Editing Mechanical calculator (section)

==The 19th century==

===Overview===
{{anchor|TotalMachinesBuilt}}
[[Luigi Torchi (inventor)| Luigi Torchi]] invented the first direct multiplication machine in 1834.<ref>{{cite web|url=http://history-computer.com/MechanicalCalculators/19thCentury/Torchi.html|title=History of Computers and Computing, Mechanical calculators, 19th century, Luiggi Torchi|website=history-computer.com|date=4 January 2021 }}</ref> This was also the second key-driven machine in the world, following that of [[James White (inventor)|James White]] (1822).<ref name="Roegel">{{cite journal|doi=10.1109/MAHC.2016.46|title=Before Torchi and Schwilgué, There Was White|year=2016|last1=Roegel|first1=Denis|journal=IEEE Annals of the History of Computing|volume=38|issue=4|pages=92–93|s2cid=28873771 }}</ref>

The mechanical calculator industry started in 1851 [[Thomas de Colmar]] released his simplified [[Arithmometer|Arithmomètre]], which was the first machine that could be used daily in an office environment.

For 40 years,<ref>This is one third of the 120 years that this industry lasted</ref> the arithmometer was the only mechanical calculator available for sale and was sold all over the world. By 1890, about 2,500 arithmometers had been sold<ref>{{cite web|url=http://www.arithmometre.org/NumerosSerie/PageNumerosSeriePayen.html|title=www.arithmometre.org|website=arithmometre.org}}</ref> plus a few hundreds more from two licensed arithmometer clone makers (Burkhardt, Germany, 1878 and Layton, UK, 1883). Felt and Tarrant, the only other competitor in true commercial production, had sold 100 comptometers in three years.<ref>{{cite book|last=Felt|first=Dorr E.|title=Mechanical arithmetic, or The history of the counting machine|publisher=Washington Institute|location=Chicago|page=4|year=1916|url=https://archive.org/details/mechanicalarithm00feltrich}}</ref>

The 19th century also saw the designs of Charles Babbage calculating machines, first with his [[difference engine]], started in 1822, which was the first automatic calculator since it continuously used the results of the previous operation for the next one, and second with his [[analytical engine]], which was the first programmable calculator, using Jacquard's cards to read program and data, that he started in 1834, and which gave the blueprint of the [[mainframe computers]] built in the middle of the 20th century.<ref name=BABBAGE>"The calculating engines of English mathematician Charles Babbage (1791–1871) are among the most celebrated icons in the prehistory of computing. Babbage's Difference Engine No.1 was the first successful automatic calculator and remains one of the finest examples of precision engineering of the time. Babbage is sometimes referred to as "father of computing." The International Charles Babbage Society (later the Charles Babbage Institute) took his name to honor his intellectual contributions and their relation to modern computers." [http://www.cbi.umn.edu/about/babbage.html Charles Babbage Institute] (page. Retrieved 1 February 2012).</ref>
[[Image:DesktopMechanicalCalculators inProduction intheXIXCentury.svg|thumbnail|upright=2.6|center|<div align="center">Desktop Mechanical Calculators in production during the 19th century</div>]]

