deletions | additions       diff --git a/subsection_The_Pressure_Signal_Full__.tex b/subsection_The_Pressure_Signal_Full__.tex  index acf566a..6b944bc 100644  --- a/subsection_The_Pressure_Signal_Full__.tex  +++ b/subsection_The_Pressure_Signal_Full__.tex 
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\end{equation}  where we've suppressed the constant factor involving the pressures.  Likewise, non-central encounters with a dust devil will distort the profile full-width/half-max, giving a full-width/half-max $\Gamma_{\rm obs}$. Having passed through its minimum at the devil's closest approach distance, the observed pressure signal reaches half its value at a time $t = \frac{1}{2} \Gamma_{\rm obs}^\prime = \frac{1}{2} \Gamma_{\rm obs}/\upsilon$ by definition. At this time, the center of the devil is a radial distance from the barometer $r(t = \Gamma_{\rm obs}^\prime) = \dfrac{b}{\cos\left[ \arctan\left( \Gamma_{\rm obs}/2b \right) \right]}$ and $P(r) $P(r(\Gamma_{\rm obs}^\prime/2))  = \frac{1}{2} P_{\rm obs} = \dfrac{P_{\rm act}/2}{1 + \left( 2 b /\Gamma_{\rm act} \right)^2} = \dfrac{P_{\rm act}}{1 + \left( 2r(\Gamma_{\rm obs}^\prime/2)/\Gamma_{\rm act} \right)^2 }$. Solving for $\Gamma_{\rm obs}$ gives \begin{equation}\label{eqn:Gamma_obs}  \Gamma_{\rm obs} = \frac{1}{2}\sqrt{\Gamma_{\rm act}^2 + \left( 2b \right)^2}.  \end{equation} 
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\begin{equation}\label{eqn:dpdGamma_obs}  \dfrac{dp}{d\Gamma_{\rm obs}} = 8 \Gamma_{\rm act}^{-2}\ \Gamma_{\rm obs}.   \end{equation}  Again combining this expression with the recovery bias gives the probability density for a devil with a given $\Gamma_{\rm act}$-value to be observed with a $\Gamma_{\rm obs}$-value, and Figure \ref{fig:} illustrates the probability density.