Referring to the preliminary remarks on cutting tools, pages 457 to 468 of the present volume, it will be seen that saws were considered to belong to the group of scraping tools, and that e and f, fig. 316, were viewed as the generic forms of the teeth, the angle of which is commonly 60 degrees, from the circumstance of the simple angular teeth being mostly produced by angular notches, filed with two of the sides of an equilateral triangular file; and therefore the points assume the same angle as the spaces, or 60 degrees.

But the angle of 60 degrees is variously placed; for instance, the teeth in fig. 643 are said to be upright, or to have no pit. and the teeth in fig. 616 to be flat, or to have considerable pitch: these may be considered as the extremes of this kind of tooth, between which every inclination or pitch is more or less used; but, for the sake of definition, four varieties have been assumed, the straight lines of which are 15 degrees asunder.

Fig. 648, as already explained, is the ordinary tooth for cross-cutting, and which, from presenting equal angles on each side, is said to be of upright pitch. The tooth that is, however, more generally used for small cross-cutting saws is fig. 644, which is inclined about 15 degrees from the last. This form of tooth, called slight pitch, is used for the cross-cutting saws for firewood; those for joiners' use; and also for those employed in cutting up ivory; in which latter case the blade is stretched in an iron frame.

Fig. 645 is the tooth in most general use: it is known as ordinary pitch or the hand-saw-tooth. The face is perpendicular, and the back inclines at an angle of 30° from the edge of the saw, or the line of work. Most of the saws used by cabinetmakers and joiners are thus toothed, or rather at an inclination intermediate between figs. 644 and 645.

The tooth, fig. 645, is likewise generally employed for saws used for metal; for circular saws used for fine work, including veneer-saws, and for many of the circular saws for cross-cutting.

In fig. 646 the face of the tooth is " set forward," or stretches beyond the perpendicular, at an inclination of 15 degrees: this kind is employed in mill-saws used abroad for soft woods, and they are the most inclined of those teeth formed by the two faces of the triangular file at the one process.

Nearly the same tooth as fig. 646 is also used for circular saws and cutters for metal. The object is then to assimilate the points to those suitable to tools for turning the metals; therefore, the angle of separation betwixt the end of the tooth and the plane to be wrought, is made small. The hook form of the point is incidental to the employment of the triangular file, and is also proper for the material to be cut.

Fig. 647 is a form of tooth that is set forward like 646, but the point is more acute than the last five, or it is about 45 degrees instead of 60. It is used for some circular saws, and occasionally also for pit saws and cross-cut saws; and is frequently employed for cutting soft Bath stone.

Sometimes the acute angular notch is not continued to an internal angle; a method adopted in some mill saws, both those of ordinary or perpendicular pitch, fig. 648, and those of great or pitch or inclination, fig. 649; the former being more common for rectilinear, the latter for circular saws. Various intermediate forms are met with.

The three kinds of teeth, figs. 647, 648, and 649, from being more acute than 60 degrees, cannot be sharpened with the ordinary three-square or equilateral file, as it will not reach to the bottoms of the teeth. The mill-saw file is then used, namely, a thin flat file with square or round edges, as the definition of the internal angle is not needful; although given by the punch in the formation of the tooth. The angular mill-saw teeth are employed, partly because they are more easily sharpened than the gullet teeth, which conclude the series of diagrams.

The teeth, figs. 650 to fig. 653, are called gullet teeth, on account of the large hollow or gullet that is cut away in front of each tooth, in continuation of the face; and they are also known as briar teeth. The tooth is in general cut by one punch filling the entire space; but two punches, an angular and a gullet punch ha\e been occasionally used.

The gullet is adopted to allow the tooth to be sharpened with a round or half-round file, by which the face of the tooth becomes concave when viewed edgeways, and acquires a thin and nearly knife-like edge, as will be explained. The increased curvilinear space allows more room for the sawdust, and is less disposed to retain it than the angular notch.

For the facility of explanation, the faces of the teeth differ fifteen degrees in pitch, and the tops of the tooth are variously inclined to the edge of the saw, as tabulated. The medium kinds, figs. 651 and 652, are perhaps more common, although the saw-maker forms the teeth originally more acute, for the facility of first sharpening; and the sawyer sometimes neglects to file the gullets in the same proportion as the tops, by which the advantage attending the gullets is in a measure lost. Each alternate tooth appears to be deeper than the others; but this only arises from the peculiar mode of sharpening the gullet with a round or half-round file, which makes a broad chamfer, the v of which is elliptical.

For the general purposes of pit saws, and also for straight and circular mill-saws,the medium teeth, 651 and 652, are suitable; but for hard woods, as mahogany, rosewood, and others, and also for cross-cutting, the form should lean towards fig. 650; and for soft woods and ripping with the grain, towards the more inclined tooth, fig. 668. The whole of the forms of teeth may be materially diverted from those originally given by the saw-maker, in the important process of sharpening, and which will be now described, as the most proper way of concluding the remarks respecting the angles or bevils given to the edges of the teeth, independently of their simple profiles.