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Quantitative estimates are
derived, describing the size and shape of a symmetric (idealized) liquid drop, resting
in gravitational equilibrium on a plane surface Π. The free surface interface is
determined by the conditions that its mean curvature be a given (increasing) linear
function of distance from Π, that it enclose with Π a prescribed volume V , and that
the angle formed with Π be a prescribed constant γ. The estimates apply to drops of
all sizes, and some are asymptotically exact in the limiting cases of large or small
wetted area on Π. It is shown that a number of qualitative features of behavior are
determined by the ratio V∕sinγ∕2. This ratio is in turn related to a ratio
that appears in the study of the circular capillary tube, thus indicating a
reciprocity between th,e two problems, which becomes exact in both limiting
cases.
As corollaries of the method, the uniqueness of the symmetric solution is proved,
and a new proof of existence is given.
The results are compared with calculations and with measurements in some
particular cases.
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