of the mass and to be gradually expanded in such a shape that
the walls consist almost entirely of two parallel planes. The distance
between the planes is supposed to be very small compared with their
ultimate diameters, but at the same time large enough to exceed the
range of the attractive forces. The work required to produce this
crevasse is twice the product of the tension and the area of one of
the faces. If we now suppose the crevasse produced by direct
separation of its walls, the work necessary must be the same as
before, the initial and final configurations being identical; and we
recognize that the tension may be measured by half the work that must
be done per unit of area against the mutual attraction in order to
separate the two portions which lie upon opposite sides of an ideal
plane to a distance from one another which is outside the range of the
forces. It only remains to calculate this work.

If [sigma]1, [sigma]2 represent the densities of the two infinite
solids, their mutual attraction at distance z is per unit of area
_
/ [oo]
2[pi][sigma]1[sigma]2 | [psi](z)dz, (30)
_/z

or 2[pi][sigma]1[sigma]2[theta](z), if we write
_
/ [oo]
| [psi](z)dz = [theta](z). (31)
_/z

The work required to produce the separation in question is thus
_
/ [oo]
2[pi][sigma]1[sigma]2 | [theta](z)dz; (32)
_/ 0

and for the tension of a liquid of density [sigma] we have
_
/ [oo]
T = [pi][sigma]^2 | [theta](z)dz. (33)
_/0

The form of this expression may be modified by integration by parts.
For
_ _ _
/ / d[theta](z) /
| [theta](z)dz = [theta](z).z - | z -----------dz = [theta](z).z + | z[psi](z)dz.
_/ _/ dz _/

Since theta(0) is finite, proportional to K, the integrated term
vanishes at both limits, and we have simply
_ _
/ [oo] / [oo]
| [theta](z)dz = | z[psi](z)dz, (34)
_/0 _/0

and
_
/