Editing Differential analyser (section)

==History==
[[Image:KayMcNultyAlyseSnyderSisStumpDifferentialAnalyzer.jpg|thumb|[[Kay McNulty]], Alyse Snyder, and Sis Stump operate the differential analyser in the basement of the [[Moore School of Electrical Engineering]], [[University of Pennsylvania]], [[Philadelphia, Pennsylvania]], c.&nbsp;1942–1945.]]
[[Image:NASA Differential Analyzer.jpg|thumb|A differential analyser at the [[National Advisory Committee for Aeronautics|NACA]] [[Glenn Research Center|Lewis Flight Propulsion Laboratory]], 1951]]
[[File:Nordsieck Differential Analyzer, 1965, Computer History Museum.jpg|thumb|Differential analyser built by [[Arnold Nordsieck]], at the [[Computer History Museum]]]]
Research on solutions for differential equations using mechanical devices, discounting [[planimeter]]s, started at least as early as 1836, when the French physicist [[Gaspard-Gustave Coriolis]] designed a mechanical device to integrate [[differential equation]]s of the first order.<ref>{{cite journal |first=Gaspard-Gustave |last= Coriolis| author-link=Gaspard-Gustave Coriolis |url=http://visualiseur.bnf.fr/ConsulterElementNum?O=NUMM-16380&Deb=11&Fin=15&E=PDF |title=Note sur un moyen de tracer des courbes données par des équations différentielles |journal=[[Journal de Mathématiques Pures et Appliquées]] |series=series I 1 |pages=5–9 |year=1836|language=fr}}</ref>

The first description of a device which could integrate differential equations of any order was published in 1876 by [[James Thomson (engineer)|James Thomson]], who was born in [[Belfast]] in 1822, but lived in [[Scotland]] from the age of 10.<ref>{{cite journal |author=Thomson, James |title=An Integrating Machine having a new Kinematic Principle |journal=Proceedings of the Royal Society |volume=24 |issue= 164–170|pages=262–5 |year=1876 |doi=10.1098/rspl.1875.0033 |url=https://zenodo.org/record/1432057 |doi-access=free }} Reprinted in {{cite book | last = Thomson | first = James | title = Collected Papers in Physics and Engineering by James Thomson | editor=Joseph Larmor & James Thomson | publisher = Cambridge University Press | year = 1912 | pages = xvii, 452–7| url = https://archive.org/details/collectedpapersi00thomrich | isbn = 0-404-06422-1 }}</ref> Though Thomson called his device an "integrating machine", it is his description of the device, together with the additional publication in 1876 of two further descriptions by his younger brother, [[William Thomson, 1st Baron Kelvin|Lord Kelvin]], which represents the invention of the differential analyser.<ref>{{Cite journal
  | last = Hartree
  | first = D.R.
  | author-link = Douglas Hartree
  | title = The Bush Differential Analyser and its Implications
  | journal = Nature
  | volume = 146
  | issue = 3697
  | page = 319
  |date=September 1940
  | doi = 10.1038/146319a0| bibcode = 1940Natur.146..319H
 | s2cid = 40727987
 }}. Lord Kelvin's descriptions: {{cite journal |author=Thomson, William |title=Mechanical Integration of Linear Differential Equations of the Second Order with Variable Coefficients |journal=Proceedings of the Royal Society |volume=24 |issue= 164–170|pages=269–71 |year=1876 |doi=10.1098/rspl.1875.0035 |s2cid=62694536 |doi-access=free }} {{cite journal |author=Thomson, William |title=Mechanical Integration of the general Linear Differential Equation of any Order with Variable Coefficients |journal=Proceedings of the Royal Society |volume=24 |issue= 164–170|pages=271–5 |year=1876 |doi=10.1098/rspl.1875.0036 |doi-access=free }}</ref>

