Amsler is also credited with conceiving a design for a planimeter that restricted the movement of the end of the tracer arm opposite the tracer point to a straight line. The collections suggest that Americans were particularly interested in further developing linear planimeters, with examples patented by John Coffin, Edward Jones Willis, and Frederick R. Williams. Another linear planimeter sold by an American company and an instrument that does not fit any of the categories of planimeters are also included on this page.
In 1875, Danish mathematician and cavalry officer Holger Prytz came up with a final form of planimeter—the hatchet planimeter. It simply consists of a rod with a tracer point at one end and a chisel edge at the other. As the tracer goes around the drawing, the chisel makes a zigzag path. The product of the length of the path and the length of the rod gives the area of the drawing. The result, though, is not as accurate as those provided by more complex forms of planimeters. At present, no examples of this instrument are known to be among the mathematics collections.
"Planimeters - Linear" showing 1 items.
- This German silver instrument consists of three pieces. The first is a seven-inch tracer arm with a tracer point at one end and a measuring wheel with vernier and a peg at the other end. The peg fits into a groove on the second piece, which is a rectangular plate with a removable sliding ruler that is divided on all four sides into 96, 120, 150, and 180 parts. A pivoting rectangular blade is at the right end of the second piece. This piece is marked: KEUFFEL & ESSER Co N.Y. Pat. Dec. 8. 1903 No 7. The third piece is a folding L-shaped ruler. The long arm is graduated to 1/4-inch and numbered from 1 to 5. The short arm is divided to tenths of an inch and numbered from 5 to 20.
- A rectangular hardwood case has green velvet lining the supports for the instrument. A small ivory plate screwed inside the lid is marked: KEUFFEL & ESSER CO. (/) NEW YORK (/) ST. LOUIS CHICAGO (/) SAN FRANCISCO.
- Frederick (Frank) R. Williams of Syracuse, N.Y., patented this planimeter. He may have been a merchant who sold his grocery store in 1906. The instrument was never advertised in Keuffel & Esser catalogs. Since this example was donated by K&E in 1971 and since the serial number is so low (7), perhaps K&E manufactured it as a prototype or for use with its own steam engine indicators, but decided not to offer it for sale to the public. Compare to the linear planimeter invented by John Coffin, MA*323708, 1987.0107.03, MA*323705, and MA*323706.
- References: Frank R. Williams, "Planimeter" (U.S. Patent 746,427 issued December 8, 1903); "Skaneateles," Syracuse Journal (January 10, 1906), 6, http://fultonhistory.com/newspapers%20Disk3/Syracuse%20NY%20Daily%20Journal/Syracuse%20NY%20Daily%20Journal%201906.pdf/Syracuse%20NY%20Daily%20Journal%201906%20-%200104.PDF; Clark McCoy, ed., "Planimeters and Integrators in K&E Catalogs by Model Number," http://www.mccoys-kecatalogs.com/PlanimeterModels/PlanimeterModels.htm; Bob Otnes, "American Planimeters," Journal of the Oughtred Society 11, no. 2 (2002): 59–64; accession file.
- Currently not on view
- date made
- Keuffel & Esser Co.
- ID Number
- catalog number
- accession number
- Data Source
- National Museum of American History, Kenneth E. Behring Center