deletions | additions       diff --git a/12 vs 13 CO.tex b/12 vs 13 CO.tex  index c0ff9b3..619ed6e 100644  --- a/12 vs 13 CO.tex  +++ b/12 vs 13 CO.tex 
...
\section{\textsuperscript{12}CO compared to \textsuperscript{13}CO}  At present, all In comparing the  results are for \textsuperscript{13}CO. Attempts to analyse \textsuperscript{12}CO obtained  in the same way have failed observations in \textsuperscript{12}CO and \textsuperscript{13}CO, we first need  to produce any significant results. It appears determine which limits are appropriate. The assumption  that \textsuperscript{12}CO both are optically thin, but we will show here that this  is not optically thin. Once I have some solutions correct. \textsuperscript{13}CO appears to be acceptably thin, but observations in \textsuperscript{12}CO are useless without a correction  for \textsuperscript{12}CO, taking into account the fact that it optical thickness. We will show suggest such a correction and show its correctness.  \subsection{\textsuperscript{12}CO  is optically thick I will add those here. thick}  A comparison between \textsuperscript{12}CO and \textsuperscript{13}CO when we assume \textsuperscript{12}CO is optically thin can be seen in the two following graphs