After the form of the cutting tool is decided upon, the next important point to be considered is the manner of its application. The principle which is usually stated for turning tools is, that the point of the tool should be nearly on a level with the axis of the matter to be turned, or rather that it should be very slightly below it. This rule when applied to the greater number of tools and tool-holders is calculated to mislead. Before applying the correct rule it is necessary to consider in each tool or tool-holder, what is the situation of that point around which the cutting point of the tool will turn when any force is put upon the tool. Let this point be called the center of flexure. Then the correct rule is, that the center of flexure should always be above the line joining the center of the work and the cutting point.

On looking at fig. 983 A c, is the line joining the cutting point a and the center of the work c. By making the tool weak about Q that point becomes the center on which the point a will bend when any unusual force occurs. On the occurrence of any such unusual force arising from any pin or point of unequal density in the matter cut, the point of the tool a, by bending around the center Q will dig deeper into the work and cause some part of the apparatus to give way or break.

If on the other hand the point P is that around which the point of the tool when resisted tends to turn, then since this point is above the line joining the cutting point and the center of the work, the tendency of the additional strain on the point is to make it sink less deeply into the work, and consequently to relieve itself from the force opposed to it.

Fortunately the position of this point can always bo commanded, for it is always possible, by cutting away matter, to make one particular part weak. This is indeed a circumstance too frequently neglected in the construction of machinery. Every piece of mechanism exposed to considerable force is liable to fracture, and it is always desirable to direct it to break at some one particular point if any unexpected strain occurs. In many cases where danger may arise from the interference of the broken part with the rest of the machinery this arrangement is essential. In all cases it is economical, because by making the breaking, if it occur, at a selected spot, provision may be made of duplicate parts and the delay arising from stopping the machine be avoided.

The results of the preceding inquiry would lead to considerable changes in the forms of tools generally used in cutting metals, and as the time employed in taking a cut is usually equal whether the shaving be thick or thin, the saving in power by taking thin cuts separately would be accompanied by a considerable expense of time Thin however need not be the case if proper tool-holders are employed, in conformity with the following several conditions: thus

The tool-holders should be so contrived as to have several cutters successively removing equal cuts. - The cutting edges should be easily adjusted to the work. - The steel of which the cutters are formed should be of the best kind, and after it is once hardened should never again be submitted to that process. - The form and position of the cutter should be such that it may, when broken or blunted, be easily ground, having but one or at the utmost but two faces requiring grinding. - 1 desirable that when being ground it should bo fixed into some temporary handle, in order that it may always be ground to the same cutting angles. - The cutters should be very securely, but also very simply tightened in their places. - The center of flexure of the cutter should, in turning, be above the line joining the center of the work and the cutting point; - whilst in planing the center of flexure should be in advance of a lino perpendicular at the cutting point to the surface of the work planed. Examples of some tool-holders of this kind will be given subsequently.

The effects of such improved tools would bo to diminish greatly the strain put upon lathes and planing machines, and consequently to enable them to turn out better work in the same time and at a less expense of power: whilst the machines themselves so used would retain their adjustments much longer without reparation.

Note AT. - To follow Note AS at foot of page 539. | The author's description of Tools and Tool-holders for turning and planing metal, constructed by C. Babbage, Esq. F.R.S.) In the course of the investigation which led Mr. Babbage to write the foregoing per, he constructed various experimental tool-holders, a port of the more successful of which I shall now attempt to describe, beginning with those in which a single cutter is used. The figures are one-fourth of the size of the actual tools, but the proportions of which may of course be enlarged or reduced according to circumstances.

Fig. 984 represents the perspective view, fig. 985 the plan, and a b c d e the details of Mr. Babbage's tool-holder, for the general purposes both of turning and planing metal: the tool itself c, being simply a short rectangular piece of steel cut off from the end of a long bar, and ground at the end with one chamfer at about 60 degrees with the length of the blade. The stock is cast of gun-metal and of a cranked form, as seen in fig. 984, the end being pierced with a vertical hole, in which is fitted the bolt a, having a long diametrical mortise to admit the tool freely as shown, and a nut and washer e, below to bind all the parts together. The bolt a, passes through two circular wedges b and d, inclined at the angle 27° on their internal faces, and loosely united by steadying pins; the lower circular wedge has a diametrical inclined mortise to serve as the seat for the tool, and which is grasped by the margins or walls of the wedges, when the bolt and nut are tightened.

Sometimes the cutter lies centrally to the shaft of the holder, as shown in fig. 984, and also by the central dotted line in the plan, the vertical branch of the holder is pierced with a mortise, then to receive the superabundant length of the steel cutter; but at other times the cutter is inclined about 45° in either direction, as represented in the plan, fig. 985, and the cutter then just escapes the stock through a little notch filed for the purpose.