  We present results on the static three- and four-quark potentials in SU(3)
and SU(4) respectively within quenched lattice QCD. We use an analytic
multi-hit procedure for the time links and a variational approach to determine
the ground state. The three- and four-quark potentials extracted are consistent
with a sum of two-body potentials, possibly with a weak many-body component.
The results give support to the $\Delta$ ansatz for the baryonic area law.
