\begin{table}%T1
\caption{A numerical example showing the mass-dependent 
relations between the different reaction rates in the oxygen isotopic 
system. In successive columns: (1) the isotopic reaction 
$^{i}$O+$^{j}$OM $\to   {}^{i}$O$^{j}$OM; (2) the reduced mass of the 
reactants for $M=5$; (3) the reduced mass ratio $\Delta \mu 
_{\rm Y-MX}^{a }$ normalized to the reaction $^{16}$O+$^{16}$OM for $a=1$; 
(4) the product of the relative abundance with $^{16}\rm O=0.9976$, 
$^{17}\rm O=4\times10^{-4}$ and $^{18}\rm O=2 \times10^{-3}$; (5) the 
product of $(3)\times(4)$.
%
The $^{17}$O/$^{16}$O ratio ($x'_{17}/x'_{16})$ of the OOM molecule (noted 
[$^{17}$O/$^{16}$O]$_{\rm OOM })$ is calculated from the values of the column 
(5); that is: $x'_{16} = \{1/2 [4.128 \times10^{-4} + 2.129 \times10^{-3} $ $+ 
4.070 \times10^{-4 }+ 2.073 \times10^{-3}] + 9.952 \times10^{-1}\}$. Similarly for 
$x'_{17}$ and $x'_{18}$. This gives:
%
[$^{17}$O/$^{16}$O]$_{\rm OOM} = (x'_{17}/x'_{16}) = 4.119 \times10^{-4}$
and [$^{18}$O/$^{16}$O]$_{\rm OOM} = (x'_{18}/x'_{16}) = 2.111 \times10^{-3}$
corresponding to $\delta ^{17}$O = ([$4.119 \times10^{-4 }/ (4 \times10^{-4}/0.9976)]-1)\times1000 = +27.3\mbox{\textperthousand}$ and similarly $\delta ^{18}\rm O = +53.2\mbox{\textperthousand}$. The 
slope in the diagram $\delta ^{17}$O versus $\delta ^{18}$O is equal to 
0.513.}\label{tab1}
%\centering

\begin{tabular}{lllll}
\hline\hline
\multicolumn{1}{c}{[1]}& \multicolumn{1}{c}{[2]}& \multicolumn{1}{c}{[3]}& \multicolumn{1}{c}{[4]}& \multicolumn{1}{c}{[5]} \\
\hline
$^{16}$O + $^{16}$OM& 9.081& $\equiv $1& 0.9952& 0.9952 
\\
$^{17}$O + $^{16}$OM& 9.395& 1.0345& $3.990\times10^{-4 }$& $4.128\times10^{-4}$
\\
$^{18}$O + $^{16}$OM& 9.692& 1.0673& $1.995\times10^{-3 }$& $2.129\times10^{-3}$
\\
$^{16}$O + $^{17}$OM& 9.263& 1.0201& $3.990\times10^{-4 }$& $4.070\times10^{-4}$
\\
$^{17}$O + $^{17}$OM& 9.590& 1.0560& $1.600\times10^{-7 }$& $1.690\times10^{-7}$
\\
$^{18}$O + $^{17}$OM& 9.900& 1.0902& $8.000\times10^{-7 }$& $8.721\times10^{-7}$
\\
$^{16}$O + $^{18}$OM& 9.436& 1.0391& $1.995\times10^{-3 }$& $2.073\times10^{-3}$
\\
$^{17}$O + $^{18}$OM& 9.775& 1.0764& $8.000\times10^{-7 }$& $8.611\times10^{-7}$
\\
$^{18}$O + $^{18}$OM& 10.10& 1.1119& $4.000\times10^{-6 }$& $4.448\times10^{-6}$
\\
\hline
\end{tabular}
\end{table}