Calculating machine Resulta BS 7
Calculating machine Walther WSR 160

A calculator , also outdated as a calculator , is a machine with the help of which mathematical calculations can be carried out automatically. A calculating machine is therefore a calculation aid that supports the calculation of more complex mathematical tasks by requiring as little cognitive effort as possible from the user of the machine . Which calculations are possible depends on the machine and the algorithms offered for this machine .

The first calculating machines were mechanically driven by hand. Up until the 1970s, the (relatively inexpensive) adding machines that only mastered addition and subtraction (hence also called two-species machines) were particularly popular, but this was sufficient in many areas of application. Expensive three- species machines could additionally perform the multiplication and four-species machines also the division more or less automatically, loudly and slowly. Occasionally there were also electromechanical calculating machines that could also pull the square root .

Three- and four-species machines were primarily designed according to two principles: staggered roller and sprocket wheel .

## Historical development

Original drawing by Wilhelm Schickard

The first calculating machine mentioned in a document was briefly described by Wilhelm Schickard in a letter to Johannes Kepler in 1623 . The machine consisted of an adding and subtracting mechanism and a device for multiplying and dividing in the manner of Napier's calculators . Schickard reported that he had also implemented this machine. It is believed that this machine was later lost during a fire in his house. It was reconstructed in 1960.

In 1645 the Frenchman Blaise Pascal demonstrated his calculating machine " Pascaline ", which works with gears and pawls. Pascal made some of these machines and sent them to European royal houses. For this reason, in addition to many replicas, there are still some original Pascalines.

There is disagreement between German and French historians as to which nation produced the first calculating machine. There is no clear answer to this question. The first construction drawing by Schickard and the first surviving machine from Pascal can be verified.

Both types of machines have a common problem. They are not suitable for everyday use as calculating machines. They contain important functional principles, but not devices that enable safe daily work.

Wilhelm Schickard's machine, for example, lacks the ability to store energy for the tens transfer of each decimal place. This means that the calculation 9 + 1 is easy to handle, but 9999 + 1 requires a lot of effort and has probably caused the machine to jam.

In Blaise Pascal's machine, pawls prevent the gears from rotating freely, they are held down by gravity. This means that the machine suffers from the phenomenon of "overturning". The problem is that gears or entire gears continue to move as inert masses even without a drive, with the result that the calculation result is falsified because the machine counts too much when adding 1 or more.

Leibniz's four-species calculating machine - original, around 1690
Replica of Leibniz's calculating machine

In 1673 Gottfried Wilhelm Leibniz presented a relay roller machine he had developed to the Royal Society in London.
Quote from Leibniz:

It is unworthy to waste the time of excellent people with servile arithmetic work, because when using a machine, even the most simple-minded can safely write down the results. "

- Gottfried Wilhelm Leibniz

How well this machine actually worked cannot be said with absolute certainty. At the end of the 19th century, the German calculating machine manufacturer Arthur Burkhardt was commissioned to repair the Leibniz machine. When investigating the original Leibniz calculating machine (made around 1700–1716), Nikolaus Joachim Lehmann discovered a fundamental mistake in the restoration work around 1894, which prevented the transmission mechanism from fully functioning. A fully functional replica of the device in original dimensions, which fully corresponds to Leibniz's intentions, was carried out at the TU Dresden. In Hanover Erwin Stein and Franz Otto Kopp carried out investigations into Leibniz's calculating machine and made a replica.

The former manufacturing technology could indeed gears finished accurately and other mechanical parts very, however, was from a interchangeability far away. The individual parts had to be manufactured manually and adapted to each other through rework. Even if the construction of the mechanics for the 10 digit was identical to the 100 digit, the moving parts could not be swapped between the two locations without reworking.

It can therefore be assumed that the original Leibniz machine was able to properly calculate the sample tasks and was blocked over time due to modifications and incorrect repairs. In any case, the replicas of the Heinz Nixdorf MuseumsForum and the Deutsches Museum work perfectly. However, they have also been created using modern manufacturing techniques.

Leibniz manufactured a calculating machine with all the necessary design features. Series production never came about.

In 1709 the Italian mathematician and astronomer Giovanni Poleni (1683–1761) published the construction drawings of his wooden adding machine. This worked on the basis of gears with a variable number of teeth, the so-called sprocket wheels . The realization of his machine failed due to the production possibilities at the time, so that Poleni destroyed his machine by hand. Replicas exist z. B. in the Museo della Scienza e della Tecnologia di Milano (Milan) and in the Arithmeum Bonn.

