\begin{table} %t9
  \caption{Beam averaged column density of various molecules using
the disk sizes listed in Table~\ref{tab:fitting_parameters}.} 
   \label{moldisks:column_density}
 %\centerline
{
 \begin{tabular}{llllll}
 \hline
\hline  
  &  & \multicolumn{4}{c}{$N  ({\rm cm}^{-2})$}\\
 \noalign{\smallskip}
 \cline{3-6}
 \noalign{\smallskip}
 & &\multicolumn{1}{c}{LkCa15}&\multicolumn{1}{c}{\object{TW~Hya}}&\multicolumn{1}{c}{\object{HD~163296}}&\multicolumn{1}{c}{MWC 480}\\
 \hline
 \noalign{\smallskip}
 \multicolumn{1}{c}{Species} & \multicolumn{1}{c}{Transition} &\multicolumn{1}{c}{$R_{\rm disk}=450$~AU}&\multicolumn{1}{c}{$R_{\rm disk}=165$~AU}&\multicolumn{1}{c}{$R_{\rm disk}=680$~AU}&\multicolumn{1}{c}{$R_{\rm disk}=400$~AU}\\
 \hline
 $^{12}$CO$^{a}$  & $^{13}$CO $J\!=\!3\!\rightarrow\!2$            & \phantom{$<$}1.9(16)  & \phantom{$<$}3.2(16) & \phantom{$<$}3.5(16)& \phantom{$<$}6.9(16)\\
 $^{13}$CO        & $J\!=\!3\!\rightarrow\!2$                      & \phantom{$<$}3.6(14)  & \phantom{$<$}5.5(14) &\phantom{$<$}5.9(14) & \phantom{$<$}1.2(15)\\
 HCO$^{+}$        & $J\!=\!4\!\rightarrow\!3$                      & \phantom{$<$}3.3(11)  & \phantom{$<$}4.4(12) & \phantom{$<$}9.4(11)& \phantom{$<$}1.0(12)\\
 HCO$^{+}$        & H$^{13}$CO$^{+}$ $J\!=\!4\!\rightarrow\!3$     & \multicolumn{1}{c}{...}  & \phantom{$<$}1.2(13) & \multicolumn{1}{c}{...}  & \multicolumn{1}{c}{...}  \\
 H$^{13}$CO$^{+}$ &  $J\!=\!4\!\rightarrow\!3$                     &           $<$1.5(11)  & \phantom{$<$}2.0(11) & \multicolumn{1}{c}{...} & \multicolumn{1}{c}{...}\\
 DCO$^{+}$        & $J\!=\!5\!\rightarrow\!4$                      & $<$2.9(11)  & \phantom{$<$}4.4(11) & \multicolumn{1}{c}{...} & \multicolumn{1}{c}{...}\\
 CN               & $J\!=\!3\frac{7}{2}\!\rightarrow\!2\frac{5}{2}$& \phantom{$<$}1.5(13)  & \phantom{$<$}6.6(13) &\phantom{$<$}1.5(13) & \phantom{$<$}1.5(13)\\
 HCN              & $J\!=\!4\!\rightarrow\!3$                      & \phantom{$<$}1.8(12)  & \phantom{$<$}9.2(12) & $<$1.0(12) & $<$1.2(12)\\
 H$^{13}$CN       & $J\!=\!4\!\rightarrow\!3$                      & \multicolumn{1}{c}{...}  & $<$4.8(11) &\multicolumn{1}{c}{...} &\multicolumn{1}{c}{...}\\
 HNC              & $J\!=\!4\!\rightarrow\!3$&             \multicolumn{1}{c}{...}   & $<$1.4(12)&\multicolumn{1}{c}{...}&\multicolumn{1}{c}{...}\\
 DCN              & $J\!=\!5\!\rightarrow\!4$&             \multicolumn{1}{c}{...}   & $<$4.0(10) &\multicolumn{1}{c}{...}&\multicolumn{1}{c}{...}\\
