The star catalogue of Wilhelm IV, Landgraf von Hessen-Kassel: Accuracy of the catalogue and of the measurements.

We analyse a manuscript star catalogue by Wilhem IV, Landgraf von Hessen-Kassel, from 1586. From measurements of altitudes and of angles between stars, given in the catalogue, we find that the measurement accuracy averages 26 arcsec for eight fundamental stars, compared to 49 arcsec of the measurements by Brahe. The computation in converting altitudes to declinations and angles between stars to celestial position is very accurate, with errors negligible with respect to the measurement errors. Due to an offset in the position of the vernal equinox the positional error of the catalogue is slightly worse than that of Brahe's catalogue, but when correction is made for the offset -- which was known to 17th century astronomers -- the catalogue is more accurate than that of Brahe by a factor two. We provide machine-readable Tables of the catalogue.