deletions | additions       diff --git a/Whether_a_devil_with_a__.tex b/Whether_a_devil_with_a__.tex  index d058972..e2ba84c 100644  --- a/Whether_a_devil_with_a__.tex  +++ b/Whether_a_devil_with_a__.tex 
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$b_{\rm max}$ can also be written in terms of a devil's central pressure $P_{\rm act}$: $b_{\rm max} = \dfrac{\Gamma_{\rm act}}{2} \sqrt{ \dfrac{P_{\rm act}}{P_{\rm min}} - 1}$, giving the following expression for the probability density:  \begin{equation}\label{eqn:dpdP_obs}  \dfrac{dp}{dP_{\rm obs}} \left(\dfrac{\partial p}{\partial P_{\rm obs}}\right)_{\Gamma_{\rm act}}  = \left( \dfrac{P_{\rm min}}{P_{\rm act} - P_{\rm min}} \right) P_{\rm act}\ P_{\rm obs}^{-2}. \end{equation}  Combining the recovery bias and distortion expression gives a probability density for a devil with a given $P_{\rm act}$ to be observed with a pressure between $P_{\rm obs}$ and $P_{\rm obs} + dP_{\rm obs}$:  
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\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.