or **Pair of Compasses**, a mathematical instrument for describing circles, measuring figures, and the like.

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 the best in which the pin or axle on which the joint turns, and also half the joint itself, are made of steel, as the opposite metals wear more equably. The perfection of compasses 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 compasses of various kinds and contrivances, accommodated to the various uses they are intended for.

**Compasses of Three Legs**, or **Triangular Compasses**, are, setting aside the excess of a leg, of the same structure with the common ones; and their use is to take three points at once, so as to form triangles; to lay down three positions of a map, to be copied at once, &c.

**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. To the cursors may be screwed points of any kind, whether steel for pencils, or the like. Beam-compasses are 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.

**Clockmaker's Compasses** are joined like the common compasses, with a quadrant or bow like the spring compasses, only of different use, as here it serves to keep the instrument firm at any opening. They are made very strong, with the points of their legs of well-tempered steel, 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, being a little bent on the ends. Their use is to take the diameter, thickness, or calibre of round or cylindrical bodies, such as cannon, pipes, &c.

**Elliptic Compasses** are used to draw ellipses, or ovals of any kind. They consist of a beam about a foot long, bearing three cursors, to one of which may be screwed points of any kind. To the bottom of the other two are rivetted two sliding dovetails, adjusted in grooves made in the cross branches of the beam. As the dovetails have a motion every way, by turning about the long branch, they 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 dovetail will have got back the whole length of the branch. The use of this compass is easy; by turning round the long branch, the ink, pencil, or other point, will draw the ellipse required.

**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 withinside, by a small adjusting screw to one of the legs, as to take an extent to a hair's breadth.

**Lapidaries' Compasses** are a piece of wood, in form of the shaft of a plane, cleft at top, as far as half its length; and with this the angles, &c., of jewels and precious stones are measured. There is in the cleft a little brass rule, fastened 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 lapidaries take the angles of the stones, laying these 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. The latter consist of two parts or sides of brass, which lie upon each other so nicely as to appear but one when they are shut. The sides open easily, and move about a centre, which is itself moveable in a hollow canal cut through the greater part of their length. To this centre, on each side, is affixed a sliding piece, 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 superficies, 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 one to twenty, the last from six to twenty.

The use of the first is to divide a line into any number of equal parts; by the second and third are found the sides of like planes or solids in any given proportions; and by the fourth, circles are divided into any number of equal parts, or any polygons inscribed in them.

**Spring Compasses**, or dividers, those with an arched head, which by its spring opens the legs; the opening being directed by a circular screw fastened to one of the legs and let through the other, worked with a nut. These compasses are made of hardened steel.

**Trisection Compasses** consist of two central rules, and an arch of circles of 120 degrees, immovable, with its radius, which is fastened with one of the central rules, like the two legs of a sector, in order that the central rule may be carried through all the points of the circumference or the arch. The radius and rule should be as thin as possible; the rule fastened to the radius should be hammered cold, to attain the greater elasticity; and the breadth of the central rule should be triple that of the radius. There must also be a groove in this rule, with a dovetail fastened on it for its motion, and a hole in the centre of each rule. The use of this instrument is to facilitate the trisection of angles geometrically.

**Turn-up-Compasses**. The body of this instrument is like the common compasses; but towards the bottom of the legs, outside, are added two other points besides the usual ones, the one of which carries a drawing pen point, and the other a port-crayon, both adjusted so as to turn round, and be in the way of use, or out of it, as occasion requires. These compasses have been contrived to save the trouble of changing the points.