CO\I PASSES, (from the French, compas) a mathematical instrument fiur describing circles and ellipses, or their arcs; also for measuring and proportioning distances.
Compasses for drawing are of four kinds : those with two legs, moveable on a joint, by which the extremities can be extended to any distance, not exceeding the sum of both legs, are called COIllIn011 compasses. Those with a beam having a fixed point at one of its ends, and a moveable collar carrying another point, which may be fixed at any distance from the fixed point by means of a screw, are called beam compasses. Those with three legs, so as to be set to any three points, of which the distance between any two may not be greater than the sum of any two legs of the compass, are called triangular compasses. Those for drawing ellipses, are called elliptic compasses.
Common compasses are of several kinds, and are furnished with fixed or moveable points, ti or carrying a pencil or ink foot.
Common compasses with sharp points, used for taking distances, are called dividers. Dividers, m hich have the lower point of one of the legs famened to the upper part by a stiff spring, and by moons of a screw will allow of slow motion in the legs, so as to extend or shorten the distance of the points to the smallest degree, are called hair compasses. Those with moveable ink and pencil feet, for describing circular lines, are called, in contradistinction, composses; the ink or pencil foot is fated into a socket in one of the legs of the compass. Besides the ink and pencil feet, there is sometimes another foot for dotting circular lines, but it is seldom used, as being apt to run two or more dots into one. Compasses for describing small circles with ink or pencil, and which shut into a bow, are called bow compasses.
Triangular compasses have two legs, which revolve on a folding joint, like comm4 »I compasses, and the third leg is fixed to the bulb by means of a projection, with a joint, so as to be moveable in every direction. The three points of the compasses may be made almost to coincide with any three assumed points, to any distance within the reach of their extension.
Compasses with a joint between the extremities, and two sharp points at each end, forming a double compass, so that the two ends may always preserve the same ratio, however extended, are called proportional compasses. When the joint is fixed, the compass is said to be simple ; but when moveable, it is called a compound proportional compass.
The simple proportional compasses, in most general use, have the two legs on one side of the centre always double those on the other, and are denominated wholes-and-halves, or bisecting compasses.
Compound proportional compasses have each branch cut with a long slit for a cursor to slide in ; in the middle of the cursor is a screw, by which the ends may be set in any pro portion to each other. One leg is generally graduated on
either side of the slit, one side for the division of right lines into any number of equal parts from 2 to 10, and the other for inscribing polygons from 6 to 20 sides in a circle of any given radius within the greatest extension of the compasses. The other leg is graduated in a similar manner, one side into divisions, showing the proportion between the areas of similar plane figures, the other into parts showing the proportion between the contents of similar solid figures. This instru ment is employed in the reduction of figures, and is extremely useful in the projection of dome departments, and in perspective.
Examples of the use of compound proportional compasses. —Let it be required to divide a straight line into four equal parts ; push the cursor till the index be just on the figure 4, and_fix it there ; then take the length of the given line with the longer legs, and the distance between the points of the other legs will be one-fourth of the length of the line.
Again, let it be required to inscribe a heptagon in a circle : push the cursor till the index or zero he on 7 ; then, with the longer legs take the radius of the circle, and the distance between the two other points will be the side of the heptagon. See PROJECTION.
To find a regular plane figure whose area shall equal one fourth of that of a given similar figure ; set the zero on the cursor to the line marked 4, take the length of one of the sides of the given figure with the longer legs, and the distance between the points of the shorter ones will give the side of a similar figure which shall contain an area equal to one fourth of the area of the given figure.
By means of the same scale of divisions, may be found the square root of any given number, thus :—Set the zero of the cursor to the given number ; open the longer legs so as to contain the same number from any scale of equal parts, then apply the points of the shorter legs to the same scale, and the distance measured between them will give the square root of the given number.
To find a sphere or cube whose solid contents shall be equal to one-fourth of those of a given square or cube : Set the zero to the division marked 4, measure the diameter of given sphere, or the side of the given cube, with the points of the longer legs, and the points of the shorter ones will give the diameter of a sphere or side of a cube such as required.
The cube root of any number may be found by this scale in a similar manner to that by which the square root is found by the opposite one.
Compasses used in the description of ellipses, are called elliptic compasses, or ellipsographs. See ELLIPSOGRAPII and PENTAGRApit.