Theory of Surface Forces. 117 
For a homogeneous agent we have : 
0^ on 
The differential equation passes therefore for a homogeneous 
agent into the equation : 
V + 4ttA-> = 0- 
According to the theory of Gauss and van der Waals the 
potential energy of the forces of attraction must be in this 
case 
Y=—2ap, 
where a denotes the coefficient of the expression for the so- 
called molecular pressure of Laplace. Hence 
2w/X 8 =a. 
For a capillary layer, having the form of a spherical shell. 
concave towards the vapour, we have therefore : 
where R denotes the radius of the sphere of equal density, 
which passes through the considered point, while dh indicates 
the differential of the normal (radius) to the surface of the 
capillary layer. This differential is reckoned positive in the 
direction : liquid »- vapour. 
If p denotes the pressure for a point of the theoretical 
isotherm, which corresponds to the density of the considered 
point in the capillary layer* we call fi=\v dp the thermo- 
dynamical potential in the considered point of the capillary 
layer. If ^ indicates the value of /x in the homogeneous 
phase of the liquid we have : 
V + 2,/ ; o- / a 1 - y uf (11) 
For the homogeneous liquid- and vapour-phases, which 
limit the capillary layer, the potential V may be expressed by 
the formula of Gauss and van der Waals : 
Y=-2ap, 
and therefore 
when fii and /i v indicate resp. the value of the thermo- 
dynamical potential in the liquid and in the vapour. In 
* We say that a point of the theoretical isotherm corresponds with a 
point in the capillary layer, when the specific volume of the first has the 
reciprocal value of the density of the latter. 
f Phil. Mag. October 1907, p. 516 ; equation (4). 
