  Using spectroscopic data presented in Magrini et al. (2003), we have analyzed
with the photoionization code CLOUDY 94.00 (Ferland et al. 1998) 11 Planetary
Nebulae belonging to the spiral galaxy M 33. Central star temperatures and
nebular parameters have been determined. In particular the chemical abundances
of He/H, O/H, N/H, Ar/H, and S/H have been measured and compared with values
obtained via the Ionization Correction Factors (ICFs) method, when available.
Chemical abundance relationships have been investigated; in particular, a
correlation between N/H and N/O similar to the Galactic one (Henry 1989), and a
feeble anti-correlation between O/H and N/O have been found.
  A gradient in O/H across the disc of M~33 is indicatively consistent with the
one found from HII regions in this galaxy (Vilchez et al 1988). Further studies
in the more external parts of M~33 are however needed to ascertain this point.
The present result shows that oxygen and helium abundances (with lower accuracy
also nitrogen, argon and sulphur) can be actually estimated from the brightest
PNe of a galaxy, even if the electron temperature cannot be measured. We also
found that the oxygen abundance is quite independent of the absolute magnitude
of the PN and consequently the brightest PNe are representative of the whole PN
population. This represents an important tool to measure the metallicity of
galaxies at the time of the formation of PNe progenitors.
