Theory of Surface Forces. 337 



. maximum density, the potential V in this plane could not 

 have the same value as the potential in the corresponding 

 points of the capillary layer which limits a large bulk of 

 liquid. Hence follows : The film must always consist of a 

 layer of liquid, limited by two complete capillary layers, and 

 the layer of liquid must have a minimum thickness, which 

 has the same value as the radius of the sphere of action. 

 The thickness of the capillary layer and the sphere of action 

 being of the same order of greatness, one can take for the 

 thickness of the complete capillary layer approximately the third 

 part of the minimum value of a liquid film. 



Hitherto we have supposed that the capillary layer was in 

 contact with saturated vapour. Let us now consider the 

 possibility of the existence of a plane capillary layer in con- 

 tact with vapour which has not the ordinary tension. 

 Using the potential function 



r 



r 



for the forces between the elements of volume, the cohesion 

 S 2 in a direction normal to the lines of force is * : 



B -5*{(£/+S}' (*•> 



and the cohesion Si in the direction of the lines of force : 



«.-^C(s;-5} <«> 



Hence 



Differentiating this equation we find 



dp _ eld _ V dX 

 dv dv 2a dv 



We have, further,//! denoting the thermodynamical poten- 

 tial of the homogeneous phase of the vapour : 



V+2«p-/i 1 - # *t (5) 



Hence 



dp _ d$ to—p rn 



dv ~ dv 2ap " w 



* Phil. Mao. Dec. 1006, p 560. 



t Phil. Mag. Oct. 1907, p. 516, equation 4. 



