70:
57:, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operationally. The original machines could not add, but then it was noticed that if the two wheels of a rear differential are turned, the drive shaft will compute the average of the left and right wheels. Addition and subtraction are then achieved by using a simple gear ratio of 1:2; the gear ratio provides multiplication by two, and multiplying the average of two values by two gives their sum. Multiplication is just a special case of integration, namely integrating a
177:, 1928–1931, comprising six mechanical integrators. In the same year, Bush described this machine in a journal article as a "continuous integraph". When he published a further article on the device in 1931, he called it a "differential analyzer". In this article, Bush stated that " present device incorporates the same basic idea of interconnection of integrating units as did . 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."
27:
93:
283:
357:
829:
1265:
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
388:. 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
1300:, 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
792:
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
1264:
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.
298:) 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
375:
parts: this meant that the machine was less costly to build, and it proved "accurate enough for the solution of many scientific problems". A similar machine built by J.B. Bratt at
Cambridge University in 1935 is now in the
134:
from the age of 10. 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,
1285:"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
817:
1437:"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
302:
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.
195:" 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
237:
and in the basement of the Moore School of
Electrical Engineering at the University of Pennsylvania during the early 1940s. The latter was used extensively in the computation of
226:
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.
1174:
1057:
814:
806:
1623:
a mechanical differential analyser: it is included because the author clearly felt that the only way to introduce such an innovation was to describe it as an "
1071:
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
455:
199:, and was, according to Hartree, " first machine of its kind in operation outside the United States". During the next five years three more were added, at
832:
519:
1074:
395:
It is estimated that "about 15 Meccano model
Differential Analysers were built for serious work by scientists and researchers around the world".
1392:
1203:
1289:
literature in 1973. However after extensive enquiries and literature searches over the last few years, no evidence can be found that the [
1091:
434:
97:
1146:
470:
249:, one of the initial contributors during the early 1930s, Bush attempted an electrical, rather than mechanical, variation, but the
371:
The model differential analyser built at
Manchester University in 1934 by Douglas Hartree and Arthur Porter made extensive use of
1387:
261:
at a cost of $ 125,000. By 1950, this machine had been joined by three more. The UCLA differential analyzer appeared in 1950's
77:
1610:, London: Longmans, Green (this is the only book that describes how to set up and operate a mechanical differential analyser).
1178:
154:, resulting in an electrically driven, mechanical analogue computer, which was completed by about 1912. Italian mathematician
1678:
955:
514:
363:
Meccano differential analyser in use at the
Cambridge University Mathematics Laboratory, c. 1937. The person on the right is
254:
174:
1293:
211:
in Farnborough. One of the integrators from this proof of concept is on display in the History of Computing section of the
146:
built by Kelvin starting in 1872–3. On Lord Kelvin's advice, Thomson's integrating machine was later incorporated into a
1286:
377:
360:
1323:
701:
571:
136:
122:
The first description of a device which could integrate differential equations of any order was published in 1876 by
793:
to allow workers to control heavy machinery, could be used to provide the necessary power. See: Stuart Bennett,
414:
268:
1369:
Some Improvements in the Construction of a Small Scale Differential Analyser and a Review of Recent Applications
1585:
Hartree, D. R.; Porter, Porter (1934–1935), "The construction and operation of a model differential analyser",
1683:
346:
230:
204:
20:
1533:"Mechanical Integration of the general Linear Differential Equation of any Order with Variable Coefficients"
661:"Mechanical Integration of the general Linear Differential Equation of any Order with Variable Coefficients"
339:
275:
208:
1619:(RLE, Technical Report 90, MIT. Note that this paper describes a very early electronic analogue computer,
1600:
A mathematical survey of computing devices with an appendix on an error analysis of differential analyzers
1688:
299:
1498:"Mechanical Integration of Linear Differential Equations of the Second Order with Variable Coefficients"
880:
Bush, V. (October 1931). "The differential analyzer. A new machine for solving differential equations".
