The surface-density of this stratum is σ = cρ. The energy per unit of area is

e = ∫c0 χρ dz = cρ (χ′ − 4πρθ(0)) + 2πρ² ∫c0 θ(z) dz + 2πρ² ∫c0 θ(z − c) dz.

Since the two sides of the stratum are similar the last two terms are equal, and

e = cρ (χ′ − 4πρθ(0)) + 4πρ² ∫c0 θ(z) dz.

Differentiating with respect to c, we find

dσ = ρ,   de = ρ (χ′ − 4πρθ(0)) + 4 πρ²θ(c).
dc dc

Hence the surface-tension

T = e − σ de4πρ² (∫c0θ(z) dz − cθ(c)).
dσ

Integrating the first term within brackets by parts, it becomes

cθ(c) − 0θ(0) −∫c0z dθdz.
dz