  The effect of the heavy b-quark mass on the two, three and four-jet rates is
studied using LEP data collected by the DELPHI experiment at the Z peak in 1994
and 1995. The rates of b-quark jets and light quark jets (l = uds) in events
with n = 2, 3, and 4 jets, together with the ratio of two and four-jet rates of
b-quarks with respect to light-quarks, R_n^bl, have been measured with a
double-tag technique using the CAMBRIDGE jet-clustering algorithm. A comparison
between experimental results and theory (matrix element or Monte Carlo event
generators such as PYTHIA, HERWIG and ARIADNE) is done after the hadronisation
phase. Using the four-jet observable R_4^bl, a measurement of the b-quark mass
using massive leading-order calculations gives: m_b(M_Z) = 3.76 +/- 0.32 (stat)
+/- 0.17 (syst) +/- 0.22 (had) +/- 0.90 (theo) GeV/c^2 . This result is
compatible with previous three-jet determinations at the M_Z energy scale and
with low energy mass measurements evolved to the M_Z scale using QCD
Renormalisation Group Equations.
