  We explore the classical version of the mapping, due to Abanov and Wiegmann,
of Calogero-Sutherland hydrodynamics onto the Benjamin-Ono equation ``on the
double.'' We illustrate the mapping by constructing the soliton solutions to
the hydrodynamic equations, and show how certain subtleties arise from the need
to include corrections to the naive replacement of singular sums by
principal-part integrals.
