  Published data for large amplitude asymptotic giant branch variables in the
Large Magellanic Cloud are re-analysed to establish the constants for an
infrared (K) period-luminosity relation of the form: Mk=rho[log P-2.38] +
delta. A slope of rho=-3.51+/-0.20 and a zero point of delta=-7.15+/-0.06 are
found for oxygen-rich Miras (if a distance modulus of 18.39+/-0.05 is used for
the LMC). Assuming this slope is applicable to Galactic Miras we discuss the
zero-point for these stars using the revised Hipparcos parallaxes together with
published VLBI parallaxes for OH Masers and Miras in Globular Clusters. These
result in a mean zero-point of delta=-7.25+/-0.07 for O-rich Galactic Miras.
The zero-point for Miras in the Galactic Bulge is not significantly different
from this value.
  Carbon-rich stars are also discussed and provide results that are consistent
with the above numbers, but with higher uncertainties. Within the uncertainties
there is no evidence for a significant difference between the period-luminosity
relation zero-points for systems with different metallicity.
