A: Paris, Île-de-France, France

1878

In 1878 Bruno Abdank-Abakanowicz, a mathematician, inventor and electrical engineer, invented the integraph, a form of integrator.

"The integraph is an elaboration and extension of the planimeter, an earlier, simpler instrument used to measure area. It is a mechanical instrument capable of deriving the integral curve corresponding to a given curve. Hence, it is capable of solving graphically a simple differential equation.

"Sets of partial differential equations are commonly encountered in mathematical physics. Most branches of physics such as aerodynamics, electricity, acoustics, plasma physics, electron-physics and nuclear energy involve complex flows, motions and rates of change which may be described mathematically by partial differential equations. A well-established example from electromagnetics is the set of partial differential equations known as Maxwell's equations.

"In practice, differential equations can be difficult to integrate, that is to solve. The integraph is capable of solving only simple differential equations. The need to handle sets of more complex non-linear differential equations, led Vannevar Bush to develop the Differential Analyzer at MIT in the early 1930s. In turn, limitations in speed, capacity and accuracy of the Bush Differential Analyzer provided the impetus for the development of the ENIAC during World War II.

"Abdank-Abakanowicz’s instrument could produce solutions to a commonly encountered class of simple differential equations of the form dy/dx = F(x) so that y = ò F(x)dx. The basic approach was to draw a graph of the function F and then use the pointer on the device to trace the contour of the function. The value of the [indefinite] integral could then be read from the dials. The concept of the instrument was taken up and soon put into production by such well known instrument makers as the Swiss firm of Coradi in Zurich" (From Gordon Bell's website, accessed 09-01-2010).

Abdank-Abakanowicz published a monograph entitled *Les Intégraphes* (Paris, 1886).

(This entry was last revised on 03-12-2018).