Compass, after another, and subtract the lesser from the next Compasses. greater: thus will you have the quantity of the several angles, and the length of the lines that include them. For the rest, see GEOMETRY. Plate CL. fig. 9. Note. All the angles of the figure taken together, must make twice as many right angles; abating two if no mistake has been committed. Azimuth COMPASS. See AZIMUTH. COMPASS-Dials, are small horizontal dials, fitted in brass or silver boxes, for the pocket, to show the hour of the day, by the direction of a needle that indicates how to place them right, by turning the dial about till the cock or style stands directly over the needle; but these can never be very exact, because of the variation of the needle itself. See COMPASS and DIALING. COMPASSES, or Pair of COMPASSES, a mathematical instrument for describing circles, measuring figures, &c. The common compasses consist of two sharp-pointed branches or legs of iron, steel, brass, or other metal, joined together at the top by a rivet, whereon they move as on a centre. Those compasses are of the best sort in which the pin or axle on which the joint turns, and also half the joint itself, is made of steel, as the opposite metals wear more equably. The perfection of them may be known by the easy and uniform opening and shutting of their legs; one of which is sometimes made to take in and out, in order to make room for two other points to describe with ink, black-lead or other materials. There are now used compasses of various kinds and contrivances, accommodated to the various uses they are intended for; as, COMPASSES of three legs, or Triangular Compasses, are, setting aside the excess of a leg, of the same structure with the common ones; their use being to take three points at once, and so to form triangles; to lay down three positions of a map, to be copied at once, &c. To the cursors Beam-COMPASSES consist of a long branch, or beam, made of brass or wood, carrying two brass cursors, the one fixed at one end, the other sliding along the beam, with a screw to fasten it occasionally. may be screwed points of any kind, whether steel for pencils, or the like. It is used to draw large circles, to take great extents, &c. To the fixed cursor is sometimes applied an adjusting or micrometer screw, by which an extent is obtained to extreme nicety. Mr Jones of Holborn has made beam-compasses to adjust to the dth of an inch. Calibre-COMPASSES. See CALiber. Clockmaker's COMPASSES are joined like the common compasses, with a quadrant, or bow, like the spring compasses; only of different use, serving here to keep the instrument firm at any opening. They are made very strong, with the points of their legs of well tempered steel, as being used to draw lines on pasteboard or copper. Cylindrical and Spherical COMPASSES, consist of four branches, joined in a centre, two of which are circular, and two flat, a little bent on the ends: their use is to take the diameter, thickness, or caliber of round or cylindric bodies; such as cannons, pipes, &c. Elliptic COMPASSES. Their use is to draw ellipses, or ovals of any kind: they consist of a beam AB 3 about a foot long, bearing three cursors; to one of Compasses. which may be screwed points of any kind to the bottom of the other two are rivetted two sliding dove-tails, adjusted in grooves made in the cross branches of the beam. The dove-tails having a motion every way by turning about the long branch, go backwards and forwards along the cross; so that when the beam has gone half-way about, one of these will have moved the whole length of one of the branches; and when the beam has got quite round, the same dove-tail has got back the whole length of the branch. Understand the same of the other dove-tail. Note. The distance between the two sliding dovetails is the distance between the two foci of the ellipsis; so that by changing that distance, the ellipsis will be rounder or slenderer. Under the ends of the branches of the cross are placed four steel points to keep it fast. The use of this compass is easy; by turning round the long branch, the ink, pencil, or other point, will draw the ellipsis required. Its figure shows both its use and construction. German COMPASSES have their legs a little bent outwards, towards the top; so that when shut, the points only meet. Hair COMPASSES are so contrived within side, by a small adjusting screw to one of the legs, as to take an extent to a hair's breadth. Lapidary's COMPASSES are a piece of wood, in form of the shaft of a plane, cleft at top, as far as half its length; with this they measure the angles, &c. of jewels and precious stones, as they cut them. There is in the cleft a little brass rule, fastened there at one end by a pin; but so that it may be moved in the manner of a brass level with this kind of square they take the angles of the stones, laying them on the shaft as they cut them. Proportional COMPASSES are those whose joint lies between the points terminating each leg: they are either simple or compound. In the former sort the centre is fixed, so that one pair of these serves only for one proportion. fig. 6. Compound proportional COMPASSES consist of two Plate CLL parts or sides of brass, which lie upon each other so nicely as to appear but one when they are shut. These sides easily open, and move about a centre, which is itself moveable in a hollow canal cut through the greatest part of their length. To this centre on each side is affixed a sliding piece A of a small length, with a fine line drawn on it serving as an index, to be set against other lines or divisions placed upon the compasses on both sides. These lines are, 1. A line of lines. 2. A line of superfices, areas, or planes. 3. A line of solids. 4. A line of circles, or rather of polygons to be inscribed in circles. These lines are all unequally divided; the three first from 1 to 20, the last from 6 to Their uses are as follow: 20. By the line of lines you divide a given line into any number of equal parts; for by placing the index A against I, and screwing it fast, if you open the compasses; then the distance between the points at each end will be equal. If you place the index against 2, and open the compasses, the distance between the points of the longer legs BB, will be twice the distance between the shorter ones CC; and thus a line is bisected, or divided into two equal parts. If the index be placed against |