An astrometric system based on radio observations of compact extragalactic sources has important possibilities in eliminating errors arising both from the proper motions of stars and from galactic rotation, and also in reducing the likelihood of large-scale inhomogeneities. The methods used for calibrating the 5-km telescope are described and an account is given of how it has been used to provide absolute measurements of declination with an accuracy of ∼0″.03 arc at δ = 45° and relative measurements of right ascension to within a few milliseconds. The absence of objects within the solar system suitable for accurate radio measurement makes it difficult to determine an absolute origin in α , but the scale of right ascension has been related to that of the FK4 system by observation of β Persei. The radio emission is associated with the 2 d. 8 binary system AB and not with component C, and the observations have made it possible to establish the 5-km scale of right ascension relative to the barycentre of β Persei with an accuracy of ±1.5 ms. Improved optical measurements are now needed to relate the position of the barycentre to other FK4 stars with comparable accuracy. It should then become possible to make a detailed comparison of the 5-km and FK4 systems by observation of compact extragalactic sources having compact optical counterparts.