If the liquid forms a stratum of thickness c, then

[chi] = [chi]' - 4[pi][rho][theta](0) + 2[pi][rho][theta](z) +

+ 2[pi][rho][theta](z - c).

The surface-density of this stratum is [sigma] = c[rho]. The energy

per unit of area is

_

/ c

e = | [chi][rho]dz = c[rho]([chi]' - 4[pi][rho][theta](0)) +

_/0

_ _

/ c / c

+ 2[pi][rho]^2 | [theta](z)dz + 2[pi][rho]^2 | [theta](z - c)dz.

_/0 _/0

Since the two sides of the stratum are similar the last two terms are

equal, and

_

/ c

e = c[rho]([chi]' - 4[pi][rho][theta](0)) + 4[pi][rho]^2 | [theta](z)dz.

_/0

Encyclopaedia Britannica, 11th Edition, "Capefigue" to "Carneades" Volume 5, Slice 3 · 第 17 / 74 题