Differential analyser
Encyclopedia
Analog computer
An analog computer is a form of computer that uses the continuously-changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved...
designed to solve differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s by integration
Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operationally.
History
Planimeter
A planimeter 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 which they are constructed varies, with the main types of mechanical planimeter being...
s, started at least as early as 1836, when the French physicist Gaspard-Gustave Coriolis
Gaspard-Gustave Coriolis
Gaspard-Gustave de Coriolis or Gustave Coriolis 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. See the Coriolis Effect...
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
James Thomson (engineer)
right|300px|James Thomson was an engineer and physicist whose reputation is substantial though it is overshadowed by that of his younger brother William Thomson .-Biography:Born in Belfast, he grew up mostly in Glasgow...
, who was born in Belfast
Belfast
Belfast is the capital of and largest city in Northern Ireland. By population, it is the 14th biggest city in the United Kingdom and second biggest on the island of Ireland . It is the seat of the devolved government and legislative Northern Ireland Assembly...
in 1822, but lived in Scotland
Scotland
Scotland is a country that is part of the United Kingdom. Occupying the northern third of the island of Great Britain, it shares a border with England to the south and is bounded by the North Sea to the east, the Atlantic Ocean to the north and west, and the North Channel and Irish Sea to the...
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
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...
, which represents the invention of the differential analyser.
On Lord Kelvin's advice, Thomson's integrating machine was incorporated into a fire-control system
Fire-control system
A fire-control system is a number of components working together, usually a gun data computer, a director, and radar, which is designed to assist a weapon system in hitting its target. It performs the same task as a human gunner firing a weapon, but attempts to do so faster and more...
for naval gunnery being developed by Arthur Pollen
Arthur Pollen
Arthur Joseph Hungerford Pollen was a writer on naval affairs in the early 1900s who recognised the need for a computer-based fire-control system...
, resulting in an electrically driven, mechanical analogue computer, which was completed by about 1912. Italian mathematician Ernesto Pascal also developed integraph
Integraph
An Integraph is an instrument used in mathematics for plotting the integral of a graphically defined function.It was invented independently about 1880 by the British physicist Sir Charles Vernon Boys and by Bruno Abakanowicz, a Polish-Lithuanian mathematician from the Russian Empire.An integraph...
s for the mechanical integration of differential equations and published details in 1914. However, the first widely practical differential analyser was constructed by Harold Locke Hazen and Vannevar Bush
Vannevar Bush
Vannevar Bush was an American engineer and science administrator known for his work on analog computing, his political role in the development of the atomic bomb as a primary organizer of the Manhattan Project, the founding of Raytheon, and the idea of the memex, an adjustable microfilm viewer...
at MIT
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
, 1928–1931, comprising six mechanical integrators. In the same year, Bush described this machine in a journal article as a "continuous integraph
Integraph
An Integraph is an instrument used in mathematics for plotting the integral of a graphically defined function.It was invented independently about 1880 by the British physicist Sir Charles Vernon Boys and by Bruno Abakanowicz, a Polish-Lithuanian mathematician from the Russian Empire.An integraph...
". When he published a further article on the device in 1931, he called it a "differential analyzer". 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." Claude Shannon was hired as a research assistant in 1936 to run the differential analyzer in Bush's lab.
Douglas Hartree
Douglas Hartree
Douglas Rayner Hartree PhD, FRS was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree-Fock equations of atomic physics and the construction of the meccano differential analyser.-Early life:Douglas Hartree was born in...
of Manchester University brought Bush's design to England, where he constructed his first "proof of concept
Proof of concept
A proof of concept or a proof of principle is a realization of a certain method or idea to demonstrate its feasibility, or a demonstration in principle, whose purpose is to verify that some concept or theory that has the potential of being used...
" 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
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, they were particularly well known for their industrial electrical equipment such as generators, steam...
, and was, according to Hartree, "[the] first machine of its kind in operation outside the United States". During the next five years three more were added, at Cambridge University
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
, Queen's University Belfast, and the Royal Aircraft Establishment
Royal Aircraft Establishment
The Royal Aircraft Establishment , was a British research establishment, known by several different names during its history, that eventually came under the aegis of the UK Ministry of Defence , before finally losing its identity in mergers with other institutions.The first site was at Farnborough...
in Farnborough.
In Norway
Norway
Norway , officially the Kingdom of Norway, is a Nordic unitary constitutional monarchy whose territory comprises the western portion of the Scandinavian Peninsula, Jan Mayen, and the Arctic archipelago of Svalbard and Bouvet Island. Norway has a total area of and a population of about 4.9 million...
, the locally built Oslo Analyser
Oslo Analyzer
Oslo Analyzer was a differential analyzer type of computer, built in Norway from 1938 to 1942. It was the largest computer of its kind....
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
Ballistic Research Laboratory
The Ballistic Research Laboratory at Aberdeen Proving Ground, Maryland was the center for the United States Army's research efforts in ballistics and vulnerability/lethality analysis....
in Maryland
Maryland
Maryland is a U.S. state located in the Mid Atlantic region of the United States, bordering Virginia, West Virginia, and the District of Columbia to its south and 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
Originally applied to any group of infantry primarily armed with projectile weapons, artillery has over time become limited in meaning to refer only to those engines of war that operate by projection of munitions far beyond the range of effect of personal weapons...
firing tables prior to the invention of the ENIAC
ENIAC
ENIAC was the first general-purpose electronic computer. It was a Turing-complete digital computer capable of being reprogrammed to solve a full range of computing problems....