One of the earliest practical uses of Thomson's concepts was a [[tide-predicting machine]] built by Kelvin starting in 1872–3. On Lord Kelvin's advice, Thomson's integrating machine was later incorporated into a [[fire-control system]] for naval gunnery being developed by [[Arthur Pollen]], resulting in an electrically driven, mechanical analogue computer, which was completed by about 1912.<ref>{{cite book |last=Pollen |first=Anthony |title=The Great Gunnery Scandal – The Mystery of Jutland |publisher=Collins |year=1980 |page=23 |isbn=0-00-216298-9}}</ref> Italian mathematician [[Ernesto Pascal]] also developed [[integraph]]s for the mechanical integration of differential equations and published details in 1914.<ref>{{cite book |title= Miei Integrafi per Equazioni Differenziali |last= Pascal |first= Ernesto |year= 1914 |publisher= B. Pellerano |location= Naples |language=it}} See also Integraph.</ref>

However, the first widely practical general-purpose differential analyser was constructed by [[Harold Locke Hazen]] and [[Vannevar Bush]] at [[Massachusetts Institute of Technology|MIT]], 1928–1931, comprising six mechanical integrators.<ref>Karl L. Wildes and Nilo A. Lindgren, ''A Century of Electrical Engineering and Computer Science at MIT, 1882-1982'' (Cambridge, Massachusetts:  MIT Press, 1985), [https://books.google.com/books?id=6ZX-GwvhcnkC&pg=PA90 pages 90-92].</ref><ref>{{Cite journal
  | last = Robinson
  | first = Tim
  | title = The Meccano Set Computers A history of differential analyzers made from children's toys
  | journal = IEEE Control Systems Magazine
  | volume = 25
  | issue = 3
  | pages = 74–83
  |date=June 2005
  |doi = 10.1109/MCS.2005.1432602| s2cid = 10075776
 | url = https://zenodo.org/record/918318
 }}. Hartree, D.R. (September 1940), ''op. cit.''</ref><ref>Bush's differential analyser used mechanical integrators. The output of each integrator was intended to drive other parts of the machine; however, the output was too feeble to do so. Hazen recognized that a "torque amplifier", which had been invented in 1925 by Henry W. Nieman and which was intended to allow workers to control heavy machinery, could be used to provide the necessary power.  See:  Stuart Bennett, ''A History of Control Engineering 1930-1955'' (London, England:  Peter Peregrinus Ltd., 1993), [https://books.google.com/books?id=VD_b81J3yFoC&pg=PA103 page 103].  See also Nieman's U.S. patents:  '''(1)''' "Servo mechanism", [http://patimg1.uspto.gov/.piw?docid=01751645&PageNum=1&&IDKey=4EA8A1F40C57&HomeUrl=http://pimg-piw.uspto.gov/ U.S. patent no. 1,751,645] (filed: 28 January 1925; issued:  25 March 1930); '''(2)''' "Servo mechanism", [http://patimg1.uspto.gov/.piw?docid=01751647&PageNum=1&&IDKey=5001BCE94739&HomeUrl=http://pimg-piw.uspto.gov/ U.S. patent no. 1,751,647] {{Webarchive|url=https://web.archive.org/web/20180807185758/http://patimg1.uspto.gov/.piw?docid=01751647&PageNum=1&&IDKey=5001BCE94739&HomeUrl=http%3A%2F%2Fpimg-piw.uspto.gov%2F |date=2018-08-07 }} (filed: 8 January 1926; issued: 25 March 1930); '''(3)''' "Synchronous amplifying control mechanism", [http://patimg2.uspto.gov/.piw?Docid=01751652&homeurl=http%3A%2F%2Fpatft.uspto.gov%2Fnetacgi%2Fnph-Parser%3FSect1%3DPTO1%2526Sect2%3DHITOFF%2526d%3DPALL%2526p%3D1%2526u%3D%25252Fnetahtml%25252FPTO%25252Fsrchnum.htm%2526r%3D1%2526f%3DG%2526l%3D50%2526s1%3D1,751,652.PN.%2526OS%3DPN%2F1,751,652%2526RS%3DPN%2F1,751,652&PageNum=&Rtype=&SectionNum=&idkey=NONE&Input=View+first+page U.S. patent no. 1,751,652] {{Webarchive|url=https://web.archive.org/web/20140628104954/http://books.google.com/books?id=VD_b81J3yFoC&pg=PA103&lpg=PA103 |date=2014-06-28 }} (filed: 8 January 1926; issued: 25 March 1930).</ref> In the same year, Bush described this machine in a journal article as a "continuous integraph".<ref>{{Cite journal
  | last1 = Bush
  | first1 = V.
  | author-link = Vannevar Bush
  | last2 = Gage
  | first2 = F.D.
  | last3 = Stewart
  | first3 = H.R.
  | title = A continuous integraph
  | journal = Journal of the Franklin Institute
  | volume = 203
  | issue = 1
  | pages = 63–84
  |date=January 1927
  | doi = 10.1016/S0016-0032(27)90097-0}}.</ref> When he published a further article on the device in 1931, he called it a "differential analyzer".<ref>{{Cite journal
  | last = Bush
  | first = V.
  | title = The differential analyzer. A new machine for solving differential equations
  | journal = Journal of the Franklin Institute
  | volume = 212
  | issue = 4
  | pages = 447–488
  |date=October 1931
  | doi = 10.1016/S0016-0032(31)90616-9}}.</ref> In this article, Bush stated that "[the] present device incorporates the same basic idea of interconnection of integrating units as did [Lord Kelvin's]. In detail, however, there is little resemblance to the earlier model." According to his 1970 autobiography, Bush was "unaware of Kelvin’s work until after the first differential analyzer was operational."<ref>Robinson, Tim (June 2005), ''op. cit.'', citing {{Cite journal
  | last = Bush
  | first = Vannevar
  | title = Pieces of the Action
  | place = New York NY
  | publisher = Morrow
  | year = 1970}}.</ref>  [[Claude Shannon]] was hired as a research assistant in 1936 to run the differential analyzer in Bush's lab.<ref>{{cite book |last=Gleick|first=James|title=The Information: A History, a Theory, a Flood (ebook) |publisher=Patheon|year=2011|page=342/1102 |isbn=978-0-00-742311-8}}</ref>

