156 



On the Theory of Surface Forces. 



The equation (57) becomes thus 



pi- pi 



«r? 



(61) 



If we now consider the plane capillary layer as a limit- 

 case of the cylindrical of small curvature, we must take in 

 (61) R = cc . As JV 2 — C 2 always remains small, we have 



lim. 



H 2 



P1-P2 



= for R = oo. 



So we have for the plane capillary layer p= " l -. 



I.e.-. if we have a plane capillary layer the volume of 

 which amounts to one cm 3 *, this capillary layer contains as 

 much matter as the totality of half a cm 3 of liquid and half 

 a cm 3 of vapour. 



For the contribution of the liquid resp. vapour at the 

 formation of the capillary layer (per unit of mass) (see 

 § 4) we found : 



Pi—P2 



p\-rp\pi 



and 



P1-P2 



For the plane capillary layer these quantities are thus : 



/l - , . pi+p2\ 

 [~=P being "-/-) 



pi 



P1 + P2 



and 



Liquid and vapour contribute consequently to the plane 

 capillary layer quantities resp. proportional <o theii densities. 



In consequence of the law of Cailletet and Mathias (the 

 so-called law of the rectilinear diameter) p x + p? is in the 

 case when the homogeneous phases of the liquid and the 

 vapour are separated by a plane capillary layer a decreasing 

 linear function of the temperature, or 



where a represents a constant, p K the critical density, and 

 T K the critical temperature. 



* For water at ordinary temperature the surface of the considered 

 capillary layer becomes about 500 ni 2 . 



