\begin{table}%t8
\par
\caption {\label{Tab:orbits}An extensive list of orbital elements for (non-symbiotic) 
M~giants. 
}
{
%\tabcolsep 2 pt
\begin{tabular}{rrrcrlllclrrrl}
\noalign{\bf New orbits}\\
\hline\hline
HD & Sp. & $N$ & $\sigma$(O$-$C) &
$\Delta t$ & 
\multicolumn{1}{c}{$P$} &
\multicolumn{1}{c}{$e$} & 
\multicolumn{1}{c}{$f(M)$} &
\multicolumn{1}{c}{$T_0$} &
\multicolumn{1}{c}{$\omega$} & 
\multicolumn{1}{c}{$K_1$} & 
\multicolumn{1}{c}{$V_0$} &
\multicolumn{1}{c}{$a_1 \sin i$} & 
\\
   & &     & 
\multicolumn{1}{c}{(\kms)} &
(d)        &
\multicolumn{1}{c}{(d)} & & 
\multicolumn{1}{c}{(\Msun)}  &
\multicolumn{1}{c}{(JD $-$2\ts400\ts000)} & 
\multicolumn{1}{c}{($^\circ$)} & 
\multicolumn{1}{c}{(\kms)} & 
\multicolumn{1}{c}{(\kms)} & 
($10^6$~km)\\ 
\hline
83~069 & M2III & 9 & 0.11 & 4450 & $4768\pm175$ & $0.36\pm0.12$ &
0.0076 & $53\ts344\pm106$ & $132\pm15$ & $2.7\pm 0.2$ & $-17.9\pm0.1$
& 163.3 \\
108~907 & M4III & 15 & 0.60 & 6821 & $1714\pm4$ & $0.20\pm0.03$ &
0.0094 & $53\ts239\pm40$ & $278\pm9$ & $3.8\pm0.2$&$-15.6\pm0.1$
& 88.6  
& (1)\\
       && 71 & 0.90 & 24~830 &  $1703\pm3$ & $0.30\pm0.05$ &
0.0076& $42\ts868\pm40$ & $244\pm9$ & $3.7\pm0.2$&$-14.3\pm0.1$
& 82.0
& (2) \\
       && 72 & 1.02 & 9451 & $1703\pm3$ & $0.33\pm0.02$ &
0.0063& $53\ts204\pm19$ & $267\pm4$ & $3.5\pm0.1$&$-14.8\pm0.1$
& $77.1$
& (3)\\
111~129& M2III &  10 & 0.18 & 3633 & $496.7\pm0.7$  & $0.14\pm0.01$ & 
0.047& $50\ts630\pm17$ & $299\pm12$ & $9.8\pm0.3$ & $-15.9\pm0.1$
& 66.3 
\\
113~406 & M1III & 12 & 0.25 & 4324 &  $1338\pm7$  & $0.30\pm0.03$ & 
0.0065 & $50\ts865\pm18$ & $18\pm5$ & $3.8\pm0.3$ & $4.8\pm0.1$
& 66.4
\\
137~853 & M1III & 11 & 0.12 & 3794 & $1373\pm15$ & $0.15\pm0.06$ &
0.0015 & $51\ts616\pm62$ & $119\pm17$ & $2.2\pm0.1$ & $-9.8\pm0.1$
& 41.7& 
\\
159~608&  M2III & 16 & 0.39 & 3981 & $599.3\pm0.4$   & $0.22\pm0.01$& 
0.0751 & $52\ts731\pm5$ & $357\pm3$ & $10.9\pm0.2$ & $-59.9\pm0.1$
& 87.8
\\
165~374&  M2III & 37 & 0.41 & 7349 & $2741\pm13$ & $0.05\pm0.02$ &
0.0782& $51\ts058\pm128$ & $74\pm17$ & $6.5\pm0.1$ & $-32.0\pm0.1$
& 245.3  
\\
182~190&  M1III & 40 & 0.30 & 5258 & $3856\pm22$& $0.57\pm0.01$ &  0.0155 & $53\ts053\pm11$ & $164\pm2$ & $4.1\pm0.1$ & $-24.4\pm0.1$
& 179.0  \\
187~372&  M1III & 16 & 0.36 & 5787 & $986\pm3$     & $0.24\pm0.03$ & 
0.0034& $50\ts201\pm22 $ & $204\pm8$ & $3.3\pm0.2$ & $0.1\pm0.1$
& 43.8  
\\
199~871&  M0III & 10 & 0.31 & 3964 & $840.2\pm0.7$   & $0.16\pm0.02$ & 
0.203& $51\ts899\pm7$ & $17\pm3$ & $13.4\pm0.1$ & $-48.2\pm0.1$
& 153.1  
\\
212~009&  M0III &  9 & 0.17 & 5008 & $791.8\pm1.1$   & $0.17\pm0.04$ & 
0.0231& $53\ts529\pm15$ & $70\pm6$ & $6.6\pm0.2$ & $-17.7\pm0.2$
&  71.3  
\\
212~047&  M4III & 12 & 0.24 & 3984 & $328.2\pm0.1$   & $0.016\pm0.012$&
0.0290& $49\ts315\pm47$ & $176\pm53$ & $9.4\pm0.1$ & $-7.5\pm0.1$
&  42.8  
\\
220~088& M0III   & 37 & 0.13 & 5874 & $2516.6\pm1.5$  & $0.639\pm0.004$           & 0.0169 &$53\ts622.5\pm2.6$  & $259.5\pm1.1$ & $5.21\pm0.05$ & $-20.48\pm0.03$ & 138.9 \\
\hline\\
\end{tabular}
}
 {
\begin{tabular}{rlrcrlll}
\noalign{
\bf Preliminary orbit
}
\smallskip\\
\hline\hline
HD  & Sp. & $N$ &  $\sigma$(O$-$C) & $\Delta t$ &  \multicolumn{1}{c}{$P$} &
