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Calculation and Computation in the Pre-electronic Era pp 75–122Cite as

“Like the Poor, the Harmonics Will Always Be with Us”

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Part of the book series: History of Computing ((HC))

Abstract

From the perspective of the degree of mechanization (machine to human capital, constant to variable capital), some of the machines presented in this chapter should be placed at the one end of the spectrum of technologies of calculation-computation of the mechanical and electrical eras, whereas some of the graphs presented in Chap. 5 should be placed at the other. The calculating machines (mechanical calculators) presented in Chap. 6 and the slide rules presented in Chaps. 2 and 3 would fill the space in between. If we had to choose one name to refer to the great variety of the machines and associated mechanisms of this chapter, this would have to be “analyzer.”

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Notes

  1. 1.

    For an introductory placement of Bush’s contribution within the history of computing in the long-run, see Brian Randell. 1982. From analytical engine to electronic digital computer : The contributions of Ludgate, Torres, and Bush. Annals of the History of Computing 4(4): 327–341. The articles by Larry Owens on Bush’s differential analyzer and MIT’s subsequent struggle to distance itself from Bush’s analyzer have set the scholarly standard for studies on the history of analog computing. See Larry Owens. 1986. Vannevar Bush and the differential analyzer : The text and the context of an early computer. Technology and Culture 27(1): 63–95, and Larry Owens. 1996, October–December. Where are we going Phil Morse? Challenging agendas and the rhetoric of obviousness in the transformation of computing at MIT, 1939–1957. IEEE Annals of the History of Computing 18(4): 34–41. For an exemplar book-length study on interwar computing and Bush’s role in it, see David Mindell. 2004. Between human and machine. Baltimore: Johns Hopkins University Press. On Bush’s top administrative role in World War II and his influential role in shaping post-World War II science and technology policy, see Larry Owens. 1994, Winter. The counterproductive management of science in the Second World War: Vannevar Bush and the Office of Scientific Research and Development. Business History Review 68: 515–576; Daniel J. Kevles. 1977. The National Science Foundation and the debate over postwar research policy, 1942–1945: A political interpretation of ‘Science: The endless frontier’. ISIS 68(241): 4–26; Stanley Goldberg. 1992. Inventing a Climate of Opinion: Vannevar Bush and the Decision to Build the Bomb. ISIS 83: 429–452; Daniel Lee Kleinman. 1994. Layers of interests, layers of influence: Business and the genesis of the National Science Foundation. Science, Technology, and Human Values 19(3): 259–282. For Bush in general, see G. Pascal Zachary. 1997. Endless frontier: Vannevar Bush, engineer of the American century. New York: Free Press. For more on the context of the development of Bush’s analyzers and MIT, see, also, Karl L. Wildes, and Nilo A. Lindgren. 1985. A century of electrical engineering and computer science at MIT, 1882–1982. Cambridge: MIT Press. For a more general angle on MIT, see Bruce Sinclair (ed.). 1986. Inventing a genteel tradition: MIT crosses the river. In New perspectives on technology and American culture, 1–18. Philadelphia: American Philosophical Society Library no. 12, and Larry Owens. 1990. MIT and the Federal ‘Angel’: Academic R&D and Federal-Private Cooperation Before World War II. ISIS 81: 188–213. Also from a more general angle, see Christophe Lecuyer. 1995. MIT, progressive reform, and ‘Industrial Service’, 1890–1920. Historical Studies in the Physical Sciences 26(1): 35–38, and Christophe Lecuyer. 1992. The making of a science based technological university: Karl Kompton, James Killian, and the reform of MIT, 1930–1957. Historical Studies in the Physical Sciences 23: 153–180. For the suggestive variance in the perception and persistence of the differential analyzer tradition according to variance of national context, see Mark D. Bowles. 1996, October–December. U.S. Technological enthusiasm and British Technological Skepticism in the Age of the Analog Brain. IEEE Annals of the H istory of Computing 18(4): 5–15.

  2. 2.

