Magnitude systems in old star catalogues

Abstract

The current system of stellar magnitudes originally introduced by Hipparchus was strictly defined by Norman Pogson in 1856. He based his system on Ptolemy's star catalogue, the Almagest, recorded in about AD137, and defined the magnitude-intensity relationship on a logarithmic scale.

Stellar magnitudes observed with the naked eye recorded in seven old star catalogues were analyzed in order to examine the visual magnitude systems. Although psychophysicists have proposed that human visual sensitivity follows a power-law scale, it is shown here that the degree of agreement is far better for a logarithmic scale than for a power-law scale. It is also found that light ratios in each star catalogue are nearly equal to 2.512, if the brightest (1st magnitude) and the faintest (6th magnitude and dimmer) stars are excluded from the study. This means that the visual magnitudes in the old star catalogues agree fully with Pogson's logarithmic scale.