  The two-dimensional sloshing problem is considered; it describes the
transversal free oscillations of water in an open, infinitely long canal of
uniform cross-section. It is proved that the fundamental eigenfrequency is
simple, whereas the corresponding velocity potential has only one nodal line
connecting the free surface and the bottom; its harmonic conjugate (stream
function) does not change sign under the proper choice of the additive
constant.
