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Mechanical Calculator Information

A mechanical calculator was a device used to perform the basic operations of arithmetic. The last mechanical calculators were comparable in size to desktop computers and were rendered obsolete by the advent of the electronic calculator.

The mechanical calculator was invented in 1642[1] and the first commercially successful device was manufactured from 1851. Machines with columns of keys were introduced in 1887 while 10 key calculators and electric motors appeared in 1902.[2] The use of electric motors allowed for the design of very powerful machines during the first half of the 20th century. In 1961, the comptometer became the first mechanical calculator to receive an all electronic calculator engine, creating the link in between these two industries and marking the beginning of its decline. The last mechanical calculators were built in the middle of the 1970s.

The mechanical calculator was preceded by and competed against clerical aids such as abaci, Napier's bones and slide rules, and various books of mathematical tables. The true precursors to the mechanical calculator were machines made of toothed gears linked by carry mechanisms like odometers, astrolabes, clocks and pedometers.[3]

Contents

History

Ancient history

Suanpan (the number represented in the picture is 6,302,715,408) Main article: Abacus

Devices have been used to aid computation for thousands of years, using one-to-one correspondence with our fingers.[4] The earliest counting device was probably a form of tally stick. Later record keeping aids throughout the Fertile Crescent included clay shapes, which represented counts of items, probably livestock or grains, sealed in containers.[5]

The first clerical aids were abathia, and were often constructed as a wooden frame with beads sliding on wires. Abathias were in use centuries before the adoption of the written Arabic numerals system and are still used by some merchants, fishermen and clerks in Africa, Asia, and elsewhere.

The counter abacus was devised by Egyptian mathematicians in Egypt in 2000 BC. It was used for arithmetic tasks. The Roman abacus was used in Babylonia as early as 2400 BC. Since then, many other forms of reckoning boards or tables have been invented. In a medieval counting house, a checkered cloth would be placed on a table, and markers moved around on it according to certain rules, as an aid to calculating sums of money (this is the origin of "Exchequer" as a term for a nation's treasury).

Other precursors to the mechanical calculator

A number of analog computers were constructed in ancient and medieval times to perform astronomical calculations. These include the Antikythera mechanism and other astrolabes from ancient Greece (c. 150-100 BC), which are generally regarded as the first mechanical analog computers.[6] Other early versions of mechanical devices used to perform some type of calculations include the planisphere and other mechanical computing devices invented by Abū Rayhān al-Bīrūnī (c. AD 1000); the equatorium and universal latitude-independent astrolabe by Abū Ishāq Ibrāhīm al-Zarqālī (c. AD 1015); the astronomical analog computers of other medieval Muslim astronomers and engineers; and the astronomical clock tower of Su Song (c. AD 1090) during the Song Dynasty. The "castle clock", an astronomical clock invented by Al-Jazari in 1206, is considered to be the earliest programmable analog computer.[7]

The 17th century

Overview

The 17th century was a turning point in the history of mechanical calculators. On one hand, it saw the invention of logarithms, logarithmic tables and the slide rule which, for their ease of use by scientists in multiplying and dividing, ruled over and impeded the use and development of mechanical calculators[8] until the production release of the arithmometer in the mid 19th century, and, on the other hand, it saw the invention of the mechanical calculator by Blaise Pascal[1] quickly followed by Gottfried Leibniz who was the first to describe a pinwheel calculator[9] and who invented the Leibniz wheel. Neither of them being successful in commercializing their machines.

Logarithms and slide rules

17th century calculators, Musée des Arts et Métiers

Scottish mathematician and physicist John Napier noted multiplication and division of numbers could be performed by addition and subtraction, respectively, of logarithms of those numbers. While producing the first logarithmic tables Napier needed to perform many multiplications, and it was at this point that he designed Napier's bones, an abacus-like device used for multiplication and division.[10]

In 1622 William Oughtred invented the slide rule, which was revealed by his student Richard Delamain in 1630.[11] Since real numbers can be represented as distances or intervals on a line, the slide rule allows multiplication and division operations to be carried out significantly faster than was previously possible.[12] The devices were used by generations of engineers and other mathematically inclined professional workers, until the invention of the pocket calculator. The engineers in the Apollo program that sent a man to the moon made many of their calculations on slide rules, which were accurate to three or four significant figures.[13]

