Jhc accuracy of t h c reduction of pliotograpliic position5 t o a gi-eii >!cteni of rrlercncc stars can lie considerably iniprovcd. o r thc niiinhrr of referrncr >tars retluccd without rcsultiiig loss of accuracy IJ) reyarding not only the plate constants. b u t also t h e Iicld stars' coordinates (and pic~pcr motions. I\ hcrc: rcqiiired) iis unknowns in a least squares solution. 'This iiirans t h a t ovcrlappiiig plates a i r "tird togethcr" ant1 that pohitions of stars rezulting from measurements on overlapping plates will n o t show systeniatic tliffrrrnccs A m e t l i d is described whercby plate constants a s well A S coordinates antl proper motions iirr c11)tairietl from the resulting complicatcd systcni of iiui iral cquatioiis, which cnii bc sol\ rtl t ) itciatici:s in such a n a y t h a t the number of unknowns in any partial systein ne\ci cxccctls thc.niiinlwi of 1)lxte ciwstnnts on an) ene plate. I t is also shown how the wrights of t h c plate constants. and of t h e coordiiiatc> and pioper motions. can be ccmputcd hy siiccessivc iterations. l h c inethod lends itself particularly \ w l l to tlic dctei niination of positicns (antl pioper motions) in a n extended area of t h e sphcie froin measurements on iniitually ovcrlappiiig plates. as in ii photographic positicn catalogue. ' h ? computations invol\*ccl a i c st:aightfoi\vard but heavy a n d can hardly be pcrfornircl withotit a n electronic coniputer. 5 -= 2' a,),* x i yk Illr cs -.