\begin{table}%t1
%\centering
\par
\caption{Relevant parameters of the observed sample of Cepheids, sorted by increasing period.
\label{cepheids_params}}
\begin{tabular}{lccccccc}
\hline\hline
\noalign{\smallskip}
\par
 & X~Sgr & $\eta$~Aql & W~Sgr & $\beta$~Dor & $\zeta$~Gem & Y~Oph & $\ell$~Car \\
  & \object{HD 161592} & \object{HD 187929} & \object{HD 164975} & \object{HD 37350} &
\object{HD 52973} & \object{HD 162714} & \object{HD 84810}\\
\hline
${m_V}^{a}$ & 4.581 & 3.942 & 4.700 & 3.731 & 3.928 & 6.164 & 3.771 \\
${m_K}^{b}$ & 2.56 & 1.966 & 2.82 & 1.959 & 2.11 & 2.682 & 1.091 \\
Sp. Type & F5-G2II & F6Ib-G4Ib & F4-G2Ib & F4-G4Ia-II & F7Ib-G3Ib & F8Ib-G3Ib & F6Ib-K0Ib\\
%Classification$^{{\rm ***}}$ & & C & C & & s & & \\
$\pi$ (mas)$^{c}$ & $3.03 \pm 0.94$ & $2.78 \pm 0.91$ & $1.57 \pm 0.93$ & $3.14 \pm 0.59$ &
$2.79 \pm 0.81$ & $1.14 \pm 0.80$ & $2.16 \pm 0.47$\\
\hline
Min $  T_{{\rm eff}}$ (K) & 5670 & 5400 & 5355 & 5025 & 5150 & &  \\
Mean $ T_{{\rm eff}}$ (K)$^{d}$ & 6150 & 5870 & 5769 & 5490 & 5430 & {\it 5300} & 5090 \\
Max $  T_{{\rm eff}}$ (K) & 6820 & 6540 & 6324 & 6090 & 5750 & &  \\
Min $\log g$ & 1.86 & 1.25 & 1.72 & 1.60 \\
Mean $\log g^{e}$ & 2.14 & 1.49 & 1.82 & 1.83 & 1.50 & {\it 1.50} & 1.50 \\
Max $\log g$ & 2.43 & 1.73 & 2.02 & 2.06 \\
$[{\rm M}/{\rm H}]^{e}$ & 0.04 & 0.05 & $-$0.01 &$-$0.01 & 0.04 & 0.05 & 0.30 \\
\hline
$T_0$ (JD-$2.452\times10^6$)$^{f}$ & 723.9488 & 519.2477 & 726.8098 & 214.2153 & 210.7407 & 715.4809 & 290.4158 \\
$P$ (days)$^{g}$ & 7.013059 & 7.176769 & 7.594904 & 9.842425 & 10.150967 & 17.126908 & 35.551341 \\
\hline
Intensity profiles$^{h}$\\
$a_1$ & $+0.7594$ & $+0.8816$ & $+0.8002$ & $+0.7969$ & $+0.8713$ & $+0.8549$ & $+0.8500$ \\
$a_2$ & $-0.4530$ & $-0.7418$ & $-0.5135$ & $-0.4596$ & $-0.6536$ & $-0.5602$ & $-0.4991$ \\
$a_3$ & $+0.0347$ & $+0.3984$ & $+0.1583$ & $+0.1341$ & $+0.3283$ & $+0.2565$ & $+0.2113$ \\
$a_4$ & $+0.0751$ & $-0.0778$ & $+0.0109$ & $+0.0082$ & $-0.0610$ & $-0.0437$ & $-0.0340$ \\
\hline
\end{tabular}
\begin{list}{}{}
\item[$^{a}$] $m_V$ from Barnes et~al.~(\cite{barnes87}) for X~Sgr,
from Barnes et~al.~(\cite{barnes97}) for $\eta$~Aql, from Moffett \& Barnes~(\cite{moffett84})
for W~Sgr and $\zeta$~Gem, from Berdnikov \& Turner~(\cite{berdnikov01})
for $\beta$~Dor and $\ell$~Car, and from Coulson \& Caldwell (\cite{coulson85}) for Y~Oph.
\item[$^{b}$] $m_K$ from Welch et~al.~(\cite{welch84}) for
X~Sgr, and W~Sgr, from Laney \& Stobie~(\cite{laney92}) for $\beta$~Dor,
Y~Oph, and $\ell$~Car, from Ducati et~al.~(\cite{ducati01}) for $\zeta$~Gem,
from Barnes et~al.~(\cite{barnes97}) for $\eta$~Aql.
%\item[$^{{\rm c}}$] Classification according to Bersier \& Burki~(\cite{bersier96}).
\item[$^{c}$] Parallaxes from the {\sc Hipparcos} catalogue (Perryman et~al.~\cite{hip}).
\item[$^{d}$] From Kiss \& Szatm\`ary~(\cite{kiss98}) for $\zeta$~Gem and $\eta$~Aql,
Bersier et~al.~(\cite{bersier97}) for W~Sgr, and Pel~(\cite{pel78}) for X~Sgr and $\beta$~Dor.
\item[$^{e}$] From Andrievsky et~al.~(\cite{andrievsky02}), Cayrel de Strobel et~al.~(\cite{cayrel}, \cite{cayrel01}),
and Pel~(\cite{pel78}), except for $\log g$ of Y~Oph.
%from Fernie's~(\cite{fernie95a}) law.
\item[$^{f}$] Reference epoch $T_0$ values have been computed near the dates of the VINCI observations,
from the values published by Szabados~(\cite{szabados89a}).
\item[$^{g}$] $P$ values from Szabados~(\cite{szabados89a}).
The periods of $\eta$~Aql, $\zeta$~Gem and W~Sgr are known to evolve.
The values above correspond to the $T_0$ chosen for these stars.
\item[$^{h}$] Four-parameters intensity profiles from Claret~(\cite{claret00}) in the $K$ band,
assuming a microturbulence velocity of 4~km~s$^{-1}$ and the average values of $ T_{\rm eff}$ and $\log g$.
\end{list}
\end{table}