deletions | additions       diff --git a/Whether_or_not_we_detect__.tex b/Whether_or_not_we_detect__.tex  index 96e1929..ac20ee6 100644  --- a/Whether_or_not_we_detect__.tex  +++ b/Whether_or_not_we_detect__.tex 
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\begin{equation}  db = \frac{1}{2}\Gamma_{\rm act}\left[ \dfrac{P_{\rm act}}{P_{\rm obs}} - 1 \right]^{-1/2} \left( \dfrac{P_{\rm act}}{P_{\rm obs}^2} \right) dP_{\rm obs} = \frac{1}{2}\left( \dfrac{\Gamma_{\rm act}}{2} \right)^2\dfrac{P_{\rm act}}{P_{\rm obs}^2} \dfrac{ dP_{\rm obs} }{b},  \end{equation}  \label{eqn:infinitesimal_area}  where we've subsumed the minus sign into the definition of $P_{\rm obs}$ (which has the opposite sign of $db$). Then using the expression for the differential probability above, we can express the probability to measure a pressure signal between $P_{\rm obs}$ and $P_{\rm obs} + dP_{\rm obs}$ for a devil with a given $P_{\rm act}$ and $\Gamma_{\rm act}$:   \begin{equation}  dp\left(P_{\rm obs}\right) = P_{\rm act} \left( \dfrac{\Gamma_{\rm act}}{2\ b_{\rm max}} \right)^2 \dfrac{ dP_{\rm obs} }{P_{\rm obs}^2}. 
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