The Greek philosophers failed, we are told, in spite of their great mental subtlety, to arrive at any true conception of the laws governing the motion of bodies. It was left to the period of the revival of learning which followed the Middle Ages to produce ideas which were in partial conformity with the truth. Galileo and his contemporaries evolved the theory of the parabolic motion of falling bodies and confirmed this brilliant discovery by experiment. Tartaglia sought to apply it to the motion of balls projected from cannon, but was held up by the opposing facts: the initial part of the trajectory was seen to be a straight line in actual practice, and even, perhaps, to have an upward curvature. So new hypotheses were called in aid, and the path of projectiles was assumed to consist of three separate motions: the _motus violentus_, the _motus mixtus_, and the _motus naturalis_. During the _motus violentus_ the path of the spherical projectile was assumed to be straight--and this fallacy, we may note in passing, gave rise to the erroneous term “point blank,” to designate the distance to which the shot would travel before gravity began to operate; during the _motus naturalis_ the ball was assumed to fall along a steep parabola; and during the _motus mixtus_, the path of the trajectory near its summit, the motion was assumed to be a blend of the other two. This theory, though entirely wrong, fitted in well with practical observation; the trajectory of a spherical shot was actually of this form described. But in many respects it had far-reaching and undesirable consequences. Not only did it give rise to the misconception of the _point en blanc_; it tended to emphasize the value of heavy charges and high muzzle velocities while at the same time obscuring other important considerations affecting range. So the gunner was primed with a false theory of the trajectory. But even this could not be relied on as constant in operation. The ranging of his shot was supposed to be affected by the nature of the intervening ground; shot were thought to range short, for some mysterious reason, when fired over water or across valleys, and the gunner had to correct, as best he could, for the extra-gravitational attraction which water and valleys possessed. In addition to all these bewilderments there was the error produced by the fact that the gun itself was thicker at the breech than at the muzzle, so that the “line of metal” sight was not parallel with the bore: a discrepancy which to the lay mind, and not infrequently to the gunner himself, was a perpetual stumbling-block.