The differential analyser is a mechanical
analogue computer designed to solve
differential equations by
integration, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operationally.
In addition to the integrator devices, the machine used an epicyclic differential mechanism to perform addition or subtraction - similar to that used on a front-wheel drive car, where the speed of the two output shafts (driving the wheels) may differ but the speeds add up to the speed of the input shaft. Multiplication/division by integer values was achieved by simple gear ratios; multiplication by fractional values was achieved by means of a multiplier table, where a human operator would have to keep a stylus tracking the slope of a bar. A variant of this human-operated table was used to implement other functions such as polynomials.
History
Research on solutions for differential equations using mechanical devices, discounting
planimeter
A planimeter, also known as a platometer, is a measuring instrument used to determine the area of an arbitrary two-dimensional shape.
Construction
There are several kinds of planimeters, but all operate in a similar way. The precise way in whic ...
s, started at least as early as 1836, when the French physicist
Gaspard-Gustave Coriolis
Gaspard-Gustave de Coriolis (; 21 May 1792 – 19 September 1843) was a French mathematician, mechanical engineer and scientist. He is best known for his work on the supplementary forces that are detected in a rotating frame of reference, le ...
designed a mechanical device to integrate
differential equations of the first order.
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
Belfast (, , , ; from ) is the capital city and principal port of Northern Ireland, standing on the banks of the River Lagan and connected to the open sea through Belfast Lough and the North Channel (Great Britain and Ireland), North Channel ...
in 1822, but lived in
Scotland
Scotland is a Countries of the United Kingdom, country that is part of the United Kingdom. It contains nearly one-third of the United Kingdom's land area, consisting of the northern part of the island of Great Britain and more than 790 adjac ...
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,
Lord Kelvin
William Thomson, 1st Baron Kelvin (26 June 182417 December 1907), was a British mathematician, Mathematical physics, mathematical physicist and engineer. Born in Belfast, he was the Professor of Natural Philosophy (Glasgow), professor of Natur ...
, which represents the invention of the differential analyser.
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
Arthur Joseph Hungerford Pollen (13 September 1866 – 28 January 1937) was an English journalist, businessman, and commentator on naval affairs who devised a new computerised fire-control system for use on battleships prior to the First World W ...
, resulting in an electrically driven, mechanical analogue computer, which was completed by about 1912. Italian mathematician
Ernesto Pascal also developed
integraphs for the mechanical integration of differential equations and published details in 1914.
However, the first widely practical general-purpose differential analyser was constructed by
Harold Locke Hazen and
Vannevar Bush
Vannevar Bush ( ; March 11, 1890 – June 28, 1974) was an American engineer, inventor and science administrator, who during World War II, World War II headed the U.S. Office of Scientific Research and Development (OSRD), through which almo ...
at
MIT
The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...
, 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 "
hepresent device incorporates the same basic idea of interconnection of integrating units as did
ord 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."
Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and the man who laid the foundations of th ...
was hired as a research assistant in 1936 to run the differential analyzer in Bush's lab.
Douglas Hartree of
Manchester University
The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The University of Manchester is c ...
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
Metropolitan-Vickers, Metrovick, or Metrovicks, was a British heavy electrical engineering company of the early-to-mid 20th century formerly known as British Westinghouse. Highly diversified, it was particularly well known for its industrial el ...
, and was, according to Hartree, "
hefirst machine of its kind in operation outside the United States". During the next five years three more were added, at
Cambridge University
The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...
,
Queen's University Belfast
The Queen's University of Belfast, commonly known as Queen's University Belfast (; abbreviated Queen's or QUB), is a public research university in Belfast, Northern Ireland, United Kingdom. The university received its charter in 1845 as part of ...
, and the
Royal Aircraft Establishment
The Royal Aircraft Establishment (RAE) was a British research establishment, known by several different names during its history, that eventually came under the aegis of the Ministry of Defence (United Kingdom), UK Ministry of Defence (MoD), bef ...
in Farnborough. One of the integrators from this proof of concept is on display in the History of Computing section of the
Science Museum
A science museum is a museum devoted primarily to science. Older science museums tended to concentrate on static displays of objects related to natural history, paleontology, geology, Industry (manufacturing), industry and Outline of industrial ...
in London, alongside a complete Manchester machine.
In
Norway
Norway, officially the Kingdom of Norway, is a Nordic countries, Nordic country located on the Scandinavian Peninsula in Northern Europe. The remote Arctic island of Jan Mayen and the archipelago of Svalbard also form part of the Kingdom of ...
, 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.