In 1727 the sprocket wheel calculator designed by Antonius Braun (1686–1728) was finished for the Viennese court. She was Emperor Charles VI. and is now in the Technisches Museum Wien . Today there is only an exact replica of this machine in the Arithmeum Bonn. When measuring and replicating the machine's usability for everyday use, it was found that it could only work correctly over three to four places: The transfer of tens did not work over a large number of places. After all, construction and fine mechanical accuracy allowed such a development at that time.

1727 published the German mechanic Jacob Leupold (1674-1727) in his technical encyclopedia Theatrum Aritmetico Geometricum construction drawings of a calculating machine he had invented, which worked according to the actuating segment principle. It is believed that Braun was familiar with this design before it was first published and that it was built around 1727. However, it was not completed until around 1736 by the French instrument maker Philippe Vayringe (1684–1746) (inscription: "Braun invenit, Vayringe fecit"). That is why Antonius Braun's calculating machine is now called the Leupold-Braun-Vayringe machine . It is located in the Deutsches Museum in Munich.

From 1770 the pastor and inventor Philipp Matthäus Hahn (1739–1790) constructed a calculating machine in the form of a can with concentrically arranged gear wheels, relay rollers and a central drive crank. He made four or five copies of this machine, some of which still exist today (one each in the Württemberg State Museum in Stuttgart and one in the Technoseum in Mannheim) and are fully functional. It is the first fully functional four-species calculating machine with a multi-digit revolution counter and two-stage tens transfer. The copy in Stuttgart counts with 11 digits and the one in Mannheim with 12 digits. The central drive crank, inspired by Leupold, the staggered roller principle and the improved manufacturing possibilities contributed to the fact that many historians see the machine of Philipp Matthäus Hahn as the first calculating machine suitable for everyday use.

Johann Helfrich von Müller (1746–1830) became known when he succeeded between 1782 and 1784 in producing a functional 3-species calculating machine that could perform the four basic arithmetic operations using a 14-digit arithmetic unit. The operands were preset using manual rotary dials. It was a machine based on the relay roller principle.

In addition to the Leibniz calculating machine, two by Hahn and three by Johann Christoph Schuster (1759–1823) have been preserved (Schuster I, 1789–1792, twelve-digit and Schuster II, 1805–1820, nine-digit in the Deutsches Museum in Munich and Schuster III, ten-digit in Arithmeum in Bonn), while the Beireis machine (11 digits) and the Herrenberger machine (14 digits) are lost today.

Abraham Stern , portrait of the inventor with his adding machine, painting by Anton Blank , 1823

From 1810, the inventor Abraham Stern manufactured a number of calculating machines in what is now Poland, which carried out the four basic arithmetic operations and took the square root.

In 1834 Luigi Torchi built the world's first machine for direct multiplication.

In 1844 Jean-Baptiste Schwilgué , builder of the current astronomical clock in the Strasbourg cathedral , patented a key adding machine. It is the third key-operated calculating machine preserved worldwide. Schwilgué also built a large mechanical calculating machine, the calculations of which were used to adjust the high-precision gear milling machine he developed.

In the Gothenburg City Museum, founded in 1861, there is a machine (already mentioned there in 1878) "from Sauter in Eßlingen [on the Neckar]" - what is probably meant is Johann Jacob Sauter junior. (born 1770 in Onstmettingen) or perhaps his brother Johann Ludwig Sauter (born 1780) - received. In the Science Museum in London there is an adding machine apparently manufactured by the same builder, "made by J. Sauter in Eßlingen [am Neckar]".

Although the technical manufacturing possibilities at that time would have allowed a limited production of these machines and at least the Hahn calculating machines were usable, none of the inventors named above were built in series. This may be due to the fact that the calculating machines were at the beginning of their development, as a result of which they were not yet mature enough for practical use and were too expensive to manufacture. The main reason, however, was that there was still no market for such machines. State administrations, the military or merchants did not suffer from time pressures or labor shortages.

## Series production

In 1820, the French Charles Xavier Thomas (1785–1870) received a French privilege (patent) for his calculating machine construction. After further attempts, he began the world's first series production of calculating machines around 1850 . Thomas was a director of two insurance companies and only ran his calculating machine production on the side. Until his death in 1870, his calculating machines were a subsidy business, the sales price was below cost .

From 1820 to 1878 around 1500 devices were manufactured. Since only two calculating machines are known from the early days, one should assume that the real focus of series production lies in the second half of the 19th century.

