  We derive mass functions (MF) for halo red dwarfs (the faintest hydrogen
burning stars) and then extrapolate to place limits on the total mass of halo
brown dwarfs (stars not quite massive enough to burn hydrogen). The mass
functions are obtained from the luminosity function of a sample of 114 local
halo stars in the USNO parallax survey (Dahn \etal 1995). We use stellar models
of Alexander \etal (1996) and make varying assumptions about metallicity and
about possible unresolved binaries in the sample. We find that the MF for halo
red dwarfs cannot rise more quickly than $1/m^2$ as one approaches the hydrogen
burning limit. Using recent results from star formation theory, we extrapolate
the MF into the brown-dwarf regime. We see that likely extrapolations imply
that the total mass of brown dwarfs in the halo is less than $\sim 3\%$ of the
local mass density of the halo ($\sim 0.3\%$ for the more realistic models we
consider). Our limits apply to brown dwarfs in the halo that come from the same
stellar population as the red dwarfs.
