  We develop the hydrodynamic theory of Fermi superfluids in the presence of a
periodic potential. The relevant parameters governing the propagation of sound
(compressibility and effective mass) are calculated in the weakly interacting
BCS limit. The conditions of stability of the superfluid motion with respect to
creation of elementary excitations are discussed.
  We also evaluate the frequency of the center of mass oscillation when the
superfluid gas is additionally confined by a harmonic trap.