===Desktop calculators produced===
[[Image:Close-up of the front panel of a Thomas Arithmometer.jpg|thumb|upright=1.8|Front panel of a Thomas Arithmometer with its movable result carriage extended]]
* In 1851, [[Thomas de Colmar]] simplified his [[arithmometer]] by removing the one-digit multiplier/divider. This made it a simple adding machine, but thanks to its moving carriage used as an indexed accumulator, it still allowed for easy multiplication and division under operator control. The arithmometer was now adapted to the manufacturing capabilities of the time; Thomas could therefore manufacture consistently a sturdy and reliable machine.<ref>Ifrah G., ''The Universal History of Numbers'', vol 3, page 127, The Harvill Press, 2000</ref> Manuals were printed and each machine was given a serial number. Its commercialization launched the mechanical calculator industry.<ref name="Chase">Chase G.C.: ''History of Mechanical Computing Machinery'', Vol. 2, Number 3, July 1980, IEEE Annals of the History of Computing, p. 204</ref> Banks, insurance companies, government offices started to use the arithmometer in their day-to-day operations, slowly bringing mechanical desktop calculators into the office.
* In 1878 Burkhardt, of Germany, was the first to manufacture a clone of Thomas' arithmometer. Until then Thomas de Colmar had been the only manufacturer of desktop mechanical calculators in the world and he had manufactured about 1,500 machines.<ref>[http://www.arithmometre.org/NumerosSerie/PageNumerosSerieEnglish.html Serial numbers and Years of manufacturing] www.arithmometre.org, Valéry Monnier</ref> Eventually twenty European companies will manufacture clones of Thomas' arithmometer until WWII.
* [[Dorr E. Felt]], in the U.S., patented the [[Comptometer]] in 1886. It was the first successful key-driven adding and calculating machine. ["Key-driven" refers to the fact that just pressing the keys causes the result to be calculated, no separate lever or crank has to be operated. Other machines are sometimes called "key-set".] In 1887, he joined with Robert Tarrant to form the Felt & Tarrant Manufacturing Company.<ref>J.A.V. Turck, ''Origin of modern calculating machines'', The Western Society of Engineers, 1921, p. 75</ref> The comptometer-type calculator was the first machine to receive an all-electronic calculator engine in 1961 (the [[Sumlock ANITA calculator|ANITA mark VII]] released by Sumlock comptometer of the UK).
* In 1890 [[Viligodt Teofil Odner|W. T. Odhner]] got the rights to manufacture his calculator back from ''Königsberger & C'', which had held them since it was first patented in 1878, but had not really produced anything. Odhner used his [[Saint Petersburg]] workshop to manufacture his calculator and he built and sold 500 machines in 1890. This manufacturing operation shut down definitively in 1918 with 23,000 machines produced. The [[Odhner Arithmometer]] was a redesigned version of the Arithmometer of Thomas de Colmar with a pinwheel engine, which made it cheaper to manufacture and gave it a smaller footprint while keeping the advantage of having the same user interface.<ref name="Trogemann">[[#TROG|G. Trogemann]], pages: 39–45</ref>
* In 1892 Odhner sold the Berlin branch of his factory, which he had opened a year earlier, to ''Grimme, Natalis & Co.'' They moved the factory to Braunschweig and sold their machines under the brand name of Brunsviga (Brunsviga is the Latin name of the town of Braunschweig).<ref>David J. Shaw: ''The Cathedral Libraries Catalogue'', The British Library and the Bibliographical Society, 1998</ref>  This was the first of many companies which would sell and manufacture clones of Odhner's machine all over the world; eventually millions were sold well into the 1970s.<ref name="Trogemann"/>
* In 1892, [[William Seward Burroughs I|William S. Burroughs]] began commercial manufacture of his printing adding calculator<ref>J.A.V. Turck, ''Origin of modern calculating machines'', The Western Society of Engineers, 1921, p. 143</ref> [[Burroughs Corporation]] became one of the leading companies in the accounting machine and computer businesses.
* [[The Millionaire (calculator)|The "Millionaire"]] calculator was introduced in 1893. It allowed direct multiplication by any digit – "one turn of the crank for each figure in the multiplier". It contained a mechanical product lookup table, providing units and tens digits by differing lengths of posts.<ref>{{Cite web|url=http://www.johnwolff.id.au/calculators/Tech/Millionaire/Intro.htm|title=The "Millionaire" Calculating Machine - Technical Description|last=Wolff|first=John|date=30 May 2007|website=John Wolff's Web Museum|access-date=2019-12-30}}</ref> Another direct multiplier was part of the [[Moon-Hopkins billing machine]]; that company was acquired by Burroughs in the early 20th century.

{|
| [[Image:EarlyComptometerMachine.png|thumb|upright=.6|19th century Comptometer in a wooden case]]
| [[File:19th-and-early-20th-centuries-calculating-machines.jpg|thumb|19th and early 20th centuries calculating machines, [[Musée des Arts et Métiers]]]]
| [[File:Odhner made before 1900.jpg|thumb|Odhner's arithmometer]]
|}

