deletions | additions       diff --git a/Thus_begin_eqnarray_label_eqn__.tex b/Thus_begin_eqnarray_label_eqn__.tex  index d8cc8d1..2de78f7 100644  --- a/Thus_begin_eqnarray_label_eqn__.tex  +++ b/Thus_begin_eqnarray_label_eqn__.tex 
...
\Rightarrow b^{-1}\ P_{\rm obs} \left( \dfrac{\partial \rho({\rm obs})}{\partial P_{\rm obs}} - \left( \dfrac{\Gamma_{\rm obs}}{2 P_{\rm obs}} \right) \dfrac{\partial \rho({\rm obs})}{\partial \Gamma_{\rm obs}} \right) & = & & b_{\rm max}^{-2}\ f(b)\ \rho({\rm act}(b))\ b & \\  \Rightarrow \rho(\Gamma_{\rm act}, P_{\rm act}) & = & & \left[ \left( \dfrac{b_{\rm max}}{b} \right)^2\ f(b)^{-1}\ P_{\rm obs} \left( \dfrac{\partial \rho({\rm obs})}{\partial P_{\rm obs}} - \left( \dfrac{\Gamma_{\rm obs}}{2 P_{\rm obs}} \right) \dfrac{\partial \rho({\rm obs})}{\partial \Gamma_{\rm obs}} \right) \right]_{\rm obs \rightarrow act} & &,  \end{eqnarray} where $\partial \Gamma_0/\partial P_{\rm obs} = 0$