Improved Willis Planimeter

The Willis planimeter is an adaptation of the standard polar planimeter that allows the user to determine mean effective pressure directly from the diagram made by a steam engine pressure indicator. The German silver instrument has two pivoted tracer arms. The length of one of these may be adjusted. This adjustable arm is graduated along one edge to 32nds of an inch from 2" to 8-1/2". The rectangular pivot attaches on the right side to a frame of three metal rods. The front rod is plain. The middle rod is made of a dark or tarnished metal and carries a brass wheel that slides on a carriage of two small double wheels. The third rod holds 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: U. S. ST'D.
Two clasps on the left side of the rectangular pivot secure the frame. That side is marked: —IMPROVED — (/) WILLIS PLANIMETER (/) MANF'D BY (/) JAMES L. ROBERTSON & SONS (/) NEW YORK, U.S.A. The right side of the pivot is marked: PAT'D SEPT. 22, 1896 (/) OCT. 6, 1896 (/) 838. A wooden case covered with black leather is lined with purple satin and velvet. The inside of the lid is marked: Improved Willis Planimeter, (/) PATENTED SEPTEMBER 22, 1896. (/) " OCTOBER 6, 1896. (/) MANUFACTURED BY (/) JAMES L. ROBERTSON & SONS, (/) New York, U. S. A.
For an attachment to this instrument, see MA*323704. Compare to 1994.0356.01 and MA*324247. Although this instrument (serial number 838) was presumably manufactured soon after 1994.0356.01 (serial number 749), note the differences in the construction of the measuring wheel on the frame attachment. Charles F. Engman (d. 1927) of New York City used this instrument. He was a marine engineer with the Clyde Line for several years and patented a device for automatically oiling engines. Around 1900, he joined the U.S. Navy. He served as chief engineer on a number of colliers, cargo ships that carried coal, until the end of World War I.
References: Edward J. Willis, "Planimeter" (U.S. Patent 529,008 issued November 13, 1894; reissued as 11,568 September 22, 1896), "Planimeter" (U.S. Patent 542,511 issued July 9, 1895), and "Planimeter" (U.S. Patent 672,581 issued April 23, 1901); Alpheus C. Lippincott, "Planimeter" (U.S. Patent 569,107 issued October 6, 1896); Charles F. Engman, "Lubricator" (U.S. Patent 596,863 issued January 4, 1898); catalog of James L. Robertson & Sons (New York, [1899]), 29–31; Hyman A. Schwartz, "The Willis Planimeter," Rittenhouse 7, no. 2 (1993): 60–64.
Currently not on view
Object Name
date made
James L. Robertson & Sons
Physical Description
german silver (overall material)
brass (overall material)
wood (overall material)
celluloid (overall material)
leather (overall material)
fabric (overall material)
case: 3.8 cm x 25.2 cm x 11.3 cm; 1 1/2 in x 9 29/32 in x 4 7/16 in
place made
United States: New York, New York
ID Number
accession number
catalog number
Naval History
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History, Kenneth E. Behring Center


Add a comment about this object