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atio of 1 2 then enables multiplication by two so addition and subtraction are achieved multiplication is just a special case of integration namely integrating a constant function 3 contents 1 history 2 use of meccano 3 see also 4 notes 5 bibliography 6 external links history edit 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 1942 1945 a differential analyser at the naca lewis flight propulsion laboratory 1951 research on solutions for differential equations using mechanical devices discounting planimeters started at least as early as 1836 when the french physicist gaspard gustave coriolis designed a mechanical device to integrate differential equations of the first order 4 the first description of a device which could integrate differential equations of any order was published in 1876 by james thomson who was born in belfast in 1822 but lived in scotland from the age of 10 5 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 lord kelvin which represents the invention of the differential analyser 6 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 7 italian mathematician ernesto pascal also developed integraphs for the mechanical integration of differential equations and published details in 1914 8 however the first widely practical general purpose differential analyser was constructed by harold locke hazen and vannevar bush at mit 1928 1931 comprising six mechanical integrators 9 10 11 in the same year bush described this machine in a journal article as a continuous integraph 12 when he published a further article on the device in 1931 he called it a differential analyzer 13 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 14 claude shannon was hired as a research assistant in 1936 to run the differential analyzer in bush s lab 15 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 16 during the next five years three more were added at cambridge university queen s university belfast and the royal aircraft establishment in farnborough 17 one of the integrators from this proof of concept is on display in the history of computing section of the science museum in london alongside a complete manchester machine in norway the locally built 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 18 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 19 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 20 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 21 in 1947 ucla installed a differential analyser built for them by general electric at a cost of 125 000 22 by 1950 this machine had been joined by three more 23 the ucla differential analyzer appeared in 1951 s when worlds collide where it was called da early computer and plotter dating to 1944 solving complex equations again 70 years after 24 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 is one of only two still operational differential analyzers produced before the end of world war ii 24 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 25 a differential analyser may have been used in the development of the bouncing bomb used to attack german hydroelectric dams during world war ii 26 differential analysers have also been used in the calculation of soil erosion by river control authorities 27 the differential analyser was eventually rendered obsolete by electronic analogue computers and later digital computers use of meccano edit motat s meccano differential analyser in use at the cambridge university mathematics laboratory c 1937 the person on the right is dr maurice wilkes who was in charge of it at the time the model differential analyser built at manchester university in 1934 by douglas hartree and arthur porter made extensive use of meccano parts this meant that the machine was less costly to build and it proved accurate enough for the solution of many scientific problems 28 a similar machine built by j b bratt at cambridge university in 1935 is now in the museum of transport and technology motat collection in auckland new zealand 28 a memorandum written for the british military s armament research department in 1944 describes how this machine had been modified during world war ii for improved reliability and enhanced capability and identifies its wartime applications as including research on the flow of heat explosive detonations and simulations of transmission lines 29 it is estimated that about 15 meccano model differential analysers were built for serious work by scientists and researchers around the world 30 see also edit torque amplifier ball and disk integrator general purpose analog computer notes edit irwin william july 2009 the differential analyser explained auckland meccano guild retrieved 2010 07 21 archived invention of the modern computer encyclopædia britannica www britannica com retrieved 2010 07 26 john von neumann the computer and the brain part 1 p 3 yale university press the silliman memorial lectures series 1958 coriolis gaspard gustave 1836 note sur un moyen de tracer des courbes données par des équations différentielles journal de mathématiques pures et appliquées series i 1 in french 5 9 thomson james 1876 an integrating machine having a new kinematic principle proceedings of the royal society 24 164 170 262 5 doi 10 1098 rspl 1875 0033 reprinted in thomson james 1912 joseph larmor james thomson ed collected papers in physics and engineering by james thomson cambridge university