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 C_{i} from
Eq. (4) as a function of the magnitude and colour index for
the
maximum digression stars:
where the symbols m_{Ni} and I_{Ni} refer to normalized magnitude and normalized colour index for each star: m_{Ni}=(mg_{i}4)/2 and I_{Ni}=(I_{i}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 
B_{1}()  
B_{2}()  
A_{1}()  
()  
 (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 BenevidesSoares (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 noncommon 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 BenevidesSoares (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 noncommon 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  
B_{1}()  
B_{2}()  
A_{1}()  
()  
 (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).