    For an introduction to the history of analog computing, see Aristotle Tympas. 2005a. Computers: Analog. In Encyclopedia of 20th–Century Technology, ed. Colin Hempstead, 195–199. London: Routledge, and Aristotle Tympas. 2005b. Computers: Hybrid. In Encyclopedia of 20th–Century Technology, ed. Colin Hempstead, 202–204. London: Routledge. See also the relevant chapter by Alan Bromley. 1990. In Computing before computers, ed. William Aspray. Ames: Iowa State University Press. For book-length historical studies, see Mindell, Between human and machine; James S. Small. 2001. The analogue alternative: The electronic analogue computer in Britain and the USA, 1930–1975. London: Routledge; Charles Care. 2010. Technology for modelling: Electrical analogies, engineering practice, and the development of analogue computing. London: Springer; Trevor Pinch, and Frank Trocco. 2004. Analog days: The invention and impact of the moog synthesizer . Cambridge, MA: Harvard University Press. For surveys of post-World War II analog computing, see, also, James S. Small. 1993. General-purpose electronic analog computing , 1945–1965. IEEE Annals of the History of Computing 15(2): 8–18, and James S. Small. 1994. Engineering, technology, and design: The Post-Second World War development of electronic analogue computers. History and Technology 11: 33–48. For a sample of case studies, see James E. Tomayko. 1985. Helmut Hoelzer’s fully electronic analog computer. Annals of the History of Computing 7(3): 227–241; Frank Preston. 2003, January–March. Vannevar Bush’s network analyzer at the Massachusetts Institute of Technology. IEEE Annals of the History of Computing: 75–78; Kent H. Lundberg. 2005, June. The history of analog computing . IEEE Control Systems Magazine: 22–28; Chris Bissell. 2007, February. The Moniac: A hydromechanical analog computer of the 1950s. IEEE Control Systems Magazine: 69–74; Jonathan Aylen. 2010. Open versus closed innovation: Development of the wide strip mill for steel in the United States during the 1920s. R&D Management 40(1): 67–80, and Jonathan Aylen. 2012, January. Bloodhood on my trail: Building the Ferranti Argus process control computer. International Journal for the History of Engineering and Technology 82(1): 1–36. The importance of analog computing in European contexts is suggested by several authors. See, for example, Jan Van Ende. 1992. Tidal calculations in the Netherlands, 1920–1960. IEEE Annals of the History of Computing 14(3): 23–33; Per A. Holst. 1996, October–December. Svein Rosseland and the Oslo Analyzer. IEEE Annals of the History of Computing 18(4): 16–26; Magnus Johansson. 1996, October–December. Early analog computers in Sweden—with examples from Chalmers University of Technology and the Swedish Aerospace Industry. IEEE Annals of the History of Computing 18(4): 27–33, and Wilfried De Beacuclair. 1986. Alvin Weather, IPM, and the development of calculator /computer technology in Germany, 1930–1945. Annals of the History of Computing 8(4): 334–350.

  3. 3.

    See Ellice M. Horsburgh (ed.). 1914. Modern instruments and methods of calculation: A handbook of the Napier Tercentenary Exhibition. London: Bell and Sons.

  4. 4.

    Vannevar Bush. 1936. Instrumental analysis. Transactions of the American Mathematical Society 42(10): 649–669. For the placement of Bush’s differential analyzer within the history of the mathematization of electrical engineering , see Susan Puchta. 1996. On the role of mathematics and mathematical knowledge in the development of Vannevar Bush’s early analog computers . IEEE Annals of the History of Computing 18(4): 49–59, and Susan Puchta. 1997. Why and how American electrical engineers developed heaviside’s operational calculus. Archives Internationales d’Histoire des Sciences 47: 57–107.

  5. 5.

    Thornton C. Fry. 1941, July. Industrial mathematics. Bell System Technical Journal 20(3): 255–292. For an earlier promotion of ‘industrial mathematics’ at Bell Labs, see George A. Campbell. 1924, October. Mathematics in industrial research. Bell System Technical Journal 3: 550–557. See, also, George A. Campbell. 1925, September. Mathematical Research. Bell Laboratories Record 1(1): 15–18.

  6. 6.

    Francis J. Murray. 1961. Mathematical machines, Volume II: Analog devices. New York: Columbia University Press.

  7. 7.

