deletions | additions       diff --git a/Problem 2.tex b/Problem 2.tex  index e1a13f7..144d400 100644  --- a/Problem 2.tex  +++ b/Problem 2.tex 
...
The total column density is then $\rm{N_H}=(\sum n_H f_V)~d\sim0.8~\rm{cm}^{-3}~d$. As a rough estimate of uncertainty, let's assume $20\%$ errors on the filling factors. The distance along the line of sight to the galactic center can be estimated as $d=8.0\pm0.6~\rm{kpc}$, e.g. \cite{Ghez}.  With these assumptions, we find an extinction due to gas in the Galactic disk (excluding Sgr B2) of $11\pm4~\rm{mag}$. In linear units, this corresponds to extinction by a factor of $\sim25,000$! Note that this value is very sensitive to the parameters adopted for the dense H$_2$ phase - assuming. a factor of 4 higher filling density or filling factor (i.e. 1 big cloud) would nearly double the total extinction.  Along those lines, when we add in Sgr B2, things get much worse for optical observers.