We present a measurement of the W boson mass using data collected with the
CDF detector during the 1994-1995 collider run at the Fermilab Tevatron. A
fit to the transverse mass spectrum of a sample of 30115 W --> ev events re
corded in an integrated luminosity of 84 pb(-1) gives a mass M-W=80.473 +/-
0.065(stat) +/-0.092(syst) GeV/c(2). A fit to the transverse mass spectrum
of a sample of 14740 W --> muv events from 80 pb(-1) gives a mass M-W=80,46
5 +/-0.100(stat)+/-0.103(syst) Ge V/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), respective
ly. The combined value for the electron and muon channel is M-W=80.470 +/-0
.089-GeV/c(2). When combined with previously published CDF measurements, we
obtain M-W=80.433 +/-0.079 GeV/c(2).