Figs. 1072 to 1076, which have convex and rectilinear edges do not admit of being sharpened by any of the guide instruments described; and the restoration of their edges is effected with small slips of oilstone delicately applied with the fingers, like a file. For reaching the square internal corners of figs. 1074 to 1076, the square edges of the oilstone slip are kept keen by rbbing it upon a piece of emery paper.

Small straight metal bars, charged with fine flour emery, oilstone powder, or crocus and oil, are sometimes used for sharpening tools of mixed forms, such as the above. These metal bars, like the metallic laps, retain their shapes longer without deterioration than the natural oilstone; they are generally made of soft brass, and similar in shape to small files of a square or half round section. Considerable practice is however required to sharpen the small ornamental drills and cutters of mixed forms, without losing the necessary accuracy of shape.

The side cutters, fig. 1077, with two quarter hollows, are made of different radii, and used for fluting concave sweeps, such as the foot of a vase, they are ground on the conical grinders of fig. 1057. The bent cutters, fig. 1078, are also made of various radii, and are principally used for small eccentric patterns on plane or spherical surfaces, such as the top of a snuff-box, or the head of a walking stick; but the bent cutters, although generally made with angular edges, do not admit of being ground on the instrument for angular tools, fig. 1047, but are sharpened with slips of oilstone. The tool, fig. 1079, is employed for turning rings of ivory or hardwood, the two half-round hollows are made of the same size, and exactly opposite to each other, in order that when the tool is fixed in the slide rest, the left hand edge may be used to turn a bead on the inside of a hollow tube, and which constitutes the first half of the ring, the second half is completed by applying the right hand edge of the tool to the outside of the tube, and the rectilinear action of the slide-rest ensures the beads being opposite to each other. The application of these various tools will however be treated of in a future volume.

Many tools from their complex forms or other reasons do not admit of being sharpened by the ordinary grinding processes, and it is frequently necessary to resort to the file for restoring their edges. Those tools that are left only of a moderate degree of hardness such as the saws, brace bits, and some circular cutters for wood and brass, may be filed without having been previously softened, other tools are lowered in temper just enough to admit of the action of the files, and still retain sufficient hardness to be tolerably durable when applied to their work, but such tools as cannot be ground, and yet are required to possess considerable hardness, are softened prior to the application of the file, and are subsequently rehardened, which processes have been already explained in the first volume of this work, but as there mentioned, the less frequently steel is passed through the fire the better, as its brittleness becomes thereby materially increased.

Moulding tools used in the sliding rest for turning do not admit of being sharpened on the flat surface of the tool, as this method would remove the edge below the center of the lathe, these tools must therefore be sharpened at the end only, and to do which in the most effective manner it is necessary that they should be first softened and then sharpened with files, or the revolving hob on which they were originally made. The edges of these moulding tools may be partially restored with slips of oilstone, or the small straight metal grinders fed with fine emery, or still better, with a temporary counterpart grinder, made by turning with the tool itself a circular moulding on a piece of boxwood, which may be afterwards charged with flour emery, and used as a grinder to restore the edges, by this method however the tools soon deteriorate, as at every sharpening they depart further from the original figure.

The fixed moulding cutters used in the large planing machines for wood, are frequently sharpened upon revolving laps with rounded edges. The tool is twisted about to expose all parts of the chamfer to the action of the lap, and which plan is tolerably manageable with tools for large mouldings. Sometimes a circular piece of oilstone turned to a round edge is used for this purpose, but the difficulty of obtaining the oilstone in sufficiently large pieces, and the numerous hard and soft places in the stone, prevent this from being so effective a tool as might at first be supposed. When the forms of the moulding cutters become depreciated, it is the better practice to resort to the use of the file, as for the small slide rest tools.

Figured cutting punches for cloth, leather, and paper, and also envelope cutters, are sharpened with oilstone slips. When they are worn down so as to become thickened so much as to render the sharpening very tedious, they are sometimes thinned by grinding them on rounded laps, but it is better that they should be softened and filed to their original forms. Circular cutting punches such as figs. 938 to 941, page 928, Vol. II. are softened and turned in the lathe; the edges are sometimes made a little keener by holding a piece of oilstone to the chamfer of the punch as it revolves in the lathe, and circular punches that are used in manufactories for cutting large quantities of gun wadding, are in some cases sharpened in the lathe by a lap which is made to revolve against the side of the punch, whilst the latter also revolves, so as to expose it equally to the action of the lap.

An instrument somewhat analogous to the patent knife sharpeners was invented by the late Sir John Robison for setting the edges of razors, penknives, and surgeon's instruments, and is shown half size in figs. 1080 & 1081, it consisted of two barrel shaped agates mounted on pivots, free to revolve in an elastic frame of sheet brass, the surface of the agates was supplied with finely pulverized corundum, emery, or oilstone powder, the edge of the blade to be sharpened was passed with slight pressure between the two agates, which from their shape could only be in contact at the central point, so that both sides of the edge were acted on at the same time, and if too much pressure was applied, the elastic frame allowed the agates to separate, and avoid injury to the edge of the blade.

The sharpening of saws with files has been already explained in Vol. II. pages 688 to 698, and the appendix, note B. L. page 1011 of the same volume describes the application of the grindstone to the teeth of large circular saws.