( 259 ) 
The Surface-tension and the Molecular Pressure. 
Let us imagine a liquid in equilibrium with its saturated vapour. 
In the transition layer we may assume the lines of force to be 
normal to the surface separating the two phases. Let us imagine 
this surface to be horizontal, therefore the lines of force in the 
capillary layer as being vertical. If the above considerations are 
correct, and if we assume that the substance fills the space contin- 
uously with a mean density, we shall find for the surface tension 
exactly the same value as is deduced from the calculations of van 
DER Waars in his “Theorie der capillariteit’. Let us first calculate 
the molecular pressure; i.e. the force, with which a column of the 
surface layer with the unity of transverse section is attracted down- 
wards in the direction of the liquid by the surrounding substance. 
Per unit of surface we found a pressure, indicated by the formula: 
ae 555 (5). 
The force we are speaking of, which we shall call £, is nothing 
but the difference between the absolute values of the pressure D on 
the upper and the lower surfaces of the column of the surface layer. 
Let us call the potential in the vapour wg and in the liquid yw, 
and let us bear in mind that both in the vapour and in the liquid 
R may be put equal to zero, then we find: 
2 2 
A ear | a 
8a f A ) 
1 
BE (iet 2) — 
1) The pressures in consideration are here negative and therefore properly speaking, 
tensions. For the rest the ideas tension and pressure are somewhat arbitrary. There 
is no objection to adding an everywhere equal amount to the pressure and the ten- 
sion through the whole mass. The new system of pressures and tensions will give a 
representation of the system of forces as well as the original. This appears immedia- 
tely from the form of the space-integral, which represents the force between two parts 
of the system : 
a kOe / ] 
x= (Ln Oe eee ee 
da dy dz 
The coefficient of dr consists of the sum of three differential coefficients. Therefore 
constant amounts may be added to per, pe, and pos. 
If the hydrostatic pressure through the whole mass is equal to the external pressure 
: 1 7 
and if only the pressure of the air acts on the system, the pressure (ts 
8x f A 
is equal to the pressure with reversed sign, leaving a constant out of account. 
