AbstractThe accuracy of the reduction of photographic positions to a given system of reference stars can be considerably improved, or the number of reference stars reduced without resulting loss of accuracy by regarding not only the plate constants, but also the field stars' coordinates (and proper motions, where required) as unknowns in a least squares solution. This means that overlapping plates are “tied together”” and that positions of stars resulting from measurements on overlapping plates will not show systematic differences.A method is described where by plate constants as well as coordinates and proper motions are obtained form the resulting complicated system of normal equations, which can be solved by iterations in such a way that the number of unknowns in any partial system never exceeds the number of plate constants on any one plate. It is also shown how the weights of the plate constants, and of the coordinates and proper motions, can be computed by successive iterations.The method lends itself particularly well to the determination of positions (and proper motions) in an extended area of the sphere from measurements on mutually overlapping plates, as in a photographic position catalogue. The computations involved are straightforward but heavy and can hardly be performed without an electronic com