  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.
