THERMODYNAMICS OF CHANGE OF STATE, ETC. 315 



If o) be the pressure of vapour at B and <o' be its value at A, and if 

 h, the intervening height, is so small that we may regard the density 

 of the vapour <r as uniform, we have 



We may express h in terms of the surface tension T and the radius of curva- 

 ture r of the surface. The pressure in the liquid just under the surface A is 



, 2T 



CO - , 



r 



therefore the pressure in the liquid at the level of the plane surface is 



where p is the density of the liquid. But this is equal to the pressure 

 of the vapour outside at the same level, viz., 



to = a/ + gcr h 



equating we get 



2T 

 ~=9(p-<r)h 



, 2T <r 



whence w-to = -- . 



r p " 



If the surface is convex, so that the liquid is depressed in the tube, we 

 have 



2T <r 



(00) = 



r p-a- 



The expression is simpler if we introduce the difference of hydrostatic 

 pressures P under the curved and under the plane surfaces. This is 



or 



P<r 



whence w w = . 



P 



If the height Ji is great we cannot take <r as uniform. We must 

 then integrate the change in pressure with the varying density as we 

 descend from A to B. 



Let dli be a small step down, and let c?co be the change in pressure in 

 the step, cr being the density. 



Then d(a 



and a) = Ko- (Boyle's law) 



whence d = gdh 



