  Measuring the top quark mass in its semileptonic decay mode, $t ->be^+\nu$
($b -> \mu^- + X$), through the mass distribution of the $e^+$--$\mu^-$ pair
has been shown to provide a good measurement of the top quark mass with an
uncertainty of $1.6\%$ for $m_t=150,250\,$GeV at the SSC. Here it is
demonstrated that an uncertainty in the polarization of the top quark can add
an additional uncertainty of about $3%$ in the mass. [Talk presented at the
Workshop on Physics at Current Accelerators and the Supercollider held at the
Argonne National Laboratory, Argonne, Illinois, 2-5 June 1993.]
