We report a measurement of the W boson mass based on an integrated luminosity of $82{\mathrm{pb}}^{\ensuremath{-}1}$ from $p\overline{p}$ collisions at $\sqrt{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.8\phantom{\rule{0ex}{0ex}}\mathrm{TeV}$ recorded in 1994--1995 by the D0 detector at the Fermilab Tevatron. We identify W bosons by their decays to $e\ensuremath{\nu}$ and extract the mass by fitting the transverse mass spectrum from 28 323 W boson candidates. A sample of 3563 dielectron events, mostly due to $Z\ensuremath{\rightarrow}\mathrm{ee}$ decays, constrains models of W boson production and the detector. We measure ${M}_{W}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}80.44\ifmmode\pm\else\textpm\fi{}0.10(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.07(\mathrm{syst})\phantom{\rule{0ex}{0ex}}\mathrm{GeV}$. By combining this measurement with our result form the 1992--1993 data set, we obtain ${M}_{W}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}80.43\ifmmode\pm\else\textpm\fi{}0.11\mathrm{GeV}$.