  We analyze the K band luminosities of a sample of galactic long-period
variables using parallaxes measured by the Hipparcos mission. The parallaxes
are in most cases re-computed from the Hipparcos Intermediate Astrometric Data
using improved astrometric fits and chromaticity corrections. The K band
magnitudes are taken from the literature and from measurements by COBE, and are
corrected for interstellar and circumstellar extinction. The sample contains
stars of several spectral types: M, S and C, and of several variability
classes: Mira, semiregular SRa, and SRb. We find that the distribution of stars
in the period-luminosity plane is independent of circumstellar chemistry, but
that the different variability types have different P-L distributions. Both the
Mira variables and the SRb variables have reasonably well-defined
period-luminosity relationships, but with very different slopes. The SRa
variables are distributed between the two classes, suggesting that they are a
mixture of Miras and SRb, rather than a separate class of stars. New
period-luminosity relationships are derived based on our revised Hipparcos
parallaxes. The Miras show a similar period-luminosity relationship to that
found for Large Magellanic Cloud Miras by Feast et al. (1989). The maximum
absolute K magnitude of the sample is about -8.2 for both Miras and
semi-regular stars, only a little fainter than the expected AGB limit. We show
that the stars with the longest periods (P>400d) have high mass loss rates and
are almost all Mira variables.
