\begin{table}%t1
\par
\caption{\label{tab:variouspresc}Various prescriptions for the softening length adopted in some simulations of self-gravitating gaseous discs (see also Fig.~\ref{fig:sys.xfig.eps}).}
%\centerline
 {\begin{tabular}{ll}
\hline\hline
Reference & Softening length $\lambda$ \\ \hline  
\cite{paplin89} & $0.056 \times (\aout-\ain)\times f(a,R,\ain,\aout)$ \\
\cite{ars89} & $0.1\times R$ \\
\cite{sayo90} & $\{0.01,0.02\} \times \aout$  \\
\cite{shu90} & $0.1 \times R$ \\
\cite{mosa94} & $0.02 \times \aout$ \\
\cite{sterzik95}$^a$ & $0.06 \times \lambda_{\rm c}$  \\
\cite{lka97} & $0.1 \times \ain$, $0.1 \times \aout$, and $0.001 \times R$ \\
\cite{lka98} & $0.0001+0.01 R \times f(a,\ain,\aout)$ \\
\cite{tremaine01} & $\beta \times R$, with $\beta \approx 10^{-4} {-} 0.2$ \\
\cite{caunt01}$^b$ & $H=2h$ \\
\cite{baruteaumasset08} & $0.3 {-} 0.5 h$ (depending on scale height)  \\
\cite{li09}$^c$ & $\approx $0.17 to $0.33 \times \Delta a$\\ \\
this work$^d$ & $\displaystyle f\left(\frac{h}{a},\frac{R}{a}\right)$\\
& $\approx$$ h/e$ at $R=a$, homogeneous case; \\ 
& see Eqs.~(\ref{eq:chispecq_explicit}), (\ref{eq:gen_chi}), (\ref{eq:root}) and~(\ref{eq:slq})\\   \hline
\end{tabular}}
\par
\smallskip
\par
$^a$ $\lambda_{\rm c}$ is the critical wave length of disturbances.\\
$^b$ concerns the magnetic potential.\\
$^c$ $\Delta a$ is the grid spacing, 3D-disc.\\
$^d$ Axisymmetric limit, finite size disc (inner edge $\ain$, outer edge $\aout$), symmetry with respect to the mid-plane, finite size layer (thickness $2h=H$), explicit function of vertical stractification, local validity. 
\end{table}