distance of the twO parts is to be adjusted, according to the thickness of the work, so that the secondary one may be flat upon the plate. The generality of dividers, instead of this contrivance, bend the index to suit the different planes of the work and plate ; but this is a very bungling method; indeed, when the borders of instruments arc re quired to be divided on feather edges, as is the case with protractors, bending is necessary : a very flexible index should in such cases be employed, in order that the pres sure of the hand may bring it in contact with the inclining plane. But even here a secondary index might be employ ed to advantage, having its position adjustable to the plane which is to receive the divisions.
The dividing-knife must next be described. This little implement is represented in full size, by Fig. 2. It con sists of a blade and handle ; the former should be made of the very best steel, and the latter of beech-wood. The cutting edge should he exactly of the same thickness that the divisions are intended to be ; it should be quite straight, and in a line with the handle. This edge must not be sharp like that of a common knife, but rounding, so as to present to the surface to be divided a small semicircle, whose radius is equal to half the breadth of the line it is to make. At the back the blade should be about a fifteenth of an inch in thickness. The left side, which is the front and downwards in the figure, should he ground flat ; but the opposite side must be chamfered in a faint curve from back to edge. The extreme end of the blade makes with the line of the edge, an angle of about 70°. A small chamfer on the side to the right, broad at the back, but vanishing at the edge, reduces the end to an equal thickness. A semi circular recess is made in the edge of the blade, near the handle, which affords a relief when the tool is sharpened, and is farther useful by receiving the inner side of the end of the middle finger. For the accommodation of this fin ger also, a part of the ferrule of the handle is cut away, as represented in the Figure. There is a convenience in the back of the blade being formed into a curve so as to make it narrow at the point, for without diminishing its strength, it enables the operator to see his work better. Such is the form of the dividing knife, an important tool in every branch of the art, as in the hands of the best workmen it has con tinued unaltered since the time of Bird. Had we, indeed,
been inclined to describe it as found in the workshop of an ordinary divider of the present time, we should only have had occasion to say, that it exactly resembles the butcher's cleaver ; and, perhaps, we might add, is commonly direct cd with about equal science.
The action of the dividing knife is directly the reverse of the graver ; the latter being pushed outwards, cuts away a fibre in the line of its course, leaving the rest of the sur face of the metal undisturbed ; but the former is drawn in wards, and without producing chips, ploughs a furrow, and the metal displaced rises in a bur on each side. The knife is held very much like a pen, only the handle must be quite home between the thumb and fore-finger, which being placed upon the ferrule, directly over the back, is, by its pressure, the chief agent in giving depth to the divisions, the thumb and middle finger acting as supporters, the other two fingers, as in writing, prop the hand. The knife is held at an angle or about 45° with the plane to be divided, and is used with the flat side in contact with the in dex before described. If it has an inclination of its own to deviate either to the right or left, it is not in a condition fit to be used ; for in the former case it would require too hard a pressure of the hand to keep it in contact with the index, and in the latter would undermine it, and in either case it would make crooked lines. It is therefore necessary to tly it in this respect, before the corumenceumit of viding. If, on drawing a line without an index, it deviates to the right, then is the vertex of the semicircular edge too near that side ; but when that vertex is too near the left, the knife will deviate the contrary way. The use of the small chamfer before described, is to make the two sides of the knife exactly similar at the point, were it not for this contrivance, the bur would not rise equally on both sides, and the strokes, where they meet the bound ing lines, woul• have an appearance of crookedness.
Preparatory to making the divisions, the circular lines must be drawn for limiting the length of the strokes: these are made with the well known apparatus called a beam-compass ; but it is only necessary to trace the lines with it. They are to be made of sufficient breadth and depth by the dividing-knife, which, when sharpened as above directed, and guided by the hand alone, will aptly follow the slightest mark.