The calculating machines were called Arithmomètre and worked on the staggered roller principle with a sliding carriage. They worked reliably, but were high technology in their day and could only be serviced and repaired in Paris .

Due to the availability of calculating machines, a market for numerical calculations slowly developed . For the first time, companies were able to perform weekly or even daily balances , and engineers were able to use algebraic methods in addition to slide rules.

In 1876 the Swede Willgodt Theophil Odhner (1845–1905) constructed a sprocket wheel machine, the construction principle of which served as a model for the later European sprocket wheel machine industry. In his opinion, the Thomas machines available at the time were too difficult to get and also not handy enough. His machine should be small, simple, easy to use and inexpensive. Since 1874 he was concerned with the construction of a sprocket calculating machine to be manufactured with the existing machine tools and probably completed the first machine in 1876.

On November 19, 1878, Odhner's business partner, a certain Koenigsberg, received the German Patent No. 7393. In 1879 Odhner received the Swedish Patent No. 123 and the Russian Patent No. 2329 for his design. Odhner did not claim the rung wheel and its rung adjustment with the help of an adjusting ring with a curved slot as his intellectual property.

The production of the calculating machines under the name Arithmometer started in 1886 in Odhner's own factory. Few machines were produced during this time. The later successful machines, which were produced by Odhner and the German company Grimme, Natalis & Co , are based on German patent No. 64 925 from 1890.

Odhner expanded his factory in 1894 and manufactured other mechanical devices in addition to calculating machines. In the Russo-Japanese War from 1904 to 1905, instruments for the naval artillery were made instead of calculating machines. The company founder W. T. Odhner did not experience the resumption of calculating machine production. He died on September 15, 1905 in Saint Petersburg . After the October Revolution of 1917, his company relocated to Gothenburg in Sweden. Up until this year, Russian production amounted to around 30,000 calculating machines, most of which were sold on the Russian market.

At the turn of the century there were already several companies that exclusively manufactured calculating machines. Charles Xavier Thomas' investment, land reforms, and social upheavals helped create a thriving market for calculating machines. In 1906, the Autarith by Alexander Rechnitzer was the first electrically powered, fully automatic calculating machine.

The pinnacle of the development of mechanical calculating machines is the Curta pocket calculator by the Austrian engineer Curt Herzstark . It was produced in large numbers in Liechtenstein by Contina AG from 1947 to 1970 .

## The end of the mechanical calculating machines

Three species machine (electric), ca.1970
Electronic desktop computer Friden 132, transistors and picture tube, 1965

With the discovery of electricity , mechanical calculating machines were supplemented and replaced by electromechanical calculating machines. Replacing hand cranks and levers with an electric motor meant a considerable saving of time and effort, especially in three- and four-species machines, but also increased noise. The further development aimed at program-controlled calculating machines, as they were first realized by Konrad Zuse and found increasingly important applications as computers .

In 1952 the ES appeared , the first German tube-based electronic computer that could process data stored on punched cards . The computer was developed by the Laboratory for Impulse Technology (LFI), the predecessor company of Nixdorf Computer AG . The LFI was the first German manufacturer of electronic computers. In 1962 the first electronic table calculating machine came on the market, the ANITA by Norman Kitz , built by the Bell Punch Company in London. She worked with tubes . At the same time, the Conti desktop calculator from LFI was the world's first desktop calculator with an integrated printer. The first transistor desktop computer was the EC-130 from the US company Friden, Inc. in San Leandro, California, available from 1963. The EC-130 computer had a tube screen with four lines of 13 digits each and was the first to work with the reverse Polish notation , which was later also used by HP. A serial dynamic memory was realized by means of magnetostrictive propagation of bits on a suitable metal wire. An electronic alternative with transistors was conceived, but was never implemented. The Italian IME 84 was also built from 1963. It was only through small integrated circuits (with many transistors) that computers became more and more powerful and compact; In addition, modern semiconductor technologies reduced power consumption.

With the Intel 4004 IC, the first mass-produced microprocessor (which was specially developed for this purpose) was used in a desktop computer from the Japanese manufacturer Busicom . The Busicom 141-PF model was launched in 1971. A year earlier, Busicom had used the fully integrated MK6010 circuit from Mostek in its Handy LE-120A model . Both components were commissioned by Busicom from the respective manufacturers Intel and Mostek specifically for the development of the most compact calculating machine possible.