Invention of the mechanical calculator

In 1642, Blaise Pascal invented the mechanical calculator while trying to help his father who had been assigned the task of reorganizing the tax revenues of the French province of Haute-Normandie.[14] After three years of effort and 50 prototypes[15] he introduced his machine to the public, dedicating it to the chancellor of France Pierre Séguier. He built twenty of these machines (called the Pascaline) in the following ten years.[16] This machine could add and subtract two numbers directly and multiply and divide by repetition.

Gottfried Leibniz invented the first calculator that could perform all four arithmetic operations automatically while adding direct multiplication and division to the Pascaline ; it was called the Stepped Reckoner. He built it around 1672, but careful examination at the end of the 19th century showed a problem with the carry mechanism. It used his Leibniz wheels which, a century and a half later, will be at the heart of the arithmometer, the first calculator to be commercialized. He also was the first to describe a pinwheel calculator in 1685[9]. Leibniz once said "It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used."[17]

Unknown prototype

Wilhelm Schickard, a German polymath, designed a calculating clock in 1623; a fire destroyed it during its construction in 1624 and Schickard abandoned his project. Two sketches of it were discovered in 1957; too late to have any impact on the development of mechanical calculators.[18]

The 18th century

Further information: pinwheel calculators Further information: Leibniz wheel

The 18th century saw the first fully functional, four operations, mechanical calculators both pinwheel calculators and Leibniz wheel calculators were built with a few unsuccessful attempts at their commercialization.

The 19th century

Machines produced

Desktop Mechanical Calculators in production during the 19th century

Prototypes and limited runs

The London Science Museum's working difference engine, built a century and a half after Charles Babbage's design.

1900s to 1970s

Mechanical calculators reach their zenith

Mechanical calculator from 1914

The first half of the 20th century saw the gradual development of the mechanical calculator mechanism.

The Dalton adding-listing machine introduced in 1902 was the first of its type to use only ten keys, and became the first of many different models of "10-key add-listers" manufactured by many companies.

An Addiator could be used for addition and subtraction.

In 1948 the miniature Curta calculator, which was held in one hand for operation, was introduced after being developed by Curt Herzstark in 1938. This was an extreme development of the stepped-gear calculating mechanism.

From the early 1900s through the 1960s, mechanical calculators dominated the desktop computing market (see History of computing hardware). Major suppliers in the USA included Friden, Monroe, and SCM/Marchant. (Some comments about European calculators follow below.) These devices were motor-driven, and had movable carriages where results of calculations were displayed by dials. Nearly all keyboards were full — each digit that could be entered had its own column of nine keys, 1..9, plus a column-clear key, permitting entry of several digits at once. (See the illustration of a 1914 mechanical calculator.) One could call this parallel entry, by way of contrast with ten-key serial entry that was commonplace in mechanical adding machines, and is now universal in electronic calculators. (Nearly all Friden calculators had a ten-key auxiliary keyboard for entering the multiplier when doing multiplication.) Full keyboards generally had ten columns, although some lower-cost machines had eight. Most machines made by the three companies mentioned did not print their results, although other companies, such as Olivetti, did make printing calculators.

In these machines, addition and subtraction were performed in a single operation, as on a conventional adding machine, but multiplication and division were accomplished by repeated mechanical additions and subtractions. Friden made a calculator that also provided square roots, basically by doing division, but with added mechanism that automatically incremented the number in the keyboard in a systematic fashion. Friden and Marchant (Model SKA) made calculators with square root. Handheld mechanical calculators such as the 1948 Curta continued to be used until they were displaced by electronic calculators in the 1970s.

Triumphator CRN1 (1958) Walther WSR160 (1960) Dalton adding machine (1930 ca.)

Typical European four-operations machines use the Odhner mechanism, or variations of it. This kind of machines included the Original Odhner, Brunsviga and several following imitators, starting from Triumphator, Thales, Walther, Facit up to Toshiba. Although most of these was operated by handcranks, there were motor-driven versions.

