Contribution à la pondération des points d'observation

Abstract

In the plate reduction, when a polynomial transformation is used, the minimum of the effect of an error calculated at the point where the error is acting does not always coincide with the plate centre (Debehogne, 1972). We have proved this property by means of a network (fictitious stars). Here, we will present a theoretical demonstration for the first and second order (straight line and parabole). For the first order, the minimum coïncides with the reference points centre (table I). For the second order, the minimum coïncides with this centre only when B = [formule], where n is the number of reference points, xt the abcisses, [xt2] = [formule] i Moreover, there are two maxima symetrically displayed around the centre for n < B. When B < n < 3 B, we have a maximum at the centre and two minima. See this extrema values in table II.