deletions | additions       diff --git a/subsection_Converting_Between_the_Observed__.tex b/subsection_Converting_Between_the_Observed__.tex  index c6186b0..7628639 100644  --- a/subsection_Converting_Between_the_Observed__.tex  +++ b/subsection_Converting_Between_the_Observed__.tex 
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\begin{eqnarray}  \label{eqn:convert_from_actual_to_observed_density}  \rho(\Gamma_{\rm obs}, P_{\rm obs}) = & \int_{b = 0}^{b_{\rm max}} & & f\ \rho(\Gamma_{\rm act}(b), P_{\rm act}(b)) &\ & \dfrac{2b\ db}{b_{\rm max}^2} & \\  = & \int_{b = 0}^{\frac{1}{2} \sqrt{\Gamma_{\rm obs}^2 - \Gamma_{\rm min}^2}} & & f\ \rho(\Gamma_{\rm act}(b), P_{\rm act}(b))& \ &  \left( \Gamma_{\rm obs}^2 - \Gamma_{\rm min}^2 \right)^{-1}\&  4b\ db &. \end{eqnarray}  Figure \ref{fig:uniform_actual_distribution_to_observed_distribution} shows the result for a uniform distribution for underlying values, $\rho(\Gamma_{\rm act}, P_{\rm act}) = \left( P_{\rm max} - P_{\rm min} \right)^{-1}\ \left( \Gamma_{\rm max} - \Gamma_{\rm min} \right)^{-1}$ and compares it to a simulated dust devil survey (blue circles).