  We combine spatially resolved ASCA temperature data with ROSAT imaging data
to constrain the total mass distribution in the cluster A401, assuming that the
cluster is in hydrostatic equilibrium. We obtain a total mass within the X-ray
core (290/h_50 kpc) of 1.2[+0.1,-0.5] 10^14 /h_50 Msun at the 90% confidence
level, 1.3 times larger than the isothermal estimate. The total mass within
r_500 (1.7/h_50 Mpc) is M_500 = 0.9[+0.3,-0.2] 10^15/ h_50 Msun at 90%
confidence, in agreement with the optical virial mass estimate, and 1.2 times
smaller than the isothermal estimate. Our M_500 value is 1.7 times smaller than
that estimated using the mass-temperature scaling law predicted by simulations.
The best fit dark matter density profile scales as r^{-3.1} at large radii,
which is consistent with the Navarro, Frenk & White (NFW) ``universal profile''
as well as the King profile of the galaxy density in A401. From the imaging
data, the gas density profile is shallower than the dark matter profile,
scaling as r^{-2.1} at large radii, leading to a monotonically increasing gas
mass fraction with radius. Within r_500 the gas mass fraction reaches a value
of f_gas = 0.21[+0.06,-0.05] h_50^{-3/2} (90% confidence errors). Assuming that
f_gas (plus an estimate of the stellar mass) is the universal value of the
baryon fraction, we estimate the 90% confidence upper limit of the cosmological
matter density to be Omega_m < 0.31.
