  The aim of this paper is to investigate the metallicity dependence of the
$PL$-relation in $V$ and $K$ based on a sample of 68 Galactic Cepheids with
individual Baade-Wesselink distances (some of the stars also have an HST-based
parallax) and individually determined metallicities from high-resolution
spectroscopy. Literature values of the $V$-band, $K$-band and radial velocity
data have been collected for a sample of 68 classical cepheids that have their
metallicity determined in the literature from high-resolution spectroscopy.
Based on a $(V-K)$ surface-brightness relation and a projection factor derived
in a previous paper, distances have been derived from a Baade-Wesselink
analysis. $PL$- and $PLZ$-relations in $V$ and $K$ are derived. The effect of
the adopted dependence of the projection factor on period is investigated. The
change from a constant $p$-factor to one recently suggested in the literature
with a mild dependence on $\log P$ results in a less steep slope by 0.1 unit,
which is about the 1-sigma error bar in the slope itself. The observed slope in
the $PL$-relation in $V$ in the LMC agrees with both hypotheses. In $K$ the
difference between the Galactic and LMC slope is larger and would favour a mild
period dependence of the $p$-factor. The dependence on metallicity in $V$ and
$K$ is found to be marginal, and independent of the choice of $p$-factor on
period. This result is severely limited by the small range in metallicity
covered by the Galactic Cepheids.
