5. “The Inner Satisfaction That Comes with Each Use of the Alignment Chart”

On Steinmetz, see Ronald R. Kline. 1987. Science and engineering theory in the invention and development of the induction motor 1880–1900. Technology and Culture 28(2): 283–313. On Kennelly, see James E. Brittain. 2006, September. Arthur E. Kennelly. Proceedings of the IEEE 94(9): 1773–1775.

Charles Proteus Steinmetz. 1917. Engineering mathematics, 3rd ed. Rev. and Enlarged, 283. New York: McGraw-Hill.

Ibid., 284.

Ibid., 288–289.

Ibid., 290.

Ibid., 293.

Ibid., 281.

Ibid., 293a.

Ibid., 293a–293b.

For computational projects that were based on computors, usually women, see David Alan Grier. 2007. When computers were human. Princeton: Princeton University Press; Jennifer S. Light. 1999, July. When computers were women. Technology and Culture 40(3): 455–483; and James E. Brittain. 1985. From computor to electrical engineer: the remarkable career of Edith Clarke. IEEE Transactions on Education E-28(4): 184–189. See, also, Margaret W. Rossiter 1980. ‘Women’s work’ in science. ISIS 71(258): 123–140; I. Gratan-Guinness. 1990. Work for the hairdressers: the production of de Prony’s logarithmic and trigonometric tables. Annals of the History of Computing 12(3): 177–185; Paul Ceruzzi. 1991. When computers were human. Annals of the History of Computing 13(1): 237–244; Lorraine Daston. 1994, Autumn. Enlightenment calculations. Critical Inquiry 21(1): 182–202; Harry Polachek. 1995, Fall. History of the journal ‘Mathematical tables and other aids to computation’ 1959–1965. IEEE Annals of the History of Computing 17(3): 67–74; Andrew Warwick. 1994. The laboratory of theory or what’s exact about the exact sciences? In The values of precision, ed. M. Norton Wise, 311–351. Princeton: Princeton University Press; Martin Campbell-Kelly, and William Aspray. 1996. Computer: A history of the information machine. New York: Basic Books, Chapter 1; Jennifer S. Light, “When Computers Were Women”; and Mary Croarken, and Martin Campbell-Kelly. 2000, October–December. Beautiful numbers: The rise and decline of the British Association Mathematical Tables Committee, 1871–1965. IEEE Annals of the History of Computing 22(4): 44–46. For Blanch, see David Alan Grier. 1997. Gertrude Blanch of the mathematical tables project. IEEE Annals of the History of Computing 19(4): 18–27; David Alan Grier. 1998. The math tables project of the work project administration: The reluctant start of the computing era. IEEE Annals of the History of Computing 20(3): 33–49, and David Alan Grier. 2000, January–March. Ida Rhodes and the dreams of a human computer, IEEE Annals of the History of Computing 22(1): 82–85.

Arthur E. Kennelly. 1925. The application of hyperbolic functions to electrical engineering problems. New York: McGraw-Hill. First edited in 1912 and reedited in 1919), Arthur E. Kennelly. 1914a. Tables of complex hyperbolic and circular functions. Cambridge, MA: Harvard University Press, Arthur E. Kennelly. 1914b. Chart Atlas of complex hyperbolic and circular functions. Cambridge, MA: Harvard University Press, and Arthur E. Kennelly. 1928. Electric lines and nets: Their theory and electrical behavior. New York: McGraw-Hill. First edited in 1917.

Kennelly, Tables of Complex Hyperbolic and Circular Functions, Preface.

Ibid., 102.

Ibid., 102.

See Edwin J. Houston, and A.E. Kennelly. Resonance in alternating current lines, AIEE Transactions 12: 139; for Pupin, see: 159–160.

Ibid., 160–161.

Ibid., 168.

Kennelly, The application of hyperbolic functions to electrical engineering problems, vii.

Arthur E. Kennelly. 1913, June 14. A convenient form of continuous-current artificial line. Electrical World 61(24): 1311.

For Kennelly, see Kennelly, A convenient form of continuous-current artificial line: 1311, and Arthur E. Kennelly. 1912, August 10. An investigation of transmission line phenomena by means of hyperbolic functions: the distribution of voltage and current over pi artificial lines in the steady state. Electrical World 60(6): 306–311. For Carson, see John Carson. 1919. Theory of the transient oscillations of the electrical networks and transmission systems. AIEE Transactions 38(1): 386.

