  We report a measurement of the W boson mass based on an integrated luminosity
of 82 pb$^{-1}$ from \ppbar collisions at $\sqrt{s}=1.8$ TeV recorded in
1994--1995 by the \Dzero detector at the Fermilab Tevatron. We identify W
bosons by their decays to $e\nu$ and extract the mass by fitting the transverse
mass spectrum from 28,323 W boson candidates. A sample of 3,563 dielectron
events, mostly due to Z to ee decays, constrains models of W boson production
and the detector. We measure $\mw=80.44\pm0.10(stat)\pm0.07(syst)$~GeV. By
combining this measurement with our result from the 1992--1993 data set, we
obtain $\mw=80.43\pm0.11$ GeV.
