Theory of Surface Forces. 513 



ordinary temperature is, in virtue of the measurements of 

 Remold and Riicker, inferior to 50 /i/jl, while tivofold the in- 

 complete capillary layer of the black spot is more than 10 fifi. 

 Putting h for the thickness of the (complete) capillary layer 

 of a soap-solution, we have also : 



50 pn >- 2Jt >► 10 fjbfju 



25 fJLjJL > Jl >- 5 fJL/JL (1) 



Observation. — That we may have in the black spots the 

 same tension as in the complete capillary layer may very well 

 bo in accordance with the expression which I have found for 

 the surface-tension H of Laplace : i. e. : 



/ denotes the constant in the used potential function for the 



forces of cohesion : — f e A and clh is the differential of the 



r 



normal to the surface of the layer. The order of greatness 

 of H is also : 



#*?*■ tiLit 



where h denotes the thickness of the capillary layer and Y 2 

 and Y 1 are successively the potentials in the vapour and 

 liquid phase. For a black spot we must change Y x into the 

 potential of a point in equal distances of the two planes 

 which limit the black film, and just as // is smaller for a black 

 spot than for a complete capillary layer, so also the difference 

 between the potential in the vapour phase Y 2 and the potential 

 in the point at equal distances from the two planes which limit 

 the black film is smaller than the difference Y 2 — V 1 for the 



* G. Bakker, " On the Theory of Surface Forces/' Phil. Mag. Dec. 

 1906, p. 562. 



t If a denotes the coefficient of the well-known expression of Laplace 

 for the so-called molecular pressure ap 2 , Gauss and van der Waals have 

 found for the potential of the forces between the volume-elements of a 

 homogeneous phase — 2ap, where p denotes the density. Formula (II.) 

 "becomes therefore 



nf h 



In this paper I find in § 3 [see formula (17)] for H the formula 



H= _6_ a 2 (P l -p 2 ) 2 . 

 orrf h 



