Theory of Surface Forces. 339 



other in their plane of maximum density the relation between 



p and - would be given by the curve of fig. 2. 



Fig. 2. 



In this manner we should have for the point P two differ- 

 ent values of -p 1 , and because this is impossible we conclude 

 dv 



that our incomplete plane capillary layer could not exist. 

 If we do not wish to use the potential function 



_ f A 



r 



for the forces between the elements of volume, we may use 

 for our consideration the equations 



p 2 = 0-S 2 



and S 2 =-VV>. (See above.) 



In the same manner as above, we can now demonstrate 

 that the curve 



*->©• 



is fully determined by the state of the vapour, from which 

 again follows the impossibility of a film consisting of two 

 incomplete capillary layers. 



/// a general manner we find thus that, for a fixed tempera- 

 ture, the plane capillary layer is fully determined and must be 

 •limited on one side by the saturated vapour (of ordinary pres- 

 sure) and on the other side lay the ''ordinary" homogeneous 

 liquid phase. 



^'2. Thickness of the plane capillary layer and surface- 

 tension of very thin liquid films. 



A case wherein a set of liquid films of different thickness 

 in the same space is in equilibrium with the vapour and with 

 each other, we have in the experiment of E. S. Johonnott, 

 Jun. In a first research about thin liquid films, Johonnott 

 has Found t that the black spots in thin liquid films may 



* j>. 2 is the pressure in a direction pea (did to the surfaces of the capillary 

 layer. 



t Phil. Mag-, xlvii. (1809) p. 501. 



