Levelling in antiquity: instrumentation, techniques and accuracies

Abstract Certain major ancient engineering constructions, such as aqueducts and qanats, testify to high accuracies in the computation of elevation differences obtained using primitive levelling instruments. Based on the typology of ancient levelling instruments and the analysis of certain key ancient structures such as the (Eupalinos) tunnel at Samos Island (Greece), it became possible to specify the accuracy, and especially the measuring techniques and procedures of levelling in antiquity, ignored so far by non-professional investigators. Ancient levelling techniques were derived on the basis of trials and errors over past centuries and include standard length sighting distances (revealing that ‘cord stretching’ may also indicate levelling), stadias with fine focussing on sliding targets adapted to the level field of view, two-way measurement in levels and stadias, repeated and redundant observations in loops, measurements by skilled professionals. These techniques permit to limit and randomise systematic errors and to obtain accuracies up to a few centimetres per kilometre are likely to indicate a real theory of error propagation and are reminiscent of the techniques used in our days in extraordinary projects (the alignment of the CERN colliders, etc.).