[[Douglas Hartree]] of [[Manchester University]] brought Bush's design to England, where he constructed his first "[[proof of concept]]" model with his student, Arthur Porter, during 1934. As a result of this, the university acquired a full-scale machine incorporating four mechanical integrators in March 1935, which was built by [[Metropolitan-Vickers]], and was, according to Hartree, "[the] first machine of its kind in operation outside the United States".<ref>Robinson, Tim (June 2005), ''op. cit.'', Hartree, D.R. (September 1940), ''op. cit.'' Hartree and Porter wrote about the model in their paper {{Cite journal
  | title = The Construction and Operation of a Model Differential Analyser
  | journal = Memoirs and Proceedings of the Manchester Literary & Philosophical Society
  | volume = 79
  | pages = 51–74
  | year = 1935}}.</ref> During the next five years three more were added, at [[University of Cambridge|Cambridge University]], [[Queen's University Belfast]], and the [[Royal Aircraft Establishment]] in Farnborough.<ref>{{Cite web | last = Robinson | first = Tim | title = Other Differential Analyzers | publisher =Tim Robinson's Meccano Computing Machinery web site | date = 2005-12-07 | url = http://www.meccano.us/differential_analyzers/other_da/index.html | access-date = 2010-07-24}} Includes summaries of "Meccano Differential Analyzers" and "Full Scale Differential Analyzers".</ref>  One of the integrators from this proof of concept is on display in the History of Computing section of the [[Science Museum (London)|Science Museum]] in London, alongside a complete Manchester machine.

