346 Dr. G. Bakker on the 



same manner as we have found for the order of greatness of 

 the thickness of a liquid film of minimal thickness circa three 

 times the thickness of a complete plane capillary layer, 

 we conclude : 



when at a fixed temperature the size of a spherical drop of liquid 

 has its minimal value, the radius of its spherical capillary layer 

 has a value of the order of greatness of the thickness of a 

 capillary layer. 



For the value of the "radius"* of a spherical capillary 

 layer Kelvin has given the formula : 



9 H 

 R = -^5 — a5) 



^liq.-.Pvap. 



where H denotes the departure from the law of Pascal for 

 the spheri-capillar y layer, and pn q . and J9 vap . respectively the 

 pressures in the corresponding liquid and vapour phases 

 which surround the capillary layer. For the case when the 

 drop has its minimal size I have calculated by the aid of the 

 formula (15) the value of B, and I have found in the following- 

 manner a value, which really is of the order of the thickness of 

 the capillary layer. The state of the liquid phase in the 

 interior of the "liquid" drop (that is to say, the homogeneous 

 part) when the drop has its minimal size and the state of the 

 homogeneous phase of the vapour which surrounds the drop, 

 are respectively given by the points A 8 and C 8 of the fig. 1 

 above. This figure has the following meaning f : — 



Every pair of points of the isotherm, for which the t her mo- 

 dynamical potential has the same value (as A 8 and C 8 , A 7 and 

 C 7 , &c), corresponds above the rectilinear part HK of the 

 empiric isotherm to a spherical drop of liquid, such, that the 

 state in the interior of the drop and the state of the vapour 

 which surrounds it, are determined in a singular ma?mer by the 

 situation of this pair of points. In the same manner, every 

 pair of points below the rectilinear part HK of the empiric 

 isotherm (A 3 and 3 , A 2 and C 2 , &c), for which the thermo- 

 dynamical potential has the same value, corresponds to a 

 spherical bubble of vapour. If we now construct the curves, 

 such as A c B 6 6? A3B3C3, &c, which present the relation between 



j 7 /» ,7 P\ -^-P'l 7 . ... 



half the sum p = x — ^-— of the maximum and minimum 



* By this radius I mean a value between the values of the radii of the 

 spheres which limit the spherical capillary layer internally and externally. 

 The effective radius would be therefore about % times the thickness of 

 the capillary layer. 



t Phil. Mag. April 1908, p. 430. 