628:"Mechanical Integration of Linear Differential Equations of the Second Order with Variable Coefficients"
1092:"From Analytical Engine to Electronic Digital Computer: The Contributions of Ludgate, Torres, and Bush"
85:
81:
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931:
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1410:
1001:
510:
409:
123:
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30:
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262:
212:
200:
143:
245:, which, in many ways, was modelled on the differential analyser. Also in the early 1940s, with
1122:
1013:
Includes summaries of "Meccano Differential Analyzers" and "Full Scale Differential Analyzers".
310:
1643:
798:
918:
737:
306:
188:
165:
However, the first widely practical general-purpose differential analyser was constructed by
116:
100:
50:
1653:
599:
196:
19:
This article is about analogue differential analysers. For the digital implementation, see
1654:
Professor Stephen Boyd at Stanford University provides a brief explanation of its working.
286:
Early computer-and-plotter dating to 1944, solving complex equations again 70 years later.
181:
was hired as a research assistant in 1936 to run the differential analyzer in Bush's lab.
8:
1226:
752:"The Meccano Set Computers A history of differential analyzers made from children's toys"
561:
147:
603:
162:
for the mechanical integration of differential equations and published details in 1914.
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1519:
1249:
1114:
771:
649:
615:
389:
246:
166:
107:
Research on solutions for differential equations using mechanical devices, discounting
76:, Alyse Snyder, and Sis Stump operate the differential analyser in the basement of the
893:
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567:
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58:
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775:
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619:
26:
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1544:
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1479:
1241:
1204:"Early computer dating to 1944 solving complex equations again after long 'reboot'"
1118:
1106:
1032:
889:
861:
763:
672:
639:
607:
547:
515:"Note sur un moyen de tracer des courbes données par des équations différentielles"
404:
324:
295:
258:
250:
192:
1559:
1297:
836:
821:
587:
500:, Part 1, p.3, Yale University Press, The Silliman Memorial Lectures Series, 1958
184:
46:
1371:, Armament Research Department Theoretical Research Memo. No. 27/44, 1944 (see
1301:
364:
178:
155:
1245:
982:
Memoirs and Proceedings of the Manchester Literary & Philosophical Society
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1049:
849:
767:
317:
223:
170:
151:
92:
1587:
Memoirs and Proceedings of the Manchester Literary and Philosophical Society
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1056:(3rd edition, 1982), Berlin, Heidelberg, New York: Springer-Verlag. p. 297.
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677:
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627:
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332:
328:
321:
1637:
1374:
734:
A Century of Electrical Engineering and Computer Science at MIT, 1882-1982
253:
built elsewhere had much greater promise and the project ceased. In 1947,
1493:
590:(September 1940). "The Bush Differential Analyser and its Implications".
385:
73:
282:
229:
In the United States, further differential analysers were built at the
108:
1036:
852:; Gage, F.D.; Stewart, H.R. (January 1927). "A continuous integraph".
1599:
1023:
Holst, P.A. (Oct–Dec 1996). "Svein Rosseland and the Oslo analyzer".
611:
356:
316:
A differential analyser may have been used in the development of the
238:
159:
1615:
1467:
535:
34:
980:"The Construction and Operation of a Model Differential Analyser".
913:
Bush, Vannevar (1970). "Pieces of the Action". New York NY: Morrow.
751:
381:
331:. Differential analysers have also been used in the calculation of
234:
131:
54:
437:. Auckland Meccano Guild. Archived from the original on 2018-11-24
191:
brought Bush's design to England, where he constructed his first "
372:
127:
1269:
560:
Thomson, James (1912). Joseph Larmor & James Thomson (ed.).
273:, where it was called "DA". A different shot appears in 1956's
219:
142:
One of the earliest practical uses of Thomson's concepts was a
139:, which represents the invention of the differential analyser.
