  We present a measurement of the W boson mass using data collected with the
CDF detector during the 1994-95 collider run at the Fermilab Tevatron. A fit to
the transverse mass spectrum of a sample of 30,115 W -> enu events recorded in
an integrated luminosity of 84 pb^(-1) gives a mass Mw = 80.473 +- 0.065(stat.)
+- 0.092(syst.) GeV/c^2. A fit to the transverse mass spectrum of a sample of
14,740 W -> munu events from 80 pb^(-1) gives a mass Mw = 80.465 +-
0.100(stat.) +- 0.103(syst.) GeV/c^2. The dominant contributions to the
systematic uncertainties are the uncertainties in the electron energy scale and
the muon momentum scale, 0.075 GeV/c^2 and 0.085 GeV/c^2, respectively. The
combined value for the electron and muon channel is Mw = 80.470 +- 0.089
GeV/c^2. When combined with previously published CDF measurements, we obtain Mw
= 80.433 +- 0.079 GeV/c^2.
