Theory of Surface Forces. 353 



The thickness of the capillary layer, which limits the 

 spherical drop, being of the order of greatness of 2 [ifi, and 

 its homogeneous part having a radius of about 1 y^i, we 

 take for the radius of the sphere, about which we distribute 

 the surface energy, a value of 2 [jljul. The collective surface 

 of the spherical drops of minimal size becomes therefore : 



4tt . 2 2 . 10- 14 _ 3 



4tt.2 3 .10 2l 2 X °*' 



or 4*5 times the value which we find for the surface of the 

 plane film. The order of greatness of the value of the depar- 

 ture from the law of Pascal of the spherical capillary layer, 

 which limits a drop of minimal size, as we have demonstrated 

 above, being the same as the capillary tension in a plane 

 capillary layer (constant of Laplace), we find thus for the 

 energy required to crumble most completely a mass of water 

 of 1 gramme a value which has the order ot" greatness of 

 4*5 x 9 = about 40 minor cal. 



The finest haze of water at ordinary temperature is therefore 

 still far remote from the vapour state. 



In his calculation of the smallest limit of the thickness of 

 water-films, Kelvin firstly supposes that the contractile force 

 of a thin plane film is independent of its thickness. "We have 

 seen that the theory as well as the experiment of Johonnott 

 gives really the same result. Supposing secondly that the 

 pint remains stabile, Kelvin finds for its minimal thickness a 

 value of about O'l /-t/x, and this would give for the thickness 

 of the capillary layer a value of about 0*03 /jl/jl. If, however, 

 my considerations above are exact, the minimum of the thick- 

 ness of the plane capillary layer of water at ordinary 

 temperatures would be about 2 fi/jb and the second supposition 

 of Kelvin may not be admitted. 



Observation II. 



By the aid of the numbers given by Loschmidr, we find at 100° 

 Celsius for the number of the molecules in a cubic millicron 

 of water : 32. Now I have found above for the order of 

 greatness of the radius of a drop of water, which has its 

 minimal size at 100° Celsius : 10 /zu. Hence follows easily 

 by calculation that the order o£ greatness of the number of 

 molecules in the considered water-drop of minimal size is about 

 80,000. Accumulations of 100 or 200 molecules for instance 

 cannot therefore form a stabile water-drop in the vapour of 

 water at 100° Celsius. Only when a kernel of sufficient size 

 is formed, is its field of force strong enough to prevent 