In [[Norway]], the locally built [[Oslo Analyzer|Oslo Analyser]] was finished during 1938, based on the same principles as the MIT machine. This machine had 12 integrators, and was the largest analyser built for a period of four years.<ref>{{cite journal |author=Holst, P.A. |title=Svein Rosseland and the Oslo analyzer |journal=IEEE Annals of the History of Computing |volume=18 |issue=4 |pages=16–26 |date=Oct–Dec 1996 |doi=10.1109/85.539912 }}</ref>

In the United States, further differential analysers were built at the [[Ballistic Research Laboratory]] in [[Maryland]] and in the basement of the Moore School of Electrical Engineering at the University of Pennsylvania during the early 1940s.<ref>[[Brian Randell|Randell, Brian]] (ed.), ''The Origins of Digital Computers Selected Papers'' (3rd edition, 1982), Berlin, Heidelberg, New York: Springer-Verlag. p. 297. [https://books.google.com/books?id=Dwj4RmcZ1AoC&dq=differential+analyzer+Moore+School+of+Electrical+Engineering&pg=PA297 Google Books]. Retrieved 25 July 2010.</ref> The latter was used extensively in the computation of [[artillery]] firing tables prior to the invention of the [[ENIAC]], which, in many ways, was modelled on the differential analyser.<ref>Bunch, B. & Hellemans, A., ''The History of Science and Technology: A Browser's Guide to the Great Discoveries, Inventions, and the People who Made Them, from the Dawn of Time to Today'' (2004), New York: Houghton Mifflin, p. 535. [https://books.google.com/books?id=MlQ7NK9dw7IC&dq=eniac+modeled+on+bush+differential+analyzer&pg=PA535 Google Books]. Retrieved 25 July 2010.</ref> Also in the early 1940s, with [[Samuel H. Caldwell]], one of the initial contributors during the early 1930s, Bush attempted an electrical, rather than mechanical, variation, but the [[digital computer]] built elsewhere had much greater promise and the project ceased.<ref>{{cite journal |author-last=Randell |author-first=Brian |author-link=Brian Randell |title=From Analytical Engine to Electronic Digital Computer: The Contributions of Ludgate, Torres, and Bush |journal=IEEE Annals of the History of Computing |volume=4 |issue=4 |pages=327–41 |publisher=IEEE Computer Society |date=Oct 1982 |url=http://www.cs.ncl.ac.uk/publications/articles/papers/398.pdf |doi=10.1109/MAHC.1982.10042 |s2cid=1737953 |access-date=2010-07-25 |url-status=dead |archive-url=https://web.archive.org/web/20130921055055/http://www.cs.ncl.ac.uk/publications/articles/papers/398.pdf |archive-date=2013-09-21 }}</ref> In 1947, [[University of California, Los Angeles|UCLA]] installed a differential analyser built for them by [[General Electric]] at a cost of $125,000.<ref name=UCLADA>{{cite magazine|url=https://news.google.com/newspapers?nid=849&dat=19780109&id=R50oAAAAIBAJ&pg=6329,375623|format=Google News|title= UCLA's Bush Analyzer Retires to Smithsonian|access-date=2010-07-22|magazine=Computerworld|date=1978-01-09}}</ref> By 1950, this machine had been joined by three more.<ref name=UCLA4DA>{{cite web|url=http://www.engineer.ucla.edu/explore/history/major-research-highlights/the-thinking-machine |title=The Thinking Machine |access-date=2010-07-22 |publisher=UCLA Engineering |url-status=dead |archive-url=https://web.archive.org/web/20100710100707/https://www.engineer.ucla.edu/explore/history/major-research-highlights/the-thinking-machine |archive-date=2010-07-10 }}</ref> The UCLA differential analyzer appeared in 1950's [[Destination Moon (film)|''Destination Moon'']], and the same footage in 1951's [[When Worlds Collide (1951 film)|''When Worlds Collide'']], where it was called "DA". A different shot appears in 1956's ''[[Earth vs. the Flying Saucers]]''.

