  Because we know little about the Galactic force-field away from the plane,
the Galactic mass distribution is very ill-determined. I show that a
microlensing survey of galaxies closer than 50 Mpc would enable us to map in
three dimensions the Galactic density of stellar mass, which should be strictly
less than the total mass density. A lower limit can be placed on the stellar
mass needed at R<R_0 to generate the measured optical depth towards sources in
the bulge. If the Galaxy is barred, this limit is lower by a factor of up to
two than in the axisymmetric case. Even our limited knowledge of the Galactic
force field suffices to rule out the presence of the amount of mass an
axisymmetric Galaxy needs to generate the measured optical depth. Several lines
of argument imply that the Galaxy is strongly barred only at R < 4 kpc, and if
this is the case, even barred Galaxy models cannot generate the measured
optical depth without violating some constraint on the Galactic force-field.
Galactic mass models that are based on the assumption that light traces mass,
for which there is significant support in the inner Galaxy, yield microlensing
optical depths that are smaller than the measured value by a factor of more
than 2.5.
