An angle - measurer which consists of a semicircular tool having degrees of arc marked on it, is made of either sheet brass or sheet steel. If to be of brass, Muntz metal is suitable, which is cut while cold, a piece about a sixteenth thick being selected for an instrument about three or four inches in length. The marking to indicate the shape of the tool is commenced by scribing a straight line along one side of the piece, and at about an eighth of an inch from the edge ; this line is made to serve as a base for a semicircle, which is scribed by means of a centre dot situated about the middle of the line, the dot being marked by C in Fig. 509. The radius with which the first semicircle is scribed is about a sixteenth longer than the radius when the tool is finished ; consequently, if cut at this line, ample metal is allowed for filing. Previous to cutting, another semicircular arc is scribed to denote the smaller or inner boundary which will surround the space in the middle of the tool; the length of this arc is rather less than that of the finished length, and the base or chord of the arc is a line parallel to the line first made, the distance between these two straight lines being the width of the straight part of the tool. This portion is termed the straight-edge, and the outer straight side is termed the true edge or base of the implement. After the shape is marked, the sheet is put upon a soft iron block and fastened with one or two screw-clamps to hold it while being cut, the cutting being effected with a sharp chisel and hammer; the piece in the middle is first cut out, and afterwards the superfluous pieces which surround the intended tool, except the superfluous eighth of an inch which adjoins the intended true edge. In addition to this piece, another small piece may be allowed to remain at the opposite side, such pieces being useful as holders or handles while marking and finishing the broad sides of the instrument.

To make large tools of this class it is necessary to cast them in sand moulds, which are shaped by wood patterns that are very nearly of the finished dimensions and shapes of the required implements. Two or three holders are provided, as for smaller work ; but large ones are planed on a machine, after which the straight lines are marked to indicate the portion termed the straight-edge, and the semicircular lines are scribed to the desired length. While in this condition the edges are shaped and the angle-measurer is made ready for the marking of the degrees.

A steel measurer of this shape is made of a piece of sheet steel, which is marked, while cold, in the same manner as for making one of sheet brass; and, when marked, the steel is heated and chiseled to its proper form, being careful to drive the chisel about halfway through at all the marks previous to cutting any part entirely through. When it is entirely forged and trimmed it is softened by slow baking, and next ground on a grindstone, which prepares the tool for filing and smoothing.

A large angle-measurer, intended to be about three or four feet long, may be made of two pieces of a hard tough iron. The metal selected consists of a bar or bars about as wide as the straight-edge portion of the intended tool. Two pieces are required, and are welded together, one of which is long enough to be curved to form the half-round portion, and the other piece being sufficient for the straight portion. This straight piece is upset for scarfing at each end, and also upset along its length; by this means it is made shorter than its finished length ; the curved piece also is upset, and both are welded together by two joints which are situated at the two corners of the implement. When the joints are finished, it is stretched to its shape and dimensions by hammering and with a flatter. During this shaping, the work is put to a diagram on a table; this diagram is a full-dimensioned outline of the tool's broad side, being about an eighth of an inch longer and wider than the work when finished.

In order to tightly hold thin tools of this class and other work of similar shape while filing their broad sides, they are held by means of screw-clamps on a wood or iron table, pieces of plate iron and leather being put under the screw-points to prevent injury to the work. Marking the degrees of arc is not done till the broad sides are smoothed, if not polished. To mark an angle-measurer without a machine, only a divider, straight-edge, and scriber are necessary, and the marking commences by making a small centre dot, termed the primary centre, in the middle of the outer straight line. From this dot two or three semicircular arcs are exscribed to distinguish the longer from the shorter divisions to be marked. At each place where one of the semicircular arcs intersects the outer straight line, another dot is made, and into one of these a divider-point is put and the legs adjusted to a radius which will scribe a short arc at a short distance beyond the ninetieth degree; another short arc is next marked with the same radius by putting one point into the dot at the other place of intersection and scribing across the arc first made; at the point where the two short arcs intersect is the ninetieth degree, and to this point and the primary centre the straight-edge is put to scribe a straight line across the instrument. The divider is next closed to the same radius which scribed the semicircle, and while thus adjusted the entire semicircular line is divided into six equal lengths, which represent thirty degrees each. These portions are next divided into three parts of ten degrees each, and afterwards each of these is bisected to make each division represent five degrees. One more bisecting process will produce marks for each two and a half degrees, which is about as small a quantity as can be marked by these operations. Such dividing processes are in daily use among engine-makers, but the accurate marking of degrees is always effected in proper arc-dividing machines.