deletions | additions       diff --git a/We_can_use_the_encounter__.tex b/We_can_use_the_encounter__.tex  index 11c3da7..5f61828 100644  --- a/We_can_use_the_encounter__.tex  +++ b/We_can_use_the_encounter__.tex 
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\label{eqn:dp_dGamma_obs}  \dfrac{dp}{d\Gamma_{\rm obs}} = \dfrac{\Gamma_{\rm obs}}{b_{\rm max}^2} = 4 \Gamma_{\rm act}^{-2} \left( \dfrac{P_{\rm min}}{P_{\rm act} - P_{\rm min}}\right) \Gamma_{\rm obs}.  \end{equation}  We require that $b \le b_{\rm max}$ in order for a devil to be detected, which limits the range of allowable values for $\Gamma_{\rm obs}$, given $P_{\rm act}$ and $\Gamma_{\rm act}$. We can use the relationship $\Gamma_{\rm obs}^2 = \Gamma_{\rm act}^2 + \left(2 b\right)^2$ Equation \ref{eqn:Gamma_obs}  to solve for $\Gamma_{\rm obs}/\Gamma_{\rm act}$: \begin{equation}  \label{eqn:Gamma_obs_limits}  1 \le \dfrac{\Gamma_{\rm obs}}{\Gamma_{\rm act}} \le \sqrt{P_{\rm act}/P_{\rm min}}.