Theory of Surface Forces. 515 



where h denotes the thickness of the capillary layer, and p 

 the average pressure in the direction of the surface, we have 



*— ?. w 



For water the surface-tension being H = 76 (dyne pro cm. 

 or erg pro cm. 2 J, and adopting in connexion with the in- 

 vestigations of Reinold and Rucker, h = \0 fjbfjb, we find for 

 water at ordinary temperature : 



p = — tttz 6 = — 76 . 10 6 or nearly —76 atmospheres. 



Whereas the black spots may be in equilibrium with the 

 complete capillary layer, and the thickness of the black spots 

 may be less than 5 fifi (Reinold and Rucker), the absolute value 

 of the negative pressure in the black spots of a film of soap- 

 solution may be larger than 150 atmospheres. 



That the pressure perpendicular to the surface of the 

 capillary layer must be equal to the vapour-pressure, we see 

 in considering the well-known statement of the theory of 

 elastic forces: 



dPzs dpyy "dPzz _ ft ». 



a* + ay + a* ' 



when we choose the --axis normal to the surface. 



The gradient of the properties of the capillary layer being 

 normal to its surface : 



0% oy 



Hence ^p 22 



-^— — =0 or p zz = constant. 



In the homogeneous phases of the liquid and the vapour 

 adjacent to the capillary layer, the pressure being the vapour- 

 pressure, we have : 



p zz = vapour-pressure =pi, 

 putting p 1 = vapour-pressure. 



§ 3. The average value p of the Pressure p 2 parallel to the 

 surface of the Capillary Layer and the Theoretical 

 Isotherm of James Thomson and van der Waals. 



When we may not neglect the vapour-pressure pi we must 

 complete the equation (2 a) to 



2 f p 2 dh-2p l h + 2~H.=0. 



* Gravitation is not considered. 