Although Dalton introduced in 1902 first ten-keys printing adding(two operations) machine, these features was not present in computing (four operations) machines for many decades. Facit-T (1932) was the first 10-keys computing machine having a large commercial diffusion. Olivetti Divisumma-14 (1948) was the first computing machine with both printer and 10-keys keyboard. Full-keyboard machines, including motor-driven ones, were also built until 60ties. Some machines had as many as 20 columns in their full keyboards. The monster in this field was the Duodecillion made by Burroughs for exhibit purposes.

Duodecillion (1915 ca.) Marchant Figurematic (1950-52) Facit NTK (1954) Olivetti Divisumma 24 (1964)

The end of an era

Mechanical calculators continued to be sold, though in rapidly decreasing numbers, into the early 1970s, with many of the manufacturers closing down or being taken over. Comptometer type calculators were often retained for much longer to be used for adding and listing duties, especially in accounting, since a trained and skilled operator could enter all the digits of a number in one movement of the hands on a Comptometer quicker than was possible serially with a 10-key electronic calculator. The spread of the computer rather than the simple electronic calculator put an end to the Comptometer. Also, by the end of the 1970s, the slide rule had become obsolete.

See also

References

  1. ^ a b Jean Marguin (1994), p. 48
  2. ^ Ernst Martin p.23,133 (1925)
  3. ^ Jean Marguin p.39-43 (1994)
  4. ^ Georges Ifrah notes that humans learned to count on their hands. Ifrah shows, for example, a picture of Boethius (who lived 480–524 or 525) reckoning on his fingers in Ifrah 2000, p. 48.
  5. ^ According to Schmandt-Besserat 1981, these clay containers contained tokens, the total of which were the count of objects being transferred. The containers thus served as a bill of lading or an accounts book. In order to avoid breaking open the containers, marks were placed on the outside of the containers, for the count. Eventually (Schmandt-Besserat estimates it took 4000 years) the marks on the outside of the containers were all that were needed to convey the count, and the clay containers evolved into clay tablets with marks for the count.
  6. ^ Lazos 1994
  7. ^ Ancient Discoveries, Episode 11: Ancient Robots. History Channel. http://www.youtube.com/watch?v=rxjbaQl0ad8. Retrieved 2008-09-06
  8. ^ Scripta Mathematica, p.128 (1932)
  9. ^ a b David Smith, p.173-181 (1929)
  10. ^ A Spanish implementation of Napier's bones (1617), is documented in Montaner i Simon 1887, pp. 19–20.
  11. ^ Slide Rules
  12. ^ Kells, Kern & Bland 1943, p. 92
  13. ^ Kells, Kern & Bland 1943, p. 82, as log(2) = 0.3010, or 4 places.
  14. ^ Maurice d'Ocagne (1893), p. 245 Copy of this book found on the CNAM site
  15. ^ (fr) La Machine d’arithmétique, Blaise Pascal, Wikisource
  16. ^ Guy Mourlevat, p. 12 (1988)
  17. ^ As quoted in Smith 1929, pp. 180–181
  18. ^ René Taton, p. 81 (1969)
  19. ^ L'ami des Sciences 1856, p.301 www.arithmometre.org (page consultée le 22-09-2010)
  20. ^ Ifrah G., The Universal History of Numbers, vol 3, page 127, The Harvill Press, 2000
  21. ^ Chase G.C.: History of Mechanical Computing Machinery, Vol. 2, Number 3, July 1980, IEEE Annals of the History of Computing, p. 204
  22. ^ J.A.V. Turck, Origin of modern calculating machines, The western society of engineers, 1921, p. 75
  23. ^ Trogemann G., Nitussov A.: Computing in Russia, GWV-Vieweg, 2001, ISBN 3-528-05757-2, p. 45
  24. ^ J.A.V. Turck, Origin of modern calculating machines, The western society of engineers, 1921, p. 143

Sources

Categories: Calculators | Mathematical tools | Office equipment

 

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