The Thousand Star Magnitudes in the Catalogues of Ptolemy, Al Sufi, and Tycho Are All Corrected for Atmospheric Extinction

Three pre-telescopic star catalogues contain about a thousand star magnitudes each (with magnitudes 1, 2, 3, 4, 5, and 6), with these reported brightnesses as the original basis for what has become the modern magnitude scale. These catalogues are those of Ptolemy (c. 137, from Alexandria at a latitude of 31.2), Al Sufi (c. 960, from Isfahan at a latitude of 32.6), and Tycho Brahe (c. 1590, from the island of Hven at a latitude of 55.9). Previously, extensive work has been made on the positions of the catalogued stars, but only scant attention has been paid to the magnitudes as reported. These magnitudes will be affected by a variety of processes, including the dimming of the light by our Earth's atmosphere (atmospheric extinction), the quantization of the brightnesses into magnitude bins, and copying or influence from prior catalogues. This paper provides a detailed examination of these effects. Indeed, I find all three catalogues to report magnitudes that have near-zero extinction effects, so the old observers in some way extinction corrected their observations.