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See also:PANTOGRAPH, or PANTAGRAPI (from the See also:Greek sravra, all, and yp64 av, to write) , an See also:instrument for making a reduced, an enlarged, or an exact copy of a See also:plane figure . In its commonest See also:form it consists of two See also:long arms, AB and AC (fig . 1), jointed together at A, and two See also:short arms, FD and FE, jointed together at F and with the long arms at D and E; FD is made exactly equal to AE and FE to AD, so that ADFE is a parallelogram whatever the See also:angle at A . The instrument is supported parallel to the See also:paper on castors, on which it moves freely- A See also:tube is usually fixed vertically at c, near the extremity of the long See also:arm AC, and similar tubes are mounted on plates which slide along the short arms BD and FD ; they are intended to hold either the See also:axle See also:pin on a weighted fulcrum See also:round which the instrument turns, or a See also:steel pointer, or a See also:pencil, interchangeably . When the centres of the tubes are exactly in a straight See also:line, as on the dotted line bfc, the small triangle bfD will always be similar to the large triangle bcA ; and then, if the fulcrum is placed under b, the pencil at f, and the pointer at c, when the instrument is moved round the fulcrum as a See also:pivot, the pencil and the pointer will move parallel to each other through distances which will be respectively in the proportion of bf to be ; thus the pencil at f draws a reduced copy of the See also:map under the pointer at c; if the pencil and the pointer were interchanged an enlarged copy would be See also:drawn; if the fulcrum and pencil were interchanged, and the sliders set for f to bisect be, the map would be copied exactly . Lines are engraved on the arms BD and FD, to indicate the positions to which the sliders must be set for the ratios 4, 4..., which are commonly required . The square See also:pantograph of See also:Adrian Gavard consists of two graduated arms which are pivoted on a See also:plain See also:bar and connected by a graduated bar sliding between them throughout their entire length, to be set at any required distance from the plain bar; a sliding See also:plate carrying a See also:vertical tube, to hold either the axle of the fulcrum, the pencil, or the pointer, is mounted on one of the arms and on a prolongation of the plain bar beyond the other arm, and also on the graduated connecting bar; and an additional arm is provided by means of which reductions below or enlargements above the scales given on the instrument can be readily effected . The eidograph (Gr . &MSos, form) is designed to supersede the panto-graph, which is somewhat unsteady, having several supports and See also:joints . It is composed of three graduated bars, one of which is held over a fulcrum and carries the others, which are lighter, one at each extremity . The three bars are movable from end to end in See also:box-sockets, each having an See also:index and a See also:vernier in contact with the graduated See also:scale . The box-socket of the See also:principal bar turns round the vertical axle of the fulcrum; that of each See also:side bar is attached to a vertical axle, which also carries a grooved See also:wheel of large See also:diameter and turns in a See also:collar at either end of the principal bar . The two wheels are of exactly the same diameter and are connected by a steel See also:band fitting tightly into the grooves, so that they always turn together through identical arcs; thus the side bars over which they are respectively mounted, when once set parallel, turn with them and always remain parallel . A pointer is held at the end of one of the side bars and a pencil at the diagonally opposite end of the other . The bars may be readily set by their graduated scales to positions in which the distances of the pencil and the pointer from the fulcrum will always be in the ratio of the given and the required map scales . Numerous other modifications have been proposed from See also:time to time; many forms are described in G . Pellehn's Der Pantograph (See also:Berlin, 1903) . |
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