deletions | additions       diff --git a/sectionResults_Eight.tex b/sectionResults_Eight.tex  index 226f2ba..f911757 100644  --- a/sectionResults_Eight.tex  +++ b/sectionResults_Eight.tex 
...
where  \begin{align}  g_K= g_I &= 1\notag\\ 1\nonumber\\  \mu^2_{el} S &= 3.8 \;\mathrm{Debye}^2\notag\\ \;\mathrm{Debye}^2\nonumber\\  Z_{rot} &= .8556\; T_{ex}-0.10\notag\\ T_{ex}-0.10\nonumber\\  F(T) &= \frac{1}{e^{h\nu/k_BT}-1}.\notag\\ \frac{1}{e^{h\nu/k_BT}-1}.\nonumber\\  \end{align}  {\bf where $\epsilon_0$ is the vacuum permittivity, $\mu_{el}$ is the permanent electric dipole moment, S is the line strength, Z$_{rot}$ is the rotational partition function, g$_K$ is the K-level degeneracy, g$_I$ is the reduced nuclear spin degeneracy, E$_u$ is the energy of the upper-transition state, T$_{ex}$ is the excitation temperature and T$_{bg}$ is the background temperature.} The dipole moment line strength ($\mu^2_{el}$ S) is taken from the JPL spectral line catalog \citep{Pickett1998}. The partition function (Z$_{rot}$) is a linear fit to JPL data between T=37 to 75 K. T$_{bg}$ was taken to be the cosmic microwave background temperature, 2.725 K. The uncertainty in the fit amplitudes and derived column densities is dominated by our flux-calibration uncertainty. Since the relationships are linear, we estimate the uncertainty in both as 20\%.