deletions | additions       diff --git a/If_a_devil_with_a__.tex b/If_a_devil_with_a__.tex  index fa7204b..10f361a 100644  --- a/If_a_devil_with_a__.tex  +++ b/If_a_devil_with_a__.tex 
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\dfrac{dp}{dP_{\rm obs}} = \dfrac{P_{\rm act}}{P_{\rm obs}^2} \left( \dfrac{\Gamma_{\rm act}}{2\ b_{\rm max}} \right)^2 = \left(\dfrac{P_{\rm act}}{P_{\rm obs}^2}\right) \left(\dfrac{P_{\rm min}}{P_{\rm act} - P_{\rm min}}\right).  \end{equation}  Combining the recovery bias and distortion expression gives a Figure \ref{fig:pres_distortion_probability} shows contours of  probability density for a devil with a given $P_{\rm act}$ to be observed with a pressure between $P_{\rm obs}$ and $P_{\rm obs} + dP_{\rm obs}$:   \begin{equation}\label{eqn:probability-density_Pobs-Pact}  f_{\Gamma_{\rm act}}\ \left(\dfrac{\partial p}{\partial P_{\rm obs}}\right)_{\Gamma_{\rm act}} = \left( \dfrac{P_{\rm min}}{P_{\rm max} - P_{\rm min}} \right) P_{\rm act}\ P_{\rm obs}^{-2}.  \end{equation}Figure \ref{fig:probabilty-density_Pobs-Pact} illustrates this density, assuming $P_{\rm min} = 0.1$ and $P_{\rm max} = 10$ in arbitrary units. density.