    “Network Calculator …Mathematician Par Excellence,” Westinghouse Engineer 4 (July 1944), editorial. For an introduction to the analyzer tradition as developed and used in the context of computing electric power networks, see Aristotle Tympas. 1996. From digital to analog and back: The ideology of intelligent machines in the history of the electrical analyzer, 1870s–1960s. IEEE Annals of the History of Computing 18(4): 42–48, and Aristotle Tympas. 2003. Perpetually laborious: Computing electric power transmission before the electronic computer. International Review of Social History 11(Supplement): 73–95, and Aristotle Tympas. 2012. A deep tradition of computing technology: Calculating electrification in the American West. In Where minds and matters meet: Technology in California and the West, ed. Volker Janssen, 71–101. Oakland: University of California Press; Aristotle Tympas, and Dina Dalouka. 2007. Metaphorical uses of an electric power network: Early computations of atomic particles and nuclear reactors. Metaphorik 12: 65–84, and Aristotle Tympas. 2007. From the historical continuity of the engineering imaginary to an anti-essentialist conception of the mechanical-electrical-electronic relationship. In Tensions and convergences: Technical and aesthetic transformation of society, ed. Reinhard Heil, Andreas Kamiski, Marcus Stippak, Alexander Unger, and Marc Ziegler, 173–184. Germany: Verlag. For articles that are focused on individual contributions, see Gordon S. Brown. 1981. Eloge: Harold Locke Hazen, 1901–1980. Annals of the History of Computing 3(1): 4–12. See, also, William Aspray. 1994. Calculating power: Edwin L. Harder and analog computing in the electric power industry. In Sparks of genius: Portraits of electrical engineering excellence, ed. Frederik Nebeker, 159–199. New York: IEEE Press, and William Aspray. 1993. Edwin L. Harder and the Anacom: Analog computing at Westinghouse. IEEE Annals of the History of Computing 15(2): 35–52. See, also, Bernard O. Williams. 1984. Computing with electricity, 1935–1945. Diss. University of Kansas. For a primary source that provided with a survey of the general uses of the various analyzers and a survey of particular uses within electrification right at the emergence of the analog-digital demarcation, see H.A. Peterson, and C. Concordia. 1945, September. Analyzers…For use in engineering and scientific problems. General Electric Review: 29–37. For an update that was focused on the spread of network analyzers , see Eric T.B. Gross. 1959. Network analyzer installations in Canada and the United States. American Power Conference Proceedings 21: 665–669. For the intervening emergence of the suggestive concept “digital differential analyzer” and the a posteriori designation of Bush’s differential analyzer as the “analog differential analyzer,” see Sprague, Fundamental methods of the digital differential analyzer method of computation,” and John F. Dovan. 1950. The serial-memory digital differential analyzer. In Mathematical tables and other aids to computation: 41–49 and 102–112 respectively. For the eventual subsuming of the history of the analyzer computing tradition under the history of analog computing, see the “Historical Survey” in Stanley Fifer. 1961. Analogue computation: Theory, techniques, and applications, vol. I. New York: McGraw-Hill, section 1.8.

  8. 8.

    See C.H. Claudy . 1914, March 7. A Great Brass Brain. Scientific American: 197.

  9. 9.

    Edmund Callis Berkeley. 1949. Giant Brains, or, machines that think. New York: Wiley.

  10. 10.

    For an overview of the history of the ideology of intelligent machines before the electronic era , which focuses on network analyzers and related artifacts, see Tympas, From digital to analog and back: The ideology of intelligent machines in the history of the electrical analyzer, 1870s–1960s.

  11. 11.

    There are several articles and books that include histories of the development and use of army, navy, and air-force fire control computing but most of them are written from a general military history perspective rather than the perspective of the history of computing technology. For a vivid description of the use of a bombsight in computing the drop of the atomic bomb, see Stephen L. McFarland. 1995. America’s pursuit of precision bombing, 1910–1945. Washington: Smithsonian Institution Press. Published reminiscences also point to the importance of the class of computing artifacts under consideration in fire control. See, for example, A. Ben Clymer. 1993. The mechanical analog computers of Hannibal Ford and William Newell. IEEE Annals of the History of Computing 15(2): 19–34, and W.H.C. Higgins, B.D. Holbrook, and J.W. Emling. 1992, July. Defense research at Bell Laboratories. Annals of the History of Computing 4(3): 218–244.

  12. 12.

    See Mindell, Between human and machine.

  13. 13.

    Tympas, Perpetually laborious: Computing electric power transmission before the electronic computer.

  14. 14.

    Tympas, A deep tradition of computing technology: Calculating electrification in the American West.

  15. 15.

