\begin{table}%t5
%\centering
\par
\caption{Derived projections factors for all stars computed from the
decomposition presented in Eq.~(\ref{Eq_pf_decomposition}).
\label{Tab_presults}}
\begin{tabular}{lcccccc}
\hline \hline \noalign{\smallskip}
\par
Name     &  HD     &  $P^{b}$   &         $p_{{\rm o}}^{c}$             &       $f_{\rm grad}^{d}$       & $f_{{\rm o-g}}^{e}$      & $p^{f}$ \\
         &         &  [days]            &                           &                        &                                             \\
\hline
R TrA       & 135592  &   $3.38925$     &  $1.396_{\pm 0.010}$         &   $0.995_{\pm 0.009}$     &   $0.967_{\pm 0.005}$     &     $1.34_{\pm 0.03}$ \\
S Cru       & 112044  &   $4.68976$     &  $1.392_{\pm 0.010}$         &   $0.996_{\pm 0.007}$      &   $0.966_{\pm 0.005}$     &  $1.34_{\pm 0.03}$   \\
Y Sgr       & 168608  &   $5.77338$     &  $1.387_{\pm 0.010}$         &   $0.991_{\pm 0.005}$  &   $0.962_{\pm 0.005}$      & $1.32_{\pm 0.02}$  \\
$\beta$ Dor & 37350   &   $9.84262$     &  $1.380_{\pm 0.010}$         &   $0.997_{\pm 0.004}$    &   $0.955_{\pm 0.005}$    & $1.31_{\pm 0.02}$   \\
$\zeta$ Gem & 52973   &   $10.14960$    &  $1.380_{\pm 0.010}$         &   $0.994_{\pm 0.005}$       & $0.953_{\pm 0.005}$      & $1.31_{\pm 0.02}$   \\
RZ Vel      & 73502   &   $20.40020$    &  $1.375_{\pm 0.010}$         &   $0.994_{\pm 0.004}$       & $0.951_{\pm 0.005}$      & $1.30_{\pm 0.02}$  \\
$\ell$~Car  & 84810   &   $35.55134$   &  $1.366_{\pm 0.010}$         &   $0.989_{\pm 0.005}$       & $0.944_{\pm 0.005}$   & $1.27_{\pm 0.02}$  \\
RS Pup      & 68860   &   $41.51500$    &  $1.360_{\pm 0.010}$         &   $0.995_{\pm 0.005}$       & $0.943_{\pm 0.005}$     & $1.28_{\pm 0.02}$ \\
\hline
$\delta~Cep ^{a}$ & 213306   &   $5.419$  &   $1.390_{\pm 0.010}$  & $0.990_{\pm 0.005}  $     &   $0.963_{\pm 0.005}$      & $1.33_{\pm 0.02}$ \\
$\ell~Car ^{a}$   & 84810   &    $35.60$  &    $1.366_{\pm 0.010}$ & $0.988_{\pm 0.005} $      &   $0.944_{\pm 0.005}$     & $1.27_{\pm 0.02}$  \\
\hline
\end{tabular}
\begin{list}{}{}
\par
\item[$^a$] $\delta$~Cep and $\ell$~Car are hydrodynamical models.
\par
\item[$^b$] The corresponding Julian dates
($T_{{\rm o}}$) can be found in Paper II.
\par
\item[$^c$] $p_{{\rm o}}$ is derived from the linear limb-darkening laws of Claret et~al. (\cite{claret00})
based on the static models of Kurucz (\cite{kurucz92}). We then apply a slight
correction based on the $\delta$~Cep and $\ell$~Car hydrodynamical
models: $p_{\rm o}[{\rm hydro}]=p_{\rm o}[{\rm geo}]-(0.0174 \log P -0.0022)$ to take
the dynamical structure of the Cepheid's atmosphere into account.
\par
\item[$^d$] $f_{\rm grad}$ is derived directly from observations
using Eq (\ref{Eq_method}). It is important to notice that the results
indicated here correspond to the \ion{Fe}{i} 4896.439~\AA\ line. In
the case of a modeled star, it is derived directly from the
hydrodynamical model (see Sect.~\ref{sss_method}).
\par
\item[$^e$] $f_{{\rm o-g}}$ is derived directly from the hydrodynamical
models (see Sect. \ref{ss_fog}).
\par
\item[$^f$] $p$-factors defined by
$p=p_{{\rm o}}f_{{\rm grad}}f_{{\rm o-g}}$.
$p_{{\rm o}}$ and $f_{{\rm o-g}}$ are derived from geometrical
and hydrodynamical models respectively. $f_{{\rm grad}}$ is
derived from observations.
\end{list}
\end{table}