planimeter

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. An instrument that measures the area of a plane figure as a mechanically coupled pointer traverses the perimeter of the figure.

Century Dictionary and Cyclopedia

1. n. 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.

Wiktionary

1. n. An integrating device used to measure the area of an irregular figure via tracing its outline

GNU Webster's 1913

1. n. An instrument for measuring the area of any plane figure, however irregular, by passing a tracer around the bounding line; a platometer.

WordNet 3.0

1. n. a measuring instrument for measuring the area of an irregular plane figure