    Vannevar Bush . 1920, October. A simple harmonic analyzer. AIEE Journal: 903.

  16. 16.

    See Michael Williams. 1982. Introduction. In Modern instruments and methods of calculation: A handbook of the Napier Tercentenary Exhibition, ed. Ellice M. Horsburgh, re-edition. Los Angeles: Tomash Publishers, xviii and xiv.

  17. 17.

    For an influential placement of the artifacts under consideration in the class of ‘mechanical methods’, see Joseph Lipka . 1918. Graphical and mechanical computation. New York: Wiley.

  18. 18.

    For the integrometer and the curvometer , see Horsburgh ed., Modern instruments and methods of calculation: A handbook of the Napier Tercentenary Exhibition, 187–189 and 181–187 respectively. For Robb, see 206–207.

  19. 19.

    Ibid., 193, 194–199, 190, 204–206, 199, and 200–206.

  20. 20.

    Ulrich Peters. 1903, July 23. The balance lever as a calculating machine. Iron Age 72: 12–13. For Carse and Urquhart and for Gibb, see Horsburgh ed., Modern instruments and methods of calculation: A handbook of the Napier Tercentenary exhibition, 220–248 and 264–265 respectively.

  21. 21.

    J.Y. Wheatley. 1903. The polar planimeter and its use in engineering calculations together with tables, diagrams, and factors, 17–18. New York: Keuffel & Esser.

  22. 22.

    Ibid., 11 and 14.

  23. 23.

    See Frederik A.P. Barnard. 1869. Paris Universal Exposition , 1867: Report on machinery and processes of the industrial arts and apparatus of the exact sciences, 620. New York: Van Nostrand.

  24. 24.

    For a sample of early references on the use of the planimeter in treatises on indicator diagram computations, see Thomas Pray. 1899. Twenty years with the indicator. Boston Journal of Commerce and Publishing 1; L. Elliott Brookes. 1905. The calculation of Horsepower made easy. Chicago: Frederik Drake and Company; William Houghtaling. 1899. The steam engine indicator and its appliances. Bridgeport: The American Industrial Publishing, and F.R. Low. 1910. The steam engine indicator, third revised and enlarged edition. New York: McGraw-Hill. For a sample of articles from the same period, see Indicator diagrams. Electrician (1894, April 20): 690–691; The Hatchet Planimeter. Electrician (1894, June 1): 137–138, and W.L. Butcher. 1905. A device for averaging certain kinds of continuous records by the planimeter. Engineering News 53(26): 685. For the persistence of the interest on the development of planimeter forms and computation methods, see 1922, May 2. Measuring area of indicator diagram. Power 55(18): 693–696; Walter Block. 1930, September. Measurements: Industrial and scientific. Instruments: 577–580, and Waldo Kliever. 1941, May. Integrator for circular ordinates. Instruments: 121. For a systematic promotion of the planimeter during the interwar period, see the cluster of articles by John L. Hodgson. 1928, November. Integration of diagrams. Instruments: 479–482, John L. Hodgson. 1929a, March. Integration of ‘Orifice Head’ charts by means of special planimeters. Instruments: 95–96, and John L. Hodgson. 1929b, July. The radial planimeter. Instruments: 227–231. For the historiographical importance of computations of relevance to the indicator diagram, see, Eugene Ferguson. 1992. Engineering and mind’s eye. Cambridge: MIT Press; Thomas L. Hankins, and Robert Silverman. 1995. Instruments and the imagination. Princeton: Princeton University Press, and Robert M. Brain, and M. Norton Wise. 1999. Muscles and engines: Indicator diagrams and Helmholtz’s graphical methods. In The science studies reader, ed. Mario Biagioli, 50–66. New York: Routledge.

  25. 25.

    See Henry S. Shaw. 1886. Mechanical integrators, including the various forms of planimeters. New York: D. Van Nostrand, Preface.

  26. 26.

    Ibid., 207 and 211.

  27. 27.

    Macon Fry . 1945, August. Designing computing mechanisms. Machine Design: 103–104.

  28. 28.

    Ibid.

  29. 29.

    Sam Flax. 1995. The tools to create. Trade Catalog, ca. 1995, 77.

  30. 30.

    Bush, A simple harmonic analyzer ”, 903.

  31. 31.

