  (Abridged version): The optical depth is widely used in Galactic microlensing
studies as a means to determine the density of MACHOs, since in theory it
depends only upon their spatial distribution and is therefore less
model-dependent than other microlensing observables. However, since the
measured optical depth is restricted to that of events with measurable
timescales, inferences of total MACHO density are dependent on the assumed
timescale distribution. Using the 2-year LMC results of the MACHO
collaboration, we illustrate this point by showing how, for an assumed
isothermal halo, the inferred MACHO halo fraction as determined from optical
depth estimates depends upon MACHO mass.
  The analysis highlights the following conclusions: (1) The MACHO density
inferred from optical depth measurements depends on the assumed MACHO mass
function for a given Galactic distribution function; (2) without extra
information on the MACHO mass function, such as can be obtained from the
rate-timescale distribution, optical depth measurements can provide a lower
limit but not an upper limit on the MACHO density for a given Galactic
distribution function; (3) a comparison between the inferred total optical
depth of different Galactic models, or of different components in a
multi-component Galactic model, requires knowledge of the underlying timescale
distribution for each model or component.