=== Automatic mechanical calculators ===
[[Image:050114 2529 difference.jpg|thumb|The London Science Museum's working difference engine, built a century and a half after Charles Babbage's design.]]
* In 1822, [[Charles Babbage]] presented a small cogwheel assembly that demonstrated the operation of his [[difference engine]],<ref>[[#WEB|James Essinger]], p.76 (2004)</ref> a mechanical calculator which would be capable of holding and manipulating seven numbers of 31 decimal digits each. It was the first time that a calculating machine could work automatically using as input results from its previous operations.<ref name=BABBAGE/> It was the first calculating machine to use a printer. The development of this machine, later called "Difference Engine No. 1," stopped around 1834.<ref>"The better part of my live has now been spent on that machine, and no progress whatever having been made since 1834...", Charles Babbage, quoted in [[#GENIUS|Irascible Genius]], 1964, p.145</ref>
* In 1847, Babbage began work on an improved difference engine design—his "Difference Engine No. 2."  None of these designs were completely built by Babbage. In 1991 the [[Science Museum (London)|London Science Museum]] followed Babbage's plans to build a working Difference Engine No. 2 using the technology and materials available in the 19th century.
* In 1855, [[Per Georg Scheutz]] completed a working difference engine based on Babbage's design. The machine was the size of a piano, and was demonstrated at the [[Exposition Universelle (1855)|Exposition Universelle]] in Paris in 1855. It was used to create tables of [[logarithm]]s.
* In 1875, [[Martin Wiberg]] re-designed the Babbage/Scheutz difference engine and built a version that was the size of a sewing machine.

=== Programmable mechanical calculators ===
[[File:Analytical Engine (2290032530).jpg|thumb|left|upright=.6|Minimal but working demonstration part of the ''mill'' from the [[Analytical engine]], finished by Babbage's son around 1906]]
* In 1834, Babbage started to design his [[analytical engine]], which will become the undisputed ancestor of the modern [[mainframe computer]]<ref>"It is reasonable to inquire, therefore, whether it is possible to devise a machine which will do for mathematical computation what the [[automatic lathe]] has done for engineering. The first suggestion that such a machine could be made came more than a hundred years ago from the mathematician Charles Babbage. Babbage's ideas have only been properly appreciated in the last ten years, but we now realize that he understood clearly all the fundamental principles which are embodied in modern digital computers" [[#FASTER|B. V. Bowden]], 1953, pp. 6,7</ref> with two separate input streams for data and program (a primitive [[Harvard architecture]]), printers for outputting results (three different kind), processing unit (mill), memory (store) and the first-ever set of programming instructions. In the proposal that [[Howard Aiken]] gave [[IBM]] in 1937 while requesting funding for the [[Harvard Mark I]] which became IBM's entry machine in the computer industry, we can read: "Few calculating machines have been designed strictly for application to scientific investigations, the notable exceptions being those of Charles Babbage and others who followed him. In 1812 Babbage conceived the idea of a calculating machine of a higher type than those previously constructed to be used for calculating and printing tables of mathematical functions. ....After abandoning the ''difference engine'', Babbage devoted his energy to the design and construction of an ''analytical engine'' of far higher powers than the ''difference engine''..."<ref>Howard Aiken, 1937, reprinted in [[#ORIGINS|The origins of Digital computers, Selected Papers]], Edited by [[Brian Randell]], 1973</ref>
* In 1843, during the translation of a French article on the analytical engine, [[Ada Lovelace]] wrote, in one of the many notes she included, [[Note G|an algorithm]] to compute the [[Bernoulli numbers]].  This is considered the first computer program.
* From 1872 until 1910, [[Henry Babbage]] worked intermittently on creating the mill, the "central processing unit" of his father's machine.  After a few setbacks, he gave in 1906 a successful demonstration of the mill which printed the first 44 multiples of pi with 29 places of figures.

=== Cash registers ===
{{further|Cash registers}}
The cash register, invented by the American saloonkeeper [[James Ritty]] in 1879, addressed the old problems of disorganization and dishonesty in business transactions.<ref>[http://www.ncr.org.uk/page106.html NCR Retrospective website]. Retrieved October, 02 2012</ref> It was a pure adding machine coupled with a [[printer (computing)|printer]], a bell and a two-sided display that showed the paying party and the store owner, if he wanted to, the amount of money exchanged for the current transaction.

