polar planimeter
Date: after 1856
Inventory Number: 1999-1-0067
Classification: Planimeter
Subject:
Maker: German
Seller: Eugene Dietzgen Company (1885-present)
Cultural Region:
Place of Origin:
Dimensions:
4.3 × 17.3 × 5.5 cm (1 11/16 × 6 13/16 × 2 3/16 in.)
DescriptionThe planimeter is stored in a rectangular black case that opens with two hinges along one of the long edges. There is a single brass clip on the front of the top half of the case that snaps onto a pin attached to the front of the bottom half of the case when the case is closed. The clasp is embellished with flourishes and engravings. The inside of the case is lined with green felt cloth. The bottom half of the case is contoured to fit the instrument pieces and hold them in place when the case is closed.
The main body of the instrument is black metal and consists of two arms of different lengths. The shorter is the tracing arm and the other will be called the second arm. Each arm has a half circle at one end. The arms are connected with a pivot at that end such that the straight extensions of the arms can be brought nearly together in parallel and a full circle forms at the pivot end.
At the opposite end to the half circle on the tracing arm, there is a metal stylus. The stylus has a brass hour glass shape above the tracing arm and a metal point extending below it. The hour glass component is the tracing handle. The tip of the pointed end rests on the surface below. The stylus is attached to the tracing arm by two metal screws.
At the opposite end to the half circle on the second arm, there is a flat brass extension screwed into a small hole. The brass extension connects to a black metal puck. Underneath this end of the second arm, there is a tiered-funnel-shaped attachment. The funnel attachment has a screw on the side.
At the half circle end of the tracing arm, there is a white measurement mechanism consisting of a white wheel, a white wheel-subsection, and a white disc. The white wheel subsection is fixed, i.e. does not rotate, and is closest to the pivot holding the two arms together. It has one increment marked "0" at one end and "10". This increment is divided in 10 by small black lines. The white wheel is marked in evenly spaced increments from 0 to 9. All the markings are in black type, etched into the white wheel. The axis of each wheel is parallel to the tracing arm. The white disc lies flat, parallel to the top surface of the tracing arm. It is marked from 0 to 9 in evenly spaced increments around the circumference. Each numeral is accompanied by a small black line. In between the white wheel and the white disc there is a metal roller whose axis is parallel to the tracing arm. There is a metal screw running from the center of this roller to a point on the tracing arm at which there is a black metal cube. It has precisely the width that remains between the two planimeter arms when they are rotated together so that the cube touches both arms.
The main body of the instrument is black metal and consists of two arms of different lengths. The shorter is the tracing arm and the other will be called the second arm. Each arm has a half circle at one end. The arms are connected with a pivot at that end such that the straight extensions of the arms can be brought nearly together in parallel and a full circle forms at the pivot end.
At the opposite end to the half circle on the tracing arm, there is a metal stylus. The stylus has a brass hour glass shape above the tracing arm and a metal point extending below it. The hour glass component is the tracing handle. The tip of the pointed end rests on the surface below. The stylus is attached to the tracing arm by two metal screws.
At the opposite end to the half circle on the second arm, there is a flat brass extension screwed into a small hole. The brass extension connects to a black metal puck. Underneath this end of the second arm, there is a tiered-funnel-shaped attachment. The funnel attachment has a screw on the side.
At the half circle end of the tracing arm, there is a white measurement mechanism consisting of a white wheel, a white wheel-subsection, and a white disc. The white wheel subsection is fixed, i.e. does not rotate, and is closest to the pivot holding the two arms together. It has one increment marked "0" at one end and "10". This increment is divided in 10 by small black lines. The white wheel is marked in evenly spaced increments from 0 to 9. All the markings are in black type, etched into the white wheel. The axis of each wheel is parallel to the tracing arm. The white disc lies flat, parallel to the top surface of the tracing arm. It is marked from 0 to 9 in evenly spaced increments around the circumference. Each numeral is accompanied by a small black line. In between the white wheel and the white disc there is a metal roller whose axis is parallel to the tracing arm. There is a metal screw running from the center of this roller to a point on the tracing arm at which there is a black metal cube. It has precisely the width that remains between the two planimeter arms when they are rotated together so that the cube touches both arms.
Signedengraved on instrument arm: Eugene Dietzgen Co.
engraved on instrument arm: GERMANY
engraved on instrument arm: GERMANY
Inscribedin white lettering on blue plastic adhesive strips on case lid: PLANIMETER / PIERCE LABS / SQUARE INCHES
engraved on instrument arm: No. 9507
engraved on instrument arm: 14885
engraved on instrument arm: 0,01 in
engraved on instrument arm: No. 9507
engraved on instrument arm: 14885
engraved on instrument arm: 0,01 in
FunctionThe polar planimeter is used for ascertaining the area of any plane surface represented by a figure drawn to any scale, such as indicator diagrams, profiles, architectural plans or sections. The planimeter is placed over top of the diagram in question and the user traces it with the stylus at the end of the short arm of the instrument. The planimeter measures the area of the traced figure. This particular planimeter was probably designed for use in analyzing steam engine indicator diagrams.
As the user traces a figure lying flat on a surface below, the metal roller on the tracing arm rolls and slides accordingly. The measurement apparatuses on the tracing arm record this motion. When the stylus returns to the starting point of the figure being traced, the recorded measurements will be proportional to the area of the figure. The end of the short arm with the half circle is restricted to circular motion as the user traces the diagram below. This is the case because it is attached by a pivot to the longer arm, the opposite end of which is attached to the black metal puck which acts as a weight restricting its motion.
This is called a polar planimeter because of the fact that the end of the short arm from the stylus is restricted to circular motion. For linear planimeters, that end of the tracer arm moves in a straight line, either in a track or on rollers. Polar planimeters were invented by Jacob Amsler in 1854. They are considered easier to use and more accurate than the linear variety.
For more information on the design and workings of linear and polar planimeters, including an animated simulation of the latter, see Robert Foote's page here. Foote is a professor of mathematics and computer science at Wabash College.
As the user traces a figure lying flat on a surface below, the metal roller on the tracing arm rolls and slides accordingly. The measurement apparatuses on the tracing arm record this motion. When the stylus returns to the starting point of the figure being traced, the recorded measurements will be proportional to the area of the figure. The end of the short arm with the half circle is restricted to circular motion as the user traces the diagram below. This is the case because it is attached by a pivot to the longer arm, the opposite end of which is attached to the black metal puck which acts as a weight restricting its motion.
This is called a polar planimeter because of the fact that the end of the short arm from the stylus is restricted to circular motion. For linear planimeters, that end of the tracer arm moves in a straight line, either in a track or on rollers. Polar planimeters were invented by Jacob Amsler in 1854. They are considered easier to use and more accurate than the linear variety.
For more information on the design and workings of linear and polar planimeters, including an animated simulation of the latter, see Robert Foote's page here. Foote is a professor of mathematics and computer science at Wabash College.
Curatorial RemarksGERMANY is inscribed on the instrument arm which means it is possible this instrument was made by the German company Faber-Castell and distributed in the United States by Eugene Dietzgen Co. According to the Sphere Research Corporations Dietzgen archives, the latter distributed many slide-rules made by Faber-Castell in the United States. See their website for details.
Primary SourcesJacob Amsler, "Uber das Planimeter", 1856.