    See Frederick S. Dellenbaugh, Jr. 1921. February. An electromechanical device for rapid schedule harmonic analysis of complex waves. AIEE Journal: 135–144, and Frederick S. Dellenbaugh, Jr. 1923a, January. Another harmonic analyzer. AIEE Journal: 58–61, and Frederick S. Dellenbaugh, Jr. 1923b. Artificial lines with distributed constants. AIEE Transactions 42: 803–819 (discussion, 820–823).

  32. 32.

    Sylvanus P. Thompson. 1905, May 5. Harmonic analysis reduced to simplicity. Electrician: 78. For Thomson, see A.C. Lynch. 1989. Sylvanus Thompson: Teacher, researcher, historian. IEE Proceedings 136(Part A, 6): 306–312. For the MIT-GE partnership see, W. Bernard Carlson. 1988, July. Academic enterpreneureship and engineering education: Dugald C. Jackson and the MIT-GE cooperative engineering course, 1907–1932. Technology and Culture 29(3): 536–567.

  33. 33.

    John Hopkinson. 1894. May 11 and 18. The relation of mathematics to Cambridge Engineering. Electrician: 41–43, and 78–80, 85 respectively. For the editorial response, see 1894, May 11. The relation of Cambridge mathematics to engineering. Electrician: 44–46. For Thompson, see Thompson, Harmonic analysis reduced to simplicity: 78. For Kinter, see S.M. Kinter . 1904, May 22. Alternating current wave-form analysis. Electrical World and Engineer 63(22): 1203. For the context that prepared for these debates, see Bruce J. Hunt. 1983. Practice vs. theory: The British electrical debate, 1888–1891. ISIS 74: 341–355; D.W. Jordan. 1985. The cry for useless knowledge: Education for a New Victorian Technology. IEE Proceedings 132(Part A, 8): 587–601.

  34. 34.

    For Slichter , see Charles S. Slichter. 1909, July 15. Graphical computation of Fourier’s constants for alternating current waves. Electrical World 54: 146. For Beattie, see R. Beattie. 1912, April 19. The best form of the resonance method of harmonic analysis. Electrician 69: 63. For the rest of the references, see P.G. Agnew. 1909a, July 15. Experimental method for the analysis of E.M.F. waves. Electrical World 54(3): 142–147, and P.G. Agnew . 1909b, July 15. An electrical device for solving equations. Electrical World 54(3): 144–146.

  35. 35.

    L.W. Chubb. 1914, February. The analysis of periodic waves. Electric Journal 11(2): 93.

  36. 36.

    The analysis of wave forms. Electric Journal 11(2) (1914): editorial.

  37. 37.

    L.W. Chubb . 1915, May. Polar and circular oscillograms and their practical applications. Electric Journal 11(5): 262. For Steinmetz’s experience and, also, for the development of oscillographs, see Edward L. Owen. 1998. A history of harmonics in power systems. IEEE Industry Applications Magazine 4(1): 6–12. For Johnson, see J.B. Johnson. 1932, January. The cathode ray oscillogram. Bell System Technical Journal 11: 1–27. For the development of oscillographs , see, also, Frederick Bedell. 1942. History of A-C wave form, its determination and standardization. AIEE Transactions 61: 864–868; V.J. Philips. 1985, December. Optical, chemical and capillary oscillographs. IEE Proceedings 132(Part A, 8): 503–511.

  38. 38.

    Westinghouse Instruments and Relays (Catalogue 3-B). East Pittsburgh: Westinghouse Electric and Manufacturing Company, July 1916; Smithsonian Institution, National Museum of American History, Trade Catalogs Collection, Mezzanine Library. For the cost of calculating machines for engineering in the mid-1910s, see P.H. Skinner. 1915, January 7. Computing machines in engineering. Engineering News: 25–27.

  39. 39.

    For the interpretation of the electrical power network as an expansive reproduction of a mechanical power network, see Tympas, From the historical continuity of the engineering imaginary to an anti-essentialist conception of the mechanical-electrical-electronic relationship.

  40. 40.

    For the integraph, see Vannevar Bush, F.D. Gage, and H.R. Stewart. 1927, January. A continuous integraph . Franklin Institute Journal: 63–84; Vannevar Bush, and Harold L. Hazen. 1927, November. Integraph solutions of differential equations. Franklin Institute Journal: 575–615, and T.S. Gray. 1931, July. A photo-electric integraph. Franklin Institute Journal: 77–102.

