About the same time that Sang and Wetli were working on planimeters, the Swiss mathematician Jacob Amsler was figuring out how to make the instrument smaller, less expensive, and easier to use. By 1854, he had eliminated most of the complex mechanisms typical of earlier designs, reducing the planimeter to two arms connected with a pivot. One arm was anchored at the end away from the pivot, and one arm traced the drawing. Because the pivot and both arms can move around the anchor, the motion of the tracer arm is graphed with polar coordinates instead of linear x-y axes. Thus, this form of planimeter is called a polar planimeter. Since the pivot moved back and forth, it traced an area whose net measurement was zero. This meant that the area traced by the tracer point exactly equaled the area of the closed curve the user was measuring. This area was equivalent to 2π multiplied by the product of the length of the tracer arm, the radius of the counting wheel on the tracer arm, and the number of revolutions completed by the counting wheel. Again, mathematicians today work out the detailed mathematics of the operation of Amsler's planimeter with Green's Theorem.
|U.S. Census geographers using planimeters similar to Amsler's model 6, ca 1940, ARC ID 6200720, Record Group 29: Records of the Bureau of the Census, 1790–2007, U.S. National Archives, College Park, MD.|
By 1857, Amsler opened a highly successful workshop that sold 50,000 polar planimeters of six different types all over the world in its first 60 years. Other manufacturers of scientific instruments also copied his design, including Hine & Robertson of New York City and American Steam Gauge & Valve Manufacturing Company of Boston. A prominent Swiss modification of the Amsler planimeter is featured on the next page. Planimeters directly from Amsler or on his design were sold by American retailers to universities, engineers, and factory managers until at least the 1930s.
"Planimeters - Polar–Amsler" showing 1 items.
- This nickel-plated instrument forms a U and is hinged around a brass measuring wheel and vernier. A cylindrical weight fits over a peg at the end of the pole arm. The plating has worn away from the handle for the tracer point. The tracer arm is stamped with a serial number: 5337. An oblong wooden case covered with black leather is lined with dark blue velvet. The top of the case is marked: AMERICAN (/) SCHAEFFER & BUDENBERG. These words are in an oval around the company logo of a globe and the words: BROOKLYN, N.Y. A torn red and white sticker on the bottom of the case originally read: UNIVERSITY OF (/) CINCINNATI (/) 33893. Compare to 1981.0301.03 and 1981.0301.04.
- In 1923 the American Steam Gauge & Valve Manufacturing Company, the Hohmann-Nelson Company, and the American division of the Schäffer & Budenberg Manufacturing Company merged to form American Schaeffer & Budenberg Corporation. The first and third companies were known for their planimeters as well as their steam-engine indicators, but American had made this particular instrument since the late 19th century, while Schäffer & Budenberg was associated with the Coffin planimeter. See MA*323706. The merged firm may have been purchased by Manning, Maxwell, and Moore in the late 1930s. The department of mechanical engineering laboratory at the University of Cincinnati owned this instrument.
- References: Barry Lee David, The Antique American Steam Gauge: A Collector's Guide (Mendham, N.J.: Astragal Press, 2003); American Steam Gauge Company, catalog (Boston, 1896), 130–135.
- Currently not on view
- date made
- after 1923
- American Steam Gauge & Valve Mfg. Co.
- ID Number
- catalog number
- accession number
- Data Source
- National Museum of American History, Kenneth E. Behring Center