Improved Willis Planimeter

This metal instrument (possibly of nickel-plated brass) has two pivoted arms with needle points. One is about 9" long, and the other is about 6-1/2" long. The longer arm is used for tracing and is graduated to 32nds of an inch from 2" to 7-7/8". The pivot is marked on that side: PAT'D SEPT. 22, 1896 (/) OCT. 6, 1896. The other side of the pivot is marked: —IMPROVED — (/) WILLIS PLANIMETER (/) MANF'D BY (/) JAMES L. ROBERTSON & SONS (/) NEW YO[RK] U.S.A. There are two clasps on that side for securing the frame with the measuring wheel. The back of one clasp and the first side of the pivot have a serial number: 749.
A metal frame has three bars. The first bar is unadorned. The second bar slides in a groove formed by two small double wheels and holds a brass wheel for measuring. The third bar 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. STD. The frame fits into three holes on the pivot that joins the arms.
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.
Edward Jones Willis (1866–1941), a steam and electrical engineer from Richmond, Va., patented a cross-shaped planimeter in 1894 and had a modified version of the patent reissued in 1896. This is the first patent mentioned on the instrument. Willis's 1895 patent for a planimeter with a frame similar to the frame on this example is not mentioned on the instrument. Alpheus C. Lippincott of New York City received the second patent mentioned on the instrument, for a different form of cross-shaped planimeter.
James L. Robertson & Sons manufactured steam engine indicators. Since planimeters were used to measure the area under curves drawn by these indicators, it was common for firms that made indicators to also produce planimeters. Indeed, Robertson sold both the Improved Willis Planimeter and the Lippincott Planimeter, so it is probable that the company mentioned Lippincott's patent on this planimeter by mistake. Around 1900, the Improved Willis Planimeter cost $18.00.
In 1901, Willis patented the form of planimeter that sold as the Improved Willis Planimeter and added a triangular ruler attachment that could be used to calculate horsepower. See MA*324247, MA*323703, and MA*323704. Note that this example of the instrument has the frame on the left side of the instrument, unlike the later and more common versions, which had the frame on the right. The mechanism for the measuring wheel is also different, and its bar does not slide on later instruments. Because the 1901 patent is not mentioned and because of the differences in design, this Willis planimeter is probably the oldest one in the collections. James Jack Scott, the superintendent of the Eagle Cotton Oil Mill in Meridian, Miss., from about 1900 to about 1935, used this planimeter to analyze the operations of the plant's steam power equipment.
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); 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
metal (overall material)
wood (overall material)
celluloid (overall material)
cloth (overall material)
leather (overall material)
case: 4 cm x 25 cm x 11.1 cm; 1 9/16 in x 9 27/32 in x 4 3/8 in
place made
United States: New York, New York
ID Number
catalog number
accession number
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History, Kenneth E. Behring Center


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