Anyone who thinks sitting in church can make you a Christian must also think that sitting in a garage can make you a car.
In 1770 the Württemberg pastor, astronomer, engineer, and entrepreneur Philipp Matthäus Hahn turned his attention to the creation of calculating machines, devising a simple calculation device (so-called Rechentrommel – calculation drum), then an adding device, and finally a more elaborate cylindrical calculating machine. The first two devices were not so innovative, but Hahn’s cylindrical calculators were the first fully functional popular four-species mechanical calculating machines in the world (the earlier machines of Anton Braun and Jacob Leupold remained relatively obscured and unknown to the public).
Philipp Hahn was a gifted mechanic, who was engaged mainly in making clocks and planetariums. He needed a calculating device, in order to calculate the parameters of his machines, that’s why sometime in the summer of 1770 he started to design several calculating devices. Let’s examine what he devised:
The Calculating Drum of Hahn
It seems the first and simplest calculating device of Hahn was the calculating drum (Rechentrommel), which he devised around 1770. It was a simple calculating device (see the lower photo), with manually rotated inscribed scales, used for adding numbers.
The Cylindrical Calculating Machine of Hahn
The first working copy of Hahn’s most advanced calculating machine, his cylindrical calculator, was ready in 1773, but it was demonstrated as late as 1778 because Hahn has difficulties with the reliability of the tens carry mechanism. Until 1779 four machines were made, till the end of his life, Hahn manufactured about 5-6 devices, two of which still exist in the Württemberg State Museum in Stuttgart and in the Technoseum in Mannheim. After his death, several calculating machines by his design were created by his apprentices, in the photo below you can see a variety of Hahn’s machine, made by Johann Christoph Schuster, an apprentice, and brother-in-law of Hahn.
Hahn certainly has been acquainted with machine of Leibniz (not only from Theatrum arithmetico-geometricum of Leupold, but also from other sources), and that’s probably the reason to use the stepped drum of Leibniz in the construction of his device. However, the arrangement of the device has some similarities not with the Stepped Reckoner of Leibniz, but with the calculating machines of Leupold and Braun.
In an article in the magazine Teutschen Merkur from 1779, Hahn mentioned his inspirator:
When my time was occupied with making astronomical clocks, I had to deal with calculations of long fractions, multiplication, and division of large numbers, and I was so overwhelmed, that my primary work was close to being stopped. Then I recalled that some time ago I read a book for Leibniz, which mentioned his calculating machine, for which he spent a lot of money, without satisfactory results. I decided to spare some time in this direction. Certainly, I also wasted much time and money experimenting and troubleshooting the construction of my device. Finally, I managed to construct a rather advanced and reliable machine. Most difficulties I met during the construction of the tens carrying mechanism.
Hahn needed quite some time to solve the problem with the tens-carry mechanism (he complained several times about the poor quality work of his mechanics), but he managed to resolve it, partly by changing the initial rectangular form of the machine with a circular. So the first working copies of the machine had ten digital positions, and the latter had 12 digital positions.
The main part of the mechanism of each digital position is a small stepped drum (see the staffelwalze in the lower drawing), mounted on an axis, which can be moved upwards and downwards.
During the rotation of the mechanisms of the machine by means of the handle in the middle of the lid, a stepped drum will be engaged with the wheel of the main counter, which is also attached to vertical axes, and according to the vertical position of the appropriate stepped drum, the wheel will be rotated to 0, 1, …, 9 teeth.
The dials are graduated with two scales. The outer ring of digits is black and is used during adding and multiplication, the inner one is red, and is used during subtraction and division. The digits of the inner scale actually are complementing to 9 of those in the outer scale (i.e. below 0 is 9, below 1 is 8, etc.).
The entered in the input mechanism (stepped drums) number is transferred to the main counter by rotating the handler. There is also an additional counter, which counters the revolutions of the handle. The module of the additional and main counter is separated by the calculating module (module with the stepped drums) in a separate ring. This means, that the calculating mechanism is separated by the displaying mechanism. Thus, by rotating the ring of the counters, we actually can move the multiplier (divisor), during the multiplication (division). This moving can be controlled by a special arrow-pointer.
An adding operation can be done as follows:
1. The dials must be set to 0 (if it is necessary). By rotating the axes of the main counter, we set the first addend in the bigger dial (with black digits).
2. Then by pulling the axes of the stepped drums we set another addend.
3. By rotating the handle to 1 revolution, the number is transferred to the main counter and the result can be seen in the windows of the dials.
The subtraction can be performed in a similar way, but the minuend is set according to the red digits, while the subtrahend is set by pulling the axes of the stepped drums. After rotating the handle to one revolution, the result can be seen in the windows of the dials.
