\begin{table}%T2
\caption{A numerical example showing the non-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 
ratio $\Delta \mu _{\rm Y-MX}^{a }= [\mu _{\rm X-MY }$/$\mu _{\rm X-MX}
]^{a}$ for $a=0.1$ and $M=5$; (3) $\Delta \mu _{\rm Y-MX}^{b }$ for $b= 
0.2$; (4) $\Delta \mu _{\rm Y-MX}^{c }$ for $c= 0.1$; (5) the 
reaction rate ratio $R$. Two situations are distinguished: (1) for 
$^{i}$O+$^{ i}$OM ($i\equiv j$), $R = \Delta \mu _{\rm Y-MY}^{a} \ \Delta 
\mu _{\rm Y-MY}^{b }$ and for (2) $^{j}$O+$^{ i}$OM ($i\ne j$), 
$R=\{\Delta \mu _{\rm Y-MX}^{a}$ 1/2 
[$\Delta \mu _{\rm Y-MX}^{b }+\kappa \ \Delta \mu_{\rm Y-MX}^{c}$]; calculations 
are performed for $\kappa  = 0.8$ (6) The product of the 
relative abundance with $^{16}\rm O =0.9976$, $^{17}\rm O=4\times10^{-4}$ and 
$^{18}\rm O=2\times10^{-3}$ (7) the product of $(5)\times(6)$.
%
The $^{17}$O/$^{16}$O ratio of the OOM molecule (noted 
[$^{17}$O/$^{16}$O]$_{\rm OOM })$ is calculated from the values of the column 
[7]; that is for the abundance of $^{16}$O: \{1/2 [$3.585 \times10^{-4} + 
1.789 \times10^{-3} + 3.587\times10^{-4 }+ 1.792 \times10^{-3}] + 9.952 
\times10^{-1}$\} and similarly for $^{17}$O and $^{18}$O. The $\delta 
^{17}$O ($\mbox{\textperthousand}$) = ([$^{17}$O/$^{16}$O]$_{\rm OOM }$/[0.0004/0.9976])$-$ 1) 
$\times$1000; similarly for $\delta ^{18}$O ($\mbox{\textperthousand}$). That is: $\delta ^{17}\rm O 
=-101.1\mbox{\textperthousand}$ and $\delta ^{18}\rm O= -102.2\mbox{\textperthousand}$ with $\delta ^{17}$O/$\delta ^{18}\rm O=0.989$.}\label{tab2}
%\centering
\par
\begin{tabular}{lllllll}
\hline\hline
\multicolumn{1}{c}{[1]}& \multicolumn{1}{c}{[2]}& \multicolumn{1}{c}{[3]}& \multicolumn{1}{c}{[4]}& \multicolumn{1}{c}{[5]} & \multicolumn{1}{c}{[6]}& \multicolumn{1}{c}{[7]}\\
\hline
$^{16}$O+$^{16}$OM & $\equiv $ 1 & $\equiv $ 1 & $\equiv $ 1 & $\equiv $ 1 & 0.9952  &
0.9952
\\
$^{16}$O+$^{17}$OM & 1.0034 & 0.9932 & 0.9966 & 0.8983 & $3.990\times10^{-4 }$ & $3.585\times10^{-4}$
\\
$^{16}$O+$^{18}$OM & 1.0065 & 0.9871 & 0.9935 & 0.8968 & $1.995\times10^{-3 }$ & $1.789\times10^{-3}$
\\
$^{17}$O+$^{16}$OM & 1.0020 & 0.9960 & 0.9980 & 0.8990 & $3.990\times10^{-4 }$ & $3.587\times10^{-4}$
\\
$^{17}$O+$^{17}$OM & 1.0055 & 0.9892 & 0.9946 & 0.9946 & $1.600\times10^{-7 }$ & $1.591\times10^{-7}$
\\
$^{17}$O+$^{18}$OM & 1.0087 & 0.9829 & 0.9914 & 0.8957 & $8.000\times10^{-7 }$ & $7.166\times10^{-7}$
\\
$^{18}$O+$^{16}$OM & 1.0038 & 0.9924 & 0.9962 & 0.8981 & $1.995\times10^{-3 }$ & $1.792\times10^{-3}$
\\
$^{18}$O+$^{17}$OM & 1.0074 & 0.9854 & 0.9927 & 0.8963 & $8.000\times10^{-7 }$ & $7.171\times10^{-7}$
\\
$^{18}$O+$^{18}$OM & 1.0107 & 0.9790 & 0.9894 & 0.9894 & $4.000\times10^{-6 }$ & $3.958\times10^{-6}$
\\
\hline
\end{tabular}
\end{table}