Bush Builds the First Differential Analyzer Summary

  • Last updated on November 10, 2022

The differential analyzer developed by Vannevar Bush and his colleagues at the Massachusetts Institute of Technology was the first modern analog computer.

Summary of Event

Calculating equipment has developed along two distinct lines: one is digital computation and the other is analog computation. Analog machines, of which the mechanical differential analyzer is an example, operate on quantities that are capable of continuous variation. These quantities—shaft rotation, electrical voltage, and so on—are physical analogues of the problem under consideration, and the use of analog machines to simulate the behavior of actual equipment can be an important engineering tool. In addition to serving as simulators of actual physical situations such as electrical power networks, analog machines are used as equation solvers. One type of analog machine was both easily portable and in common use—the slide rule—but was replaced by electronic calculators in the 1970’s. Another type, the differential analyzer, was developed to provide solutions for differential equations through a process of successive integration in a closed-loop configuration. Early mechanical differential analyzers were extremely large, composed of many different parts, and often weighed thousands of tons. In addition, these early analyzers required several days of setup before a problem or series of problems could be run. [kw]Bush Builds the First Differential Analyzer (1928) [kw]First Differential Analyzer, Bush Builds the (1928) [kw]Differential Analyzer, Bush Builds the First (1928) Differential analyzer Analog computers Computers;analog Inventions;analog computer [g]United States;1928: Bush Builds the First Differential Analyzer[06960] [c]Science and technology;1928: Bush Builds the First Differential Analyzer[06960] [c]Inventions;1928: Bush Builds the First Differential Analyzer[06960] [c]Mathematics;1928: Bush Builds the First Differential Analyzer[06960] [c]Engineering;1928: Bush Builds the First Differential Analyzer[06960] [c]Computers and computer science;1928: Bush Builds the First Differential Analyzer[06960] Bush, Vannevar Kelvin, Baron (William Thomson) Babbage, Charles

Vannevar Bush.

(Library of Congress)

Calculating devices are as old as humanity, but most have relied on treating variables as being counted as discrete entities. The abacus and its modern counterpart, the digital computer, both embody this assumption of counting discrete units; the analog computer does not. Instead, the analog computer measures variables along a continuous range of values in much the same way that a thermometer can measure temperature at any point or an odometer measures miles. Further, whereas digital calculators have an ancestry reaching back to antiquity, analog computers are a comparatively recent development. Because digital computers are based on counting, simple machines to aid humanity in establishing the presence or absence of discrete units were developed in a variety of places and cultures. The abacus dates from at least five thousand years ago and is still used in many countries. In 1642, Blaise Pascal, the noted French philosopher-scientist, constructed a calculating machine to assist him in computing business accounts. A few years later, a German mathematician, Gottfried Wilhelm Leibniz, built a machine that he called a “stepped reckoner.”

Not until 1820, however, did a reliable calculating machine capable of addition, subtraction, multiplication, and division become commercially available. It was not until 1835, when Charles Babbage designed his “Analytical Engine,” Analytical Engine that a computer in the modern sense appeared, at least on paper. Had it been built, it would have been the first digital computer to incorporate the principles of sequential control.

The first mechanical analog computers also appeared in the nineteenth century. Baron Kelvin (Sir William Thomson, known as Lord Kelvin), an English physicist, attempted to build one of the earliest known analog computers in 1872 to serve as a tide predictor. The first modern working analog computer, however, was designed and built by a team headed by Vannevar Bush at the Massachusetts Institute of Technology (MIT) in the late 1920’s. The machine was a forerunner of the specialized type of analog computers known as differential analyzers and was designed to solve a specific form of differential equation. When completed in 1928, the device could perform eighteen different functions.

When Bush joined the MIT faculty in 1919, his research focused on electrical power transmission. Calculating precisely the distribution of power within a network entailed solving large problems of simultaneous linear equations. This was a difficult and time-consuming procedure because the calculations frequently involved differential equations that were particularly intractable. Lord Kelvin had attempted to build a machine to solve such equations almost fifty years earlier but had been unsuccessful in going beyond second-order differential equations. Lord Kelvin showed that coupling together two of the integrators described by James Clerk Maxwell Maxwell, James Clerk in the 1873 paper “Treatise on Electricity and Magnetism” "Treatise on Electricity and Magnetism" (Maxwell)[Treatise on Electricity and Magnetism] would work to solve for second-order derivatives. In principle, Lord Kelvin also contended that combining Maxwell’s integrators in various configurations also should allow solutions for higher-order differential equations to be found. Simple integrators, such as the one described by Maxwell, have become common in a variety of settings. Perhaps the most familiar example is household electrical meters, which measure current and voltage and integrate their product, power or kilowatts, with respect to time.

When Bush began working on a differential analyzer, he used an electrical meter as the core of the machine. Working under Bush’s supervision, a graduate student completed the first simple computer, a continuous integraph, in 1926. It was constructed to evaluate integrals that contained a product but was limited to the solution of first-order differentials. Having obtained both accurate and useful results from the continuous integraph, Bush and his students added a second integrating unit to the first computer. They discovered, however, that they could not use another electrical meter. Bush turned to the Kelvin device as a possible solution, as the rotation of the meter appeared ideally suited to rotate the disk of a mechanical integrator. Unfortunately, as soon as a load was placed on the moving parts of the machine, its accuracy dropped. Connecting the two integrators with a servomotor solved the problem, and a Kelvin device capable of solving for second-order derivatives became a reality. It still had limitations, however: It could not solve higher-order differential equations or systems of simultaneous differential equations. Bush decided to try to build a true differential analyzer, a machine that would connect integrator after integrator.

