Now this irregularity can only arise from the track of the bullet being incurvated sideways as well as downwards. The reality of this doubly incurvated track being demonstrated, it may be asked what can be the cause of a motion so different from what has been hitherto supposed. ~1st cause of increase, deflection.~ 1st Cause. Is owing to the resistance of the air acting obliquely to the progressive motion of the body, and sometimes arises from inequalities in the resisted surface. ~2nd cause, from whirling motion.~ ~Direction of a shot influenced by position of axis round which it whirls.~ 2nd Cause. From a whirling motion acquired by the bullet round its axis, for by this motion of rotation, combined with the progressive motion, each part of the bullet’s surface will strike the air in a direction very different from what it would do if there was no such whirl; and the obliquity of the action of the air arising from this cause will be greater, according as the rotatory motion of the bullet is greater in proportion to its progressive motion; and as this whirl will in one part of the revolution conspire in some degree with the progressive, and in another part be equally opposed to it, the resistance of the air on the fore part of the bullet will be hereby affected, and will be increased in that part where the whirling motion conspires with the progressive; and diminished where it is opposed to it. And by this means the whole effort of resistance, instead of being in a direction opposite to the direction of the body, will become oblique thereto, and will produce those effects we have already mentioned. For instance, if the axis of the whirl was perpendicular to the horizon, then the incurvation would be to the right or left. If that axis were horizontal to the direction of the bullet, then the incurvation would be upwards or downwards. But as the first position of the axis is uncertain, and as it may perpetually shift in the course of the bullet’s flight, the deviation of the bullet is not necessarily either in one certain direction, nor tending to the same side in one part of its flight that it does in another, but it more usually is continually changing the tendency of its deflection, as the axis round which it whirls must frequently shift its position during the progressive motion. ~Doubly incurvated track.~ It is constantly found in practice that a shot will deviate in a curved line, either right or left, the curve rapidly increasing towards the end of the range. This most probably occurs from the velocity of rotation decreasing but slightly, compared with the initial velocity of the shot, or, if a strong wind is blowing across the range during the whole time of flight, the curve would manifestly be increased according as the velocity of the ball decreased. ILLUSTRATIONS OF ROBINS’ THEORY OF ROTATION. ~With ball and double string.~