The multiplication can be done (by performing successive additions) thus:
1. The dials must be set to 0 (if it is necessary). The multiplicand is set by pulling the axes of the stepped drums.
2. The handle must be rotated to the revolutions, equal to the number of the units of multiplier (the number of revolutions can be seen in the small dials).
3. Then we have to multiply the multiplicand by the tens of the multiplier, so we have to shift the multiplicand one digital position to the left, by rotating the ring with the dials.
4. The handle must be rotated to the revolutions, equal to the number of the tens of multiplier.
5. If it is necessary, the same actions must be repeated for hundreds, thousands… of the multiplier.
The division is done in a way, similar to multiplication, but in this case, are used the red digits of the dials and it is based on successive subtractions.
The calculating machine of Hahn became popular in Germany at the end of the 18th century and was demonstrated to many “celebrities” like Kaiser Joseph II, Johann Wolfgang von Goethe (Goethe visited Hahn in 1779 in his workshop in Kornwestheim), Herzog Carl von Weimar zu Gast, and described in the press.
The Adding Machine of Hahn
It is known also that Hahn designed and manufactured several simple adding machines, which he sold during his lifetime. These devices have been used for monetary calculations (for mechanizing the changeover between Kreuzer and Gulden, where 1 Gulden = 60 Kreuzer). Unfortunately, none of these survived to our time, there is only one copy of a machine, attributed to Hahn, kept now in the collection of Arithmeum Museum, Bonn (see the lower photo).
The adding device in Arithmeum has a brass and steel mechanism, put in a leather-covered wooden box. It has six dials in a row, and the dials are set by means of a stylus. Obviously, only addition is possible, as there is no inscription for complemented to 9 digits. The dials are returned to zero by turning them backward. The tens-carry mechanism is simple but fully functional. Later one of Hahn’s apprentices, Jakob Auch, will create a similar machine, but with an improved tens-carry mechanism.
The construction principles of Hahn’s machines were continued by his eldest son, Christoph Matthäus Hahn (1767-1833), who worked as a court mechanic in Stuttgart, by his apprentices Jakob Auch (1765-1842) and Johann Christoph Schuster (1759-1823, Schuster married one of Hahn’s sisters), by Johann Jakob Sauter (1743-1805, Sauter worked for Hahn in his workshop since 1868 as an assistant for making clocks and balances) and his sons, and by his friend Philipp Gottfried Schaudt.
Biography of Philipp Matthäus Hahn
Already at his lifetime the German vicar Philipp Matthäus Hahn was known in church circles through his theological writings, with princes and nobles by his large astronomical clocks and machines, and the upper middle class through his pocket watches, scales, and calculating machines.
Philipp Matthäus Hahn was born on 25 November 1739, in Scharnhausen auf den Fildern (near Stuttgart), as the second of eight children (Philipp had an elder sister, Juliane Felicitas, b. 18 Feb 1737) in the family of the pastor Georg Gottfried Hahn (b. 18 Oct 1705 Untersielmingen, d. 25 May 1764 Ostdorf) and Juliana Kunigunde Justine Hahn, nee Kaufmann (b. 18 May 1711 Maichingen, d. 26 Feb 1752 Scharnhausen), who married on 8 May, 1736.
Hahns was a rather prominent and wealthy local family, known to live in Scharnhausen since the 16th century. Philipp Matthäus got his name after his grandfathers—Johann Philipp Kaufmann (1661-1748), a pastor from Stuttgart, and Matthäus Hahn (1670-1759), a merchant from Sielmingen auf den Fildern. Juliana Hahn died in February 1752, and in November 1852, Georg Hahn married a second time to Charlotte Dorothea Maichel (b. 6 Feb 1733 Tübingen, d. 7 May 1780 Stuttgart), and the new family had five more children.
As a little boy, Philipp was taught by his father and by his maternal grandfather for four years in ancient languages and religions (Latin, Greek, and Hebrew). Being only 8 y.o. he became interested in astronomical observations and found in his father’s library a book with a description of the celestial sphere, which delighted him for a long time. Two years later, Philipp constructed a simple sundial.
From 1749 to 1754 Philipp attended Latin schools in Esslingen and in Nürtingen, studying religion, but also painting, and especially mathematics. During this time he kept his interest in astronomical observations and sundials and was promoted by Tobias Mayer, the future director of the Göttingen Observatory. In May 1756, the Hahn family moved to Onstmettingen, in the Swabian Jura (in 1755 Georg Hahn was transferred for disciplinary reasons by the consistory there for drunkenness). There Philipp Hahn met his future assistant—the local schoolmaster Philipp Gottfried Schaudt (1739-1809), who had learned the art of watch-making with the local craftsmen—brothers Johannes and Paulus Sauter. This meeting marked the beginning of a lifelong friendship and successful cooperation between the two because Hahn used to use Schaudt’s technical skills to implement his ideas into practice.