When he attempted to build the larger machine, Bush discovered that the servomotor provided only a partial solution. It proved difficult to set properly and oscillated wildly at times when transmitting large magnifications of turning force, or torque. In 1927, a new device appeared: the torque amplifier. Torque amplifiers Use of torque amplifiers meant there was no longer a limit to the number of integrators that could be interconnected and a true differential analyzer could be built. The first had six integrators and could be used to solve most of the differential equations engineers were likely to encounter, including systems of two or three simultaneous second-order equations.

The increase in scale and the addition of torque amplifiers required that a large room be used to house the differential analyzer with its complex mass of interconnected metal axles, gears, disks, handles, and electric motors. The six integrators consisted of glass disks on movable tables. One set of measurements determined the movement of the table, another determined the rotation of the disk, and a metal wheel on the glass disk measured a third variable by its distance from the disk. The torque amplifiers controlled all of this by permitting the wheels and shafts running the differential analyzer to move easily without slippage. In an analog computer, the physical movement of parts performs the actual computation, so all parts must move precisely. A collection of shafts and straps connected to servomotors through the torque amplifiers moved the integrators, but the differential analyzer itself was purely mechanical. Electricity was used only for powering the amplifiers, the shafts, and the printers.


The differential analyzer was the first serious attempt to build a computer for use by scientists. When Bush described the differential analyzer in a paper published in 1931, other scientists and engineers immediately began to build similar machines. The differential analyzer quickly found a variety of applications in civilian and military settings, as it could be used both to simulate complex systems, such as electrical power grids, and to solve the difficult equations posed by ballistics problems.

As political conditions in Europe and the Far East deteriorated during the 1930’s, the U.S. War Department became involved increasingly in both computer research and the use of computers. The U.S. Navy was particularly interested in applying the differential analyzer to solving ballistics problems and funded such research actively. This research support soon was extended to include work on digital computers, and mathematicians such as Grace Hopper, who later became known as the inventor of COBOL, were recruited to work as programmers on these projects.

In addition to spin-offs such as an increased interest in digital computers, the successful development of an analog computer meant that scientists and engineers could perform simulations of complex technical systems at a considerable savings over the expense of actual tests of those systems. The analog computer proved to be an invaluable tool in the development of aircraft, guided missiles, automobiles, and the like. By using simulator studies, researchers could obtain large databases before trial flights or test drives commenced, and those studies also could suggest how a limited number of physical trials could be most efficiently utilized. The development of the analog computer corresponded to a number of other significant developments within the history of technology, such as research in nuclear power and the development of jet aircraft, and contributed significantly to them.

It would have been impossible to build actual working prototypes of some large technological systems, such as nuclear power plants, and to construct preliminary design models for jet aircraft, which would be prohibitively expensive if done for every proposed design change or modification. Analog computers allowed engineers and scientists to progress in the development of new technological devices and systems more economically and more quickly than they could have otherwise.

Bush’s successful work with the differential analyzer may have helped to shape future science policy in the United States. Although his own research interests moved away from analog computing in the 1930’s, the interest the differential analyzer aroused in the scientific community contributed to Bush’s personal influence and success. As chairman of the National Research Committee and director of the Office of Scientific Research and Development during World War II, Bush helped to forge connections among the federal government, universities, and private industry that led to the priorities that were set for basic research in the physical sciences for generations. Bush’s personal influence on the American scientific community will persist long after the mechanical differential analyzer has been relegated to the status of a historical curiosity. Differential analyzer Analog computers Computers;analog Inventions;analog computer

Further Reading
  • citation-type="booksimple"

    xlink:type="simple">Ashurst, F. Gareth. Pioneers of Computing. London: Frederick Muller, 1983. Explains differences between digital and analog computers in addition to providing biographies of John Napier, Pascal, and others.
  • citation-type="booksimple"

    xlink:type="simple">Campbell-Kelly, Martin, and William Aspray. Computer: A History of the Information Machine. 2d ed. Boulder, Colo.: Westview Press, 2004. Comprehensive history begins with the work of mathematicians in the nineteenth century and covers developments through the beginning of the twenty-first century. Includes notes, bibliography, and index.
  • citation-type="booksimple"

    xlink:type="simple">Hartley, M. G. An Introduction to Electronic Analogue Computers. New York: John Wiley & Sons, 1962. Provides a brief history of computers and explains the difference between analog and digital computers.
  • citation-type="booksimple"

    xlink:type="simple">Heyn, Ernest V. A Century of Wonders: One Hundred Years of Popular Science. Garden City, N.Y.: Doubleday, 1972. Presents easy-to-understand explanations of the evolution of a variety of technologies, including electronic computers. Excellent illustrations.
  • citation-type="booksimple"

    xlink:type="simple">Shurkin, Joel. Engines of the Mind: The Evolution of the Computer from Mainframes to Microprocessors. Updated ed. New York: W. W. Norton, 1996. General history of computers attempts to explain priority disputes without taking sides. Focuses more on the social history of computer development and the personalities of the persons involved than on the technical aspects of computing.
  • citation-type="booksimple"

    xlink:type="simple">Williams, Raymond Wilson. Analogue Computation: Techniques and Components. New York: Academic Press, 1961. Provides background in both the history and theory of analog computers.

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