, which, in many ways, was modelled on the differential analyser. Also in the early 1940s, with Samuel H. Caldwell
Samuel H. Caldwell
Samuel Hawks Caldwell was an American electrical engineer, known for his contributions to the early computers....
, 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. In 1947, UCLA
University of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...
installed a differential analyser built for them by General Electric
General Electric
General Electric Company , or GE, is an American multinational conglomerate corporation incorporated in Schenectady, New York and headquartered in Fairfield, Connecticut, United States...
at a cost of $125,000. By 1950, this machine had been joined by three more.
In Canada, a differential analyser was constructed at the University of Toronto
University of Toronto
The University of Toronto is a public research university in Toronto, Ontario, Canada, situated on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution of higher learning in Upper Canada...
in 1948 by Beatrice Helen Worsley
Beatrice Helen Worsley
Beatrice "Trixie" Helen Worsley was the first female computer scientist in Canada. -Education:Beatrice Helen Worsley was born in Mexico, but graduated from Bishop Strachan School in Toronto in 1939, receiving the Governor General’s Award for the highest overall grade...
, but it appears to have had little or no use.
A differential analyser may have been used in the development of the bouncing bomb
Bouncing bomb
A bouncing bomb is a bomb designed specifically to bounce to a target across water in a calculated manner, in order to avoid obstacles such as torpedo nets, and to allow both the bomb's speed on arrival at the target and the timing of its detonation to be pre-determined...
, used to attack German
Nazi Germany
Nazi Germany , also known as the Third Reich , but officially called German Reich from 1933 to 1943 and Greater German Reich from 26 June 1943 onward, is the name commonly used to refer to the state of Germany from 1933 to 1945, when it was a totalitarian dictatorship ruled by...
hydroelectric dams
Hydroelectricity
Hydroelectricity is the term referring to electricity generated by hydropower; the production of electrical power through the use of the gravitational force of falling or flowing water. It is the most widely used form of renewable energy...
during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
. Differential analysers have also been used in the calculation of soil erosion 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 MeccanoMeccano
Meccano is a model construction system comprising re-usable metal strips, plates, angle girders, wheels, axles and gears, with nuts and bolts to connect the pieces. It enables the building of working models and mechanical devices....
parts: this meant that the machine was cheaper 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
Museum of Transport and Technology
The Museum of Transport and Technology is a museum located in Western Springs, Auckland, New Zealand. It is located close to the Western Springs Stadium, Auckland Zoo and the Western Springs Park. The museum has large collections of civilian and military aircraft and other land transport vehicles...
(MOTAT) collection in Auckland
Auckland
The Auckland metropolitan area , in the North Island of New Zealand, is the largest and most populous urban area in the country with residents, percent of the country's population. Auckland also has the largest Polynesian population of any city in the world...
, New Zealand
New Zealand
New Zealand is an island country in the south-western Pacific Ocean comprising two main landmasses and numerous smaller islands. The country is situated some east of Australia across the Tasman Sea, and roughly south of the Pacific island nations of New Caledonia, Fiji, and Tonga...
. 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. In 1948, this machine was bought by Professor Harry Whale of Auckland, for 100 pounds sterling, and he then took it to Auckland for use at the Seagrave Radio Research Centre.
It is estimated that "about 15 Meccano model Differential Analysers were built for serious work by scientists and researchers around the world". More recently, building differential analysers with Meccano parts has become a popular project among serious Meccano hobbyists. An example is the differential analyser built at Marshall University
Marshall University
Marshall University is a coeducational public research university in Huntington, West Virginia, United States founded in 1837, and named after John Marshall, the fourth Chief Justice of the United States....
, which is now used for educational purposes, in that a student not only solves a differential equation but also becomes the "calculator" by operating the machine, and so develops a better understanding of what a differential equation is.
Cultural references
A differential analyser at UCLA is shown in operation in the 1951 film When Worlds CollideWhen Worlds Collide (film)
When Worlds Collide is a 1951 science fiction film based on the 1933 novel co-written by Philip Gordon Wylie and Edwin Balmer. The film was shot in Technicolor, directed by Rudolph Maté and was the winner of the 1951 Academy Award for special effects....
and the 1956 film Earth vs. the Flying Saucers
Earth vs. the Flying Saucers
Earth vs. the Flying Saucers is an American black and white science fiction film, directed by Fred F. Sears and released by Columbia Pictures. The film is also known as Invasion of the Flying Saucers. It was ostensibly suggested by the non-fiction work Flying Saucers from Outer Space by Donald...
. After UCLA's machines were retired, one was donated to the Smithsonian Institute
Smithsonian Institution
The Smithsonian Institution is an educational and research institute and associated museum complex, administered and funded by the government of the United States and by funds from its endowment, contributions, and profits from its retail operations, concessions, licensing activities, and magazines...
.
External links
- Vannevar Bush bio which focuses on the Differential Analyzer