deletions | additions       diff --git a/In_the_next_section_we__.tex b/In_the_next_section_we__.tex  index b9675ef..3b89504 100644  --- a/In_the_next_section_we__.tex  +++ b/In_the_next_section_we__.tex 
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In the next section, we apply Equation \ref{eqn:convert_from_observed_to_actual_density} to datasets from real surveys, but as an example, consider the simple observed distribution $\rho(\Gamma_{\rm obs}, P_{\rm obs}) = k P_{\rm obs}^{-2}$. Applying Equation \ref{eqn:convert_from_observed_to_actual_density} gives a distribution of actual parameters as follows:   \begin{equation*}  \rho(\Gamma_{\rm act}, P_{\rm act}) = 8 k b_{\rm max}^2 A_{\rm max} \kappa^{-1}\ \upsilon^{-1} \Gamma_{\rm act}^{-11/3} \left( \dfrac{P_{\rm min}}{P_{\rm act} - P_{\rm min}} \right)^{3/2} P_{\rm act}^{-2} = k^\prime\ \Gamma_{\rm act}^{-11/3} \left( \dfrac{P_{\rm min}}{P_{\rm act} - P_{\rm min}} \right)^{3/2} P_{\rm act}^{-2}.  \end{equation*} The shaded contour plot in Figure \ref{fig:} illustrates this $\rho(\Gamma_{\rm act}, P_{\rm act})$ distribution.