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LX. On the Equilibrium of Vapour at a Curved Surface of 

 Liquid. By Sir William Thomson, F.R.S.* 



IN a closed vessel containing only a liquid and its vapour, all 

 at one temperature, the liquid rests, with its free surface 

 raised or depressed in capillary tubes and in the neighbour- 

 hood of the solid boundary, in permanent equilibrium according 

 to the same law of relation between curvature and pressure as 

 in vessels open to the air. The permanence of this equilibrium 

 implies physical equilibrium between the liquid and the vapour 

 in contact with it at all parts of its surface. But the pressure 

 of the vapour at different levels differs according to hydrostatic 

 law. Hence the pressure of saturated vapour in contact with a 

 liquid differs according to the curvature of the bounding surface, 

 being less when the liquid is concave and greater when it is con- 

 vex. And detached portions of the liquid in separate vessels all 

 enclosed in one containing vessel cannot remain permanently 

 with their free surfaces in any other relative positions than those 

 they would occupy, if there were hydrostatic communication of 

 pressure between the portions of liquid in the several vessels. 

 There will be evaporation from those surfaces which are too high, 

 and condensation into the liquid at those surfaces which are too 

 low — a process which will go on until hydrostatic equilibrium, 

 as if with free communication of pressure from vessel to vessel, 

 is attained. Thus, for example, if there are two large open 

 vessels of water, one considerably above the other in level, and 

 if the temperature of the surrounding matter is kept rigorously 

 constant, the liquid in the higher vessel will gradually evaporate 

 until it is all gone and condensed into the lower vessel. Or if, 

 as illustrated by the annexed diagram, a capillary tube with a 

 small quantity of liquid occupying it from its bottom up to a 

 certain level be placed in the neighbourhood of a quantity of the 

 same liquid with a wide free surface, vapour will gradually be- 

 come condensed into the liquid in the capillary tube until the 

 level of the liquid in it is the same as it would be were the lower 

 end of the tube in hydrostatic communication with the large 

 mass of liquid. Whether air be present above the free surface 

 of the liquid in the several vessels or not, the condition of ulti- 

 mate equilibrium is the same ; but the processes of evaporation 

 and condensation through which equilibrium is approached will 

 be very much retarded by the presence of air. The experi- 

 ments of Graham and the kinetic theory of Clausius and Max- 

 well scarcely yet afford us sufficient data for estimating the 

 rapidity with which the vapour proceeding from one of the 

 liquids will diffuse itself through the air and reach the surface 



* From the Proceedings of the Royal Society of Edinburgh, Session 

 1869-/0. Communicated by the Author, 



