deletions | additions       diff --git a/subsection_Converting_Between_the_Observed__.tex b/subsection_Converting_Between_the_Observed__.tex  index f40b4ec..c4ca17c 100644  --- a/subsection_Converting_Between_the_Observed__.tex  +++ b/subsection_Converting_Between_the_Observed__.tex 
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= 2\ A_{\rm max}^{-1}\ \upsilon\ \kappa\ b_{\rm max}^{-2} P_{\rm min}^{-1/2}\ \int_{b^\prime = 0}^{b({\rm obs})} \left( \Gamma_{\rm act}(b^\prime)/{\rm m} \right)^{5/3} \left( P_{\rm act}(b^\prime) - P_{\rm min} \right)^{1/2} \ \rho({\rm act}(b^\prime))\ b^\prime\ db^\prime \label{eqn:convert_from_actual_to_observed_density},   \end{equation}  where $\kappa = 40\ {\rm s}$ and $\Gamma_{\rm act}$ is measured in meters, m. Figure \ref{fig:uniform_actual_distribution_to_observed_distribution} shows the result for a uniform distribution of actual values, $\rho({\rm act}) = \left( P_{\rm max} - P_{\rm min} \right)^{-1}\ \left( \Gamma_{\rm max} - \Gamma_{\rm min} \right)^{-1}$ and compares it to a simulated dust devil survey (blue circles). (For the uniform distribution, the integral has a closed form expression that is unwieldy, so we opt to perform the integration numerically.)