  Recently a brane world perspective on the cosmological constant and the
hierarchy problems was presented. Here, we elaborate on some aspects of that
particular scenario and discuss the stability of the stationary brane solution
and the dynamics of a probe brane. Even though the brane is unstable under a
small perturbation from its stationary position, such instability is harmless
when the 4-D cosmological constant is very small, as is the case of our
universe. One may also introduce radion stabilizing potentials in a more
realistic scenario.
