| Abstract
| - This paper concerns the calibration of the K period-luminosity relation for Mira variables using Hipparcos parallaxes. K magnitudes are available for 255 Mira-like variables which were observed by Hipparcos. Period-luminosity zero-points are evaluated for various subgroups of data. The best solution for oxygen-rich Miras, which uses 180 stars, omitting the short-period red group (which had different kinematics from the short-period blue stars) and the low-amplitude variables, provides a zero-point of which implies a distance modulus for the Large Magellanic Cloud of or perhaps slightly greater if a metallicity correction is required, in good agreement with the value derived from Cepheids. The zero-point of the period-luminosity relation for carbon stars is briefly discussed. Linear diameters are derived for red variables with measured angular diameters and parallaxes, and are used to examine the long-standing question of the pulsation mode(s) of these stars. Evidence is presented to suggest that most of them are pulsating in the same mode and, if published model atmospheres are correct, this is probably the first overtone. Some discussion is given of sequences in the period-luminosity and period-colour diagrams and their bearing on the pulsation mode problem.
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