deletions | additions       diff --git a/section_Analysis_We_examined_the__.tex b/section_Analysis_We_examined_the__.tex  index 9d2e5bc..07fe94a 100644  --- a/section_Analysis_We_examined_the__.tex  +++ b/section_Analysis_We_examined_the__.tex 
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We examined the GMC properties as in \citet{Solomon_1987}. M83 clouds exhibit similar relationships for velocity line width to radius, which confirms our assumption of the clouds being in virial equilibrium (Figure 1). As well, the virial mass to luminous mass and luminous mass to radius relationships are also consistent with previous findings (Figures 2 and 3). We then binned the clouds by equal surface area on the disk as in \citet{Adamo_2015}, and for each bin examined the cumulative mass function:  \begin{equation}   N(>M)=\int^\infty_M \frac{dN}{dM}dM=\frac{\beta M_\odot}{\alpha+1}\left(\frac{M}{M_\odot}\right)^\alpha=\frac{N_{max}}{M_{max}}\left[\left(\frac{M}{M_{max}}\right)^{\alpha+1}-1\right] \frac{dN}{dM}dM  \end{equation}  The {\sc powerlaw} fit function is   \begin{equation}