111:, started at least as early as 1836, when the French physicist
338:
The differential analyser was eventually rendered obsolete by
242:
1316:
Electronic Brains: Stories from the Dawn of the Computer Age
563:
Collected Papers in Physics and Engineering by James Thomson
1227:"Beatrice Helen Worsley: Canada's Female Computer Pioneer"
305:
In Canada, a differential analyser was constructed at the
1468:"An Integrating Machine having a new Kinematic Principle"
536:"An Integrating Machine having a new Kinematic Principle"
978:
Hartree and Porter wrote about the model in their paper
1644:
The Differential Analyser Explained (updated July 2009)
1377:. Tim Robinson's Meccano Computing Machinery web site
1004:. Tim Robinson's Meccano Computing Machinery web site
948:
The Information: A History, a Theory, a Flood (ebook)
566:. Cambridge University Press. pp. xvii, 452–7.
257:
installed a differential analyser built for them by
215:
in London, alongside a complete Manchester machine.
1584:
1342:
1224:
809:(filed: 28 January 1925; issued: 25 March 1930);
694:The Great Gunnery Scandal – The Mystery of Jutland
797:(London, England: Peter Peregrinus Ltd., 1993),
1660:
1530:
1492:
1201:
1054:The Origins of Digital Computers Selected Papers
824:(filed: 8 January 1926; issued: 25 March 1930);
658:
625:
454:: CS1 maint: bot: original URL status unknown (
848:
839:(filed: 8 January 1926; issued: 25 March 1930).
313:, but it appears to have had little or no use.
1557:
1465:
736:(Cambridge, Massachusetts: MIT Press, 1985),
533:
1564:Bulletin of the American Mathematical Society
1367:Cairns, W. J., Crank, J., & Lloyd, E. C.
1304:, but neither could substantiate the rumour."
1147:"UCLA's Bush Analyzer Retires to Smithsonian"
1649:Tim Robinson's Meccano Differential Analyser
1404:For the "Armament Research Department", see
1225:Campbell, Scott M. (October–December 2003).
1073:(2004), New York: Houghton Mifflin, p. 535.
828:"Synchronous amplifying control mechanism",
520:Journal de Mathématiques Pures et Appliquées
241:firing tables prior to the invention of the
1022:
1640:which focuses on the Differential Analyzer
1593:: 51–73, reprinted as a pamphlet July 1935
1440:"Computing History Displays: The Displays"
795:A History of Control Engineering 1930-1955
719:Miei Integrafi per Equazioni Differenziali
115:designed a mechanical device to integrate
1575:
1548:
1513:
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676:
643:
551:
1372:
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999:
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355:
281:
91:
68:
25:
1234:IEEE Annals of the History of Computing
1167:
1099:IEEE Annals of the History of Computing
1086:
1025:IEEE Annals of the History of Computing
586:
559:
1661:
1192:
1139:
945:
716:
691:
78:Moore School of Electrical Engineering
1332:
1313:
732:Karl L. Wildes and Nilo A. Lindgren,
435:"The Differential Analyser Explained"
432:
367:, who was in charge of it at the time
150:for naval gunnery being developed by
1105:(4). IEEE Computer Society: 327–41.
912:
879:
801:. See also Nieman's U.S. patents:
1616:An electronic differential analyzer
1291:differential analyser held by MOTAT
721:(in Italian). Naples: B. Pellerano.
13:
1268:For more on Beatrice Worsley, see
1240:(4). IEEE Computer Society: 53–4.
1177:. UCLA Engineering. Archived from
974:, Hartree, D.R. (September 1940),
780:. Hartree, D.R. (September 1940),
471:"Invention of the modern computer"
378:Museum of Transport and Technology
101:Lewis Flight Propulsion Laboratory
14:
1705:
1631:
882:Journal of the Franklin Institute
854:Journal of the Franklin Institute
351:
267:, and the same footage in 1951's
1597:Worsley, Beatrice Helen (1947).
