compensating polar planimeter with magnified fixed tracing arm
Date: 1960-1969
Inventory Number: 1999-1-0005
Classification: Planimeter
Dimensions:5.1 × 23.2 × 9.3 cm (2 × 9 1/8 × 3 11/16 in.)
Accessories: plush-lined, hard green case
white card with instrument information in case
DescriptionThis polar planimeter with magnifying tracing arm is stored in a green, rectangular case that opens with two hinges along one of the long edges. There are two metal clips on the front of the top half of the case that snap onto knobs fixed to the front of the bottom half. The inside of the case is lined with green velvet. The bottom half of the case is contoured to fit the pieces and hold them in place when the case is closed.
The instrument breaks down into two main pieces with one accessory. One main part is a long, rectangular, black metal bar with a large black puck attached at one end and a silver metal pin attached to the other end. The second main piece is the instrument's tracing arm. It consists of a shorter, rectangular metal bar with a round magnifying glass at one end and a measuring mechanism encased in a black metal box at the other. The metal arm is colored with faded red pigment.
The black-cased measurement apparatus has six visible components. There is a metal roller attached to the outside of the box, a white disk whose axis is parallel to the tracing arm half exposed from the top of the casing, a hole next to this disc, a metal button next to a metal screw on the outside of the case, and two windows displaying white measurement readers. The window at the furthest end of the black box, covered by a clear membrane, displays two side-by-side white wheels whose axes are parallel to the tracing arm. The top wheel (when the measurement markings are right side up) has one increment marked "0" on the left and "10" on the right with 10 small lines. The bottom wheel (when the measurement markings are right side up) is marked with ten equally spaced increments marked from "0" to "9" increasing in ones, each increment further divided in ten by small black lines. The second window, nearly centered in the black casing, displays a partial white disc lying parallel to the top panel of the casing. The disc is slightly more than half hidden behind a metal plate fixed beneath the glass window. The disc is marked from "0" to "9" increasing in ones. Each number is written near the circumference of the disc and meets a black line coming from the center of the disc. The metal plate has a rounded "m" shape cut out of it such that the central point lines up with one of the lines on the disc beneath. The metal plate thus acts as an arrow for the measurements obtained by the disc.
The opposite end of the tracing arm is equipped with a fixed magnifying glass. It is in the shape of a disc parallel to the top panel of the measurement device casing and consists of five layers. Each layer, excepting the lens on top, forms a hollow circle. The bottom layer, that lies contacts the surface below, consists of the same metal with faded red pigment as the central bar of the tracing arm. Above that is a metal layer of slightly larger diameter. Above that is a black layer that serves to attach the magnifying glass to the metal bar. Next is a coarsely textured metal band that acts as a grip for the user. Finally, the glass magnifying lens sits on top.
The instrument has one further piece. It is a flat metal strip in the shape of a "u" with a flattened bottom a short, flat extension from either extremity parallel to the flat bottom. The two extensions are colored with the same faded red pigment as the central bar of the tracing arm. There is a thin metal wire attached to one of the extensions that arches over the dip in the "u". It appears to originally have been attached to the other extension as well but this connection has come undone.
When the instrument is assembled, the pin at one end of the long black arm fits in to the hole in the top of the measurement device casing. The user traces the figure in question using the magnifying glass as a stylus.
The Keuffel & Esser Co. Manual for compensating polar planimeters that details the design and function of the instruments can be found here. This specific model is not treated in the manual.
For an explanation of how polar planimeters work and alternate photos of magnifying stylus compensating polar planimeters, see Robert's Foote's website. Robert Foote is a professor of mathematics and computer science at Wabash College.
Signedin gold lettering on instrument case: K + E
on white card inside case: K + E / KEUFFEL & ESSER CO.
in white lettering on instrument arm: K + E. GERMANY
Inscribedin white lettering on instrument arm: 61030
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 tracer arm. The planimeter measures the area of the traced figure. This particular model of planimeter magnifies the diagram below, thus scaling it up for easier measurement of small areas.
This is a polar planimeter because the intersection point of the tracing arm and the second arm is restricted to circular motion. This is the case because the other end of the second arm is fixed in place by the weight of the black puck. For linear planimeters, the end of the tracer opposite the stylus moves in a straight line, either in a track or on rollers.
As the user traces a figure on the surface below, the metal roller attached to the outside of the measurement device casing rolls and slides along accordingly. The measurement mechanisms record this motion and when the user arrives back at the starting point, the recorded motions will be proportional to the area of the figure below.
The Keuffel & Esser Co. Manual for compensating polar planimeters that details the design and function of the instruments can be found here. This specific model is not treated in the manual.
For an explanation of how polar planimeters work and alternate photos of magnifying stylus compensating polar planimeters, see Robert's Foote's website. Robert Foote is a professor of mathematics and computer science at Wabash College.
Primary SourcesKeuffel & Esser Co., "Directions for the Use, Care, and Adjustment of Compensating Polar Planimeters", printed in the United States, 1938.
ProvenanceAcquired from Professor John Michael Harrison of the Department of Psychology at Boston University, 64 Cummington Street, Boston, MA 00215, on 23 February 1999.