 CS               & $J\!=\!7\!\rightarrow\!6$&             \phantom{$<$}5.1(12)   & \multicolumn{1}{c}{...} &\multicolumn{1}{c}{...} &\multicolumn{1}{c}{...}\\
 \noalign{\smallskip}
 \hline
 \noalign{\smallskip}
 H$_{\rm 2}$CO    &$J\!=\!2_{12}\!\rightarrow\!1_{11}$ & \phantom{$<$}5.1(12) & \multicolumn{1}{c}{...}          &$<$2.1(12) &$<$2.7(13)\\
 H$_{\rm 2}$CO    &$J\!=\!3_{03}\!\rightarrow\!2_{02}$ & \phantom{$<$}1.7(12) & \multicolumn{1}{c}{...}          &$<$2.6(12) & \multicolumn{1}{c}{...}\\
 H$_{\rm 2}$CO    &$J\!=\!3_{22}\!\rightarrow\!2_{21}$ & $<$1.4(13)& \multicolumn{1}{c}{...}     &$<$9.4(12) & \multicolumn{1}{c}{...}\\
 H$_{\rm 2}$CO    &$J\!=\!3_{12}\!\rightarrow\!2_{11}$ & \phantom{$<$}7.1(11) & \multicolumn{1}{c}{...}          &$<$1.5(12) &$<$9.4(11) \\
 H$_{\rm 2}$CO    &$J\!=\!5_{15}\!\rightarrow\!4_{14}$ & \phantom{$<$}2.4(12) & $<$8.0(11)& $<$1.1(12) & $<$1.5(12)\\
 \noalign{\smallskip}
 \hline
 \noalign{\smallskip}
 CH$_{\rm 3}$OH   &$J\!=\!2_K\!\rightarrow\!1_K$ &   $<$7.1(13)         & \multicolumn{1}{c}{...}          & $<$2.8(13)&\multicolumn{1}{c}{...} \\
 CH$_{\rm 3}$OH   &$J\!=\!4_{\rm 2}\!\rightarrow\!3_1$ E$^+$ & $<$4.3(14)    &  \multicolumn{1}{c}{...}    & \multicolumn{1}{c}{...}
  &$<$6.9(13)\\   
 CH$_{\rm 3}$OH   &$J\!=\!5_K\!\rightarrow\!4_K$ &  $<$2.4(13)     &  \multicolumn{1}{c}{...}  & \multicolumn{1}{c}{...} &\multicolumn{1}{c}{...} \\
 CH$_{\rm 3}$OH   &$J\!=\!7_K\!\rightarrow\!6_K$ & \multicolumn{1}{c}{...} & $<$1.1(13)&\multicolumn{1}{c}{...} & \multicolumn{1}{c}{...}\\
 \noalign{\smallskip}
 \hline
 \noalign{\smallskip}
 N$_{\rm 2}$H$^+$          &$J\!=\!4\!\rightarrow\!3$ &             $<$1.4(12)   & $<$1.0(13) & \multicolumn{1}{c}{...} & $<$1.5(12) \\
 H$_{\rm 2}$D$^+$       &$J\!=\!1_{10}\!\rightarrow\!1_{11}$ &   $<$8.7(11)   & $<$4.4(12) & \multicolumn{1}{c}{...} & $<$1.0(12)\\
 \noalign{\smallskip}
 \hline
 \noalign{\smallskip}
 SO & $J\!=\!8_8\!\rightarrow\!7_7$ &\multicolumn{1}{c}{...}& $<$4.3(12)&\multicolumn{1}{c}{...}&\multicolumn{1}{c}{...} \\
 \hline
 \end{tabular}}
 \smallskip
   {\it Note.}
   The excitation temperature is assumed to be 25~K for all lines;
  uncertainties in the column densities are of the order of 30\%, not
including uncertainties in the disk size. \\
   $a(b)$ means $a$ $\times$ 10$^b$. \\
   $^a$ $^{12}$CO column density derived from $^{13}$CO intensity assuming [$^{12}$C]/[$^{13}$C] = 60. \\
  \end{table}