∫∞z ψ(z) dz = θ(z),
then 2πmρθ(z) will express the work done by-the attractive forces, while a particle m is brought from an infinite distance to a distance z from the plane surface of a mass of the substance of density ρ and infinitely thick. The function θ(z) is insensible for all sensible values of z. For insensible values it may become sensible, but it must remain finite even when z = 0, in which case θ(0) = K.
If χ′ is the potential energy of unit of mass of the substance in vapour, then at a distance z from the plane surface of the liquid
χ = χ′ − 2πρθ(z).
At the surface
χ = χ′ − 2πρθ(0).
At a distance z within the surface
χ = χ′ − 4πρθ(0) + 2πρθ(z).
If the liquid forms a stratum of thickness c, then
χ = χ′ − 4πρθ(0) + 2πρθ(z) + 2πρθ(z − c).