We are all born ignorant, but one must work hard to remain stupid.

*Benjamin Franklin*

In 1767 the pastor (and self-taught genius engineer) of Onstmettingen village in Württemberg—Philipp Matthäus Hahn designed, and together with his friend and local schoolmaster Philipp Gottfried Schaudt constructed a big brass and iron astronomical clock, presented to Duke Karl Eugen, the Herzog of Württemberg, who admired the inventor and ordered a larger machine for the Library of Ludwigsburg. At that time Hahn engaged as an apprentice and journeyman a young successor of the famous local family of blacksmiths Sauter—Johann-Jakob Sauter (1743-1805), who was a student of Schaudt, and his relatives, deaf blacksmiths and watchmakers Johann Sauter (1723–1786) and Paulus Sauter (1732–1794), taught Schaudt how to work with brass and steel.

Later Sauter assisted Hahn in creating his calculating machines also, because, after the death of the pastor in 1790, Sauter not only established himself as а past-master of clocks and balances but continued his occasions with calculating devices and created two remarkable calculators, similar to Hahn’s adding machine and Hahn’s circular calculating machine. In fact, we are not sure what is the exact participation of the abovementioned Johann-Jakob Sauter in the creation of these two calculators, because two of his sons (he had six of them) were also named Johann (Johann-Jakob Sauter Jr. (born 1770), and Johann Ludwig Sauter (born 1780)), they also became very good watchmakers and technicians and continued the activities of their father.

**Sauter’s adding machine**

In the collection of Science Museum, London, is included an adding machine (see the photo below), which probably was commenced by Johann Jakob Sauter Sr. at the end of 1790s, but finished around 1820 in Esslingen by one of his sons: Johann Jakob Sauter Jr. or Johann Ludwig Sauter. Napoleonic wars from the beginning of the 19th century strongly affected Württemberg, so the members of the Sauter family scattered all around Europe, some of them moving north in the vicinity of Stuttgart.

Sauter’s adding machine (in fact, with some additional efforts the device can be used for subtraction, multiplication, and division also) is quite similar to Hahn’s adding machine (which in turn has certain similarities to Pascaline), although far more ornate in appearance. The original stylus for moving the number wheels is preserved and shown in the photo below.

It was a stylus-operated 7-positional adding device. The box is carried by five lions, thus the machine seems to float above its base. Sauter used star-shaped gear wheels (often found in repeating watches) at the upper row of his calculating machine. The tens transfer is implemented by a single tooth that hits a crescent-shaped transfer rocker. As a result, it is moved slightly further so that its end can reach the next position and turn the next star-shaped gear wheel one position further. Interestingly, this calculator is the first machine that has a reset device for the revolution counter, by means of a rectangular strip with teeth at the bottom of the device. The Arithmeum Museum in Bohn, Germany, created a replica of the London device and published a very good animated presentation of this device.

**Sauter’s circular calculating machine**

It is believed that this especially impressive and aesthetically appealing mechanical calculator for all four arithmetic operations was built by Johann Jakob Sauter around 1796. Only one example of the device survived to our time, and it is kept in Gothenburg City Museum (see the photo below).

It is believed that Johann Jakob Sauter sold this mechanical calculator around 1804 to the Swedish royal house for 1000 krones (a huge sum for the time). Then in 1808, Johann Jakob Sauter (obviously Jr., not Sr., who died in 1805) received the right to run the manufacture of watches, etc. in Stockholm, accepting the position of *royal mechanic*.

The device is made of brightly colored brass and English steel and has a round form with dimensions of 7½ inches wide, and 2 inches high. There is a plate with engraved text: “Maschine / ohne nachzudenken / geschwind und sicher / damit rechnen zu können / von Sauter in Esslingen”, in English: Machine to calculate swiftly and safely without thinking by Sauter of Esslingen. The device has a wooden base with brass details, 5 brass lion paws, and a drawer.

On the right horizontal plate are mounted 3 rows of enameled number plates (display discs), 9 in each row. The innermost small discs are denoted by the 10 digits from 0 to 9, the middle discs show these digits 2 times, black in larger and red in smaller range (red digits present complementation to 9 of black digits, e.g. over black 5 is inscribed red 4). Black digits are used for addition and multiplication, while red digits are used for subtraction and division.

The entire upper plate, with all these discs, can be rotated around the center of the machine, by means of the arm standing next to the crank, which in the drawing is denoted by *A*. The rotation of the upper plate by means of arm *A* takes place only on multiplication and division.

