Theory of Surface Forces. 139 



Surface of the capillary layer, while R' signifies the radius 

 of the sphere we construct through the considered point 

 concentric to the surface of the little drop. By integration 

 of (2) I found : 



Pi-]h- = 2\ J — w (3) 



The quantity R K of Kelvin is at curvatures not too strong* 

 consequently represented by: 



Generally R K is not identical with R= — —' 9 — -. 



> We now wish to bring R K and R into connexion with 

 each other. For that reason we consider the equilibrium of 

 the spherical capillary layer under the influence of the pres- 

 sures resp. of the liquid (inside R x ) and of the vapour around 

 the little di;op in the same way as the hemispheres in the 

 celebrated experiment of Otto von Guericke on the atmo- 

 spherical pressure. If the thickness of the capillary layer is 

 represented by f, and the pressure parallel to the surface for 

 a point of the capillary layer is denoted by p. r , we find as the 

 condition for the equilibrium: 



M^-m 2 Jh-^(^ + m 2 pr=-27r\ 2 pT R'dh 



«. i 



= -2>ir\ 2 p T (R—JiZ+'h)dh. . . (4) 



As the thickness of a capillary layer only amounts to few 

 millimicrons, we may, in the case when R is of the order of a 

 micron or larger, neglect the terms with f 2 /R 2 > an( l have: 



Pir-Pv 



2f (£±&-£)t 



R 



* The surface-tension being the integral of the departure from Pascal's 

 law with respect to the volume elements, and not with respect to dh. 



t If f * pidlr is represented by pr'( 2 , the complete equation is 



