Theory of Surface Forces. 335 



layer in a direction parallel to their surface, we have, further, 



p 2 = 6 — S 2 , 



and we see thus that in the corresponding points of the 

 capillary layers, which are touched by the same vapour. 

 Pi, jt> 2 , anc l V have the same values. Now, we consider the 

 capillary layer as a continuous series of states between two 

 fixed densities. Each state (phase) is determined by its 

 density p and the hydrostatic pressures p x and p 2 . This 

 density p and the hydrostatic pressures pi and p 2 having the 

 same values in the corresponding points of the considered 

 capillary layers, we see that a set of films touched by the 

 saturated vapour must be limited by congruent capillary 

 layers or parts of congruent capillary layers. The capil- 

 lary layer which limits a large bulk of liquid is, of course, 

 complete. For the two capillary layers, however, which 

 limit a black spot, we must examine the question further, 

 and we shall find that the capillary layers in this case must 

 be also complete. Indeed, if we could have a black spot, 

 which could consist of two incomplete capillary layers, which 

 touch each other in their plane of maximum density, this 

 plane should divide the black spot in two congruent layer- of 

 smaller thickness, and because this plane should be a plane 

 of symmetry the intensity of the force of cohesion must be 

 null in this plane. In my theory, the departure from the law 

 of Pascal being proportional to the square of the intensity 

 of the force of cohesion*, we must have for each point of the 

 plane of symmetry : 



Pi=P2 ; 



and, further, 



Now, for every plane capillary layer (complete or incom- 

 plete) the hydrostatic pressure in a direction perpendicular 

 to its surface must be a constant t, and therefore the pres- 

 sure p must have in the considered plane the same value as 

 the vapour-pressure. In fig. 1 the curve HFK gives for a 

 complete plane capillary layer, for each point, the relation 

 between the pressure p and the reciprocal value of the 

 density. Now, if we could have a black spot, which might 

 consist of two 'incomplete capillary layers, which touch each 

 other in their plane of maximum density, the relation between 



|? and for each of the two symmetric incomplete layers, out 



* Phil. Mag. Oct. 1907, p. 523, Formula (22). t L. c. p. 515. 



2 A 2 



