# planimeter

## Definitions

• WordNet 3.6
• n planimeter a measuring instrument for measuring the area of an irregular plane figure
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Webster's Revised Unabridged Dictionary
• n Planimeter An instrument for measuring the area of any plane figure, however irregular, by passing a tracer around the bounding line; a platometer.
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Century Dictionary and Cyclopedia
• n planimeter An instrument for measuring a plane area by carrying a tracer round its periphery, and noting the change of reading of a scale. Planimeters are of various constructions; but the most interesting is the polar planimeter (see the first figure). This consists of an inner arm OJ, turning about a fixed center O, and an outer arm JP, turning about a joint J, and resting upon a point or tracer P, and upon a wheel W, having its axis coincident with or just below the line .JP, and provided with a counting-apparatus, so that the turns and fractions of a turn it makes can be read off. In order to see that the instrument will accurately show the area, consider the second figure, where the tracer is supposed to follow the outline of an infinitesimal parallelogram, P1P2P3P4, so Placed that when the tracer moves from P2to P3 and from P4 to P1 the wheel moves from W2 to W3 and from W4to W1, both these paths of the wheel being in the direction of its axis, so that it only turns in passing from W1to Wo2 and from W3 to W4, during which motions the inner arm is stationary. The area of the parallelogram described by the tracer is equal to the base P1P2 = W1 W2(JP2 ÷ JW2) multiplied by the altitude, which is evidently equal to W2W3, so that the area is W1W2 × W2W3 × (JP2 ÷ JW2). The wheel turns one way in passing from W2 to W3, and the opposite way in passing from W4 to W1. But these two paths are not exactly equal, their difference being plainly W1W2 × W2W3 ÷ JW2. The algebraic sum of the rolling multiplied by the constant length JP2 gives the area. Now, any finite area may be conceived as formed of such infinitesimal parallelograms, and were the peripheries of all these traced out in the direction of the motion of clock-hands, every boundary between two of them would be traced once forward and again backward, so that the final reading of the wheel would be the same as if only the outer boundary of the area were traced. This is illustrated in the third figure. Also called platometer.
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Chambers's Twentieth Century Dictionary
• Planimeter an instrument for measuring the area of a plane figure
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## Etymology

Webster's Revised Unabridged Dictionary
Plani-, + -meter,. Cf. Planometer
Chambers's Twentieth Century Dictionary
Fr.,—L. planus, plain.

## Usage

### In literature:

The simple finding of areas we may omit, as the planimeter will do that equally well.
"Scientific American Supplement, No. 794, March 21, 1891" by Various
He showed a polar planimeter in which the integrating surface is a sphere.
"Scientific American Supplement, No. 315, January 14, 1882" by Various
In this it differs from Amsler's planimeter.
"Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4" by Various
Areas were measured with a planimeter; distances traveled by individuals were measured with a cartometer.
"Natural History of the Ornate Box Turtle, Terrapene ornata ornata Agassiz" by John M. Legler
At least two such readings were taken for each home range; then these planimeter values were converted into square feet.
"Comparative Ecology of Pinyon Mice and Deer Mice in Mesa Verde National Park, Colorado" by Charles L. Douglas
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