On 22 October 1756, Hahn enrolled in the Protestant theological seminary Tübinger Stift in Tübingen to study theology, and there continued his occasions with clocks. (It is amazing, that some 150 years before Hahn, in the same college studied also theology the inventor of the first mechanical calculating machine—Wilhelm Schickard, however Hahn, in contrast to Schickard, later on, will reject the proposed to him professorship there.)
Hahn had a hard time in Tübingen, because his father couldn’t support his children through university. In 1758 Philipp managed to get a two years grant from the Widerholt’s family foundation, and also got some money from his stepmother. In the same 1758 he (for the first time) also had been paid out for his technical knowledge and his mechanical skill—during the semester break, he got thirty guilders to make a sundial for a church. During this period his best friend was Schaudt, as both teenagers shared a pronounced scientific curiosity and technical enthusiasm. Together the young men cut glass, and built mouthpieces, telescopes, microscopes, and sundials. When Hahn was able to spend the lecture-free periods in Onstmettingen, the two friends sat together all night, dismantling clocks, building mechanical equipment, and watching the starry sky.
In 1760 Hahn obtained a Master’s degree in Philosophy in Tübingen, then worked for about a year as a private teacher in the Benedictine monastery in Lorch in Lorch bei Schwäbisch Gmünd. At that time Hahn worked on the construction of a Perpetuum Mobile, but soon he realized it is impossible to build such a machine. In 1761 Hahn started his way in Church as a Vicar, then moved to Herrenberg (the hometown of Wilhelm Schickard), to receive in 1764 a Vicariate in Onstmettingen, succeeding his father, who had died suddenly. There he (together with his old friend and local schoolmaster Schaudt) organized a workshop for the construction of scales, astronomical clocks, and machines to glory of God.
In 1766 Hahn designed, and in 1667 Schaudt constructed a big brass and iron astronomical clock, presented to Duke Karl Eugen, the Herzog of Württemberg, who admired the inventor (he later became his patron and used to dub Hahn as “the watchmaker God”), gave him a reward of 300 guilders (quite a sum for the time), and promptly ordered a larger machine for the Library of Ludwigsburg (this device, known as Astronomic World Machine, now stands in the Stuttgart Landesmuseum). In Onstmettingen Hahn constructed also many solar, steeple, pocket and pendant watches, and invented a new type of weightless balance—the pendulum balance.
On 24 May 1764, Philipp Hahn married 15 y.o. Anna Maria Rapp (1749-1775), a daughter of the mayor of Schorndorf Ulrich Rapp. The family had six sons, but two of them died as babies, so left four—Christoph Matthäus (1767-1833), Christian Gottfried (1769-1831), Gottlieb Friedrich (1771-1802), and Immanuel (1773-1833). All the sons shared Hahn’s interests in mechanics and mathematics, and two of them—Christof Matthäus and Christian Gottfried also became skillful watchmakers.
In 1770 Duke Karl Eugen proposed a mathematics professorship at Tübingen to Hahn, but he refused it (he still needed to be in the bosom of the church.) In the same 1770 however, Hahn accepted another position, arranged by the Duke, and in March moved to serve in the well-paid parish Kornwestheim, where he lived in the new rectory (see the upper photo) and arranged a large workshop, where he invited to work his brothers—Georg David Polykarp (1747-1814) and Ägidius Stephanus Gottfried (1749-1827). There unfortunately his wife Anna died too young, on 10 July 1775, giving birth to their seventh child. In 1776 Hahn married a second time to Beate Regine Flattich (1757-1824), a daughter of the Münchinger parson Johann Friedrich Flattich (1713-1797). The new family had eight children.
In June 1779 Hahn was appointed as a member of the Erfurt Academy of Sciences. In 1781 Duke Karl Eugen again arranged a new profitable position for Hahn, in the best-paid parish in the whole country, Echterdingen, near Stuttgart. In Echterdingen Hahn dealt mainly with pocket watches and even wrote a treatise in this regard.
In 1772-1774 Hahn published several theological books: The main cause of the Apocalypse (1772), Clue to the understanding of the Kingdom of God (1774), and two sermon books. The printing of books he financed from the profits, which dropped from the workshop. So does the technical work of Hahn was indirectly working for the kingdom of God:-) Hahn certainly published also several technical books: Beschreibung mechanischer Kunstwerke in 1774, and Von Verbesserung der Taschenuhren in 1784.
Philipp Matthäus Hahn had a tireless nature. A working day of 16 to 18 hours was the norm for him, despite suffering most of his life from a stomach illness. He was a pedantic boss, both in his workshop and in the house. This remarkable man died of lung disease (pneumonia or lung cancer) on 2 May 1790, in Echterdingen, and was buried in Kirchfriedhof von Echterdingen.