Difference between the declination δ_h computed from the altitude with Eqs. (7)–(9) and the declination δ_W listed in Manuscript for ϕ_G = 51° 19′. With few excaptions, the computations are exact for superior and southern culminations. The values δ_h from inferior culmination are systematically too high for low altitudes. Values for which δ_h ≠ δ_W are labelled with W for those entries for which only one altitude is listed, and for W 9. The solid curve gives the refraction R_R according to Rothmann. Stars to the right of the vertical dashed line have R = 0, according to Rothmann.