Meres, Eng

Literature (Arber's Eng. Garner, II. 96). Plani (plā'nī), n. pl. [NL., pl. of L. plan us, flat: see plane1.] In Cuvier's cla ification. the second family of sub brachiate malacopterygian fishes; the flatfishes: same as Pleuro nectidæ in a wide sense and the suborder Hete rosomata. plan i caudate (plā-ni-ka'dāt), a. [L. plan us , flat, + cauda , tail, + -atel (see caudate ).] Having a flattened tail: said of reptiles. planicipital (plā-ni-sip'i-tal), a. [L. plan us , flat, + caput ( cap it- , in comp. -cipit- ), head, + -al.] Having a flat head, as an insect. plan i dors ate (plā-ni-dôr'sāt), a . [ plan us , flat, + dorsum , back, + -atel .] Having a flat back. plan i form (plāʼni-fôrm), a . [ plan us , flat, + form a , form.] In an at . , presenting a plane or flat surface: said of the articular surface of bones whose jointing is arthrodial. planigraph (plan'i-graf), n. [ planum , a plane, + Gr. γράφειν , write.] An instrument for reducing or enlarging drawings. It consists of two scales graduated in a definite ratio to each other, attached end to end, and rotating about a pivot at their common origin. Measurements taken on a copy at one side are marked by the operator at the corresponding gradations on the other arm of the instrument. Interchangeable scales are provided for different degrees of enlargement or reduction. planimeter (plā-nim'e-ter), n. [= F. plan i mètre ; planum , a plane, + Gr. μέτρον, measure.] 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 IMG:content-0334.png:[blocks in formation] ner arm is stationary. The area of the parallelogram described by the tracer is equal to the base P1P2 = W1 W2 (JP2JW2) multiplied by the altitude, which is evident ly equal to W2W3, so that the area is W1W2 × W2W3 × (JP2JW2). The wheel turns one way in pa ing from W2 to W3, and the opposite way in pa ing from W4 to W1. But these two paths are not exactly equal, their difference being plainly W1 WWW JW. 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 . planimetric (plan-i-met'rik), a . [= F. plan i métrique = Pg. plan i met rico ; as planimetr -y + -ic.] Pertaining to planimetry or the mensuration of plane surfaces. - Planimetric function. See function .