\multicolumn{1}{c}{$e$} & Rem.\\
    &     &     &                &   (d)       &  \multicolumn{1}{c}{(d)} \\
\hline\\
203~525& M0III &  10 & 0.12 & 4741 & 7290:          & 0.4:          \\
\hline\\
\end{tabular}
\par
\begin{tabular}{r@{}llllll}
\noalign{
\bf Orbits from the literature
}
\smallskip\\
\hline\hline
HD  &  & Sp. & $P$  &  $e$ &  $f(M)$    &  Ref. \\
    &  &     & (d)   &      & (\Msun)\\
\hline
9053   & & M0III & 193.8 & 0.0 & 0.083 & $\gamma$ Phe: \citet{Luyten-1936}\\	 
41~511  & & M4III & $260.34\pm1.80$ & $0.024\pm0.005$ & $0.261\pm0.005$ &  (4)\\
42~995  & & M3III & 2983 & 0.53  & 0.13  & $\eta$ Gem: \citet{McLaughlin-1944}\\
80~655  & & gM & 834  & 0.0   & 0.0074&  \citet{Griffin-1983}\\  
89~758  & & M0III & $230.089\pm0.039$ & $0.061\pm0.022$ & 0.01 & $\mu$~UMa:  \citet{Jackson-1957,Lucy-Sweeney-71}\\
108~815 & & M     & $4448\pm20$   & $0.73\pm0.03$    & $0.012\pm0.003$ & Griffin, priv. comm.\\ 
111~307 & & M0 & $18000\pm3000$ & 0:  & $0.10\pm0.04$  & Griffin, priv. comm.\\
115~521 &Aa+b & M2III & $>$7000  & $>$0.5 & .. & Sect.~\ref{Sect:115521} \\ 
115~521 &A+a &      & $475.1\pm1.4$  & $0.15\pm0.06$ & $9.3\times 10^{-5}$  & (5), revised but orbital 
nature doubtful 
(Sect.~\ref{Sect:115521}) \\
117~673 & & M0III & $1360.8\pm2.3$ & $0.26\pm0.02$  & 0.0095 & \citet{Griffin-2008}\\ 
126~947 & & M3III & $2812.3\pm9.4$   & $0.432\pm0.021$  & 0.045 &  \citet{Prieur-2006}\\ 
132~813 & & M4.5III & 748.9          & 0.13           & 0.0043 & RR UMi (SRb, $P = 43.3$ d):\\
       & &         &                &                &        & \citet{Dettmar-1983,Batten-1986}\\ 
147~395 & & M2III & 335.5          & 0.24           & 0.154 & \citet{Carquillat-96}\\
187~076 & &  M2II+late B & $3704.2\pm3.2$       & $0.45\pm0.01$           & $0.135\pm0.005$ &  Griffin, priv.comm.\\
       & &            &                       &                       &   & $\delta$~Sge: A $\zeta$~Aur/VV~Cep-like system  
  \citep{Reimers-Schroeder-1983}\\
190~658 & & M2.5III & 198.7           & 0.05           & 0.045 &  (6) \\
192~867 & & M1III   & 5929           & 0.64           & 0.032 &    \citet{Griffin-1990}\\  
220~007 & & M3III   & 1520           & 0.51           & 0.013 &    \citet{Griffin-1979}\\  
\hline\\
\end{tabular}
}
Remarks: (1) this work; (2) \citet{Reimers-1988}; (3) combined solution (see text);
(4) SS Lep: M4III + accreting A1 star \citep{Welty-1995}. \citet{Verhoelst-2007} shows, from interferometric measurements of the M-giant radius,  that the giant fills its Roche lobe (see also Paper~III); 
(5) possibly a triple system,
formerly a radial-velocity standard star; 
\citet{Duquennoy-Mayor-91} found a preliminary  509~d period for the inner pair, but the
orbital nature of the short-period variations is questionable (Sect.~\ref{Sect:115521});
(6) HD 190~658 = V1472 Aql = HIP~98~954: semiregular or most likely
eclipsing or ellipsoidal variable with  $P = 100.37$~d, almost
exactly half the orbital period \citep{Samus-1997}. Orbital elements
from \citet{Lucke-Mayor-1982}. A (physical?) companion is present at
2.3\arcsec\ \citep{Tokovinin-1997,Frankowski-2007}.
\end{table}