deletions | additions       diff --git a/Analysis.tex b/Analysis.tex  index 265119d..dfeabfa 100644  --- a/Analysis.tex  +++ b/Analysis.tex 
...
\begin{equation}  B_{mod} =B_0 \frac{h^2\nu^{3+\beta}}{c^3}\frac{1}{e^{\frac{h\nu}{kT}}-1}  \end{equation}  where $\beta$ is assumed to be 2 (\cite{D_sert_2008}). \cite{D_sert_2008}.  B$_0$ and T were taken as free parameters and a Levenberg–Marquardt algorithm was used to find the best-fit. The fitting was done to the flux density in Jy, so B$_0$ carries these units. The total column density was calculated following Miettinen \& Harju (2010). Briefly, we used the following relations: \begin{equation}  N_{tot} = \frac{I}{B_\nu \mu m_H \kappa R_d}\\  B_\nu = \frac{2 h \nu^3}{c^2 (e^\frac{h \nu}{kT}-1)}\\  I = 3.73\times 10^{-16} B_{mod} \left(\frac{1"}{\theta}\right)^2\\  \kappa = \kappa_{1.3mm} \left(\frac{\lambda}{1.3mm}\right)^{-\beta}\\  \end{equation}  where 3.73 x 10$^{-16}$ converts the surface brightness from Jy/(1" beam) to SI units. We make the following assumptions: $\kappa_{1.3mm}$ = 0.11 $\frac{m^2}{kg}$, appropriate for ice-covered dust grains from OH94, $\theta$=15.0", the beamsize of the GBT at 49 GHz, the mean molecular weight $\mu$ = 2.3 and dust to mass ratio $R_d$ = 1/100. Note that B$_\nu$, B$_{mod}$ and $\kappa$ all require a choice of frequency or wavelength. However, these dependencies cancel in the final calculation of N$_{tot}$. These results are summarized in Table \ref{mbb}, where we report the flux density at five wavelength bands for each CS detection, the best-fit temperature, the total column density and the CS abundance. For those sources where the modified blackbody model was a poor fit, as judged by eye, we have excluded the temperature, column density and abundance. The cause for the poor fit in these cases appeared to be caused by the Herschel band emission not fitting nicely within extending well outside the  the GBT beam. As a result, For these poorly-fit sources,  the fluxes reported here probably do not represent the emission from the same object. For those sources with a double-Gaussian CS line profile, we add the CS column densities calculated using both Gaussians. \begin{table}  \begin{tabular}{rrrrrrrrr}  Name & Blue (Jy) & Red (Jy) & PSW (Jy) & PMW (Jy) & PLW (Jy) & Temperature (K) & Total Column Density ($\times$10$^{21}$ cm$^{-2}$) & CS Abundance ($\times$10$^{-7}$)\\ 
...