If the material of which our cutting instruments are made would allow it, that is to say if it was perfectly hard, perfectly rigid and incapable of being crushed or torn apart, the proper shape of a cutting instrument would be a wedge of the most acute form possible. But since the steel which we use is limited in its hardness and its power of resisting crushing and bending influences, the blades of our knives must have a certain strength or thickness, depending upon the character of the material to be cut. For very hard substances the knife must be stout and the edge ground to a comparatively obtuse angle; for moderately soft substances, such as wood, the angle may be more acute, while for very soft tissues the thinnest blade and the sharpest edge are most suitable. [Illustration: Fig. 1.] The various angles to which cutting tools of different kinds are ground are shown in the accompanying illustrations, which explain themselves. [Illustration: Fig. 2.] In the diagrams just given, the sides of the wedge are carried in straight lines to the very edge. In practice, however, this is never done, there being two strong objections to such a form. In the first place if the sides were as shown in the figures, every time the tool was ground or set, the entire side would have to be ground off, and this would involve great labor. But another difficulty, quite as great, would occur in the use of the instrument, for since the wedge keeps growing constantly and proportionately thicker, the friction between the sides of the wedge and the material would rapidly become very great. Therefore most cutting edges are ground to a second angle, much more obtuse than the first, and it is this second angle which forms the true cutting edge. And it is obvious that the mass of material required to carry out the ultimate angle in any case is wholly unnecessary, for if the tool be strong enough at _a b_ (Fig. 2) it will certainly be strong enough at _c d_. An extreme illustration of this principle is shown in the cold chisel used for cutting iron, the edge of which is shown in Fig. 2, and the angle of 80° to which it is ground is carried out by dotted lines. The angle which the sides of the chisel (not the sides of the extreme cutting edge however) make with each other is 25°. [Illustration: Fig. 3.] [Illustration: Fig. 4.]