The inner 2 rows of number plates can be turned back and forth by means of a small button (input pin), on which it may be possible to place each desired number under the open sheet metal windows. And since each sheet has 9 number plates, it is clear that on this machine each number can be produced up to a million. For the convenience of counting, the value of each digit is prescribed below its plate, whether it is tens, hundreds, thousands, etc.

In the center of the machine, crank *C* is provided with several devices and a small bell, screwed on by means of a screw nut. This crank can only be turned to the right, and since it always has to stand still in a certain place, when you want to count the numbers in the windows or want to turn the plate, then on a fixed piece placed on the surface is an elevation and end hook, on which the crank must rest, which therefore has a spring under the handle or button, in order to be able to raise and release it slightly before turning.

Sauter equipped his calculating machine with several indicator bells. They ring to show that tens carry has been triggered, which exceeds the highest place, so cannot be displayed, or the crank has been turned too many times on the same number place. In fact, Sauter improved the tens carry mechanism of Hann, moreover, this machine is the first mechanical calculator with an automated zero-setting mechanism, which makes calculating more comfortable and saves time.

The addition is done as follows:

First, you place on the middle row of number plates by means of the buttons or the dedicated arms *D* and *E* all on black zeros (resetting), then you set on the outer half-boards a given number (e.g. 2516) using the input pins, as the other digits which stand before or are not needed are all set to zeros. Now you raise the arm *C* a little and move it around until it reaches the same place again, then the number 2516 appears in the openings or windows on the middle row of numbers. Then you put on the half boards another number (e.g. 629), but so that units always stand under units, tens under tens, and so on: if you now turn the crank around again, the number in the middle window turns into the sum 3145. If more than two numbers are added together, e.g. to the first two numbers another third 1802 must be added, then 1802 must be set on the outer semicircles again and the crank must be turned once more than the sum of all three numbers (4947) becomes visible, in the same way, you can continue with adding many numbers.

Subtraction:

The minuend (e.g. 87950) must be set in red digits under the windows in the middle row of number plates, the subtrahend (e.g. 7058) must be set on the half boards (the others all at zeros), then after a rotation of the crank C, the minuend consisting of red numbers will show the result: 80892.

Multiplication:

If one of the numbers only consists of one digit, e.g. if you want to multiply 1905 by 4, you put the larger number (1905) on the arcs or semicircles, as all the numbers in front of you are set to black zeros, then you turn the crank until the first small board in the innermost row of the number 4 becomes visible, which takes place after 4 rotations, instead of the zeros previously placed on the paintings, and the product 7620 should be visible under the windows. If the smaller number consists of more than one digit, e.g. instead of 4, the multiplier is 24, you first proceed with the 4 as it was described, let all the numbers stand, and push the whole upper plate by means of the arm *A* while you with the left-hand finger press the button *B*, so far forward until the little blue steel pointer which shows the small enameled arches, shows the arc denoted by tens. Then you turn the crank again until on the second of the innermost small discs two appear, then on the middle paintings the product of 7620 with 24 namely 45720. The same action also continues when the multiplier has even more digits. Thanks to the implementation of the so-called *arithmetic shift*, during the multiplication an operator must turn the crank not “multiplier” times (in this case 24), but only “multiplier units”+”multiplier tens”+… times (in this case 2+4=6).

Division:

The dividend, e.g. 1643, is set by means of the red numbers. The divisor 64 is set on the semicircles, both in their proper places, the small number plates and all other preceding digits are set to zero. Now the whole upper plate is turned by arm *A* and the button so that the highest number of the divisor falls below the highest number of the dividend, and then the crank is turned until the first number in the dividend becomes smaller than the one below. In our example it should occur when the crank has been turned twice, consequently, the first digit of result 2 appears on the small innermost digits, standing red number would be the rest. But if this is greater than the divisor, which in this example the remainder 363 is greater than 64, then the plate is moved by its arm *A* a little to the left further or so far that the highest number in the divisor has a higher number standing over it and turns the crank again until as long as the upper number becomes smaller than the lower, and the quotient 25 finally appears on the small boards and instead of the dividend, the remainder 43 appears.

The Arithmeum Museum in Bohn, Germany, created a replica of this Sauter’s calculator also and published a perfect animated presentation.

#### Biography of Johann Jakob Sauter

Sauter family lived in Onstmettingen, a village south of Stuttgart, in the Swabian mountains, for many centuries (the first Sauter is mentioned in 1571). The Sauters were versatile and skilled as farriers and ordnance blacksmiths, building amongst other things balances for rural use. There is a church record from 1650, stating that the village blacksmith Konrad Sauter (b. 1619) and his wife Anna-Maria baptized their daughter Anna (they had 9 children—2 sons and 7 daughters). The next known Sauter was Melchior (1660-1731), who was not only a blacksmith and weapon smith but had also a successful plough leasing business.