1537:Proceedings of the Royal Society
1502:Proceedings of the Royal Society
1472:Proceedings of the Royal Society
1408:, and cf. the entry for 1944 in
665:Proceedings of the Royal Society
632:Proceedings of the Royal Society
540:Proceedings of the Royal Society
1577:10.1090/S0002-9904-1936-06390-1
1459:
1427:
1361:
1307:
1275:
1218:
1080:
1069:Bunch, B. & Hellemans, A.,
1063:
1043:
1016:
993:
964:
939:
901:
873:
842:
786:
743:
415:General purpose analog computer
342:and, later, digital computers.
96:A differential analyser at the
1343:Hartree & Porter 1934–1935
1002:"Other Differential Analyzers"
726:
710:
685:
624:. Lord Kelvin's descriptions:
580:
527:
523:. series I 1 (in French): 5–9.
503:
490:
463:
426:
335:by river control authorities.
1:
1416:. Ploughshare Innovations Ltd
1393:"Piece reference DEFE 15/751"
950:. Patheon. p. 342/1102.
894:10.1016/S0016-0032(31)90616-9
866:10.1016/S0016-0032(27)90097-0
756:IEEE Control Systems Magazine
347:Digital differential analyzer
340:electronic analogue computers
231:Ballistic Research Laboratory
21:Digital Differential Analyzer
1679:Electro-mechanical computers
1386:). The memorandum is now in
1373:Robinson, Tim (2008-06-07).
1208:The Asahi Shimbun/Technology
1000:Robinson, Tim (2005-12-07).
433:Irwin, William (July 2009).
276:Earth vs. the Flying Saucers
209:Royal Aircraft Establishment
16:Mechanical analogue computer
7:
1411:"MoD History of Innovation"
970:Robinson, Tim (June 2005),
907:Robinson, Tim (June 2005),
750:Robinson, Tim (June 2005).
398:
300:Tokyo University of Science
10:
1710:
1433:Irwin, William (2009-07).
1281:Irwin, William (2009-07).
498:The Computer and the Brain
344:
205:Queen's University Belfast
86:Philadelphia, Pennsylvania
82:University of Pennsylvania
64:
18:
1608:The Differential Analyser
1531:Thomson, William (1876).
1246:10.1109/MAHC.2003.1253890
1202:Hisatoshi Kabata (2014),
1077:. Retrieved 25 July 2010.
1060:. Retrieved 25 July 2010.
830:U.S. patent no. 1,751,652
815:U.S. patent no. 1,751,647
807:U.S. patent no. 1,751,645
659:Thomson, William (1876).
626:Thomson, William (1876).
511:Coriolis, Gaspard-Gustave
292:Osaka Imperial University
1627:differential analyser").
1445:. University of Auckland
1350:. Auckland Meccano Guild
768:10.1109/MCS.2005.1432602
717:Pascal, Ernesto (1914).
692:Pollen, Anthony (1980).
420:
410:Ball-and-disk integrator
113:Gaspard-Gustave Coriolis
31:Ball-and-disc integrator
1603:(Master's Thesis, MIT).
1560:"Instrumental analysis"
1558:Bush, Vannevar (1936).
1466:Thomson, James (1876).
1395:. The National Archives
1348:"Differential Analyser"
1111:10.1109/MAHC.1982.10042
696:. Collins. p. 23.
534:Thomson, James (1876).
476:Encyclopædia Britannica
144:tide-predicting machine
1550:10.1098/rspl.1875.0036
1515:10.1098/rspl.1875.0035
1485:10.1098/rspl.1875.0033
1318:, Granta, p. xx,
1175:"The Thinking Machine"
946:Gleick, James (2011).
926:Cite journal requires
678:10.1098/rspl.1875.0036
645:10.1098/rspl.1875.0035
553:10.1098/rspl.1875.0033
380:(MOTAT) collection in
368:
311:Beatrice Helen Worsley
287:
130:in 1822, but lived in
117:differential equations
104:
89:
51:differential equations
38:
1613:MacNee, A.B. (1948).
