Change of State: Solid-Liquid. 39 



a liquid rises in a capillary tube so that its surface is concave 

 upwards, and (we may add) the pressure of the liquid is less 

 than at the plane surface, then the equilibrium vapour-tension 

 is less than at the plane surface. If the liquid falls in the tube, 

 so that the surface is convex and the pressure greater than 

 at the plane surface, then the equilibrium vapour-tension is 

 greater. It has been supposed that this difference of vapour- 

 tensions is due to the curvature of the surface; and Fitzgerald 

 has suggested that we may thus perhaps obtain a connexion 

 between "two apparently unrelated quantities," the evapo- 

 ration and the surface-tension (Phil. Mag. [5] viii. p. 384). 

 But while a very slight impurity in a liquid can greatly alter 

 the surface-tension, it has not been shown that it alters the 

 evaporation to the same degree. I think that we must look 

 for the explanation elsewhere than in the curvature of the 

 surface; and I shall endeavour to show that we may account 

 for the effect by the difference of pressures of the liquid at the 

 curved and plane surfaces. The curvature of the surface is 

 then, as it were, an accidental accompaniment of the difference 

 of pressure, and not the cause of the variation in the vapour- 

 tension. We might therefore expect to find the variation 

 taking place also at flat surfaces if the pressure be altered, 

 and with solid as well as with liquid bodies. We cannot 

 directly investigate the vapour-tension of flat surfaces under 

 pressure ; but I shall assume that we may here take, instead, 

 the rate at which exchange takes place when the solid and liquid 

 are in contact with each other. 

 Sir W. Thomson's formula is 



2T<t 

 P = *~^Z^> ( 5 > 



where 

 p is the vapour-tension in contact with the concave surface, 

 -ex is the vapour-tension in contact with the plane surface, 

 T is the surface-tension of the liquid, 



p and a the densities of the liquid and its vapour respectively, 

 r the radius of curvature of the curved surface. 

 If P be the difference between the hydrostatic pressures 

 just beneath the curved surface and just beneath the plane 

 surface, equation (5) may easily be put in the form 



p'-w-p? («) 



or a pressure P in the liquid increases the vapour-tension by 



an amount P — 



The following/proof of this formula,^ = w— P -, is, I believe, 



r 



