If the direction of the force does not pass through the centre of gravity, the progressive motion will be altered, and the body will then also acquire a rotatory motion round an axis passing through the centre of gravity, and perpendicular to a plane passing through the direction of the force and this centre. CASES BEARING UPON THE FOREGOING THEORY. ~When ball is perfectly round, centre of gravity coincides with figure, and no windage.~ 1st Case. Suppose the ball to be perfectly round, its centre of gravity and figure to coincide, and let there be no windage. In this case the force of the powder not only passes through the centre of gravity of the shot, but proceeds in a direction parallel to the axis of the bore, and there would be but small friction due to the weight of the shot. ~If windage then rotation.~ 2nd Case. But as there is a considerable amount of friction between the bore and the projectile in the case where there is windage, the direction of this force being opposite to that of the gunpowder, and upon the surface of the ball, it will therefore give rotation to the shot. ~Eccentricity causes rotation.~ 3rd Case. Suppose the ball to be perfectly round, but its centre of gravity not to coincide with the centre of figure. In this case the impelling force passes through the centre of the ball, or nearly so, and acts in a direction parallel to the axis of the piece; but if the centre of gravity of the ball lie out of the line of direction of the force of the powder, the shot will be urged to turn round its centre of gravity. ~Angular velocity.~ The angular velocity communicated to the body will depend, firstly, upon the length of the perpendicular from the centre of gravity upon the direction of the impelling force, and secondly, upon the law of density of the material or the manner in which the metal is distributed. The direction of rotations will depend upon the position of the centre of figure with regard to that of gravity. (Plate 23, fig. 6.) ~Robins’ remarks.~ Robins remarks, bullets are not only depressed beneath their original direction by the action of gravity, but are also frequently driven to the right or left of that direction by the action of some other force. If it were true that bullets varied their direction by the action of gravity only, then it ought to happen that the errors in their flight to the right or left of the mark, should increase in proportion to the distance of the mark from the firer only. ~Deflection not in proportion to distance.~ But this is contrary to all experience, for the same piece which will carry its bullet within an inch at ten yards, cannot be relied upon to ten inches in one hundred yards, much less to thirty inches in three hundred.