  41. 41.

    See Robert N. Varney. 1942, January. An all electric integrator for solving differential equations. Review of Scientific Instruments 13: 10. For Norbert Wiener’s involvement in the MIT development of analyzers for harmonic analysis, see Norbert Wiener. 1929, April. Harmonic analysis and the quantum theory. Franklin Institute Journal 207: 525–534, and Norbert Wiener. 1930. Generalized harmonic analysis. Acta Mathematica 55: 118–258.

  42. 42.

    Morris Blair. 1943, March. An improved current integrator. Review of Scientific Instruments 14(3): 64–67; Otto H. Schmitt, and Walter E. Tolles. 1942, March. Electronic differentiation. Review of Scientific Instruments 13: 115–118. See, also, S. Leroy Brown , and Lisle L. Wheeler. 1941, March. A mechanical method for graphical solution of polynomials. Franklin Institute Journal 231(3), and S. Leroy Brown , and Lisle L. Wheeler. 1942, November. Use of a mechanical multiarmonograph for graphic types of functions and for solution of Pairs of non-linear simultaneous equations. Review of Scientific Instruments 13: 493–495.

  43. 43.

    Varney, An all electric integrator for solving differential equations, 15.

  44. 44.

    Bush, Gage, and Stewart, A continuous integraph, 63.

  45. 45.

    Leo Teplow. 1928, July. Stability of synchronous motors under variable-torque loads as determined by the recording product integraph. General Electric Review 31(7): 356. For the cooperative climate between MIT and GE, see Carlson, Academic entrepreneurship and engineering education: Dugald C. Jackson and the MIT-GE cooperative engineering course, 1907–1932: 536–567.

  46. 46.

    Teplow , Stability of synchronous motors under variable-torque loads as determined by the recording product integraph, 363.

  47. 47.

    Vladimir Karapetoff. 1925. Double integraph for electric line transients. Sibley Journal of Engineering 39: 243–260.

  48. 48.

    See Sibley Journal of Engineering XXXII (1918, January): 550.

  49. 49.

    See AIEE Transactions XXXVII, Part I (1918): 329.

  50. 50.

    See AIEE Journal XLI (1922): 107.

  51. 51.

    Vladimir Karapetoff. 1922, January. Generalized proportional dividers. Sibley Journal of Engineering XXXVI(1): 5–6.

  52. 52.

    Vladimir Karapetoff. 1923a, February. The ‘Blondelion’: A kinematic device which indicates the performance of a polyphase synchronous generator or motor. AIEE Transactions 42: 144–156.

  53. 53.

    Vladimir Karapetoff. 1923b, February. The ‘Heavisidion’: A computing kinematic device for long transmission lines. AIEE Transactions 42: 42–53.

  54. 54.

    It was “in preparation” in February 1923, see Karapetoff, The ‘Heavisidion’: A computing kinematic device for long transmission lines: 44, and The ‘Blondelion’: A kinematic device which indicates the performance of a polyphase synchronous generator or motor: 145.

  55. 55.

    Karapetoff, Double integraph for electric transients, 259–260.

  56. 56.

    Karapetoff, The ‘ Heavisidion ’: A computing kinematic device for long transmission lines.

  57. 57.

    R.L. Wegel, and C.R. Moore . 1924, February. An electrical frequency analyzer. AIEE Transactions: 457–466; J.W. Horton. 1928, June. The empirical analysis of complex electrical waves. Bell Telephone Laboratories Record Reprints B-320; C.R. Moore, and A.S. Curtis. 1927, April. An analyzer for the voice frequency range. Bell System Technical Journal 6: 217–247; H.C. Montgomery. 1938, July. An optical harmonic analyzer. Bell System Technical Journal 27: 406–415; F.G. Marble. 1944, April. An automatic vibration analyzer. Bell Laboratories Record 22(7): 376–380; J.D. Cockroft, R.T. Coe, J.A. Tyacke, and Miles Walker. 1925, January. An electric harmonic analyzer. IEE Journal 63(337): 69–113, and A. Blondel. 1925, March 7. Une Methode Potentiometrique d’Analyze Harmonique des Orders des Comants Alternatifs des Alternateurs. Revue Generale de l’ Electricite. For the parallel development of the theory of harmonic analysis, see George A. Campbell . 1928, October. The practical application of the Fourier integral. Bell System Technical Journal 7, 639–707, and George A. Campbell, and Ronald M. Foster. 1931, September. Fourier integrals for practical applications. Bell Telephone System Monographs B-584.

