On the Equilibrium of Vapour at a Curved Surface of Liquid. 449 



of another liquid at a lower level. With air at any thing ap- 

 proaching to ordinary atmospheric density to resist the pro- 

 cess, it is probable it would be too slow to show any results 

 unless in very long-continued experiments. But if the air be 

 removed as perfectly as can be done by well-known practical 

 methods, it is probable that the process will be very rapid ; it 

 would indeed be instantaneous, were it not for the cold of eva- 

 poration in one vessel and the heat of condensation in the other. 

 Practically, then, the rapidity of the process towards hydrostatic 

 equilibrium through vapour between detached liquids depends 

 on the rate of the conduction of heat between the several sur- 

 faces through intervening solids and liquids. "Without having 

 made either the experiment or any cal- 

 culations on the rate of conduction of 

 heat in the circumstances, I feel con- 

 vinced that in a very short time water 

 would visibly rise in the capillary tube 

 indicated in the diagram, and that, 

 provided care is taken to maintain 

 equality of temperature all over the 

 surface of the hermetically sealed ves- 

 sel, the liquid in the capillary tube 

 would soon take very nearly the same 

 level as it would have were its lower 

 end open — sinking to this level if the 

 capillary tube were in the beginning 

 filled too full, or rising to it if (as in- 

 dicated in the diagram) there were not 

 enough of liquid in it at first to fulfil 

 the condition of equilibrium. 



The following formulae show pre- 

 cisely the relations between curvatures, 

 differences of level, .and differences of 

 pressure with which we are concerned. 



Let p be the density of the liquid and o- that of the vapour, 

 and let T be the cohesive tension of the free surface per unit of 

 breadth, in terms of weight of unit mass as unit of force. Let 

 h denote the height of any point P of the free surface above 

 a certain plane of reference, which I shall call for brevity the 

 plane level of the free surface. This will be sensibly the actual 

 level of the free surface in regions (if there are any) with no part 

 of the edge (or bounding line of the free surface where liquid 

 ends and solid begins) at a less distance than several centimetres. 

 Lastly, let r and r 1 be the principal radii of curvature of the sur- 

 face at P. By Laplace's well-known law we have, as the equation 

 of equilibrium, , w m /l 1\ 



(1) 





Phil Mag. S. 4. Vol. 42. No. 282. Dec, 1871. 2 G 



