On the relationship between conventional and overlap reduction techniques in positional astronomy

It is shown that the familiar night-to-night or plate-to-plate reduction of astrometric observations, if iterated after removal of mean star residuals, is equivalent to the more sophisticated overlap reduction. As an example, the reduction of a meridian circle differential program in right ascension is considered in detail. It is shown that the iteration is convergent even in the present case, where the Jacobian matrix is rank deficient. Practical means to deal with the indeterminacy which arises from the singularity are outlined