The first commercially available electronic calculators with accumulators were the Sharp QT-8B and the Sanyo ICC 82-D in 1970 . The Sharp EL-8 , which appeared at the end of 1970 and is usually considered to be the first pocket calculator , contained the same circuitry as the QT-8B and was a lot more compact, but still 7 cm thick. However, the development went so fast that devices came on the market as early as 1971 that can really be called pocket calculators.

By the late 1970s, electronic pocket and desk calculators had practically completely displaced mechanical machines.

Today the term calculating machine is commonly used for electronic desktop calculators, which are often equipped with a small printer, which enables the calculation to be checked. Up until around 1980, machines of this type often had no LED display at all, only a printing unit.

The calculating machines also include pocket calculators and, in a broader sense, also freely programmable computers , which are also used for tasks that have nothing to do with arithmetic, e.g. B. the storage of data. Today, personal computers have taken over the tasks of classic calculating machines in many areas.

## Types of mechanical calculating machines

In the literature, in addition to the calculating machines mentioned above, a wide variety of objects such as abacus , slide rules or Napier slide rules are referred to as mechanical calculating machines . In order to distinguish the calculating machines explained here from these devices, the term mechanical calculating machines must be defined in more detail:

The mechanical calculating machines referred to here have at least one setting mechanism, one result mechanism and an automatic tens transfer in common. The automatic transfer of tens does not have to capture the full capacity of the machine and may only be available inside the machine. The tens carry must therefore not only be partially automatic, as is usual when calculating with column adding machines.

The restriction that a mechanical calculating machine should work with gears would exclude the multiplying machines of Eduard Selling (1834–1920), which work on the principle of the Nuremberg scissors .

The following section is intended to give an overview of the different types of mechanical calculating machines:

The subdivision made here primarily concerns the functionality and area of ​​application of the calculating machines; A distinction is made between adding machines (also adding machines) and four-species machines. A calculating machine is referred to here as an adding machine, the concept of which is primarily geared towards the rapid addition of columns of numbers. The definition of the term four-species machines makes it clear that this division does not lead to a clear distinction between different computing machines .

In Europe , adding machines are often referred to as two-species machines . This does not do justice to their use, especially in the USA . On full keyboard adding machines, which have a separate key column with the digits 1 to 9 for each entry point, it is possible to multiply and divide quickly and efficiently. When multiplying on a full-keyboard adding machine, the hand position essentially replaces the slide of a European four-species machine . So multiplying two numbers can like on an adding machine Comptometer of Felt and Tarrant Manufacturing Company of Chicago be performed more quickly than on a Brunsviga - Sprossenrad -Rechenmaschine from Braunschweig . With continued calculation and division, however, the sprocket calculating machine again shows its advantages.

This fact may be due to the fact that in Europe mainly sprocket and staggered roller machines are manufactured, while full-keyboard adding machines form the backbone of adding machines in the USA. The corresponding comparative competitions and advertising statements from the heyday of mechanical calculating machines may still have a late effect here.

Column adding machines are intended to add up each column individually when several numbers are added, as one is used to with written addition. There are also examples of these machines that are also suitable for multiplication. For example, the pen of Adolf Bordt Mannheim ( Ref : Lenz, K., calculators).

In adding machines with direct transmission, pressing a key immediately triggers the calculation process, which is why these machines are often referred to as the fastest adding machines. They are usually equipped with a full keyboard.

The torpedo high-speed adding machine from Torpedo Works and the Plus from Bell Punch Ltd. London are an exception here: You have keys 1 to 5 for each column, i.e. half a full keyboard or a reduced keyboard .

#### Adding machines with drive lever

Calculating machine Astra model B from Chemnitz Astrawerke , approx. 1922.

On these machines, you key in a number and start the calculation with a separate lever. The word drive lever is to be understood here in a broader sense, it can also be a button or a crank. In addition, some makes were equipped with motors in which the drive lever only had a releasing function. Adding machines with drive levers were equipped with the abovementioned full keyboard or with a numeric keyboard, as is known from today's pocket calculators .

The disadvantage of adding machines with drive levers compared to machines without drive levers is that they require an additional keystroke per number. On the other hand, the keystroke is usually easier because the drive lever supplies the energy for the mechanism. The construction of a machine with a drive lever is easier to control, in particular they have a simpler tens transmission mechanism. An aspect that is interesting for beginners in machine computing is the ability to control the input and correct it without problems, which is not possible on machines with direct transfer.

