Provenance: Grimme Calculating Machine Museum, Natalis & Co AG, Braunschweig.Waldbauer Collection No. 2397 Lit.: The Braunschweig GNC monthly magazine November/December 1925, Braunschweig: p. 524 with illustration. Described there as follows: Hahn machine. Invention of the pastor Philipp Matthäus Hahn, Echterdingen 1774. Manufactured in 1805 to1820 by the watchmaker Joseph Christian Schuster, Ansbach, who worked as a journeyman for Hahn from 1778-1780 and later married her sister.

Shuster's calculator was one of the last of the highly individually built and elaborately ornamented calculators of the pre-industrial era; it has 1052 parts. Calculating machines of the 17th and 18th centuries are extremely rare. There are in fact only a ten calculating machines remaining from that period, which are four species, that is can perform all four basic operations of arithmetic, (addition, subtraction, multiplication and division). During the baroque age there was neither a commercial nor a scientific need for mechanical calculating machines. Tradesmen still calculated using calculation boards, tables and reckoning counters. And in the sciences, calculating methods were unknown or just beginning to be developed. Thus, the clergyman Philipp Matthäus Hahn (1739-1790), Schuster's mechanical master and brother-in-law, had built his calculating machines 'for the propagation of the Gospel'.

At the time they were built, these calculating machines were not used practically. They were destined for the curiosity cabinets; the 'Kunstkammer' of princes and nobility. Some, such as the gloriously decorated machine by Johann Jakob Sauter could have no other purpose!

The first calculating machine put in serial production was the Arithmomètre (arithmometer) by the French entrepreneur Charles-Xavier Thomas de Colmar (1785-1870).

Colmar conceived the idea of the arithmometer during his lengthy stay with the armies of Marchall Soult, where he needed to perform a lot of calculations. This became even more important in his eyes when, in 1819, he was appointed General Manager of the Phoenix insurance company and, later, when he founded the insurance companies Soleil (1829) and Aigle (1843). He did build upon the idea of the stepped drum design first used in Leibnitz machine.

Of course, others had tried before him to make calculating machines in quantities: mention only Pascal, Leibniz, Braun, Morland, Hahn, Sauter, Schuster, Müller, Stanhope  (especially Hahn tried to manufacture in quantity his machines but without success). Also these machines, often defective and very expensive, made it impossible to commercialize. Moreover, it was too early to produce in large quantities a calculator in the 17th or 18th century. Human society did not yet need such devices and the technologies, needed for such mass production, have not been yet been perfected. In the middle of the 19th century, with the industrial revolution, technological obstacles were overcome. More and more enterprises, scientific, military and government institutions became eager to accept a calculator. In the nick of time, came Thomas de Colmar.¹

The first calculating machine for the four basic arithmetic operations was invented by Gottfried Wilhelm Leibniz in the 1670s. During his lifetime he made several copies or had them built by skilled craftsmen, but none of them worked reliably. However, the stepped roller used by Leibniz, an elongated gear wheel with teeth of different widths, later made practicable devices possible. The first working calculator of this type came from pastor Philipp Matthäus Hahn residing in the Swabia region of Bavaria, Germany. He was born in Scharnhausen, South-East of Stuttgart, Germany in 1739 and died in Echterdingen in 1790.
In addition to his main job as a pastor, Philipp Mathäus Hahn (1739-1790) ran a workshop in which he constructed clocks,  orreries, planetariums and other intricate astronomical machines for which complex arithmetic operations had to be solved correctly. One day he wrote: “Today, 10 p.m., I’ve miscalculated again: Now I’m building a calculating machine!” So he invented a fully functioning calculating machine that was operated by a few turns of a crank. The original machine has survived and is now on display in the Württembergischen Landesmuseum in Stuttgart. A copy, made in 1992, can be seen in the Arithmeum Museum in Bonn. The specimen here has been constructed in 2020 by a very skilled German engineer, Michael Leibfritz. From photographs he worked out three dimensional computer drawings of all the parts and then took on the giant task of producing and assembling more than a thousand parts to construct the machine. The sides are transparent so one can see the machine as it operates.

After the Arithmometer, the pinwheel calculator was the next major mechanical innovation. It used retractable pins instead of the stepped drum for decimal input. The first practical implementation was that of Polini in 1709, then Braun in 1720s, and Roth and Staffel around 1840, but was first made successfully for mass production by Willgodt Theophil Odhner a Swedish immigrant to Russia. Production began in St Petersburg in 1890 and was very successful until the Russian revolution of 1917 when the factory was shut down. From 1892 to the middle of the 20th century, independent companies were set up all over the world to manufacture Odhner's clones and, by the 1960s, with millions sold, It became one of the most successful type of mechanical calculator ever designed.

The Carl Walther company was one of these clones and introduced a line of pinwheel calculators in 1924 to supplement their primary business in sporting firearms. Production continued until the 1939-45 war, then resumed in 1947 in West Germany. This pre-war Model RMKZ was built at the original plant in Zella-Mehlis in the 1930s.

The machine is built from aluminum-alloy castings and is relatively light in weight. It has a setting check dial and tens-carry on the counter, but no back-transfer mechanism. The carriage is spring-loaded towards the left, and is moved one step at a time by the two vertical levers next to the winding handle. A button at the front releases the carriage detent to allow continuous movement. The accumulator register has small thumbwheels next to each numeral wheel to allow values to be entered directly, eg, in setting up a division.