\begin{table}%T4
\par
\caption{Predicted numbers of QSOs, $3<z<8$.}
\label{results}%\centerline
{
\begin{tabular}{ccccc}
\hline\hline
Sample & Observed at $z>3$ & Analysis type& Contributors & Predicted$^\dag~3<z<8$ \\
\hline
%&&&&\\
\multicolumn{3}{l}{Single survey cutoff:} &    &      \\
3 &11.4 & single cutoff, $\alpha = +0.2$ & 73(86) & 64.7(66.7) \\
3 &11.4 & single cutoff, $\alpha = \ \ 0.0$ & 49(57) & 40.3(40.4) \\
3 &11.4 & single cutoff, $\alpha = -0.2$ & 39(43) & 25.0(25.1) \\
\multicolumn{3}{l}{Source-by-source analysis, "Single-source survey'':}  &    &      \\
2 &17.8 &  $S_{2.7}, S_{5.0}$ & 71(89) & 51.5(53.5) \\
2 &17.8 &  $S_{0.365}, S_{1.40}, S_{2.7}, S_{5.0}$ & 67(89) & 48.5(54.0) \\
2 &17.8 &  $S_{0.365}, S_{1.40}, S_{2.7}, S_{5.0}, S_{8.40}$ & 53(65) & 28.8(30.1) \\
2 &17.8 &  $S_{0.365}, S_{1.40}, S_{2.7}, S_{5.0}, S_{8.87}$ or $S_{8.40}$& 57(70) & 38.6(38.6) \\
2 &17.8 &  $S_{0.365}, S_{1.40}, S_{2.7}, S_{5.0}, S_{8.87}$ & 70(88) & 50.5(52.9) \\
%&&&&\\
\hline
\end{tabular}}
\par
\medskip
$^\dag$ Calculated in the geometry adopted for this paper; bracketed numbers are
for $\Omega_{\rm m} = \Omega_{\rm tot} = 1.0$, the Einstein-de~Sitter
Universe.
\end{table}