The present high accuracy of stellar positions and proper motions allows us to determine the positional accuracy of old stellar catalogues. This has already been done for the most important catalogues from before the 18th century. Our aim is to extend this study to several 18th century catalogues. To do this, I studied ten catalogues: those of Flamsteed and Romer, four catalogues of La Caille, and catalogues of Tobias Mayer, Bradley, Piazzi, and Lalande. A comparison with modern data, mostly from Hipparcos, compiled in the Simbad data base of the CDS allowed me to determine the position errors of these catalogues. I also compared the stellar visual magnitudes given in eight of these catalogues with photometric V magnitudes. Thanks to novel instruments, the r.m.s. positional accuracy improved from thousands to hundreds of arc seconds in older catalogues to less than one minute in that of Flamsteed, and to 2-6 arcseconds in the other catalogues I examined. These improvements allowed for the first time relatively accurate proper motions to be determined by 19th century astronomers.