[[File:ImgAJ201412020061M-b.png|thumb|Early computer-and-plotter dating to 1944, solving complex equations again 70 years later.<ref name="KABATA"/>]]
At [[Osaka Imperial University]] (present-day [[Osaka University]]) around 1944, 
a complete differential analyser machine was developed (illustrated) to calculate the movement of an object and other problems with mechanical components, and then draws graphs on paper with a pen. It was later transferred to the [[Tokyo University of Science]] and has been displayed at the school's Museum of Science in Shinjuku Ward. Restored in 2014, it is one of only two still operational differential analyzers produced before the end of World War II.<ref name="KABATA">{{citation  
 | author=Hisatoshi Kabata 
 |year =2014 
 |url=http://ajw.asahi.com/article/sci_tech/technology/AJ201412020060 
 |title=Early computer dating to 1944 solving complex equations again after long 'reboot'
 |journal= The Asahi Shimbun/Technology 
 |archive-url=https://web.archive.org/web/20160304051419/http://ajw.asahi.com/article/sci_tech/technology/AJ201412020060 
 |archive-date=2016-03-04 
 |url-status=dead
}}</ref>

In Canada, a differential analyser was constructed at the [[University of Toronto]] in 1948 by [[Beatrice Helen Worsley]], but it appears to have had little or no use.<ref>{{cite journal |author=Campbell, Scott M. |title=Beatrice Helen Worsley: Canada's Female Computer Pioneer |journal=IEEE Annals of the History of Computing |volume=25 |issue=4 |pages=53–4 |publisher=IEEE Computer Society |date=October–December 2003 |url=http://individual.utoronto.ca/scampbell/campbell03.pdf |doi=10.1109/MAHC.2003.1253890 |s2cid=13499528 |access-date=2010-07-24 |quote= [Worsley's] research was suggested by Samuel H. Caldwell, of MIT’s electrical engineering department, who had helped Vannevar Bush design recent analyzers. … Over six weeks during summer 1948, Worsley constructed a differential analyzer using Meccano…, based on Douglas Hartree and Arthur Porter’s 1935 article. Constructed from about CAD$75 worth of Meccano, the analyzer was minimally modified from the original design but offered slight improvements to the electrical power distribution system, the design of the torque amplifiers, and the output pen support. Unfortunately, there is no information regarding what use, if any, the analyzer was put to or why Worsley built it}} For more on Beatrice Worsley, see [[UTEC#UTEC|UTEC]].</ref>

A differential analyser may have been used in the development of the [[bouncing bomb]], used to attack [[Nazi Germany|German]] [[Hydroelectricity|hydroelectric dams]] during [[World War II]].<ref>Irwin, William (2009-07). ''Op. cit.'' "It is rumoured that a differential analyser was used in the development of the "bouncing bomb" by Barnes Wallis for the "Dam Busters" attack on the Ruhr valley hydroelectric dams in WW2. This was first mentioned in [[Museum of Transport and Technology|MOTAT]] [New Zealand] literature in 1973. However after extensive enquiries and literature searches over the last few years, no evidence can be found that the <nowiki>[</nowiki>[http://www.nzmuseums.co.nz/account/3031/object/955 differential analyser held by MOTAT] {{Webarchive|url=https://web.archive.org/web/20180226165410/http://nzmuseums.co.nz/account/3031/object/955 |date=2018-02-26 }}, nor any other differential analyser, was used for this purpose. Considering the secrecy surrounding war time activities at the time it could still be possible, but most people from that era are now deceased. Two remaining personalities still alive from that era were consulted, namely Arthur Porter and [[Maurice Wilkes]], but neither could substantiate the rumour."</ref> Differential analysers have also been used in the calculation of [[soil erosion]] by river control authorities.<ref>{{citation|title=Electronic Brains: Stories from the Dawn of the Computer Age|first=Mike|last=Hally|publisher=Granta|year=2005|isbn=9781862076631|page=xx}}.</ref>

The differential analyser was eventually rendered obsolete by [[electronic analogue computer]]s and, later, digital computers.

{{Further|Digital differential analyzer}}