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.
- Even after the apparent commercial success of his "improved planimeter," Edward Jones Willis (1866–1941), a steam and electrical engineer from Richmond, Va., continued to experiment with planimeter designs. On January 17, 1922, he received a patent for a planimeter that had the measuring wheel on a spindle instead of a wheeled carriage, and had a magnifying glass attachment.
- Willis noted that date on this instrument, but it bears little resemblance to the patent drawings. A brass arm with metal tracers at both ends moves perpendicularly to a brass frame. The arm is evenly divided in increments marked 99, 88, 77, 66, 55, 44, and 33. A metal bar at the front of the frame has a brass slide. Next are two brass wheels on spindles fastened to a brass plate in the center. At the back is a wooden triangular ruler with six scales on white celluloid. These scales divide the inch into 100, 50, 60, 30, 80, and 40 parts. The ruler is marked: J. L. ROBERTSON & SONS, N.Y. Presumably, the ruler came from one of the Improved Willis Planimeters made by Robertson between 1896 and the 1910s. The back of the frame is marked: E. J. WILLIS (/) RICHMOND, VA. (/) PAT. APL'D FOR.
- A metal rod has rectangular brass ends. A triangular metal plate has brass bolts holding prickers and a brass post that holds one end of the rod. A small brass clamp is loose in the crudely made wooden case, which appears to be made from a shipping crate. Handwriting on the inside of the lid reads: Edward J. Willis (/) Room 119 Mutual Bldng (/) P.O. Box 416 Richmond Va (/) Jany 17h 1922 (/) WILLIS TWO WHEEL PLANIMETER. There is no record of a patent that applies specifically to this apparent prototype.
- For information on Willis's earlier patents and planimeters, see 1994.0356.02, MA*324247, MA*323703, and MA*323704. At the same time that Willis worked on his later planimeters, he became interested in celestial navigation and published two textbooks on the subject. He invented a navigating machine and an altitude-azimuth instrument in the 1930s.
- References: Edward J. Willis, "Planimeter" (U.S. Patent 1,404,180 issued January 17, 1922); Hyman A. Schwartz, "The Willis Planimeter," Rittenhouse 7, no. 2 (1993): 60–64; Willem F.J. Mörzer Bruyns, "The Willis Navigating Machine: A Forgotten Invention," Rittenhouse 14 (June 2000): 13–25.
- Currently not on view
- date made
- Willis, Edward Jones
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- catalog number
- accession number
- Data Source
- National Museum of American History, Kenneth E. Behring Center