  This report describes a measurement of the top quark mass in $\ppbar$
collisions at a center of mass energy of 1.8 TeV. The data sample was collected
with the CDF detector during the 1992--95 collider run at the Fermilab
Tevatron, and corresponds to an integrated luminosity of 106 \pb. Candidate
$t\bar{t}$ events in the ``lepton+jets'' decay channel provide our most precise
measurement of the top quark mass. For each event a top mass is determined by
using energy and momentum constraints on the production of the $\ttbar$ pair
and its subsequent decay. A likelihood fit to the distribution of reconstructed
masses in the data sample gives a top mass in the lepton+jets channel of
$176.1\pm 5.1 (stat.)\pm 5.3 (syst.) \gevcc$. Combining this result with
measurements from the ``all-hadronic'' and ``dilepton'' decay topologies yields
a top mass of $176.1\pm 6.6 \gevcc$.
