deletions | additions       diff --git a/Consider_how_the_contours_behave__.tex b/Consider_how_the_contours_behave__.tex  index e1170f5..6635d65 100644  --- a/Consider_how_the_contours_behave__.tex  +++ b/Consider_how_the_contours_behave__.tex 
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Given a number density for the distribution of $P_{\rm act}$-values, $n(P_{\rm act})$, we can use this density expression to calculate the resulting distribution of $P_{\rm obs}$-values, $n(P_{\rm obs})$:  \begin{equation}  n(P_{\rm obs}) = \left( \dfrac{P_{\rm min}}{P_{\rm max} - P_{\rm min}} \right) P_{\rm obs}^{-2} \int_{P_{\rm act} = P_{\rm obs}}^{P_{\rm max}} n(P_{\rm act}) P_{\rm act}\ dP_{\rm act}.  \label{eqn:n_Pobs_from_Pact}  \end{equation}  The integral extends between $P_{\rm obs}$ and $P_{\rm max}$ since only devils with $P_{\rm act}$ in that range can contribute.