The clergyman, astronomer and inventor Philipp Matthäus Hahn from Kornwestheim (1739-1790) began building a mechanical calculating machine in 1770. He completed his first machine in 1774, which today is housed in the Württemberg State Museum, Stuttgart, and is known as the “Stuttgart Version“. The fully functional replica shown is a copy of this first machine and consists of 1260 parts, 733 of which had to be made by hand. Its construction took about 1800 working hours. It is cylindrical in shape and has vertically aligned stepped drums which can be moved vertically by means of vertically sliding bars protruding through the top-plate. The centrally driven stepped drums transfer their set values to the adjacent result mechanism. The revolutions of the crank are counted by a central revolution counter (without tens-carry). The two-step tens-carry steps are also carried out by the rotating segment after having been primed in an earlier step. In this way Hahn produced the first fully functional tens-carry mechanism in a stepped drum machine. The crank, however, turns only in one direction, as opposed to the two-way stepped drum machine of Leibniz. Thus, for subtraction and division one must, as with Pascal’s 2-species machine, utilize the complementary number inscriptions. The inner cylindrical part of the machine can be shifted with respect to the outer setting mechanism, analogous to the carriage shift with the Leibniz machine. The inscription on the top-plate reads “Rechnungs=Maschine von M. Hahn, Pfarrer zu Kornwestheim erfunden 1770;74“. A second machine built by Hahn, the “Urach Version“, dates from the period 1770-1776 and is today housed in the Museum of Technology and Labor in Mannheim. Further machines were built by Hahn’s brother-in-law Schuster, of which three have survived (two in the Deutsches Museum, Munich, and one in the Arithmeum, Bonn, since March 2000.