deletions | additions       diff --git a/Likewise_non_central_encounters_with__.tex b/Likewise_non_central_encounters_with__.tex  index a18aa24..2f0e20b 100644  --- a/Likewise_non_central_encounters_with__.tex  +++ b/Likewise_non_central_encounters_with__.tex 
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Likewise, non-central encounters with a dust devil will distort the profile full-width/half-max, giving a full-width/half-max $\Gamma_{\rm obs} > \Gamma_{\rm act}$. Having passed through its minimum at $b$, 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 $r(\Gamma_{\rm obs}^\prime) = \dfrac{b}{\cos\left[ \arctan\left( \Gamma_{\rm obs}/2b \right) \right]}$ and $P(r) = \frac{1}{2} P_{\rm obs} =\frac{1}{2}  \dfrac{P_{\rm act}}{1 act}/2}{1  + \left( 2 b /\Gamma_{\rm act} \right)^2} = \dfrac{P_{\rm act}}{1 + \left( 2r(\Gamma_{\rm obs}^\prime/2)/\Gamma_{\rm act} \right)^2 }$. Solving for $\Gamma_{\rm obs}$ gives $\Gamma_{\rm obs} = \sqrt{\Gamma_{\rm act}^2 + \left( 2b \right)^2}$. Using this equation and the encounter geometry again, we find that the probability density for $\Gamma_{\rm obs}$ is   \begin{equation}