381 Tension of Vapours near Curved Surfaces of their Liquids. 



case of a surface curved in the opposite direction. From the 

 considerations mentioned in the beginning of the paper, it is 

 obvious that Nj must be positive when the surface is convex. 

 In order to obtain the numbers admitted to the surface, we 

 should have to substitute in the foregoing investigation the 

 function corresponding to vapour f or f(r) that corresponds to 

 the liquid ; but the rest of the investigation is the same, it 

 being recollected that when the surface of the liquid is convex 

 that of the vapour is concave, and vice versa. Hence in the 

 case of a convex liquid surface, we may write those emitted as 



and those admitted as 



and for equilibrium we must have 



N^o=N +(N 1 .+^ 1 )(l + g). 



In discussing this result, it is to be observed that an increase 

 in the tension of the vapour probably produces little or no 

 effect upon the numbers emitted, and that consequently N 

 depends only upon the nature and temperature of the liquid ; 

 and it is the number that would be emitted or admitted if the 

 surface were flat, and the tension the maximum corresponding 

 to its state. On the other hand, the change in the numbers 

 that would be admitted to a flat surface is proportional to the 

 change in tension at that surface; so that changes in W are 

 proportional to the changes in tension of the vapour. We thus 

 at once conclude that the maximum tension of vapour in con- 

 tact with a convex surface of a liquid must be greater than 

 that at a flat one by a quantity which varies directly as the 

 sum of the curvatures of the surface. We know from Sir W. 

 Thomson's investigation, that the coefficient by which this sum 

 of curvatures is multiplied is proportional to the tension of the 

 surface of the liquid ; and we can thus connect two apparently 

 unrelated quantities, namely the rate of evaporation with the 

 superficial tension. As f(r) is the only unknown in the fore- 

 going investigation, it might be possible to determine it by 

 observing the rates of evaporation from drops of various sizes. 

 That the tension of the vapour was connected with the sum 

 of the curvatures might also have been suspected from the 

 equilibrium of the surface requiring the normal pressure to 

 vary with this same sum. 



