In this section, we show the results obtained by the three ways discussed in Sects. 2.1, 2.2 and 2.3.
We used the same instrument to observe at two different zenith
distances (
and 
) at Valinhos.
This should be quite effective in avoiding
instrumental systematic differences. On the other hand, a single
instrument obviously cannot make
simultaneous observations in both zenith distances. As a
consequence, latitude
values 
and 
are themselves not simultaneous,
and some
interpolation scheme must be introduced for the utilization of
Eq. (6).
In the present results, we have computed the mean latitude with respect to the Bureau International de l'Heure (BIH/IERS) for both programmes.
The final computed values from Eq. (6) are:
Before the application of Eq. (5), we must take into account
instrumental problems
affecting the computation of declinations. In fact the
are
obtained as an addition of the east and west residuals, which
means that they may
contain instrumental effects such as magnitude and colour index
equations.
To isolate these effects, we developed the term Ci from
Eq. (4) as a function of the magnitude and colour index for
the
maximum digression stars:
where the symbols mNi and INi refer to normalized magnitude and normalized colour index for each star: mNi=(mgi-4)/2 and INi=(Ii-0.8)/1.2, (Basso 1991).
The results obtained by a least squares method for VL1, VL2 and VL3 catalogues are showed in Table 1 (click here).
| catalogues | ||
|
| VL1 | VL2 | VL3 |
B1( ) |  |  |
 |
|
B2() |  |  |
 |
|
A1() |  |  |
 |
 () |  |  |
 |
|
| (Martin | & Clauzet 1990) | |
|
|
The larger values of VL3 than those in the other catalogues are
probably
due to the zenith distance observations. The high values
confirm the
importance of colour and magnitude equations in astrolabe data,
as shown by
Benevides-Soares (1988) and Chollet & Sanchez (1990).
All declinations 
and
from Eq. (5) were computed considering the colour and
magnitude
function above. After this we computed the values of 
and 
by means of Eqs. (5) and (6).
These values, applied in Eq. (4), render the
declinations absolute.
It is important to note that, through the values of 
, we
can also extend the results to non-common stars.
The system represented by Eq. (7) was reduced for 29 common
stars of
VL1 () and VL3 () and 10 common stars of VL2
()
and VL3 ().
The values C(m,I) for both catalogues are very similar to those obtained with the maximum digression stars presented in Table 1 (click here). These results are in agreement with those obtained by Benevides-Soares (1988), Boczko (1989) and Martin & Clauzet (1990) with different procedures.
The equator corrections obtained by the Method of differences are:
The strong value of 
confirms the contamination by
the colour
and magnitude effects.
We used 381 different stars belonging to the VL1, VL2 and VL3
catalogues
obtained at the OAM. Our goal was to determine 269
declination corrections (), taking into account
that 112 stars were at maximum digression condition.
An analysis of the individual values of as
obtained from global
reduction, as well as the extension to the non-common stars,
was made based on FK5 system.
The were obtained
as sums of the east and west mean residuals, which means
that they may contain
instrumental effects such as magnitude and colour equations.
In Table 2 (click here), we have given the
magnitude and colour index coefficients (instrumental effects)
obtained by the global reduction that are comparable with the
results obtained
by Krejnin's method.
| catalogues | ||
| VL1 | VL2 | VL3 | |
|
B1() |  | |
 |
|
B2() |  |  |
 |
|
A1() |  |  |
 |
|
() |  |  |
|
|
| (Basso 1991) | ||
|
|
These results are comparable with the best results presented in the literature. As we have seen in Table 1 (click here), the results for the VL3 catalogue are stronger and confirm the importance of colour and magnitude function in astrolabe data.
The general standard deviation obtained by the global reduction
is 0.13
, and the value of
is 0.028 
0.034 (Basso 1991).
Thus, the quality of the results is contaminated by the low quality of colour and magnitude errors.
The equator correction obtained is small, confirming the equator used in the FK5 system in the observed zone is compatible with the dynamical values for the equator correction taken with other techniques (Leister 1989), as shown in Fig. 1 (click here).