1388:The National Archives
359:
345:Further information:
307:University of Toronto
285:
189:Manchester University
95:
72:
43:differential analyser
29:
1684:Mechanical computers
1314:Hally, Mike (2005),
479:. www.britannica.com
222:, the locally built
201:Cambridge University
197:Metropolitan-Vickers
119:of the first order.
88:, c. 1942–1945.
1508:(164–170): 269–71.
813:"Servo mechanism",
805:"Servo mechanism",
723:See also Integraph.
638:(164–170): 269–71.
604:1940Natur.146..319H
270:When Worlds Collide
148:fire-control system
1689:Mathematical tools
1606:Crank, J. (1947).
1543:(164–170): 271–5.
1478:(164–170): 262–5.
1296:2018-02-26 at the
835:2014-06-28 at the
820:2018-08-07 at the
671:(164–170): 271–5.
546:(164–170): 262–5.
496:John von Neumann,
390:transmission lines
369:
325:hydroelectric dams
288:
247:Samuel H. Caldwell
167:Harold Locke Hazen
126:, who was born in
105:
90:
49:designed to solve
39:
1638:Vannevar Bush bio
1037:10.1109/85.539912
957:978-0-00-742311-8
365:Dr Maurice Wilkes
320:, used to attack
59:constant function
47:analogue computer
1701:
1674:Analog computers
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1494:Thomson, William
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296:Osaka University
264:Destination Moon
259:General Electric
251:digital computer
193:proof of concept
45:is a mechanical
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1570:(10): 649–69.
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1375:"Bibliography"
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1302:Maurice Wilkes
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1088:Randell, Brian
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1050:Randell, Brian
1042:
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988:: 51–74. 1935.
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888:(4): 447–488.
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156:Ernesto Pascal
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1447:. Retrieved
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1379:. Retrieved
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1352:. Retrieved
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1257:. Retrieved
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1212:the original
1207:
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1179:the original
1169:
1158:. Retrieved
1156:. 1978-01-09
1153:
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1130:. Retrieved
1123:the original
1102:
1098:
1090:(Oct 1982).
1082:
1075:Google Books
1070:
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329:World War II
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738:pages 90-92
386:New Zealand
309:in 1948 by
137:Lord Kelvin
109:planimeters
74:Kay McNulty
55:integration
1663:Categories
1625:electronic
1449:2010-07-22
1420:2010-07-26
1399:2010-07-26
1381:2010-07-26
1354:2010-07-21
1259:2010-07-24
1185:2010-07-22
1160:2010-07-22
1132:2010-07-25
1008:2010-07-24
483:2010-07-26
441:2010-07-21
207:, and the
160:integraphs
1694:Integrals
911:, citing
239:artillery
1524:62694536
1496:(1876).
1435:Op. cit.
1294:Archived
1283:Op. cit.
1254:13499528
976:op. cit.
972:op. cit.
909:op. cit.
850:Bush, V.
833:Archived
818:Archived
799:page 103
782:op. cit.
776:10075776
654:62694536
620:40727987
513:(1836).
460:Archived
450:cite web
399:See also
382:Auckland
235:Maryland
132:Scotland
1119:1737953
1052:(ed.),
600:Bibcode
373:Meccano
361:MOTAT's
327:during
128:Belfast
65:History
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1390:, UK:
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592:Nature
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322:German
220:Norway
103:, 1951
1520:S2CID
1443:(php)
1414:(PDF)
1287:MOTAT
1250:S2CID
1230:(PDF)
1126:(PDF)
1115:S2CID
1095:(PDF)
772:S2CID
650:S2CID
616:S2CID
421:Notes
243:ENIAC
35:tides
1320:ISBN
1270:UTEC
952:ISBN
932:help
698:ISBN
568:ISBN
456:link
255:UCLA
169:and
98:NACA
41:The
1621:not
1572:doi
1545:doi
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1480:doi
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