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Date: circa 1906

Inventory Number: 2006-1-0002b

Classification: Planimeter

Subject:

Maker: Jakob Amsler (1823 - 1912)

Cultural Region:

Place of Origin:

Dimensions:

8 x 208 x 10.5 cm (3 1/8 x 81 7/8 x 4 1/8 in.)

Description:

This is the rail along which the large cylinder of the Amsler integrator no. 4 slides. The rail itself is a long rectangular steel strip. It has a groove that runs along one entire long edge of the rectangle. There is a brass handle in the center of each short edge at either end of the strip.

The track is stored in a long rectangular wooden box. The box opens with three hinges attached on a long edge of the box. Parts of the box appear to have been replaced, including on of the small end walls and the lid given that they have either no finish or a different finish from the rest of the box. There are two metal hooks on the outside of the bottom half of the box for attaching it to the top half when the box is closed.

The track is stored in a long rectangular wooden box. The box opens with three hinges attached on a long edge of the box. Parts of the box appear to have been replaced, including on of the small end walls and the lid given that they have either no finish or a different finish from the rest of the box. There are two metal hooks on the outside of the bottom half of the box for attaching it to the top half when the box is closed.

Signedunsigned

Inscribedengraved on the track: No. 1124

FunctionThe planimeter is used to determine the area of an arbitrary, two-dimensional figure: it gives the area between the graphically defined curve and a horizontal x-axis. Users manually trace the figure in question with the attached tracing arm. The tracing motion is communicated through the device such that the large, solid brass cylinder will slide along the track. The distance that the cylinder has moved when the tracing is complete (i.e. when the tracer has returned to the point from which she started), is proportional to the area inside the figure. This motion transfer is guaranteed by the trigonometric relations of the main mechanism consisting of the large circle, and the three connected smaller circle. The white plastic discs attached to the tracing arm are used to record the area. This instrument, unlike some of its close relatives, does not have a drawing mechanism.

Instruments of this kind were later referred to as 'moment planimeters' because the integrals of f(x)^2 and f(x)^3 give respectively the static moment and the moment of inertia for the figure's area.

For supplementary images of a similar model and mathematical explanation of the Amsler Planimeter, click here.

For a detailed description of how the rolling sphere planimeter measures area, see the article in the Primary Sources.

Instruments of this kind were later referred to as 'moment planimeters' because the integrals of f(x)^2 and f(x)^3 give respectively the static moment and the moment of inertia for the figure's area.

For supplementary images of a similar model and mathematical explanation of the Amsler Planimeter, click here.

For a detailed description of how the rolling sphere planimeter measures area, see the article in the Primary Sources.

Curatorial RemarksA letter from Prof. William Brower continaing the complete history of ownership and use is listed in accessories but it is currently missing.

Primary SourcesJ.C. Maxwell, "Descriptions of a New Form of Planometer, an Instrument for Measuring the Areas of Plane Figures Drawn on Paper," in *The Scientific Papers of James Clerk Maxwell, Vol. 1*, ed. W. D. Niven (Mineola, NY: Dover Publications, 2003), 230-237. [Reprint of original 1890 publication by Cambridge University Press.]

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