  The current system of stellar magnitudes first introduced by Hipparchus was
strictly defined by Norman Robert Pogson in 1856. He based his system on
Ptolemy's star catalogue `Almagest', recorded in about 137 A.D., 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.
Despite that psychophysists have proposed that human's sensitivities are on a
power-law scale, it is shown that the degree of agreement is far better for a
logarithmic magnitude than a power-law magnitude. It is also found that light
ratios in each star catalogue nearly equal to 2.512, excluding the brightest
(1st) and the dimmest (6th and dimmer) stars being unsuitable for the
examination. It means that the visual magnitudes in old star catalogues fully
agree with Pogson's logarithmic scale.
