Polar–Amsler

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
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.

This German silver instrument has a 4" arm with tracer point and 6" pole arm with short cylindrical weight. The arm lengths are fixed.
Description
This German silver instrument has a 4" arm with tracer point and 6" pole arm with short cylindrical weight. The arm lengths are fixed. The tracer arm and pole arm are connected by a hinge and form a circle around the measuring wheel, vernier, and registering dial when the instrument is closed. The top of the pole arm is marked in script: Crosby Steam Gage & Valve Co. Boston. The top of the weight is marked: 16378 (/) 10 [square] in. A serial number is marked underneath the tracer arm and the weight: 10259.
A wooden case is covered with black leather and lined with purple velvet. The top of the case is marked: CROSBY STEAM GAGE & VALVE Co (/) BOSTON.
To measure the areas of diagrams produced by its steam engine indicators, Crosby imported and sold Amsler polar planimeters of types 1, 2, and 3. The presence of a registering dial and the screw thread on the post extending from the measuring wheel indicates that this example is a type 2. Planimeter expert Joachim Fischer dated this object to about 1882. Charles W. Batchelor (1845–1910), the father of the donor, used it in his work as one of Thomas A. Edison's chief assistants. For instance, between 1884 and 1888, he managed the Edison Machine Works, where a planimeter may have been especially useful. From 1888 to at least 1907, Crosby sold the Amsler type 2 in a case for $25.00. For information on Amsler and his invention, see 1987.0107.10. Compare to 1989.0305.01.
This instrument was received by the Smithsonian in 1960.
References: Crosby Steam Gage & Valve Co. Catalogue (Boston, 1888), 104–109; Crosby Steam Gage & Valve Co. Catalogue (Boston, 1900), 170–176; Crosby Steam Gage & Valve Co. Catalogue (Boston, 1907), 203–210; Crosby Steam Gage & Valve Company, Practical Instructions Relating to the Construction and Use of the Steam Engine Indicator (Boston, 1911), 43–46, 83–86; Craig Bliss, The Crosby Steam Gage & Valve Co., http://www.crosby-steam.com/index.htm.
Location
Currently not on view
date made
1880s
distributor
Crosby Steam Gage & Valve Company
maker
Amsler, Jacob
ID Number
MA.318485
catalog number
318485
accession number
233749

Our collection database is a work in progress. We may update this record based on further research and review. Learn more about our approach to sharing our collection online.

If you would like to know how you can use content on this page, see the Smithsonian's Terms of Use. If you need to request an image for publication or other use, please visit Rights and Reproductions.