In the middle of the 18th century, Sauters turned their attention to the watchmaking business. In 1723 came into the world Johannes Sauter (1723-1786), and as he was born deaf and dumb, and was so frail, that he could never be made into a blacksmith, his father Mathias decided to train him in something not demanding physical power—watchmaking. The same applied to his younger brother, Paulus Sauter (1732-1799), who also was born deaf and dumb. Johannes and Paulus taught watchmaking to the village schoolmaster of Onstmettingen, Philipp Gottfried Schaudt, who in turn transferred the knowledge to his friend Philipp Matthäus Hahn, the son of a local pastor.

Johann Jakob (or Jacob) Sauter was born on 26 April 1743 in Onstmettingen. He was the son of Johannes Sauter (b. 1712) and Anna Barbara Schaeffer (b. 1714). Johann Jakob had two elder brothers: Johannes (b. 4 May 1736 – d. 2 Dec 1803), and Gottfried (b. 8 Jan 1740 – d. 22 Jul 1809).

Johann-Jakob Sauter married Anna Maria Eppler (b. 28 July 1744 – d. 18 Oct 1789) in May 1769 in Duerrwangen, Wuerttemberg. They had six sons and two daughters, all born in Onstmettingen: Johann Jacob Sauter (b. 27 May 1770), Johann Gottfried Sauter (b. 20 Jan 1773), Johannes Sauter (b. 18 Sep 1774), Dorothea Sauter (b. 23 Jan 1776), Rosina Sauter (18 Apr 1778 – 28 Aug 1778), Johann Ludwig Sauter (b. 5 May 1780, Simon Sauter (3 Oct 1784 – 6 May 1831), and Matthaus Sauter (b. 9 Apr 1788). After the death of Anna Maria in 1789, Johann Jakob Sauter married a second time to Anna Rehfuss (7 Nov 1763 – 11 Dec 1855). They had three children: Andreas Sauter (b. 30 Oct 1791 ), Christina Sauter (b. 22 Oct 1794), and Johann Friederich Sauter (5 Oct 1797 – 7 Feb 1799).

We know that Johann Jakob was taught watchmaking by his relatives and was a pupil of the young local teacher Philipp Gottfried Schaudt, who was only four years older than him. In 1867 Hahn and Schaudt hired him as an assistant at their workshop. When in 1769 Hahn invented a new type of balance (with inclination scale), which is still in use today, Sauter assisted in manufacturing, and from that point, balance manufacture has never left the Sauter family (the Sauter family-owned company *Kern & Sohn* is still existing as a balance manufacturer). When Hahn left the village in 1770, Sauter continued to work with Schaudt, as Schaudt was responsible for mathematics and theory, while Sauter was looking after practical matters.

The next generation of Sauters, the six sons and one (survived) daughter of Johann-Jakob Sauter’s first marriage, all were taught in the field of mechanics, and (at least) four of them (Johann Jakob Sauter Jr., Johannes, Johann Ludwig, and Simon) became excellent engineers. It is known that only Simon remained in Onstmettingen (and took over his father’s workshop after his death), while the other sons moved to France (Strasbourg, Johannes), Russia (S. Petersburg, Johann Jakob), and Sweden (Stockholm, Johann Jakob), and towns around Stuttgart (Johann Ludwig and Johann Jakob).

In the early 1790s, Sauter had a workshop in Kornwestheim, near Stuttgart (interestingly, Hahn also served and had a workshop in Kornwestheim from 1770 until 1881), then in the late 1790s moved to Esslingen, near Stuttgart.

Little is known about Johann Jakob Sauter Jr. In the 1790s he worked (probably together with his father) in Kornwestheim and Esslingen, then around 1800 moved for several years to St. Petersburg, Russia, then relocated to Stockholm, Sweden, titled as a *royal mechanic*. He married Maria Catharina Griesin in 1791 in Kornwestheim, and they had four sons: Amand Andreas Sauter (b. 23 Apr 1796), John Amandus Sauter (b. 23 Mar 1798 – d. 20 Apr 1848), Johann Eberhardt Sauter (b. 8 Dec 1800), and Ferdinand Carl Sauter (b. 24 Dec 1802).

Johann-Jakob Sauter Sr. died on 13 December 1805 in Onstmettingen.