Planimeters
Resources

A planimeter with a closed curve.

Resources

In addition to the instruments discussed in this object group, the National Museum of American History's Division of Work and Industry owns a few planimeters as well as steam engine indicators whose output was measured with planimeters. Catalogues from manufacturers and distributors are part of the trade literature collections of the Smithsonian Institution Libraries.

Additionally, these museum databases include planimeters among their collections:

Further Reading

Care, Charles. "Illustrating the History of the Planimeter." Undergraduate 3rd Year Project, University of Warwick, 2004.http://empublic.dcs.warwick.ac.uk/projects/planimeterCare2004/Docs/report.pdf. Focuses on early history of the instrument and assesses computer models of the instrument's operation.

Carse, G. A., and J. Urquhart. "Planimeters." In Handbook of the Napier Tercentenary Celebration, edited by E. M. Horsburgh, 190–206. Edinburgh, 1914. One of two articles on planimeters that the Royal Society of Edinburgh solicited for a memorial volume on "modern instruments and methods of calculation." Reprinted by the Charles Babbage Institute in 1982.

Dawes, Howard. Instruments of the Imagination: A History of Drawing Instruments in Britain 16001850. Worcestershire: The Dawes Trust Ltd., 2009. General introduction to British makers of mathematical and drawing instruments with two pages on planimeters.

Eggers, John. "The Compensating Polar Planimeter." University of California-San Diego, 2010. http://www.math.ucsd.edu/~jeggers/Resources/planimeter_slides.pdf. Walks readers through the mathematics of the instrument.

Fischer, Joachim. "Instrumente zur Mechanischen Integration." In Brückenschläge – 25 Jahre Lehrstuhl für Geschichte der exakten Wissenschaften und der Technik an der Technischen Universität Berlin 1969–1994, edited by H.-W. Schütt and B. Weiss, 111–156. Berlin, 1995. Summary article by the world's leading expert on planimeters.

Foote, Robert L., Mark Levi, and Serge Tabachnikov. "Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture." American Mathematical Monthly 120 (2013): 199–216. Shows the correlations between the motion of a bicycle and the motion of a hatchet planimeter.

Foote, Robert L., and Ed Sandifer. "Area Without Integration: Make Your Own Planimeter." In Hands on History: A Resource for Teaching Mathematics, edited by Amy Shell-Gellasch, 71–88. Historical background on planimeters and suggestions for several classroom activities, including constructing a polar planimeter from TinkerToys®. Foote has several working papers housed on arXiv and a companion website, http://persweb.wabash.edu/facstaff/footer/Planimeter/PLANIMETER.HTM.

Green, David R. The Planimeter Vault. June 16, 2008. http://www.planimetervault.com. Information on Coffin and hatchet planimeters.

Hawkins, Nehemiah. Hawkins' Indicator Catechism. New York: Theo. Audel & Co., 1903. Discussion of the steam engine indicator, including descriptions of several versions of planimeters that were used to read the diagrams produced by indicators.

Heather, J.F. Mathematical Instruments: Their Construction, Adjustment, Testing, and Use. Rev. ed. 3 vol. London: Crosby Lockwood and Co., 1870. Describes the use of various drawing and mathematical instruments, including Amsler's polar planimeter.

Henrici, Olaus. "On Planimeters." In Report of the Sixty-fourth Meeting of the British Association for the Advancement of Science, 496–523. London, 1894. Classic history of the instrument.

Kidwell, Peggy Aldrich. "Planimeter." In Instruments of Science: An Historical Encyclopedia, edited by Robert Bud and Deborah Jean Warner, 467–469. London: Garland Publishing, 1998. Summary history of the various forms of planimeters.

Klein, Felix. Elementary Mathematics from an Advanced Standpoint: Geometry. Translated by E. R. Hedrick and C. A. Noble. Reprint; Mineola, N.Y.: Dover, 1949. 11–15. Lecture by the famed German mathematician and educator on the operation of Amsler polar planimeters.

Leise, Tanya. "As the Planimeter's Wheel Turns: Planimeter Proofs for Calculus Class." College Mathematics Journal 38, no. 1 (2007): 24–31. Gives formulas for a variety of forms of planimeter.

McCoy, Clark, ed. Keuffel & Esser Catalogs and Price Lists for Slide Rules, [1881–1972]. 2002-2012. http://www.mccoys-kecatalogs.com/. Planimeter models sold by K&E are also explained and linked to relevant catalog pages.

Morin, Henri de. Les Appareils d'Intégration. Paris: Gauthier-Villars, 1913. Discusses the mathematical principles and construction of planimeters, integrators, integraphs, and harmonic analyzers.

Otnes, Bob. "American Planimeters." Journal of the Oughtred Society 11, no. 2 (2002): 59–64. Brief explanation of polar, linear, and radial planimeters that were used to measure steam engine indicator diagrams.

Schwartz, Hyman A. "The Willis Planimeter." Rittenhouse 7 (1993): 60–64. Account of the planimeter invented by American engineer Edward Jones Willis.