Kennelly, Chart Atlas of complex hyperbolic and circular functions.

See Vannevar Bush. 1943. Arthur Edwin Kennelly, 1861–1939. National Academy of Sciences Biographical Memoirs 22: 89, and Edith Clarke. 1944. Trends in power system analysis. Midwest Power Conference Proceedings 7: 177.

M. Campbell-Kelly, M. Croarken, R. Flood, and E. Robson. 2003. The history of mathematical tables: From sumer to spreadsheets. Oxford/New York: Oxford University Press. For the diversity or the roles of those involved in table-making and using, the difference between tables based on empirical data and mathematical formula, the role of communities of table makers and users, and the styles of table making, see pages 2, 4, 5–9, and 9, respectively.

Steven Bradley Smith. 1983. The great mental calculators, 343–344. New York: Columbia University Press.

See F.A. (Tony) Furfari. 1999. Benjamin Garver Lamme: Electrical engineer. IEEE Industry Applications Magazine 5(6): 13.

For an example of the historiographical promotion of Steinmetz as being gifted with exceptional mental faculties, see Jonathan Norton Leonard. 1932. Loki: The life of Charles Proteus Steinmetz , 148–149. Garden City: Doubleday, Doran, and Company. For Brittain’s corrective account, see the chapter on Steinmetz in James E. Brittain . 1970. B. A. Behrend and the beginnings of electrical engineering, 1870–1920, diss., Case Western University.

See page xiv in the “Introduction” by Williams R. Williams in the reprint edition (Los Angeles: Tomash Publishers, 1982) of E.M. Horsburgh. (ed.). 1914. Modern instruments and methods of calculation: A handbook of the Napier tercentenary exhibition. London: Bell and Sons.

For Warwick, see Warwick, The laboratory of theory or what’s exact about the exact sciences?, 343.

See M.W. Franklin. 1909, September. Transmission line calculations, Part I. General Electric Review 12(9): 447–451; William Nesbit. 1919–1920. Electrical characteristics of transmission circuits. Electric Journal. article series; Dressel Dewit Ewing. 1923. Tables of transmission line constants. Lafayette: Purdue University Press; Frederick Kurt Kirsten. 1923–1929. Transmission line design, series of publications. Seattle: University of Washington Press; David Eugene Pernot. 1916. Formulae and tables for the design of air-core inductance coils. Berkeley: University of California Press, and T.R. Rosebrugh. 1919. The calculation of transmission line networks, Bulletin of the School of Engineering Research 1. Toronto: University of Toronto Press. For Kennelly’s and Pernot’s more general tables, see Kennelly, Tables of complex hyperbolic and circular functions, and Frederick Eugene Pernot. 1918. Logarithms of hyperbolic functions to twelve significant figures. Berkeley: University of California Press.

See Kennelly, Tables of complex hyperbolic and circular functions, Preface and 209–212.

See Kennelly, Chart Atlas of complex hyperbolic and circular functions, appendix. For Woodruff, see L.F. Woodruff. 1938. Principles of electric power transmission, 115–116. New York: Wiley, and Complex hyperbolic function charts. Electrical Engineering (May 1935).

See Lemuel Serrell. 1889, May 25. Calculations for long-distance power transmission. Electrical World: 292. For Franklin and Nesbit, see Franklin, Transmission line calculations, Part I, and Nesbit, Electrical characteristics of transmission circuits.

See Charles F. Scott. 1905, April. How to remember the wire table . Electric Club Journal 11(4): 220–223; Harold Pender. 1905, May. Formulae for the Wire Table. Electric Club Journal 11(5): 327; Y. Sakai. 1905, October. How to use the slide-rule on the wire table. Electric Club Journal 11(10): 632–633; and Miles Walker. 1905, November. Calculating temperature rises with a slide rule. Electric Club Journal 11(11): 694–696. For Scott’s sustained interest on the issue, see Charles F. Scott. 1919, July. Finding the size of wire. Electric Journal 16(7): editorial.

Walker, Calculating temperature rises with a slide rule: 694.

