The evaluation of stellar positions from overlapping plates by rigorous block-adjustment methods leads to a very large system of normal equations containing both stellar positions and plate constants as unknowns. These general normal equations can be reduced to a subsystem with banded-bordered coefficient matrix, containing only the plate constants as unknowns. In the case of a large photographic net covering a hemisphere or sphere with multiple overlap of the plates, the actual number of unknown plate constants may exceed 20000, depending on the adopted reduction model.