlviii. p. 12, and Koninkl. Akad. van ll'etcn- 

 scJutppen Amsterdam, Proceedings, Dec. 20, 1899, pp. 260 & 261. 



