  We report on measurements of an elementary surface mode in an ultracold,
strongly interacting Fermi gas of 6Li atoms. The radial quadrupole mode allows
us to probe hydrodynamic behavior in the BEC-BCS crossover without being
influenced by changes in the equation of state. We examine frequency and
damping of this mode, along with its expansion dynamics. In the unitarity limit
and on the BEC side of the resonance, the observed frequencies agree with
standard hydrodynamic theory. However, on the BCS side of the crossover, a
striking down shift of the oscillation frequency is observed in the
hydrodynamic regime as a precursor to an abrupt transition to collisionless
behavior; this indicates coupling of the oscillation to fermionic pairs.
