Resources: Les integraphes (in French)
 Integrating with the Coradi Integraph Invented by AbdankAbakanowicz, Report 1951
 Sur un integrateur, Comptes Rendus, 92, 1881
 Sur integration mecanigue, Comptes Rendus, 94, 1882
 Sur un Nouvel Integrometre, Comptes Rendus, 95, 1882
 Abakanowicz Instruments in CNRS Museum in France
 Graphical Integration History
 Pearson's Integrator, 1889
 Abakanowicz Train Bell
Bruno AbdankAbakanowicz [pron. abahkahNOHvitch] was born on October 6, 1852 in Wilkomierz, Poland, now Ukmerge, Lithuania, near Vilnius (Wilno, Vilna) and died on August 29, 1900, in ParcSt. Maur, east of Paris. He studied at the Polytechnic in Riga, Latvia, then became a professor at the Polytechnic Institute in Lwów, and in 1881 settled in France. While in Poland, he published several books, including works on statistics, integrators and popular scientific works, such as the one describing his integraph [14]. He’s made fortune for his inventions and ultimately settled on a little island of Costaérès, at the shores of Brittany. He contributed to the electrification of Lyon and has been known for having "electrified France." He was decorated in 1889 by Légion d'honneur, the highest distinction from the French government.
Major Contribution: Invention of an integraph 1878 [311].
Basic Questions What is an integraph? As Gordon Bell states on his website [12], “The integraph is a noteworthy development in the history of calculating instruments. While the principle on which it is based was introduced by Coriolis in 1836, it was in 1878 that AbdankAbakanowicz first developed a practical working model. 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. (…) AbdankAbakanowicz’s instrument could produce solutions to a commonly encountered class of simple differential equations of the form dy/dx = F(x) so that y = integral(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 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.” A very recent historical discussion of integrating devices, with all the theoretical underpinning, going back to Euler, Bernoulli and Coriolis, can be found in [13].
In developing a workable version of his integraph, AbdankAbakanowicz had to overcome several difficulties. Between 1880 and 1889, he “tried out a substantial number of different mechanisms in order to solve the problem, so important for integraphs, to transfer a direction extracted from a given curve on a knifeedged wheel. A fruitful cooperation came into being around 1885 with David Napoli (18401890), the chief inspector and director of the workshop of the French Eastern Railway”, whom he had met in 1883 at the Vienna Exhibition [14]. Napoli had the idea to use cogwheels in order to solve the problem of transfer of direction. This solution resulted in the model which made use of wheels connected by a filament [15]. But it was further collaboration with a Swiss engineer and manufacturer, Gottlieb Coradi (18471929), that led to a successful solution that enabled the construction of a commercial product [16]. As AbdankAbakanowicz observed: “Mr. Coradi in Zurich, the renowned maker of precision instruments, has dealt with the construction of our integraphs; these are now manufactured by him in a correct way. Mr. Coradi has kept from the earlier integraphs only the basic principle; the mechanical realization of that principle and the transfer of the movement of the directrix to the wheel, which is extraordinarily solved, are solely his merit.” [11]
How is an integraph different from integrator? It can be stated as briefly as Karl Pearson said over a century ago [17]: “In the language of the mathematician, the integrator gives only that miserly result, a definite integral, but the integraph yields an indefinite integral, a picture of the result at all times or all points – a much greater boon in most mechanical and physical investigations.”
Significance Referring to the early era of predigital computing, one researcher states [13]: “In the period which precedes the appearance of computers, needs in calculation of scientists and engineers led to an important development of graphic methods of integration.” Other researchers and historians confirm the importance of an integraph in the development of computational capabilities by mankind, but one statement seems to make a crucial point in assessing the value of the invention of an integraph. This is from a key figure in computer engineering, Gordon Bell, one of the designers of the PDP line of minicomputers from Digital Equipment Corporation, inventor of the first universal asynchronous receiver transmitter (UART) and author of two seminal books that had tremendous impact on computing and computer engineering [18,19]. Summarizing the contents of AbdankAbakanowicz’ book, Mr. Bell states on his website [12]: “The integraph is capable of solving only simple differential equations. The need to handle sets of more complex nonlinear 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.” AbdankAbakanowicz’ work has been referenced in professional publications for over a century, most recently in relevance to nonholonomic manipulators [2123].
Findings The historical contribution of this website is in bringing for the first time to the attention of the general public the name of Bruno AbdankAbakanowicz, which has been somehow neglected and almost never before mentioned in any articles or textbooks on computing history. In addition to his role in computing (developing an integraph), AbdankAbakanowicz invented a variety of other instruments, such as parabolograph for drawing paraboles, spirograph for drawing spirals and multiple other devices, including the electric bell used in trains [20], and an electric lamp of his own design. For completeness, it must be noted that at the end of the nineteenth century in Britain, Sir Charles Vernon Boys invented a slightly different version of integraph, independently of AbdankAbakanowicz, and published his results a few years later [13,17].
