Improved Willis Planimeter

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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 8-1/2". A screw on top of the rectangular pivot joining the arms allows the longer arm to be set at different lengths. The pivot is marked on the left side: —IMPROVED — (/) WILLIS PLANIMETER (/) MANF'D BY (/) JAMES L. ROBERTSON & SONS (/) NEW YORK U.S.A. There are two clasps on the left side. The right side of the pivot is marked: PAT'D SEPT. 22, 1896 (/) OCT. 6, 1896 (/) APRIL 23, 1901 (/) 8390.
A metal frame has three bars, and the first bar is unadorned. The second bar is made of a dark-colored metal. A dark-colored metal wheel slides along the bar in a carriage made of four small wheels. 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: J. L. ROBERTSON & SONS, N.Y. The frame fits into three holes on the right side of the pivot that joins the arms. A second triangular scale in the case divides the inch into 70, 20, 16, 12, 10, and 8 parts. It is also marked: J. L. ROBERTSON & SONS, N.Y.
A wooden case is covered with black leather and lined with purple satin and velvet. The inside of the lid is marked: Improved Willis Planimeter, (/) PATENTED SEPTEMBER 22, 1896. (/) " OCTOBER 6, 1896. (/) " APRIL 23, 1901 (/) MANUFACTURED BY (/) JAMES L. ROBERTSON & SONS, (/) INC. (/) New York, U. S. A. Three blue thumbtacks are inside the case.
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 and a horsepower attachment is not mentioned on the instrument; see MA.323704. Alpheus C. Lippincott of New York City received the second patent mentioned on this 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.
In 1901 Willis patented the form of wheel mount found on this instrument, which Robertson manufactured and sold as the Improved Willis Planimeter. Its price was $18.00 in 1905. The company apparently ceased operations in the 1910s. The serial number (8390) and patent references on this instrument indicate that it postdates 1994.0356.01 and MA.323703. Willis made further design changes in the 1920s; see 1983.0173.01. Lincoln F. Spencer, a stationary engineer in Massachusetts, used this instrument in the early 20th century.
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); James L. Robertson & Sons, Steam-Engine Indicators and Their Attachments (New York, 1905), 21–22; Hyman A. Schwartz, "The Willis Planimeter," Rittenhouse 7, no. 2 (1993): 60–64.
Currently not on view
date made
1901-ca 1910
James L. Robertson & Sons
place made
United States: New York, New York
Physical Description
wood (overall material)
metal (overall material)
celluloid (overall material)
fabric (overall material)
leather (overall material)
case: 14.7 cm x 26 cm x 11.5 cm; 5 25/32 in x 10 1/4 in x 4 17/32 in
ID Number
accession number
catalog number
Credit Line
Gift of R. S. Spencer
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History