  We consider the possibility of extracting the bottom quark mass from LEP
data. The inclusive decay rate for $\zbb +\cdots$ is obtained at order $\as$ by
summing up the one-loop two-parton decay rate to the tree-level three-parton
rate. We calculate the decay width of the $Z$-boson into two and three jets
containing the $b$-quark including complete quark mass effects. In particular,
we give analytic results for a slight modification of the JADE clustering
algorithm. We also study the angular distribution with respect to the angle
formed between the gluon and the quark jets, which has a strong dependence on
the quark mass. The impact of higher order QCD corrections on these observables
is briefly discussed. Finally, we present numerical results for some popular
jet-clustering algorithms and show that, indeed, these three-jet observables
are very sensitive to the $b$-quark mass and well suited for its determination
at LEP.
