  We report on a multi-epoch study of the Fornax dwarf spheroidal galaxy, made
with the Infrared Survey Facility, over an area of about 42'x42'. The
colour-magnitude diagram shows a broad well-populated giant branch with a tip
that slopes down-wards from red to blue, as might be expected given Fornax's
known range of age and metallicity. The extensive AGB includes seven Mira
variables and ten periodic semi-regular variables. Five of the seven Miras are
known to be carbon rich. Their pulsation periods range from 215 to 470 days,
indicating a range of initial masses. Three of the Fornax Miras are redder than
typical LMC Miras of similar period, probably indicating particularly heavy
mass-loss rates. Many, but not all, of the characteristics of the AGB are
reproduced by isochrones from Marigo et al. for a 2 Gyr population with a
metallicity of Z=0.0025.
  An application of the Mira period-luminosity relation to these stars yields a
distance modulus for Fornax of 20.69+/-0.04 (internal), +/-0.08 (total) (on a
scale that puts the LMC at 18.39 mag) in good agreement with other
determinations. Various estimates of the distance to Fornax are reviewed.
