deletions | additions       diff --git a/Three_sources_N62_1_N90_2_and__.tex b/Three_sources_N62_1_N90_2_and__.tex  index 437ea6d..417cb76 100644  --- a/Three_sources_N62_1_N90_2_and__.tex  +++ b/Three_sources_N62_1_N90_2_and__.tex 
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v_{in} \approx \frac{\sigma^2}{v_{red} - v_{blue}} \ln\left( \frac{1+e T_{BD}/T_D}{1+e T_{RD}/T_D}\right)  \end{equation}  When the optical depth and V$_{in}$/$\sigma$ are sufficient large, the red peak can disappear (see Myers et al. 1996 for discussion of this effect). Thus, we are limited in our numerical analysis tojust  N117_3. Our line profile measurements and infall velocity calculation are given in Table X. Since we do not have an optically thin measurement of this source, we have assumed the value of the velocity dispersion.  \begin{table}[]  \begin{tabular}{rr}  Object &N117_3\\  T_{BD} &0.9 K\\  T_{RD} &0.2 K\\  T_D &1.1 K\\  v_{blue} &38.4 km/s\\  v_{red} &40.9 km/s\\  $\sigma$ &1.0 km/s\\  \end{tabular}  \end{table}