Editing Difference engine (section)

===Charles Babbage's difference engines===
Charles Babbage began to construct a small difference engine in {{circa|1819}}<ref>{{Cite book |url=https://books.google.com/books?id=tXBVAgAAQBAJ&pg=PT22 |title=It Began with Babbage: The Genesis of Computer Science |last=Dasgupta |first=Subrata |date=2014 |publisher=Oxford University Press |isbn=978-0-19-930943-6|page=22}}</ref> and had completed it by 1822 (Difference Engine 0).<ref name=":0">{{Cite book |title=The Turing Guide |author-link1=Jack Copeland |last1=Copeland |first1=B. Jack |author-link2=Jonathan Bowen |last2=Bowen |first2=Jonathan P. |author-link3=Robin Wilson (mathematician) |last3=Wilson |first3=Robin |last4=Sprevak |first4=Mark |date=2017 |publisher=[[Oxford University Press]] |isbn=9780191065002 |page=251 |title-link=The Turing Guide }}</ref> He announced his invention on 14 June 1822, in a paper to the [[Royal Astronomical Society]], entitled "Note on the application of machinery to the computation of astronomical and mathematical tables".<ref>{{cite web |last1=O'Connor |first1=John J. |last2=Robertson |first2=Edmund F. |author-link2=Edmund F. Robertson |date=1998 |url=http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Babbage.html |title=Charles Babbage |work=MacTutor History of Mathematics archive |publisher=School of Mathematics and Statistics, University of St Andrews, Scotland |access-date=2006-06-14 |archive-url=https://web.archive.org/web/20060616002258/http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Babbage.html |archive-date=2006-06-16 }}</ref> This machine used the decimal number system and was powered by cranking a handle. The [[British government]] was interested, since producing tables was time-consuming and expensive and they hoped the difference engine would make the task more economical.<ref name="Campbell-Kelly 2004">{{cite book |title=Computer: A History of the Information Machine 2nd ed. |last=Campbell-Kelly |first=Martin |publisher=Westview Press |date=2004 |isbn=978-0-8133-4264-1 |location=Boulder, Colorado |author-link=Martin Campbell-Kelly |url-access=registration |url=https://archive.org/details/computerhistoryo02edcamp }}</ref>

In 1823, the British government gave Babbage £1700 to start work on the project. Although Babbage's design was feasible, the metalworking techniques of the era could not economically make parts in the precision and quantity required. Thus the implementation proved to be much more expensive and doubtful of success than the government's initial estimate. According to the 1830 design for Difference Engine No. 1, it would have about 25,000 parts, weigh 4 [[ton]]s,<ref>{{Cite web |title=The Engines {{!}} Babbage Engine |url=https://www.computerhistory.org/babbage/engines/ |publisher=Computer History Museum |access-date=2022-07-10 }}</ref> and operate on 20-digit numbers by sixth-order differences. In 1832, Babbage and [[Joseph Clement]] produced a small working model (one-seventh of the plan),<ref name=":0" /> which operated on 6-digit numbers by second-order differences.<ref name=":1">{{Cite book |url=https://books.google.com/books?id=QqrItgm351EC&pg=PA204 |title=A Brief History of Computing |last=O'Regan |first=Gerard |date=2012 |publisher=Springer Science & Business Media |isbn=978-1-4471-2359-0|page=204}}</ref><ref name=":2">{{Cite book |url=https://books.google.com/books?id=JckCvpOQDOoC&pg=PP1 |title=The Philosophical Breakfast Club: Four Remarkable Friends Who Transformed Science and Changed the World |last=Snyder |first=Laura J. |date=2011 |publisher=Crown/Archetype|isbn=978-0-307-71617-0 |pages=192, 210, 217 }}</ref> [[Lady Byron]] described seeing the working prototype in 1833: "We both went to see the thinking machine (or so it seems) last Monday. It raised several Nos. to the 2nd and 3rd powers, and extracted the root of a Quadratic equation."<ref>{{Cite book |title=Ada, the Enchantress of Numbers |last1=Toole |first1=Betty Alexandra |last2=Lovelace |first2=Ada |date=1998 |publisher=Strawberry Press |isbn=978-0912647180 |location=Mill Valley, California |oclc=40943907 |page=[https://archive.org/details/adaenchantressof00tool/page/38 38] |url=https://archive.org/details/adaenchantressof00tool/page/38 }}</ref> Lady Byron's daughter [[Ada Lovelace]] would later become fascinated with and work on creating the first computer program intended to solve Bernoulli's equation utilizing the difference engine. Work on the larger engine was suspended in 1833.

By the time the government abandoned the project in 1842,<ref name=":2" /><ref>{{Cite book |url=https://books.google.com/books?id=UmNJAAAAYAAJ&pg=PA387 |title=A History of the Royal Society: With Memoirs of the Presidents |last=Weld |first=Charles Richard |date=1848 |publisher=J. W. Parker |pages=387–390 }}</ref> Babbage had received and spent over £17,000 on development, which still fell short of achieving a working engine. The government valued only the machine's output (economically produced tables), not the development (at unpredictable cost) of the machine itself. Babbage refused to recognize that predicament.<ref name="Campbell-Kelly 2004" /> Meanwhile, Babbage's attention had moved on to developing an [[analytical engine]], further undermining the government's confidence in the eventual success of the difference engine. By improving the concept as an analytical engine, Babbage had made the difference engine concept obsolete, and the project to implement it an utter failure in the view of the government.<ref name="Campbell-Kelly 2004" />

The incomplete Difference Engine No. 1 was put on display to the public at the [[1862 International Exhibition]] in [[South Kensington]], London.<ref>{{Cite book |url=https://books.google.com/books?id=aDJRAAAAYAAJ |title=Cyclopaedia of useful arts, mechanical and chemical, manufactures, mining and engineering: in three volumes, illustrated by 63 steel engravings and 3063 wood engravings |last=Tomlinson |first=Charles |date=1868 |publisher=Virtue & Co. |page=136 }}</ref><ref>{{Cite book |url=https://archive.org/details/bub_gb_z7MpAAAAYAAJ|title=Official catalogue of the industrial department |date=1862 |page=[https://archive.org/details/bub_gb_z7MpAAAAYAAJ/page/n70 49] }}</ref>

Babbage went on to design his much more general analytical engine, but later designed an improved "Difference Engine No. 2" design (31-digit numbers and seventh-order differences),<ref name=":1" /> between 1846 and 1849. Babbage was able to take advantage of ideas developed for the analytical engine to make the new difference engine calculate more quickly while using fewer parts.<ref>{{cite book |title=The Philosophical Breakfast Club |last=Snyder |first=Laura J. |publisher=Broadway Brooks |date=2011 |isbn=978-0-7679-3048-2 |location=New York |url-access=registration |url=https://archive.org/details/philosophicalbre0000snyd}}</ref><ref>{{Cite book |title=The Dawn of Innovation: The First American Industrial Revolution |last=Morris |first=Charles R. |url=https://books.google.com/books?id=hRQBAwAAQBAJ&pg=PA63 |date=October 23, 2012 |publisher=PublicAffairs |isbn=9781610393577 |page=63 }}</ref>