The solar observations with astrolabes are per force a routine procedure. Eventhough each observation is carefully performed to avoid introducing systematic errors, and the relevant effects are thoroughly modelled, as discussed in item (4.), the seasonal characteristics are bound to bias the distribution of observations at a certain zenith distance on a certain site. We took a direct approach to the problem, by producing exagerately biased subsets of the actual data and investigating the outcome from these hypothetical distributions.
Table 1 presents the results obtained in Paper I for the Standard Weighted Global Solution. There, they are compared with several independent investigations and found in overal agreement. The value for the correction to the obliquity of the ecliptic is however outstanding and shall be focused upon in the analysis that follows.
Firstly the observations, inside each original subset, were divided in two groups. Queueing up the observations by order, they were sorted out into the ``even group'' or into the ``odd group''.
The main results are shown in Table 2. They show complete agreement with the Standard Weighted Global Solution, after allowance for the halved sample size, both in regard with the derived corrections and standard deviations.
Table 2: Solution for the ``even'' and ``odd'' subsets
As counterproof for the biasing introduced by the previous arrangement
of the data, we next produced five trials where 50% of the data
were picked up, regardless of the original subsets distribution.
The results so obtained are presented in Table 3. The outcome reinforces
the previously obtained inference, namely that the results are
essentially independent from any ``fair'' data sampling.
, 
, 
and 
vary within
reasonable bounds with respect to the formal standard desviation.
and 
keep the tendency shown in the Standard Weighted Global
Solution.
Table 3: Solutions for the subsets including 50% of the
observations, chosen at random
The above conclusion does not hold in the case of intentionally biased data sampling. Such would be the case of selecting only northern or southern hemisphere data points. The advantages gained by grouping complementary data sites is well discussed elsewhere (Paper I; Leister 1979, 1989; Chollet 1981; Penna 1982; Bougeard et al. 1983; Journet 1986 and Poppe 1994) and do not need further consideration.
We proceed now to assert whether the weighting system was
determinant for the solution of the unknowns. The
applied test consists on varying the weight of each subset by 
.
In this way the variation ranges from 10%, for the best quality,
less numerically dense, small zenith distance subsets, to 40%, for
the large zenith distance, numerically denser, worst observational
quality subsets. The test is applied upon each subset in turn.
It is then possible to obtain numerically the partial derivative of
each unknown with respect to the weight of each subset. The results
are presented in Table 4. The only important values are the ones
relative to the unknowns 
and 
, for the subsets
corresponding to large zenith distances (
). The response
of these two unknowns is, non-surprisingly, quite similar.
Notwithstanding their difference is well determined and independent
from the weighting scheme. The corrections to the eccentricity and
to the longitude of the perihelion do not vary, their derivative
being practically null. Nearly the same outcome happens in relation to the
equator correction, which exhibits a very small variation. As for
the correction to the obliquity of the ecliptic, it presents a
significant partial derivative only relatively to the 
zenith distance subset, that is numerically sparse and has the lowest
weight in the Standard Weighted Global Solution.
Table 4: Partial derivative of the unknowns relatively to the weight,
in arcseconds
The test allows us to conclude that the values obtained for the
unknowns show very small dependence on the weighting system.
For all subsets corresponding to zenith distances smaller than
the variation as function of weight is truly
negligible.