4242 compensating polar planimeter

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4242 compensating polar planimeter


Engineering; Mathematics


Physical Description: The Keuffel and Esser polar planimeter is composed of two individual pieces. One being the main body, and the other a tracer arm. Both sections are comprised of tarnished silver square rods with black markings indicating distance in millimeter; these rods being made of some black painted metal. Two dials are attached to the main body or larger section; one is horizontal, the other vertical. These dials are made of black painted metal with white lines and white numbers. The tracer arm is composed of a long square sections with a large balled pin on one end, and a large cylindrical mass on the other end that has a small pin on the bottom. The main body has a long square rod made of tarnished silver, with a black painted metal portion attached. This metal portion holds the aforementioned two dials. On the end of the silver square rod is a spike, this being attached to the rod via a black metal tab. The tracer arm and main body are combined by inserting the large balled pin into a hole on the surface of the main body.

The object's case is a black rectangular box with a metallic clip latch. The inside of the case is lined with pear green felt material. On the inside of the lid is a white paper card with black old-style lettering. Inside the case and screwed to the bottom is a bronze stamped nameplate.

Functional Description: The planimeter was used to measure the area of a 2d surface. It did this by having a tracer arm that remained stationary about a point, while the main body rotated and translated with the area’s curve. The dials attached measured the rotation and translation, and the resulting values could be used to calculate the area of the section enclosed by the device.


Cooper Sheldon, John Wyrzykowski, Ben Weigand, Nick Silvestri




Physical Medium




Mechanical Engineering-Engineering Mechanics Building, 3rd Floor, Second Case from the Left

Physical Dimensions

Tracer arm: 2.25 cm width x 25.5 cm length x 3.5 cm depth

Body: 23.5 cm length x 6 cm width x 2.25 cm depth


Device: Steel, Bronze, and Silver

Case: Leather and Felt


Keuffel and Esser Co.


To the left: K&E 4242 Compensating Polar Planimeter | When Tracer Arm is set to: 2024 | One revolution of dial = 100.00 sq. in. | One revolution of wheel = 10.00 “ “ | Distance between wheel Nos. = 1.00 “ “ | Distance between graduations = 0.10 “ “ | One unit on Vernier = 0.01 “ “ | Standard setting of Pole Arm for measuring in square inches, | ”pole inside figure”. 30.79 | See instructions for other settings of arms | 12,806-9. Keuffel & Esser Co.

To the right: Serial NO. | 109768 | 32.35 | 1000.0 sq. cm. | 100.0 “ “ | 100.0 “ “ | 10.0 “ “ | 1.0 “ “ | 0.1 “ “

History of the Object

This object's history is connected to the model number "4242". The Keuffel & Esser Company of New York sold this instrument model from 1901 to 1972. The price was $46.50 in 1909, $33.50 in 1915, and $55.00 in 1921; presumably, World War I affected Coradi's ability to export planimeters. By 1936, a German firm was manufacturing model 4242 for K&E's Paragon product line. Compare to 1998.0032.03. See 1991.0882.02 for a later instruction manual.


Mechanical Engineering-Engineering Mechanics Building, 3rd Floor, Second Case from the Left


Clark McCoy, "Collection of Pages from K&E Catalogs for the 4242 Family of Polar Planimeters," http://www.mccoys-kecatalogs.com/PlanimeterModels/ke4242family.htm;

Catalogue of Keuffel & Esser, 33rd ed. (New York, 1909), 322;

Catalogue of Keuffel & Esser, 35th ed. (New York, 1915), 315;

Catalogue of Keuffel & Esser, 36th ed. (New York, 1921), 257;

Catalogue of Keuffel & Esser, 38th ed. (New York, 1936), 340.

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Cooper Sheldon, John Wyrzykowski, Ben Weigand, Nick Silvestri, “4242 compensating polar planimeter,” Michigan Tech Inventory of Historic Scientific Instruments, accessed April 17, 2021, https://ihsi.omeka.net/items/show/182.