CYCLOGRAPH, (from the Greek, truttA,og, a circle. and yoacbetv, to describe) in practical geometry. an instrument for describing the arc of a circle to any chord and versed sine; but chiefly used in flat segments, or those whose curvatures approach to straight lines. There are several constructions of cyelographs, of which the following is one. The principle consists of two rules, A B, and e n, connected by a folding E, the pin, 1•, of which projects upwards. and is mortised to receive a bar, is g, which is fastened, hut movable round the centre of the folding joints; upon the connected rules, A B and c D, at equal distances, from the centre of the folding joint, are fastened the ends i and K, of two other equal bars c I. c K, connected by a movable joint, c, so as to form a rhombus, h li c 1, movable round each of the joints, cIhK; then the bar, is g. which passes the centre, is, of the two first rules, being made also to pass through a projection of the pin. r. of the opposite angle of the rhombus, is made to slide into the mortise as at r. The use of the bar is to fasten the instrument in any position by means of a screw inserted from the middle of the top of the upright pillar at c, which receives the sliding end of the bar.
The instrument being supposed to be placed upon a level plane, and the pin, h, of the folding joint being made to project upwards; another bar, L SI N, bent to a right angle with a longitudinal slit, op, is fitted upon it, so as to have a motion upon the pin h, in the section of the slit, but may be fastened at any required point, by means of a screw from the top. The other end, N, of this bar is mortised in the
direction of the slit, to receive the lower bar, h g, so as to have a longitudinal motion. The middle line of the upper bar stands in the same vertical plane with the middle line of the lower bar, and these two lines are parallel in all positions of the instrument.
The end of the bar, L NI, at the external side of the folding joint, has a deep socket for holding ft pin or pencil, perpendicular to the plane of the instrument. The advan tage of the upper bar being movable, to which the pin or pencil is attached, is to admit the point of the pin or pencil to he brought into the intersection of the sides It A, C D, of the instrument.
To describe the segment of a circle by means of the eyelo graph. fasten two pins in the plane, or steel edges made on purpose, and adjust the angle of the instrument ; place the outer edges upon the pins, and the angle close upon one of them ; move the instrument laterally close to the pins, and a pen or pencil w ill describe the curve.
The principle of this instrument is founded upon the twentv-first proposition of the third Book of Euclid's Elements. in which it is announced and proved that "the angles in the same segment of a circle, are equal to one another." This instrument may also be applied to the drawing of lines to any inaccessible points, by means of the middle bar, which always bisects the angle. and therefore will be indis pensably useful in the practice of perspective.