  We verify an upper bound of Pach and T\'oth [Combinatorica 17(1997), 427-439,
Discrete and Computational Geometry 36(2006), 527-552] on the midrange crossing
constant. Details of their $\frac{8}{9\pi^2}$ upper bound have not been
available. Our verification is different from their method and hinges on a
result of Moon [J. Soc. Indust. Appl. Math. 13(1965), 506-510]. As Moon's
result is optimal, we raise the question whether the midrange crossing constant
is $\frac{8}{9\pi^2}$.
