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XII. On the Theory of Surface Forces. — V. Thermodynamics 



of the Capillary Layer between the Homogeneous Phases of 

 the Liquid and the Vapour. By G. Barker*. 





t 



§ 1. Some definitions and mathematical significations. 



HE surface-tension of Laplace may be conceived in two 

 ways. Firstly, as the increase of the available energy, 

 when a part of the liquid- and vapour-phase is converted 

 isothermally into the matter of the capillary layer, in con- 

 sequence of which the surface of the latter has increased by 

 a unit of surface. The contributions of both homogeneous 

 phases to the formation of the capillary layer are here com- 

 pletely determined, as we assume that liquid and vapour 

 are present in abundance, while the influence of the walls of 

 the vessel is not considered. We imagine the process to be 

 very slow. 



What we call a unit of surface for a plane capillary 

 layer is evident. For a spherical capillary layer we deter- 

 mine it as follows. The spherical capillary layer lies between 

 two concentric spheres. The radius of the smaller sphere 

 we call R x and that of the larger one R 2 . We take as 

 the " surface ?' of the capillary layer that of the sphere the 



radius of which has the value R= — ^ — -. The capillary 



energy that belongs to one unit of this spherical surface 

 we call the capillary energy or constant of Laplace. If the 

 •curvature of the capillary layer is small (e. g. measurable) 

 it is unnecessary to distinguish R 1? R 2 , and R. However, 

 if the curvature is very large (R 2 — R x and R may be of the 

 same order of magnitude f) we conceive a great many parts 

 •of spherical capillary layers of equal curvature, the collective 

 surface of the resp. spherical surfaces with radius R being 

 unity. The surface energy or the available energy, pro- 

 duced at the formation of the capillary layer per unit of 

 surface (radius R) we represent by H. Fuchs proposed 

 another conception for the surface-tension of Laplace. He 

 perceived that the cohesion in directions respectively perpen- 

 dicular and parallel to the surface of the capillary layer has 

 not the same value. The difference between these cohesions 

 he considered as the cause of the surface-tension. He has 

 however in this way not calculated the surface energy J. 



* Communicated bv the Author. 



t G. Bakker, Phil. Mag. March 1909, p. ?A6. 



% K. Fuchs, Wiener Ber. xcviii. 2 Nov. 1889. 