The cash register was easy to use and, unlike genuine mechanical calculators, was needed and quickly adopted by a great number of businesses.  "Eighty four companies sold cash registers between 1888 and 1895, only three survived for any length of time".<ref>[http://www.cashregistersonline.com/history.asp History of the cash register]. Retrieved October, 05 2012</ref>

In 1890, 6 years after [[John Henry Patterson (NCR owner)|John Patterson]] started [[NCR Corporation]], 20,000 machines had been sold by his company alone against a total of roughly 3,500 for all genuine calculators combined.<ref>[[#TotalMachinesBuilt|See the number of machines built in 1890]] in this paragraph</ref>

By 1900, NCR had built 200,000 cash registers<ref>[http://www.brasscashregister.net/learn_more/articles/how_to_date_your_national_or_ncr_cash_register/ Dick and Joan's antique]. Retrieved October, 02 2012</ref> and there were more companies manufacturing them, compared to the "Thomas/Payen" arithmometer company that had just sold around 3,300<ref>[http://www.arithmometre.org/NumerosSerie/PageNumerosSeriePayen.html List of serial numbers by dates] arithmometre.org. Retrieved 10 October 2012</ref> and Burroughs had only sold 1,400 machines.<ref>Before the computer, James W. Cortada, p.34 {{ISBN|0-691-04807-X}}</ref>

===Prototypes and limited runs===
[[File:Arithmometer - Detail of Multiplier pre 1851.jpg|right|thumb|<div align="center">Arithmometers built from 1820 to 1851 had a one-digit multiplier/divider cursor (ivory top) is on the left. Only prototypes of these machines were built.</div>]]
* In 1820, [[Thomas de Colmar]] patented the Arithmometer. It was a true four operation machine with a one digit multiplier/divider (The [[The Millionaire (calculator)|''Millionaire'' calculator]] released 70 years later had a similar user interface<ref>A notable difference was that the Millionaire calculator used an internal mechanical product lookup table versus a repeated addition or subtraction ''until a counter was decreased down to zero and stopped the machine'' for the arithmometer</ref>). He spent the next 30 years and 300,000 Francs developing his machine.<ref>[http://www.arithmometre.org/Bibliotheque/BibNumerique/AmiDesSciences1856/AmidesSciences1856.pdf L'ami des Sciences 1856, p. 301] www.arithmometre.org (page. Retrieved 22 September 2010)</ref> This design was replaced in 1851 by the simplified arithmometer which was only an adding machine.
* From 1840, Didier Roth patented and built a few calculating machines, one of which was a direct descendant of [[Pascal's calculator]].
* In 1842, Timoleon Maurel invented the [[Arithmaurel]], based on the Arithmometer, which could multiply two numbers by simply entering their values into the machine.
* In 1845, [[Izrael Abraham Staffel]] first exhibited a machine that was able to add, subtract, divide, multiply and obtain a square root.
* Around 1854, [[Andre-Michel Guerry]] invented the Ordonnateur Statistique, a cylindrical device designed to aid in summarizing the relations among data on moral variables (crime, suicide, etc.)<ref>Larousse, P. (1886), ''Grand dictionnaire universel du XIX siècle'', Paris, entry for A-M Guerry</ref>
* In 1872, [[Frank Stephen Baldwin|Frank S. Baldwin]] in the U.S. invented a [[pinwheel calculator]].
* In 1877 [[George B. Grant]] of Boston in the United States began producing the Grant mechanical calculating machine capable of addition, subtraction, multiplication and division.<ref>[[#CYBERSPACE|Hook & Norman]] p.252 (2001): "Grant developed two models of his calculating machine: a ''Barrel model'', which he exhibited at the Centennial Exposition along with his difference engine; and a ''Rack and Pinion'' model, of which he was able to sell 125 examples.  Although Grant never made much money from his calculating machines, his experiences in designing and constructing them led him to establish the highly successful ''Grant Gear Works'', which helped to pioneer the gear-cutting industry in the United States."</ref> The machine measured 13x5x7 inches and contained eighty working pieces made of brass and tempered steel. It was first introduced to the public at the 1876 Centennial Exposition in Philadelphia.<ref>''"Improved Calculating Machine"'', "Scientific American" Vol. XXXVI, No. 19, 12 May 1877 p.294 New York: Munn &Company (Publisher)</ref>
* In 1883, Edmondson of the United Kingdom patented a circular stepped drum calculator.<ref>[http://www.ami19.org/BrevetsFrancais/1883Edmonson/1883Edmonson.pdf Patent application in French] from www.ami19.org scanned by Valéry Monnier (retrieved on 12 January 2012)</ref>

{|
| [[File:Detail of a Roth Calculating machine.png|thumb|Detail of an early calculating machine invented by Didier Roth around 1840.  This machine is a direct descendant of [[Pascal's calculator]].]]
| [[File:Grant mechanical calculating machine 1877.jpg|thumb|left|Grant's Barrel, 1877]]
|}