ace to contract
itself is called the surface-tension of liquids.

[Illustration: FIG. 1.]

+-----------------------+
|///////////////////////|
|///////////////////////|
|//A+---------------+A//|
|///| |///|
|///| |///|
B =========================== B
|///|C C|///|
+---+ +---+

Dupre has described an arrangement by which the surface-tension of a
liquid film may be illustrated. A piece of sheet metal is cut out in
the form AA (fig. 1). A very fine slip of metal is laid on it in the
position BB, and the whole is dipped into a solution of soap, or M.
Plateau's glycerine mixture. When it is taken out the rectangle AACC
if filled up by a liquid film. This film, however, tends to contract
on itself, and the loose strip of metal BB will, if it is let go, be
drawn up towards AA, provided it is sufficiently light and smooth.

Let T be the surface energy per unit of area; then the energy of a
surface of area S will be ST. If, in the rectangle AACC, AA = a, and
AC = b, its area is S = ab, and its energy Tab. Hence if F is the
force by which the slip BB is pulled towards AA,

d
F = --- Tab = Ta, (6)
db

or the force arising from the surface-tension acting on a length a of
the strip is Ta, so that T represents the surface-tension acting
transversely on every unit of length of the periphery of the liquid
surface. Hence if we write
_
/ [epsilon]
T = | ([chi] - [chi]0) [rho] d[nu], (7)
_/0

we may define T either as the surface-energy per unit of area, or as
the surface-tension per unit of contour, for the numerical values of
these two quantities are equal.

If the liquid is bounded by a dense substance, whether liquid or
solid, the value of [chi] may be different from its value when the
liquid has a free surface. If the liquid is in contact with another
liquid, let us distinguish quantities belonging to the two liquids by
suffixes. We shall then have
_
/ [epsilon]1
E1 - M1[chi]01 = S | ([chi]1 - [chi]01) [rho]1 d[nu]1, (8)
_/ 0
_
/ [epsilon]2
E2 - M2[chi]02 = S | ([chi]2 - [chi]02) [rho]2 d[nu]2. (9)
_/ 0

Adding these exp