3 Reduction

In view of the large number of plates and of stars it was possible to subdivide the observational material for the purpose of determining the field distortion into several groups. For the general distortion the material was divided by right ascension into four groups of six hours each, with a certain amount of overlap. In view of the possibility of introducing a systematic error periodic with the displacement from field to field, as was pointed out in the previous chapter, a relatively high weight was given to the plate-catalogue links. This is even more justified because of the high accuracy of the HIPPARCOS positions which were used as the reference system. In the process we find:
1.- the exact coordinates of the plate centers,
2.- plate by plate the exact scale factor (i.e. focal length),
3.- four different and independent vector diagrams of the field distortion.

  

Figure 1: Position residuals as function of the coordinates X and Y after the first step of the reduction process when block adjustment and a linear plate model were applied. Higher weights have been assigned to the residuals formed with the HIPPARCOS catalogue than to those formed with average positions from several plates

  

Figure 2: Position residuals as function of the coordinates X and Y after correcting the measured coordinates by the pattern indicated in Fig. 1. The residuals are plotted for four different intervals of the apparent magnitude

  

Figure 3: Position residuals as function of the coordinates X and Y after correcting the measured coordinates by the pattern indicated in Fig. 1 and Fig. 2. The residuals are plotted for four different color intervals

The vector diagrams for the four groups, of which one is shown in Fig. 1, are all very similar. Since the underlying data for the four groups are independent we may conclude not only that the field distortion is well determined, but also that is is independent of the season of the year, hence the telescope temperature.

It was found that the scale factors can be divided into two clearly distinct groups with the values 3460.0 and 3436.0 mm. This difference is clearly related to the declination zones. The different zones were observed mixed throughout the entire observing period which lasted for about two decades. The plates, however, were measured strictly in succession of declination zones. The mentioned discontinuity of the scale factor is almost certainly due to a change in the supposed scale of the reseau which was imprinted on the plates, as reported by the authors of the original coordinate measurements.

An analysis of the true plate centers shows that in the beginning of the series of observations insufficient attention was paid to the precession, a fact which is also pointed out by the authors of the original data.

For the determination of a magnitude-dependent systematic error the material was divided into several magnitude intervals (Fig. 2), with no subdivision by right ascension. The latter was justified since the general distortion, as was shown above, did not depend on the right ascension. It was attempted to use a similar process for the determination of a color dependent systematic error (Fig. 3). No reliable results could be obtained because information on the color is available only for an insufficient number of stars.

The average rms error of individual measurements in right ascension and declination was determined for different magnitude intervals after every step of the reduction. The results are given in Table 1. The first block of data contains the errors after the first linear block adjustment. As explained above, this solution led to the vector diagrams. Once these had been applied to the original X and Y coordinates, a new block adjustment was carried out, leading to the second block of data in Table 1. Finally magnitude dependent corrections are determined and subsequently applied to the already distortion corrected X and Y and a new block adjustment is carried out, leading to the third block of data in Table 1.

The total observing period covers almost three decades, from 1890 to 1918. The telescope performance, including its field distortion, may have changed during that time. A crude test of this possibility can be made by determining the above errors (after all corrections have been applied) separately for different plate epoch intervals, as shown in Table 2. No significant and well established change of the errors is observed between the first three intervals. A slight increase in the last interval may not be real because the number of data involved is considerably smaller.

  

Table 1: Partial and final errors for the totality of the S. Fernando Zone Plates

  

Table 2: Final errors for the S. Fernando Zone AC, for different observing periods

Acknowledgements

We thank S. Urban and T. Corbin of the United States Naval Observatory (USNO) for supplying us the original (x,y) coordinates, corresponding to S. Fernando's plates of the AC in a electronic form. We also thank J. Stock for his collaboration during the elaboration of this paper.