The published V-magnitudes (Carlsberg Meridian Catalogue, Nos. 6-8)
were corrected to unit heliocentric and geocentric distances to obtain
the reduced magnitude H(
):
where r and 
are the distances of the asteroid
from the Sun and the Earth, respectively, and 
is
the solar phase angle.
In the standard HG magnitude system,
as adopted at the IAU General Assembly in 1985 (Bowell et al. 1989),
the reduced magnitude is modeled by the relation:
which has two free parameters, the absolute magnitude H
and the slope parameter G.
The phase functions 
and 
are defined in Bowell et al. (1989).
The formulation is based on a semi-empirical-semi-theoretical analysis.
No physical interpretation of the slope parameter G is tied to the
HG-system, although it is clear that it is related to the albedo
and the proportion of multiple-scattered light.
In practice, the parameters H and G are not constants for an asteroid, but depend on the aspect angle, the obliquity angle, and the rotational phase. We take the first dependence into account by fitting Eq. (1) to the data from each apparition of the asteroid individually. This works quite well since the aspect angle is almost constant during an apparition for main-belt asteroids. Thus we get an HG-pair for each asteroid and apparition. This is in contrast to Paper I in which the G-value was constrained to be a constant for each asteroid, independent of apparition.
We will ignore the obliquity-dependence since it is probably insignificant for the moderate solar phase angles for observations of main-belt asteroids.
The dependence on rotational phase is usually removed by averaging the magnitude over a rotation cycle in the observed lightcurve. Unfortunately, the nightly sampling rate of CAMC complicates this. For objects with a high lightcurve amplitude and a rotation cycle not comensurate with a day we have added a 2nd order Fourier series to HGsystem in order to take this into account. For practical reasons we iteratively fitted the solar phase dependence and the rotational phase dependence until it converged, instead of a single least-squares fit.