For 1895, see N. Hawkins. 1895. Handbook of calculations for engineers and firemen, 79–82 and 296. New York: Audel. For 1932, see Frank D. Graham. 1932. Audel’s new electric library, mathematics-calculations, vol. XI. New York: Audel.

Compare Graham, Audel’s new electric library, mathematics-calculations to Kennelly, Tables of complex hyperbolic and circular functions.

For the historiographical significance of studying technical journals, see Eugene Ferguson . 1989. Technical journals and the history of technology. In In context: History and the history of technology (Essays in Honor of Melvin Kranzberg). eds. Stephen H. Cutliffe, and Robert C. Post, 53–70. Bethlehem: Lehigh University Press; James E. Brittain. 1989. The evolution of electrical and electronics engineering and the proceedings of the IRE: 1913–1937 and 1938–1962. Proceedings of the IEEE 77(6): 837–856 and 78, no. 1 (1990): 5–30; and P. Strange. 1979. Early periodical holdings in the IEE Library. Proceedings IEE 126(9): 941–94, and P. Strange. 1985. Two electrical periodicals: The electrician and the electrical review 1880–1890. IEE Proceedings 132, part A(8): 575–581.

General Electric Company. 1911a, September. Hydro-electric calculations. Engineering Department Technical Letter, no. 316 and 316A (November, 1913). Schenectady/New York: General Electric Archives.

General Electric Company. 1909, September. Transmission line calculations. Engineering Department Technical Letter (no. 309, September 1909 and no. 309A, July 1911). Washington, DC: Smithsonian Institution, National Museum of American History, Trade Catalogs Collections, Mezzanine Library.

General Electric Company. 1911b, July. Tables for transmission line calculations. Engineering Department Technical Letter, no. 309-A. Washington, DC: Smithsonian Institution, National Museum of American History, Trade Catalogs Collections, Mezzanine Library.

General Electric Company. 1911c, November. Overhead line calculations. Engineering Department Technical Letter, no. 318. Schenectady: General Electric Archives.

General Electric Company. 1919, February. Overhead line calculations. Engineering Department Technical Letter, no. 335D. Schenectady: General Electric Archives.

Franklin, Transmission line calculations, Part I: 447–451.

Edith Clarke. 1943. Circuit analysis of A-C power systems: Symmetrical and related components, vol. I. New York: Wiley.

Scott, Finding the size of wire: editorial.

Nesbit, Electrical characteristics of transmission circuits: parts I–XIII.

Scott, Finding the size of wire: editorial.

William Nesbit. 1926. Electrical characteristics of transmission circuits, 3rd Edn. East Pittsburgh: Westinghouse Technical Night School Press.

Nesbit, Electrical characteristics of transmission circuits: part I, 279.

Ibid.

Ibid., part XIII, 1920, 531.

Frederick S. Dellenbaugh, Jr. 1923. Artificial lines with distributed constants. AIEE Transactions 42: 803–819. Discussion: 820–823.

Herbert Bristol Dwight. 1925. Transmission line formulas: A collection of methods of calculation for the electrical design of transmission lines, 2nd Rev. and enlarged edition. New York: Van Nostrand, first edition, 1913).

Nesbit, Electrical characteristics of transmission circuits: part XIII, 532.

Donald M. Simons. 1925, August. Calculation of the electrical problems of transmission by underground cables. Electric Journal 22(8): 366–384.

Frederick S. Dellenbaugh, Jr. 1921, February. An electromechanical device for rapid schedule harmonic analysis of complex waves. AIEE Journal: 142.

Ibid., 142.

Ibid., 143.

Alfred E. Wiener. 1894, June 1/June 15. Practical notes on dynamo calculation. The Electrical Engineer: 640–641 and 701–703.

L.E. Imlay. 1925, February. Mechanical characteristics of transmission lines II: Span formulae and general methods of calculation. Electric Journal 22(2): part II, 53–57.

L. Maggi. 1946. The calculation of block foundations for transmission line towers. International Conference on Large Electric Systems (CIGRE) 2(220): 1.

Frederick Eugene Pernot. 1919. Formulae and tables for the design of air-core inductance coils and logarithms of hyperbolic functions to twelve significant figures and an extension of the step-by-step method of transmission line computation. Berkeley: University of California Press.

Ewing, Tables of transmission line constants.

Kirsten, Transmission line design.

