Propriétés remarquables de la réfraction astronomique dans une atmosphère à symétrie sphérique

The general theoretical properties and various approximate formulas for the angle χ S of astronomical refraction at are presented, beginning with its fundamental expression by integral immediately leading to Simpson formula. Assuming a spherically symmetric atmosphere, many additional results show up, starting Oriani’s “theorem” Bouguer’s equation. From these, an usual form is derived. A approximation follows deduce Laplace formula, then series expansions that generalize it but divergent isothermal atmosphere—because made. Two results, free from any approximation, exist presented: Biot’s Biot–Sang–Meyer–Fraser–White’s theorems. It leads link extinction, as found Laplace, Sh points on horizon. We compute chromatic effects , —and (in document associated this article) characteristics optical ducts considered in air—and original “local vertical angular distortion coefficient” horizon Annexe B).