Theory of Surface Forces. 341 



capillary layers, may be also expressed in the following 

 manner : — 



The metastabile phases of the theoretical isotherm of Thomson- 

 van der Waa/s cannot be in equilibrium unless this set of phases 

 of different densities is limited on both their sides by a homo- 

 geneous phase. 



Johonnott has also measured the surface-tensions of the 

 films and he has found that the surface-tension teas independent 

 of the thickness of the films. This fact follows immediately 

 from my considerations above. Indeed, when the films 

 always consist of a liquid film limited by two complete capil- 

 lary layers, the tension of the film must be always twice that 

 of the capillary tension of Laplace, and for a fixed tempera- 

 ture the surface-tension in the film must be independent of 

 their thickness. 



In this periodical* I have endeavoured to explain the 

 apparition of the black spots in very thin liquid films as the 

 vanishing of the phases of the theoretical isotherms of James 

 Thomson, which would be unstable if they were isolated. 

 From my considerations above, however, it follows that the 

 capillary layer must be always complete, and the apparition 

 of the black spots cannot be explained otherwise than as the 

 consequence of a temporary and local diminution of the 

 surface-tension in the considered points, in consequence of the 

 temporary and local increase of the evaporation in these points. 



If H denotes the surface-tension of Laplace, p r and p 2 re- 

 spectively the densities of the liquid and saturated vapour, 

 the ascending of a liquid in a capillary tube which is wetted 

 by the liquid is proportional to the expression 



H 



Pi- P-i 

 Now, this expression being proportional to T, — T f. where 

 T^. denotes the critical temperature, while T denotes the 

 (absolute) temperature of observation, we have 



P1-P2 V T*/ 



T 



or, putting 7^=3, 



_ H =«(1-S) (7) 



Pi — P<2 



* Phil. Ma- Oct. 1907, p. oil. 



t J. E. Verscliaftelt, Comm. from the Lab. of Phys. Leiden, Nr. 28, 

 p. J 5, andE. C. de Vries. Inaugural-dissertation and Arch. Nierl. Science, 

 xxvii'i. (1894) pp. 210-219. 