M.L. Thielemans. 1920. Calculs et Diagrammes Des Lignes De Transport De Force A Longue Distance. Comptes Rendus, 1170, and P. Thielemans. 1920. Calculs, Diagrammes et Regulation Des Lignes De Transport D’ Energie A Longue Distance. Revue Generale De L’Electricite: 403, 435, 475, 515, and (1921): 451.

Frank D. Graham, Audel’s New Electric Library, Mathematics-Calculations, Preface.

Hawkins, Handbook of calculations for engineers and firemen, 296.

N. Hawkins. 1897. New catechism of electricity: A practical treatise. New York: Audel, 331.

Ibid., 329.

Alfred E. Wiener . 1898. Practical notes of dynamo -electric machines: A manual for electrical engineers and a text-book for students of electro-technics. New York: W. J. Johnston, and Frederick Bedell, and A. C. Crehore. 1893. Alternating currents: An analytical and graphical treatment for students and engineers. New York: W. J. Johnston Company. For Bedell and Crehore, see James E. Brittain, B. A. Behrend and the Beginnings of Electrical Engineering, 1870–1920.

Charles Proteus Steinmetz, Engineering mathematics, advertisement (First edition, 1911).

Ibid.

Ibid.

Charles Proteus Steinmetz (with the Assistance of Ernst J. Berg). 1897. Theory and calculation of alternating current phenomena. New York: W. J. Johnston Company, advertisement.

Aristotle Tympas, and Fotini Tsaglioti. 2016. L’usage du calcul à la production: le cas des nomogrammes pour machines-outils au XXe siècle. In Le monde du génie industriel au XXe siècle: Autour de Pierre Bézier et de machines-outils, eds. Serge Benoit and Alain Michel, 63–73. Paris: Collection Sciences Humaines et Technologie, Pôle editorial de l’UTBM.

Thomas L. Hankins. 1999. Blood, dirt, nomograms: A particular history of graphs . ISIS 90: 71.

H.A. Evesham. 1986, October. Origins and development of nomography. Annals of the History of Computing 8(4): 331. On Pebble’s article (actually a series of articles), see J.P. Pebble. 1908, May 30, September 19, and November 13. The construction of graphical charts. American Machinist.

Hankins, Blood, dirt, nomograms: A particular history of graphs: 74–76.

Thomas L. Hankins, and Robert J. Silverman. 1995. Instruments and imagination. Princeton: Princeton University Press.

Constance Areson Clark. 2001, March. Evolution for John Doe: pictures, the public, and the scopes trial debate. Journal of American History 87(4): 1278–1279, footnote no. 5.

See Steven Lubar. 1995, April. Representation and power. Technology and Culture 36(2 Suppl): 54–82.

See John K. Brown. 2000, April. Design plans, working drawings, national styles: Engineering practice in Great Britain and the United States, 1775–1945. Technology and Culture 41(2): 195–238.

W.L. Heard . 1946. Coordinated graphic symbols for electric power and control drawings. Edison Electric Institute Bulletin 14(9): 311, and Central Station Engineers of the Westinghouse Manufacturing Company. 1944. Electrical transmission and distribution reference book, 612–618. East Pittsburgh: Westinghouse Electric and Manufacturing Company.

See Steinmetz, Engineering mathematics. For articles on the history of nomography, see Evesham, Origins and development of nomography: 323–333, and Hankins, Blood, dirt, nomograms: A particular history of graphs: 50–80.

For Whittaker, see Warwick, The laboratory of theory or what’s exact about the exact sciences?, 311–351. For d’ Ocagne, see H.A. Evesham, “Origins and Development of Nomography”. For Lipka’s reference to Whittaker’s pioneering mathematical laboratory, see the opening pages in Joseph Lipka. 1918. Graphical and mechanical computation. New York: Wiley. For Whittaker’s role in the organization of the 1914 Edinburgh Exhibition, see the opening pages in Horsburgh, Modern instruments and methods of calculation: A handbook of the Napier tercentenary exhibition.

See Maurice d’ Ocagne. 1928. Le Calcul Simplifie par les Procedes Mecaniques et Graphiques, troisieme edition. Paris: Gauthier-Villars. For the interpretation of d’ Ocagne as having made the analog-digital demarcation central, see the recent edition of d’Ocagne’s treatise in English, which was translated by J. Howlett and M.R. Williams (Los Angeles: Tomash Publishers, 1986).

