We study a sample of 257 Galactic disk M dwarfs (8 less than or equal
to M(V) less than or equal to 18.5) found in images obtained using the
Hubble Space Telescope (HST). These include 192 stars in 22 fields im
aged with the repaired Wide Field Camera (WFC2) with mean limiting mag
I = 23.7 and 65 stars in 162 fields imaged with the prerepair Planeta
ry Camera (PC1) with mean limiting mag V = 21.3. We find that the disk
luminosity function (LF) drops sharply for M(V) > 12 (M < 0.25 M(.)),
decreasing by a factor greater than or equal to 3 by M(V) similar to
14 (M similar to 0.14 M(.)). This decrease in the LF is in good agreem
ent with the ground-based photometric study of nearby stars by Stobie,
Ishida, & Peacock, and in mild conflict with the most recent LF measu
rements based on local parallax stars by Reid, Hawley, & Gizis. The lo
cal LF of the faint Galactic disk stars can be transformed into a loca
l mass function using an empirical mass-M(V) relation. The mass functi
on can be represented analytically over the mass range 0.1 M(.) < M <
1.6 M(.) by log(phi) = -1.35 - 1.33 log (M/M(.)) - 1.82[log(M/M(.))](2
), where phi is the number density per logarithmic unit of mass. The t
otal column density of M stars is only Sigma(M) = 12.4 +/- 1.9 M(.) pc
(-2), implying a total ''observed'' disk column density of Sigma(obs)
similar or equal to 40 M(.) pc(-2), lower than previously believed, an
d also lower than all estimates with which we are familiar of the dyna
mically inferred mass of the disk. The measured scale length for the M
-star disk is 3.0 +/- 0.4 kpc. The optical depth to microlensing towar
d the Large Magellanic Cloud (LMC) by the observed stars in the Milky
Way disk is tau less than or similar to 1 x 10(-8), compared to the ob
served optical depth found in ongoing experiments tau(obs) similar to
10(-7). The M-stars show evidence for a population with characteristic
s intermediate between thin disk and spheroid populations. Approximati
ng what may be a continuum of populations by two separate components,
we find a vertical density profile nu(z) proportional to 0.80 sech(2)
(z/323 pc) + 0.20 exp (-\z\/656 pc). If we combine the HST data with g
round-based measurements of the local density of M dwarfs, then a trad
itional double-exponential vertical density profile is strongly exclud
ed.