  We propose an experiment that would demonstrate the ``dc'' and ``ac''
Josephson effects in two weakly linked Bose-Einstein condensates. We consider a
time-dependent barrier, moving adiabatically across the trapping potential. The
phase dynamics are governed by a ``driven-pendulum'' equation, as in
current-driven superconducting Josephson junctions. At a critical velocity of
the barrier (proportional to the critical tunneling current), there is a sharp
transition between the ``dc'' and ``ac'' regimes. The signature is a sudden
jump of a large fraction of the relative condensate population. Analytical
predictions are compared with a full numerical solution of the time dependent
Gross-Pitaevskii equation, in an experimentally realistic situation.