In the United States, further differential analysers were built at the
Ballistic Research Laboratory
The Ballistic Research Laboratory (BRL) was a research facility under the U.S. Army Ordnance Corps and later the U.S. Army Materiel Command that specialized in ballistics as well as vulnerability and lethality analysis. Situated at Aberdeen Pr ...
in
Maryland
Maryland ( ) is a U.S. state, state in the Mid-Atlantic (United States), Mid-Atlantic region of the United States. It borders the states of Virginia to its south, West Virginia to its west, Pennsylvania to its north, and Delaware to its east ...
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
artillery
Artillery consists of ranged weapons that launch Ammunition, munitions far beyond the range and power of infantry firearms. Early artillery development focused on the ability to breach defensive walls and fortifications during sieges, and l ...
firing tables prior to the invention of the
ENIAC
ENIAC (; Electronic Numerical Integrator and Computer) was the first Computer programming, programmable, Electronics, electronic, general-purpose digital computer, completed in 1945. Other computers had some of these features, but ENIAC was ...
, which, in many ways, was modelled on the differential analyser. 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
A computer is a machine that can be programmed to automatically carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic sets of operations known as ''programs'', wh ...
built elsewhere had much greater promise and the project ceased. In 1947,
UCLA
The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school then known as the southern branch of the C ...
installed a differential analyser built for them by
General Electric
General Electric Company (GE) was an American Multinational corporation, multinational Conglomerate (company), conglomerate founded in 1892, incorporated in the New York (state), state of New York and headquartered in Boston.
Over the year ...
at a cost of $125,000.
By 1950, this machine had been joined by three more.
The UCLA differential analyzer appeared in 1950's
''Destination Moon'', and the same footage in 1951's
''When Worlds Collide'', where it was called "DA". A different shot appears in 1956's ''
Earth vs. the Flying Saucers''.

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.
In Canada, a differential analyser was constructed at the
University of Toronto
The University of Toronto (UToronto or U of T) is a public university, public research university whose main campus is located on the grounds that surround Queen's Park (Toronto), Queen's Park in Toronto, Ontario, Canada. It was founded by ...
in 1948 by
Beatrice Helen Worsley, but it appears to have had little or no use.
A differential analyser may have been used in the development of the
bouncing bomb, used to attack
German hydroelectric dams during
World War II
World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
. Differential analysers have also been used in the calculation of
soil erosion
Soil erosion is the denudation or wearing away of the Topsoil, upper layer of soil. It is a form of soil degradation. This natural process is caused by the dynamic activity of erosive agents, that is, water, ice (glaciers), snow, Atmosphere of Ea ...
by river control authorities.
The differential analyser was eventually rendered obsolete by
electronic analogue computers and, later, digital computers.
Use of Meccano
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".
[,] 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
Auckland ( ; ) is a large metropolitan city in the North Island of New Zealand. It has an urban population of about It is located in the greater Auckland Region, the area governed by Auckland Council, which includes outlying rural areas and ...
,
New Zealand
New Zealand () is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and List of islands of New Zealand, over 600 smaller islands. It is the List of isla ...
.
[ 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.
It has been estimated, by Garry Tee that "about 15 Meccano model Differential Analysers were built for serious work by scientists and researchers around the world".][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 ]
See also
* Torque amplifier
A torque amplifier is a mechanical device that amplifies the torque of a rotating shaft without affecting its rotational speed. It is mechanically related to the capstan (nautical), capstan seen on ships. Its most widely known use is in power steer ...
* Ball-and-disk integrator
The ball-and-disk integrator is a key component of many advanced mechanical computers. Through simple mechanical means, it performs continual integration of the value of an input. Typical uses were the measurement of area or volume of material in ...
* General purpose analog computer
Notes
Bibliography
*
*
*
*
*
*Worsley, Beatrice Helen (1947).
A mathematical survey of computing devices with an appendix on an error analysis of differential analyzers
' (Master's Thesis, MIT).
*Crank, J. (1947). ''The Differential Analyser'', London: Longmans, Green (this is the only book that describes how to set up and operate a mechanical differential analyser).
*MacNee, A.B. (1948).
An electronic differential analyzer
' (RLE, Technical Report 90, MIT. Note that this paper describes a very early electronic analogue computer, ''not'' 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 "''electronic'' differential analyser").
External links
{{commons category, Differential analysers
which focuses on the Differential Analyzer
Professor Stephen Boyd at Stanford University provides a brief explanation of its working.
Early computers
Analog computers
Electro-mechanical computers
Mechanical computers
Mathematical tools
Integrals