Sang Platometer

In 1851 Scottish civil engineer John Sang (1809–1887) exhibited a form of rolling planimeter at the Crystal Palace Exhibition in London. He called the instrument a "planometer," which he changed to "platometer" when he described the instrument to the Royal Scottish Society of Arts a few months later. Like all planimeters, this object measures the area bounded by a closed curve. Sang's device is also significant because it inspired James Clerk Maxwell to work on planimeters, which in turn gave James and William Thomson ideas that helped them develop a mechanical integrator.
This example is an improved version of Sang's original instrument. A brass cone is on a steel rod that connects two brass rollers. An open brass frame surrounds the rod. It has four brass rollers that slide along a brass base to which the rod is anchored. The frame has a tracer with an ivory handle, a silver measuring wheel that rolls against the side of the cone, and a small magnifying glass. The handle on the tracer arm and the construction of the measuring wheel are changed from Sang's original design.
The measuring wheel rotates only when the tracer arm's movement is perpendicular to the axis of the cone. The rate at which the wheel moves depends on its distance from the vertex of the cone. For example, when the tracer arm moves a distance S perpendicular to the axis, its reading changes by an amount equal to the area of a rectangle with sides equal to S times the distance from the vertex. The instrument is in a wooden case.
References: John Sang, "Description of a Platometer, an Instrument for Measuring the Areas of Figures Drawn on Paper," Transactions of the Royal Scottish Society of Arts 4 (1852): 119–129; "Description of Sang's Platometer, or Self-Acting Calculator of Surface," Journal of the Franklin Institute 23 (1852): 238–241; Charles Care, "Illustrating the History of the Planimeter" (Undergraduate 3rd Year Project, University of Warwick, 2004), 39–44; Charles Care, "A Chronology of Analogue Computing," The Rutherford Journal 2 (2006–2007),
Currently not on view
Object Name
date made
Sang, John
Physical Description
brass (overall material)
steel (overall material)
ivory (overall material)
glass (overall material)
overall: 7.5 cm x 33 cm x 16 cm; 2 15/16 in x 13 in x 6 5/16 in
place made
United Kingdom: Scotland, Kirkcaldy
owner, prior
United States: New York, Hastings-on-Hudson
ID Number
accession number
catalog number
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Measuring & Mapping
Data Source
National Museum of American History, Kenneth E. Behring Center


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