Almost without exception, the column adding machines mentioned have no drive lever.

#### Printing and writing adding machines

Printing adding machines can put the invoice and result on paper. With a writing adding machine you can add more text to the calculation.

### Four species calculators

The generic term four-species calculating machine is generally intended to be a calculating machine on which at least all four basic arithmetic operations can be calculated. For more information, see the article on four-species machines .

The operating principles listed below were primarily used for four-species machines:

#### Staggered roller machines

See the article relay roller

#### Proportional lever and ratchet machines

Both functional principles go back to the most important German calculating machine designer Christel Hamann (1870–1948). Hamann developed the proportional lever principle in 1902 and 1903. The first example of his Euclid calculating machine based on this principle was sold in 1908.

The first Hamann-Manus ratchet machine was produced by the Berlin company DeTeWe from 1925 onwards . The external shape of the ratchet machines was matched to the Brunsviga sprout wheel machines established on the market in order to make it easier for users to switch to this new type of machine.

Neither principle of operation found the spread of the sprocket wheel and the relay roller .

### More calculating machines

#### Multiplication body calculators

Multiplier from Léon Bollée

Multiplication body calculating machines have as a central functional element a multiplication body on which all the products of the simple multiplication are represented in rods of different lengths.

Leibniz is said to have dealt with the idea of ​​a multiplication body . The Spaniard Ramón Verea (1838–1899), who lives in New York, developed a multiplication body calculator in 1878, of which probably only a prototype was built. In the years 1888 to 1892, the French automobile designer and inventor Léon Bollée (1870–1913) built three models of calculating machines with a single unit, which were, however, quite unwieldy to use. The Swiss Otto Steiger designed a machine that was produced in large numbers: his Millionaire was built from 1893 to around 1935.

#### Accounting machines and cash registers

Booking machines are office machines that can be used to process documents about business transactions. They evolved from typewriters and calculating machines.

Although accounting machines and cash registers usually also have the function of machine computing , they are generally not counted as calculating machines.

#### Special mechanical calculating machines

There are many devices that are designed for specific math tasks. Important representatives are the Antikythera mechanism , the difference machines of the Englishman Charles Babbage (1791–1871) and the Swedes Georg and Edvard Scheutz .

## Exhibitions of calculating machines

The Arithmeum in Bonn has historically accurate and functioning replicas of the calculating machines of Wilhelm Schickard , Blaise Pascal , Samuel Morland , Gottfried Wilhelm Leibniz , Anton Braun , Giovanni Poleni , Philipp Matthäus Hahn , Johann Helfrich von Müller , Charles Stanhope , Johann Christoph Schuster , Jacob Auch and Ramón Verea .

The Heinz Nixdorf MuseumsForum in Paderborn dedicates an exhibition area to arithmetic from simple arithmetic aids to the pocket calculator wall with current models. In addition to replicas and rare machines, it is worth mentioning that the exhibition is based on original machines from the 1920s.

The Deutsches Museum in Munich has a large pool of calculating machines. Since the Deutsches Museum already existed at the beginning of the twentieth century, many original machines that were made available by the manufacturers at the time can be seen in the exhibition. In particular, there are also very valuable unique items, for example by Philipp Matthäus Hahn or Eduard Selling .

## Individual evidence

1. The first calculating machine. Retrieved March 13, 2019 .
2. ▷ VIDEO: Masterpieces of Art: Pascaline. In: museum television. June 3, 2016, accessed on March 13, 2019 (German).
3. Jan-Willem Liebezeit: Leibniz calculating machines .
4. Korte, pp. 23-30
5. Silvio Hénin: Two early Italian key-driven calculators. IEEE Annals of the History of Computing 32.1 (2010).
6. Denis Roegel: Before Torchi and Schwilgué, There Was White. IEEE Annals of the History of Computing 38.4 (2016), pp. 92-93.
7. Computer dictionary: Walther Multa 32. Retrieved on July 31, 2012 .
8. Ulrich Fritsch: The new dimension. Future strategies of international top managers, Düsseldorf, Vienna 1986, p. 138: "In 1952 Heinz Nixdorf founded the laboratory for pulse technology in Essen "
9. Friden EC-130 Electronic calculator (1963)
10. Activity report of a Swiss engineer in California.
11. computermuseum.informatik.uni-stuttgart.de IME 84
12. computermuseum.informatik.uni-stuttgart.de Sanyo ICC 82-D
13. www.schlepptops.de Printing desk calculators without display

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