deletions | additions       diff --git a/12 vs 13 [1].tex b/12 vs 13 [1].tex  index 619ed6e..43091ad 100644  --- a/12 vs 13 [1].tex  +++ b/12 vs 13 [1].tex 
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\section{\textsuperscript{12}CO compared to \textsuperscript{13}CO}  In comparing One of  the results obtained in observations in \textsuperscript{12}CO and \textsuperscript{13}CO, we first need to determine which limits are appropriate. The assumption key assumptions made is  that both are the gas is  optically thin, thin. This holds for 12CO, which is signficantly rarer than 12CO,  but it is unclear whether it holds for 12CO. To analyse 12CO  we will either need to  showhere  that this it  is not correct. \textsuperscript{13}CO appears to be acceptably optically  thin, but observations in \textsuperscript{12}CO are useless without a correction for optical thickness. We will show suggest such or develop  a correction and show its correctness. if it is optically thick.  \subsection{\textsuperscript{12}CO is optically thick}  A comparison between \textsuperscript{12}CO and \textsuperscript{13}CO when we assume \textsuperscript{12}CO is optically thin can be seen in thetwo  following graphs graph.