Table 2: 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 ⁱO+^jOM $\to {}^{i}$ O^jOM; (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 ⁱO+ⁱOM ( $i\equiv j$ ), $R = \Delta \mu _{\rm Y-MY}^{a} \ \Delta \mu _{\rm Y-MY}^{b }$ and for (2) ^jO+ⁱOM ( $i\ne j$ ), $R=\{\Delta \mu _{\rm Y-MX}^{a}$ 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 $^{16}\rm O=0.9976$ , $^{17}\rm O=4\times 10^{-4}$ and $^{18}\rm O=2 \times 10^{-3}$ (7) the product of $(5)\times (6)$ . The ¹⁷O/¹⁶O ratio of the OOM molecule (noted [¹⁷O/¹⁶O] $_{\rm OOM })$ is calculated from the values of the column [7]; that is for the abundance of ¹⁶O: {1/2 [ $3.585 \times 10^{-4} + 1.789 \times 10^{-3} + 3.587\times 10^{-4 }+ 1.792 \times 10^{-3}] + 9.952 \times 10^{-1}$ } and similarly for ¹⁷O and ¹⁸O. The $\delta ^{17}$ O ( $\mbox{\textperthousand}$ ) = ([¹⁷O/¹⁶O] $_{\rm OOM }$ /[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/ $\delta ^{18}\rm O=0.989$ .
[1] [2] [3] [4] [5] [6] [7]

¹⁶O+¹⁶OM $\equiv$ 1 $\equiv$ 1 $\equiv$ 1 $\equiv$ 1 0.9952 0.9952

¹⁶O+¹⁷OM 1.0034 0.9932 0.9966 0.8983 $3.990\times10^{-4 }$ $3.585\times10^{-4}$

¹⁶O+¹⁸OM 1.0065 0.9871 0.9935 0.8968 $1.995\times10^{-3 }$ $1.789\times10^{-3}$

¹⁷O+¹⁶OM 1.0020 0.9960 0.9980 0.8990 $3.990\times10^{-4 }$ $3.587\times10^{-4}$

¹⁷O+¹⁷OM 1.0055 0.9892 0.9946 0.9946 $1.600\times10^{-7 }$ $1.591\times10^{-7}$

¹⁷O+¹⁸OM 1.0087 0.9829 0.9914 0.8957 $8.000\times10^{-7 }$ $7.166\times10^{-7}$

¹⁸O+¹⁶OM 1.0038 0.9924 0.9962 0.8981 $1.995\times10^{-3 }$ $1.792\times10^{-3}$

¹⁸O+¹⁷OM 1.0074 0.9854 0.9927 0.8963 $8.000\times10^{-7 }$ $7.171\times10^{-7}$

¹⁸O+¹⁸OM 1.0107 0.9790 0.9894 0.9894 $4.000\times10^{-6 }$ $3.958\times10^{-6}$

**Table 2:** 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 ⁱO+^jOM $\to {}^{i}$ O^jOM; (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 ⁱO+ⁱOM ( $i\equiv j$ ), $R = \Delta \mu _{\rm Y-MY}^{a} \ \Delta \mu _{\rm Y-MY}^{b }$ and for (2) ^jO+ⁱOM ( $i\ne j$ ), $R=\{\Delta \mu _{\rm Y-MX}^{a}$ 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 $^{16}\rm O=0.9976$ , $^{17}\rm O=4\times 10^{-4}$ and $^{18}\rm O=2 \times 10^{-3}$ (7) the product of $(5)\times (6)$ . The ¹⁷O/¹⁶O ratio of the OOM molecule (noted [¹⁷O/¹⁶O] $_{\rm OOM })$ is calculated from the values of the column [7]; that is for the abundance of ¹⁶O: {1/2 [ $3.585 \times 10^{-4} + 1.789 \times 10^{-3} + 3.587\times 10^{-4 }+ 1.792 \times 10^{-3}] + 9.952 \times 10^{-1}$ } and similarly for ¹⁷O and ¹⁸O. The $\delta ^{17}$ O ( $\mbox{\textperthousand}$ ) = ([¹⁷O/¹⁶O] $_{\rm OOM }$ /[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/ $\delta ^{18}\rm O=0.989$ .
[1]	[2]	[3]	[4]	[5]	[6]	[7]
¹⁶O+¹⁶OM	$\equiv$ 1	$\equiv$ 1	$\equiv$ 1	$\equiv$ 1	0.9952	0.9952
¹⁶O+¹⁷OM	1.0034	0.9932	0.9966	0.8983	$3.990\times10^{-4 }$	$3.585\times10^{-4}$
¹⁶O+¹⁸OM	1.0065	0.9871	0.9935	0.8968	$1.995\times10^{-3 }$	$1.789\times10^{-3}$
¹⁷O+¹⁶OM	1.0020	0.9960	0.9980	0.8990	$3.990\times10^{-4 }$	$3.587\times10^{-4}$
¹⁷O+¹⁷OM	1.0055	0.9892	0.9946	0.9946	$1.600\times10^{-7 }$	$1.591\times10^{-7}$
¹⁷O+¹⁸OM	1.0087	0.9829	0.9914	0.8957	$8.000\times10^{-7 }$	$7.166\times10^{-7}$
¹⁸O+¹⁶OM	1.0038	0.9924	0.9962	0.8981	$1.995\times10^{-3 }$	$1.792\times10^{-3}$
¹⁸O+¹⁷OM	1.0074	0.9854	0.9927	0.8963	$8.000\times10^{-7 }$	$7.171\times10^{-7}$
¹⁸O+¹⁸OM	1.0107	0.9790	0.9894	0.9894	$4.000\times10^{-6 }$	$3.958\times10^{-6}$

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