press pp xvii 452 7 isbn 0 404 06422 1 hartree d r september 1940 the bush differential analyser and its implications nature 146 3697 319 bibcode 1940natur 146 319h doi 10 1038 146319a0 s2cid 40727987 lord kelvin s descriptions thomson william 1876 mechanical integration of linear differential equations of the second order with variable coefficients proceedings of the royal society 24 164 170 269 71 doi 10 1098 rspl 1875 0035 s2cid 62694536 thomson william 1876 mechanical integration of the general linear differential equation of any order with variable coefficients proceedings of the royal society 24 164 170 271 5 doi 10 1098 rspl 1875 0036 pollen anthony 1980 the great gunnery scandal the mystery of jutland collins p 23 isbn 0 00 216298 9 pascal ernesto 1914 miei integrafi per equazioni differenziali in italian naples b pellerano see also integraph karl l wildes and nilo a lindgren a century of electrical engineering and computer science at mit 1882 1982 cambridge massachusetts mit press 1985 pages 90 92 robinson tim june 2005 the meccano set computers a history of differential analyzers made from children s toys ieee control systems magazine 25 3 74 83 doi 10 1109 mcs 2005 1432602 s2cid 10075776 hartree d r september 1940 op cit 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 page 103 see also nieman s u s patents 1 servo mechanism u s patent no 1 751 645 filed 28 january 1925 issued 25 march 1930 2 servo mechanism u s patent no 1 751 647 filed 8 january 1926 issued 25 march 1930 3 synchronous amplifying control mechanism u s patent no 1 751 652 filed 8 january 1926 issued 25 march 1930 bush v gage f d stewart h r january 1927 a continuous integraph journal of the franklin institute 203 1 63 84 doi 10 1016 s0016 0032 27 90097 0 bush v october 1931 the differential analyzer a new machine for solving differential equations journal of the franklin institute 212 4 447 488 doi 10 1016 s0016 0032 31 90616 9 robinson tim june 2005 op cit citing bush vannevar 1970 pieces of the action new york ny morrow cite journal cite journal requires journal help gleick james 2011 the information a history a theory a flood ebook patheon p 342 1102 isbn 978 0 00 742311 8 robinson tim june 2005 op cit hartree d r september 1940 op cit hartree and porter wrote about the model in their paper the construction and operation of a model differential analyser memoirs and proceedings of the manchester literary philosophical society 79 51 74 1935 robinson tim 2005 12 07 other differential analyzers tim robinson s meccano computing machinery web site retrieved 2010 07 24 includes summaries of meccano differential analyzers and full scale differential analyzers holst p a oct dec 1996 svein rosseland and the oslo analyzer ieee annals of the history of computing 18 4 16 26 doi 10 1109 85 539912 randell brian ed the origins of digital computers selected papers 3rd edition 1982 berlin heidelberg new york springer verlag p 297 google books retrieved 25 july 2010 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 google books retrieved 25 july 2010 randell brian oct 1982 from analytical engine to electronic digital computer the contributions of ludgate torres and bush pdf ieee annals of the history of computing ieee computer society 4 4 327 41 doi 10 1109 mahc 1982 10042 s2cid 1737953 archived from the original pdf on 2013 09 21 retrieved 2010 07 25 ucla s bush analyzer retires to smithsonian google news computerworld 1978 01 09 retrieved 2010 07 22 the thinking machine ucla engineering archived from the original on 2010 07 10 retrieved 2010 07 22 a b hisatoshi kabata 2014 early computer dating to 1944 solving complex equations again after long reboot the asahi shimbun technology archived from the original on 2016 03 04 campbell scott m october december 2003 beatrice helen worsley canada s female computer pioneer pdf ieee annals of the history of computing ieee computer society 25 4 53 4 doi 10 1109 mahc 2003 1253890 s2cid 13499528 retrieved 2010 07 24 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 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 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 differential analyser held by motat 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 hally mike 2005 electronic brains stories from the dawn of the computer age granta p xx isbn 9781862076631 a b hartree porter 1934 1935 differential analyser auckland meccano guild retrieved 2010 07 21 cairns w j crank j lloyd e c some improvements in the construction of a small scale differential analyser and a review of recent applications armament research department theoretical research memo no 27 44 1944 see robinson tim 2008 06 07 bibliography tim robinson s meccano computing machinery web site retrieved 2010 07 26 the memorandum is now in the national archives uk piece reference defe 15 751 the national archives retrieved 2010 07 26 for the armament research department see fort halstead and cf the entry for 1944 in mod history of innovation pdf ploughshare innovations ltd retrieved 2010 07 26 irwin william 2009 07 op cit it is estimated by garry tee of auckland university that about 15 meccano model differential analysers were built for serious work by scientists and researchers around the world for garry tee see computing history displays the displays php university of auckland retrieved 2010 07 22 bibliography edit thomson james 1876 an integrating machine ha...