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XX. On the Law of Molecular Force. 

 By William Sutherland, M.A., B.Sc* 



[Concluded from p. 134.] 



IT is not difficult to illustrate how profoundly the relations 

 of pressure and density of saturated vapour may be 

 affected by capillary action at temperatures near the critical. 

 Sir William Thomson has shown (Proc. Roy. Soc. Edinb., 

 Feb. 1870) that, if inside a closed vessel containing a liquid 

 and its vapour a capillary tube dips into the liquid, the 

 pressure of saturation p of the vapour in contact with the 

 free curved surface of the liquid in the capillary tube is con- 

 nected with w, the pressure of saturation of the vapour in 

 contact with the plane surface, by the equation 



E<7 /l 1\ 



P = <UT— — — -+ ~~ f l 



r p — <r\r r/ 



where E is the surface energy of the liquid per unit area, 

 a the average density of the vapour between the levels of the 

 free surfaces of the liquid inside and outside the capillary 

 tube, p the density of the liquid, r and r' are the principal 

 radii of curvature of the curved surface of the liquid in the 

 tube, reckoned as positive when the surface is concave to the 

 vapour, that is when the liquid rises in the tube. 



At temperatures near the critical, when cr becomes nearly 



equal to p, the factor becomes very large. It has been 



assumed by some writers that E( - + — j vanishes at the 



critical temperature, and therefore becomes very small at 

 temperatures near the critical, on the supposition that, as the 

 critical temperature is the limiting temperature at which 

 capillary elevation or depression can occur in a tube, the 

 plane surface is naturally the limiting form which the free 

 surface of the liquid in a capillary tube attains at the critical 

 temperature. But that the plane surface is not a limiting 

 case is shown by such an ordinary example as the convex 

 meniscus of mercury in a glass tube. However, we have the 

 definite experiments of Wolf (Ann. de Chim. et de Pliys. 

 3 ser. xlix., 1857) to show that the plane surface is not the 

 limiting form of a capillary meniscus at the critical tem- 

 perature ; for he found that sulphuric ether, sulphide of 

 carbon, naphtha, and alcohol at temperatures near their 

 * Communicated by the Author. 



