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We study a sample of 257 Galactic disk M dwarfs (8<M_V<18.5) found in imagesobtained using HST. These include 192 stars in 22 fields imaged with therepaired WFC2 with mean limiting mag I=23.7 and 65 stars in 162 fields imagedwith the pre-repair Planetary Camera with mean limiting mag V=21.3. We findthat the disk luminosity function (LF) drops sharply for M_V>12 (M<0.25 \ms),decreasing by a factor \gsim 3 by M_V~14 (M~0.14\ms). This decrease in the LFis in good agreement with the ground-based photometric study of nearby stars byStobie et al. (1989), and in mild conflict with the most recent LF measurementsbased on local parallax stars by Reid et al. (1995). The local LF of the faintGalactic disk stars can be transformed into a local mass function using anempirical mass-M_V relation. The mass function can be represented analyticallyover the mass range 0.1\ms<M<1.6\ms by \log(\phi)=-1.35-1.34\log(M/\ms)-1.85[\log(M/\ms)]^2 where \phi is the number density per logarithmic unit of mass.The total column density of M stars is only \Sigma_M=11.8\pm 1.8\ms\pc^{-2},implying a total `observed' disk column density of \Sigma_\obs~=39\ms\pc^{-2},lower than previously believed, and also lower than all estimates with which weare familiar of the dynamically inferred mass of the disk. The measured scalelength for the M-star disk is 3.0\pm 0.4 kpc. The optical depth to microlensingtoward the LMC by the observed stars in the Milky Way disk is \tau~1x10^{-8},compared to the observed optical depth found in ongoing experiments \tau_\obs~10^{-7}. The M-stars show evidence for a population with characteristicsintermediate between thin disk and spheroid populations. Approximating what maybe a continuum of populations by two separate component, we find characteristicexponential scale heights of ~210 pc and ~740 pc.Comment: 30 pages, uuencoded postscript, includes 3 figures, 2 table

Disk M Dwarf Luminosity Function from Hubble Space Telescope Star Counts