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\section{Eclipse Statistics}  It The authors note it  is straightforward to show the probability of an eclipse at any depth is $P_e = r_s + r_g$ but where $r_s$ and $r_g$ are  the authors radii of the greater and smaller stars respectively, but in this case they  wish to study the probability of an eclipse of \textbf{any specified} magnitude depth. depth, which calls for a different approach.  \paragraph{}  In order to calculate this probability, the function $i(\Delta m)$ must be derived. Although the maximum primary eclipse depth $\Delta m$ is a well defined function of the inclination angle i, iteration is needed to find this inverse function $i(\Delta m)$