References [hide]
[1] B. AbdankAbakanowicz, Zarys statyki wykresnej. Cz. 1, Przeglad Techniczny, Lwów, 1876 [2] B. AbdankAbakanowicz, Teorya astronomiczna gwiazd spadajacych wedlug Schiaparelliego, Polskie Towarzystwo Przyrodników im. Kopernika, Lwów, 1876 [3] B. AbdankAbakanowicz, Integrator: krzywa calkowa i jej zastosowania w mechanice budowniczej, Red. „Inzynierji i Budownictwa”, Warszawa, 1880 [4] B. AbdankAbakanowicz, Prace Brunona Abdanka Abakanowicza. Tom I z portretem autora, Warszawa, Staraniem redakcyi „Prac matematycznofizycznych”, Warszawa, 1907. [5] B. AbdankAbakanowicz, Les intégraphes  la courbe intégrale et ses applications. Étude nouveau système d’intégrateurs mècaniques. GauthierVillars, Paris, 1886. [6] B. AbdankAbakanowicz, Die Integraphen. Die Integralkurven und ihre Anwendung, Teubner, Leipzig, 1889 (slightly extended translation of [5]). [7] B. AbdankAbakanowicz, Sur un integrateur, instrument servant a l’integration graphique, Comptes rendus hebdomadaires des seances de l’Academie des sciences, Vol. 92, pp. 402405, 1881 [8] B. AbdankAbakanowicz, Sur un integrateur, Comptes rendus hebdomadaires des seances de l’Academie des sciences, Vol. 92, pp. 515519, 1881 [9] B. AbdankAbakanowicz, Sur l’integration mecanique, Comptes rendus hebdomadaires des seances de l’Academie des sciences, Vol. 94, pp. 783785, 1882 [10] B. AbdankAbakanowicz, Sur un nouvel integrometre, Comptes rendus hebdomadaires des seances de l’Academie des sciences, Vol. 95, pp. 10471048, 1882 [11] B. AbdankAbakanowicz, D. Napoli, Sur un nouveau modele d’integraphe, Comptes rendus hebdomadaires des séances de l’Academie des sciences, Vol. 101, pp. 592595, 1885 [12] Collection of rare and historical books collected by Gwen and Gordon Bell. http://research.microsoft.com/~gbell/CyberMuseum_files/Bell_Book_Files/books.htm [13] D. Tournès, L’intégration graphique des equations différentielles ordinaires, Historia Mathematica, Vol. 30, 457493, 2003 http://steiner.math.nthu.edu.tw/disk5/js/history/graphicalintegration.pdf [14] Integraph with transfer of direction by cogwheels, system AbdankAbakanowicz/Napoli http://www.rehseis.cnrs.fr/calculsavant/Exposition/ArtsetMetiers/133000001e.html [15] Integraph with transfer of direction by filament, system AbdankAbakanowicz/Napoli http://www.rehseis.cnrs.fr/calculsavant/Exposition/ArtsetMetiers/135880000e.html [16] Integraph with transfer of direction by a linkage parallelogram, system AbdankAbakanowicz/Coradi (large model) http://www.rehseis.cnrs.fr/calculsavant/Exposition/ArtsetMetiers/134240000e.html [17] K. Pearson, A New Integrator, Scientific American Supplement, No. 794, March 21, 1889 http://books.jibble.org/1/5/7/0/15708/157088/ScientificAmericanSupplementNo4.html http://www.dominiopublico.gov.br/download/texto/gu011761.pdf [18] C.G. Bell, A. Newell, Computer Structures: Readings and Examples, McGrawHill, New York, 1971 [19] C.G. Bell, C. Mudge, J. McNamara, Computer Engineering, Digital Press, Maynard, Mass., 1978 [20] B. AbdankAbakanowicz, Nouvel appel magnétoélectrique, La Nature, Revue des sciences et de leurs applications aux arts et à l'industrie, Vol. 8, No. 2, p. 176, 1883 http://cnum.cnam.fr/CGI/fpage.cgi?4KY28.21/180/100/432/0008/0420 [21] H. Lossier, G. Coradi, L’integraphe AbdankAbakanowicz, Zürich, 1903 [22] H. Schilt, Integrating with the Coradi Integraph Invented by AbdakAbakanowicz. Practical Technical Problems with Examples of Solutions. G. Coradi, Zürich, 1951 [23] W. Chung, Nonholonomic Manipulators, SpringerVerlag, Berlin, 2004.