See Ijzebrand Schuitema. 1999, Spring. Articles on Dutch contribution to slide rule history in the 20th century, Number 2: F.J. Vaes. Journal of the Oughtred Society 8(2): 39–42; G.S. Merrill. 1946, June. Slide-disk calculator . General Electric Review 49: 30–33; Antonin Svoboda. 1948. Computing mechanisms and linkages. New York: McGraw-Hill; Douglas P. Adams. 1964. Nomography: Theory and application. Hamden: Archon; Vladimir Kaparetoff. 1923, February. The ‘Heavisidion’: A computing kinematic device for long transmission lines. AIEE Transactions 42: 42–53; Ijzebrand Schuitema. 1993, October. The ALRO circular slide rule. Journal of the Oughtred Society 2(2): 24–37; and Steve M. Slaby’s introduction in John H. Fasal. 1968. Nomography. New York: Frederick Ungar.

See Kaparetoff, The ‘Heavisidion’: A computing kinematic device for long transmission lines: 53, and C. Harold Berry. 1921, August 2. The chilling of condensate. Power 54(5): 182.

See Graham, Audels’ new electric library, mathematics-calculations, 93.

Horsburgh, Modern instruments and methods of calculation: A handbook of the Napier tercentenary exhibition, 279.

See the review of the recent English edition of d’ Ocagne’s book by H.A. Evesham in the Annals of the History of Computing 9 (no.3/4, 1988), 376.

For Ferguson ’s introduction to nomography, see Eugene S. Ferguson. 1992. Engineering and the mind’s eye, 151–152. Cambridge: MIT Press.

See Maurice d’ Ocagne. 1915. Numerical tables and nomograms. In Napier Tercentenary Memorial Volume, ed. Gargil Gilston Knott, 279–280. London: Longmans, Green, and Company and Royal Society of Edinburgh.

For Bush’s 1920 analyzer and nomogram, see Vannevar Bush. 1920a, October. A simple harmonic analyzer. AIEE Journal: 903–905, and Vannevar Bush. 1920b, July. Alignment chart for circular and hyperbolic functions of a complex argument in rectangular coordinates. AIEE Journal 39: 658–659. For a comparison with Kennelly’s charts, see Arthur Edwin Kennelly, Chart Atlas of complex hyperbolic and circular functions.

See William M. Schlesinger. 1982, March 5. Power transmission,” Electrical World XIX(10): 154–155, and Edith Clarke. 1925, May. Simplified transmission line calculations. General Electric Review 29(5): 321–329.

For Kennelly’s charts, see Kennelly, Chart Atlas of complex hyperbolic and circular functions. For Clarke’s history of power analysis, see Clarke, Trends in power analysis: 172–180.

See Clarke, Simplified transmission line calculations: 321.

Schlesinger, Power transmission: 154.

See H.C. Stanley. 1918, February. Graphical representation of resistances and reactances in multiple. General Electric Review 21(2): 133; Charles Carter, Jr. 1963. Graphic representation of the impedance of networks containing resistances and two reactances. American Power Conference Proceedings 25: 834–837, and Fr. Jacobsen. 1946. Diagram for calculating the sag and strain of conductors of overhead lines. CIGRE 2(214).

C.R. Van Trump. 1901. A station load diagram. National Electric Light Association ( NELA ) 24th Convention: 363–364, and 368.

Allan C. Haskell. 1919. How to make and use graphic charts, 527. New York: Codex.

Ibid., iii–iv and 1.

Ibid. On Fry, see Thornton C. Fry. 1941, July. Industrial mathematics. Bell System Technical Journal 20(3): 280, and Haskell, How to make and use graphic charts, iii.

Haskell, How to make and use graphic charts, 2 and 4.

Ibid., 6.

Hankins, Blood, dirt, nomograms: A particular history of graphs: 77.

Ronald R. Kline. 1992. Steinmetz : Engineer and socialist, 91. Baltimore: The John Hopkins University Press.

For a general introduction to the relative difference between the mode of production at General Electric and at Westinghouse, see Philip Scranton. 1997. Endless novelty: Specialty production and American industrialization. Princeton: Princeton University Press.

