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XLII. On the Tension of Vapours near Curved Surfaces of their 

 L iq u ids. By Geo. Francis Fitzgerald, M.A., F. T. CD* 



SIR W. THOMSON showed, in the Proc. Roy. Soc. of 

 Edinburgh, Feb. 7, 1870, that the maximum tension of a 

 vapour at the curved surface of its liquid when convex was 

 greater, and when concave less than when flat. He deduced 

 this as a consequence of the ascent of liquids in capillary 

 tubes, by pointing out that the tension of vapour at the top 

 and bottom of the column of liquid differs by the weight of a 

 column of the vapour of that length, while it is impossible to 

 suppose that there can be a continual distillation from the flat 

 surface of the liquid to the curved one in the tube. He does 

 not seem, however, to have observed how this result is con- 

 nected with the ordinary theories of evaporation; and it is this 

 connexion which I desire to point out. 



Assuming, as seems very probable, that evaporation is due 

 to the escape of molecules of the liquid, not from the surface 

 only, but from a very small depth indeed beneath it as well, 

 and that the chances of escape are less the longer the path of 

 the molecule within the liquid, it is at once obvious that a mo- 

 lecule situated at a given depth below the surface will have a 

 much better chance of escape if the surface be convex than if 

 it be flat, and better still than if concave. On the other hand, 

 one tending to enter the liquid from a given depth in the va- 

 pour has a less chance of entering a convex surface than a flat 

 one, and still less than of entering a concave one. Hence, in 

 order that the equality between the numbers entering and 

 leaving the surface may be maintained (i. e. in order to pre- 

 vent either evaporation or condensation), the tension of the 

 vapour would have to be greater when in contact with a con- 

 vex surface than when in contact with a flat, and still greater 

 than when in contact with a concave surface. 



If the matter be investigated mathematically, it may be treated 

 very generally indeed if we assume that the depth from which 

 evaporation takes place is so small compared with the radii of 

 curvature of the surface of the liquid, that powers of the ratio 

 of the former to the latter above the first may be neglected. 

 This is certainly legitimate in all cases that can be observed ; 

 for the depth from which evaporation takes place must be very 

 small indeed compared with the radii of curvature of the sur- 

 faces with which we have to deal. 



* Communicated by the Author, having been read at the Meeting of 

 the British Association in Sheffield. 



