  We use a new method to trace backwards the star formation history of the
Milky Way disk, using a sample of M dwarfs in the solar neighbourhood which is
representative for the entire solar circle. M stars are used because they show
H_alpha emission until a particular age which is a well calibrated function of
their absolute magnitudes. This allows us to reconstruct the rate at which disk
stars have been born over about half the disk's lifetime. Our star formation
rate agrees well with those obtained by using other, independent, methods and
seems to rule out a constant star formation rate.
  The principal result of this study is to show that a relation of the
Schmidt-Kennicut type (which relates the star formation rate to the
interstellar gas content of galaxy disks) has pertained in the Milky Way disk
during the last 5 Gyr. The star formation rate we derive from the M dwarfs and
the interstellar gas content of the disk can be inferred as a function of time
from a model of the chemical enrichment of the disk, which is well constrained
by the observations indicating that the metallicity of the Galactic disk has
remained nearly constant over the timescales involved. We demonstrate that the
star formation rate and gas surface densities over the last 5 Gyrs can be
accurately described by a Schmidt-Kennicutt law with an index of Gamma = 1.45
(+0.22,-0.09). This is, within statistical uncertainties, the same value found
for other galaxies.
