  The bottom quark 1S mass, $M_b^{1S}$, is determined using sum rules which
relate the masses and the electronic decay widths of the $\Upsilon$ mesons to
moments of the vacuum polarization function. The 1S mass is defined as half the
perturbative mass of a fictitious ${}^3S_1$ bottom-antibottom quark bound
state, and is free of the ambiguity of order $\Lambda_{QCD}$ which plagues the
pole mass definition. Compared to an earlier analysis by the same author, which
had been carried out in the pole mass scheme, the 1S mass scheme leads to a
much better behaved perturbative series of the moments, smaller uncertainties
in the mass extraction and to a reduced correlation of the mass and the strong
coupling. We arrive at $M_b^{1S}=4.71\pm 0.03$ GeV taking
$\alpha_s(M_Z)=0.118\pm 0.004$ as an input. From that we determine the
$\bar{MS}$ mass as $\bar m_b(\bar m_b) = 4.20 \pm 0.06$ GeV. The error in $\bar
m_b(\bar m_b)$ can be reduced if the three-loop corrections to the relation of
pole and $\bar{MS}$ mass are known and if the error in the strong coupling is
decreased.
