deletions | additions       diff --git a/12 vs 13 [3].tex b/12 vs 13 [3].tex  index b4b7c4d..1f213d8 100644  --- a/12 vs 13 [3].tex  +++ b/12 vs 13 [3].tex 
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To correct for the fact that \textsuperscript{12}CO is opticaly thick, we use the following equation:  \begin{equation} %\label{eqn:mass-energy}   \frac{ T_{\rm mb 12}}{T_{\rm mb 13}} = \frac{[^{12}{\rm CO}]}{[ ^{13}{\rm CO}]} \frac{1 - e^{-\tau_{12}}}{\tau_{12}} \\  \frac{1 - e^{-\tau_{12}}}{\tau_{12}} = \frac{ T_{\rm mb 12}}{T_{\rm mb 13}} \frac{[ ^{13}{\rm CO}]}{[^{12}{\rm CO}]}  \end{equation}