Woodruff, Principles of electric power transmission.

Brittain, B. A. Behrend and the beginnings of electrical engineering, 1870–1920, 142.

Ibid., 139–140.

See Robert D. Evans and H.K. Sels. 1924, February. Power limitations of transmission systems. AIEE Transactions 43: 26–38 and 71–103 (discussion); Edith Clarke. 1926, February. Steady-state stability in transmission systems: Calculation by means of equivalent circuits or circle diagrams. AIEE Transactions 45: 22–41 and 80–94 (discussion); Woodruff, Principles of electric power transmission, chapter VI, and Central Station Engineers of the Westinghouse Manufacturing Company, Electrical Transmission and Distribution Reference Book.

See P.J. Ryle. 1948. Practical long line A.C. Transmission line calculations and the design and use of a circle diagram calculating board. The International Conference on Large Electric Systems, 12th session 8, no. 402: 1–12, and E. Raymond-Barker. 1903, August 28. The calculator board and graphic methods. Electrical Review 53: 329–331.

Raymond-Barker, The Calculator Board and Graphic Methods: 329–331.

Yu Wang. 1916, June 15. The slide rule replaced by a new computer. Engineering News 75(24): 1120, and Yu Wang. 1917. New parallel-line slide rule to replace slide-rule for rapid calculations. Electrical Review and Western Electrician 70(10): 22.

Ryle, Practical long line A.C. Transmission line calculations and the design and use of a circle diagram calculating board: 6.

See Ryle, Practical long line A.C. Transmission line calculations and the design and use of a circle diagram calculating board: 1–2; Edith Clarke. 1923, June. A transmission line calculator . General Electric Review 26(6): 380–390; and Houston and Kennelly, Resonance in alternating current lines: 133–169.

O.S. Bragstad. 1924. Determination of efficiency and phase displacement in transformers by measurement on open circuit and short circuit tests. Transactions of the First World Power Conference 3: 1021.

See Arthur A. Boelsterli. 1925. Charts for regulation of transformers. IEE Journal 63: 692; Central Station Engineers of the Westinghouse Manufacturing Company, Electrical transmission and distribution reference book, 407 and 418; and Perry Shelley. 1947, January. The Oklahoma gas and electric company method for load determination on distribution transformers. Edison Electric Institute Bulletin: 17–19.

G. Combet. 1929, April 6. Methode Graphique de Calcul des Reseaux de Distribution d’ Energie Electrique. Revue Generale de l’ Electricite 25(14): 535–542; Leonard H. Gussow. 1946, January 5. Calculating voltage drop in industrial A. C. circuits. Electrical World: 60–63; and Leonard H. Gussow. 1941, October. Kurman Calculator . Instruments 14(10).

See Joergen Rybner. 1930, March. Nomograms. General Electric Review 33(9): 164, and A.H. Canada. 1948, March. Nomographs for computing exponential relationships. General Electric Review 51: 48.

See Richard A. Epperly, G. Erich Heberlein, and Lowry G. Eads. 1999. Thermography: A tool for reliability and safety. IEEE Industry Applications Magazine 5(1 and 3): 28–36 and 8, respectively; Randolph P. Hoelscher, Joseph Norman Arnold, and Stanley H. Pierce. 1952. Graphic aids in engineering computation. New York: McGraw-Hill, v; H.J. Allcock. 1950. The Nomogram: The theory and practical construction of computation charts . London: Pitman; A. Giet, J.W. Head, and H.D. Pippen. 1956. Abacs or nomograms: An introduction to their theory and construction illustrated by examples from engineering and physics. New York: Philosophical Library; and Norman H. Crowhurst. 1965. Graphical calculators and their design, 2–4. New York: Hayden.

For Slaby, see Fasal, Nomography, v. For Adams, see Adams, Nomography: Theory and application, v.

See Adams, Nomography : Theory and application, 176. For references to the incorporation of graphic representation into electric power analysis by the use of electronic computers, see Don Bissell. 1998, April–June. Was the IDIIOM the first stand-alone CAD platform? IEEE Annals of the History of Computing 20(2): 17, and Kristine K. Fallon. 1998, April–June. Early computer graphics developments in the architecture, engineering, and construction industry. IEEE Annals of the History of Computing 20(2): 23.