  The MACHO project has been monitoring about ten million stars in the Large
Magellanic Cloud in the search for gravitational microlensing events caused by
massive compact halo objects (Machos) in the halo of the Milky Way. In our
standard analysis, we have searched this data set for well sampled, long
duration microlensing lightcurves, detected several microlensing events
consistent with Machos in the 0.1 < m < 1.0 M_sun mass range, and set limits on
the abundance of objects with masses 1e-5 < m < 0.1 M_sun. In this paper, we
present a different type of analysis involving the search for very short time
scale brightenings of stars which is used to set strong limits on the abundance
of lower mass Machos. Our analysis of the first two years of data toward the
LMC indicates that Machos with masses in the range 2.5e-7 < m < 5.2e-4 M_sun
cannot make up the entire mass of a standard spherical dark halo. Combining
these results with those from the standard analysis, we find that the halo dark
matter may not be comprised of objects with masses 2.5e-7 < m < 8.1e-2 M_sun.
