  A measurement of the mass of the $W$ boson is presented based on a sample of
5982 $W \rightarrow e \nu$ decays observed in $p\overline{p}$ collisions at
$\sqrt{s}$ = 1.8~TeV with the D\O\ detector during the 1992--1993 run. From a
fit to the transverse mass spectrum, combined with measurements of the $Z$
boson mass, the $W$ boson mass is measured to be $M_W = 80.350 \pm 0.140
(stat.) \pm 0.165 (syst.) \pm 0.160 (scale) GeV/c^2$.
