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We re-examine a deep {\it Hubble Space Telescope} pencil-beam search for reddwarfs, stars just massive enough to burn Hydrogen. The authors of this search(Bahcall, Flynn, Gould \& Kirhakos 1994) found that red dwarfs make up lessthan 6\% of the galactic halo. First, we extrapolate this result to includebrown dwarfs, stars not quite massive enough to burn hydrogen; we assume a$1/{\cal M}$ mass function. Then the total mass of red dwarfs and brown dwarfsis $\leq$18\% of the halo. This result is consistent with microlensing resultsassuming a popular halo model. However, using new stellar models and parallaxobservations of low mass, low metallicity stars, we obtain much tighter boundson low mass stars. We find the halo red dwarf density to be $<1\%$ of the halo,while our best estimate of this value is 0.14-0.37\%. Thus our estimate of thehalo mass density of red dwarfs drops to 16-40 times less than the reportedresult of Bahcall et al (1994). For a $1/{\cal M}$ mass function, this suggestsa total density of red dwarfs and brown dwarfs of $\sim$0.25-0.67\% of thehalo, \ie , $(0.9-2.5)\times 10^9\msun$ out to 50 kpc. Such a low result wouldconflict with microlensing estimates by the \macho\ group (Alcock \etal1995a,b).Comment: 13 pages, 2 figures. Figure one only available via fax or snail-mail  To be published in ApJL. fig. 2 now available in postscript. Some minor  changes in dealing with disk forground. Some cosmetic changes. Updated  reference

Analysis of a [ITAL]Hubble Space Telescope[/ITAL] Search for Red Dwarfs: Limits on Baryonic Matter in the Galactic Halo