  58. 58.

    R.G. McCurdy, and P.W. Blye. 1929. Electrical wave analyzers for power and telephone systems. Bell Telephone Laboratories Reprints B-439: 2–3.

  59. 59.

    Antonin Svoboda. 1948. Computing mechanisms and linkages. New York: McGraw-Hill.

  60. 60.

    See Horsburgh ed., Modern instruments and methods of calculation: A handbook of the Napier Tercentenary Exhibition, 267–269, 253–258, and Section I.

  61. 61.

    Joseph Eugene Row. 1928, August. Instruments for the solution of triangles and other polygons. Instruments: 355.

  62. 62.

    C.F. Amor. 1986. The graphical methods of Sumpner, Drysdale, and Marchant: Solving the Kelvin Equation. IEE Proceedings 133(Part A, 6): 389.

  63. 63.

    R.L. Dietzold . 1937, December. The isograph: A mechanical root finder. Bell Laboratories Record 36(4): 131.

  64. 64.

    Ibid.

  65. 65.

    Harmonic analyzer for power circuits , NELA , Publication Number 278–22. Washington, DC: Edison Electric Institute Library Archives. This publication was a Serial Report by the Inductive Coordination Committee of the 1927–1928 Engineering National Section.

  66. 66.

    Chubb , The analysis of periodic waves: 93, and Fry, Industrial mathematics: 281.

  67. 67.

    Fry , Industrial mathematics, 280–281.

  68. 68.

    We introduced to human computers in Chapter 3, in the context of discussing the case of Edith Clarke. For a book-length study on the history of human computers, see David Alan Grier. 2007. When computers were human. Princeton: Princeton University Press.

  69. 69.

    Bush , F.D. Gage, and H.R. Stewart, A continuous integraph ; Karapetoff, Double integraph for electric transients: 244, and R.L. Dietzold, The isograph: A mechanical root finder: 134.

  70. 70.

    R.O. Mercner . 1937, December. The mechanism of the isograph. Bell Laboratories Record 26(4): 140.

  71. 71.

    Dietzold , The isograph: A mechanical root finder, 130.

  72. 72.

    Mercner , The mechanism of the isograph, 137 and 140.

  73. 73.

    Karapetoff, The ‘Heavisidion’: A computing kinematic device for long transmission lines, 53.

  74. 74.

    Karapetoff, Double integraph for electric transients, 245.

  75. 75.

    Dellenbaugh , Another harmonic analyzer, 60.

  76. 76.

    Fry, Industrial mathematics, 280. For the concept of the imago as used in the context of the three Lacanian orders—Real, Imaginary, Symbolic, see Ellie Rangland-Sullivan. 1996. Jacques Lacan and the philosophy of psychoanalysis. Chicago: University of Illinois Press.

  77. 77.

    Karapetoff, The ‘Heavisidion’: A computing kinematic device for long transmission lines, 50.

  78. 78.

    A I have shown elsewhere, Bush did the same with the artificial line . See Tympas, A deep tradition of computing technology: calculating electrification in the American West.”

  79. 79.

    For the Nyquist diagram , see David Mindell. 2000, July. Opening black’s box: Rethinking feedback’s myth of origin. Technology and Culture 41(3): 405–434.

  80. 80.

    Bush , A simple harmonic analyzer, 903.

  81. 81.

    Charles Proteus Steinmetz. 1917. Engineering mathematics, 3rd Rev. and Enlarg ed., 255. New York: McGraw-Hill.

  82. 82.

    Bedell, History of A-C wave form, its determination and standardization, 866.

  83. 83.

    Owen, A history of harmonics in power systems, 11.

  84. 84.

    Bedell, History of A-C wave form, its determination and standardization, 866. For the quote from Fisken, see Owen, A history of harmonics in power systems, 6.

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    Aristotle Tympas

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Tympas, A. (2017). “Like the Poor, the Harmonics Will Always Be with Us”. In: Calculation and Computation in the Pre-electronic Era. History of Computing. Springer, London. https://doi.org/10.1007/978-1-84882-742-4_4

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