The simplest and most effective form of trenchant instrument intended for cutting only is the American broad-axe used by squatters in the backwoods. This revival of the proto-historic celt and headman’s instrument is a plain, heavy wedge of steel, fixed on a light, tough wooden helve or heft, thus concentrating all the force in the head that strikes the blow. Here there is no uncertainty about the use; and, were it not necessary in swordsmanship to ‘recover guard’ and to save self as well as disable the assailant, it would be the best, as it is one of the oldest, weapons derived from the club. But the cutting Sword, which in the short curved form is its congener, has a long blade that allows a choice of cut—a good choice and a bad choice. If the blow be made, for instance, at a tree-branch with the Sword-point (the ‘whole-weak’), its sole effect will be to jar wrist and arm unpleasantly. The same result will follow a blow with the ‘whole-strong.’ In either case the vibration of the blade shows a waste of strength. By the experiment of cutting along the entire length, inch after inch, and by comparing the effect, the swordsman comes at last to a point, about the end of the ‘half-weak,’ speaking roughly, where there is no jar, and where, consequently, the whole force of the blow becomes effective. But our ‘centre of percussion’ must not be confounded with the ‘centre of gravity.’ This balance-position is situated in the middle of the ‘whole-strong,’ the proper part for guarding, and for guarding only. The late Mr. Henry Wilkinson, of London, a practical man of science, first proposed a formula for determining the centre of percussion without the tedious process of experimenting with each and every blade. His system was based upon the properties of the pendulum. A light rod, exactly 39·2 inches long, capped with a heavy leaden ball, and swung to and fro upon a fixed centre, vibrates seconds or sixty times per minute in the latitude of London, and the three centres of percussion, of oscillation, and of gravity are concentrated within the ball. If it were a mathematical pendulum—a rod without weight—these three points would lie precisely in the core of the ball, or 39·2 inches from the place of suspension. The blade, to be graduated, is suspended, tight-fastened at the point on which it would turn when making a cut, and is converted by swinging into a pendulum. As the length is shorter, so the oscillations are quicker: the blade makes eighty movements to sixty of the pendulum. A simple formula determines the length of such an eighty-vibrations pendulum to be twenty-two inches. This distance, measured from the point at which the blade was suspended, is marked on the back as the centre of percussion, where there is no jar, and where the most effective cut can be delivered. [Illustration: FIG. 113.—THE INFANTRY ‘REGULATION’ SWORD. C.G. Centre of Gravity; C.P. Centre of Percussion.]