But the resistance of the air, acting upon the groove of the projectile, produces, on the lower part of this groove, an action which tends to bring back its point upon the trajectory, yet with so little force, that often, in its descent, the projectile turns over, and moves breadthways at ranges of 1000 and 1200 yards. The lower side of the projectile, therefore, moving in the compressed air, and the upper in the rarified air, deviation must ensue, for, as the upper part of the bullet moves from left to right, the bottom must move from right to left. But the lower resistance to the motion of rotation being produced by the friction of the compressed air, is greater than the upper resistance, which depends on the friction of the rarified air. By combining these two resistances, there results a single force, acting from left to right, which produces what Captain Tamisier termed “derivation,” and it was to overcome this derivation that this officer proposed the circular grooves to the bullet, which he considered would act, like the feathers of the arrow, to maintain the moving body in its trajectory. ~How to obtain knowledge of the bullet’s rotation.~ ~By the arrow.~ ~Use of feathers on arrows.~ If, however, we would wish to obtain some idea of the rotatory motion of a bullet in its path through the air, let us consider the action of the arrow, and see how it is constructed, so that the resistance of the air should not act in an unfavourable manner. First, nearly all its weight is concentrated at the point, so that its centre of gravity is close to it. At the opposite end feathers are placed, the heaviest of which does not affect the centre of gravity, but gives rise to an amount of resistance in rear of the projectile, and which prevents its ever taking a motion of rotation perpendicular to its longer axis, and keeps it in the direction of its projection. This difficulty which the arrow finds in changing its direction must concur in preventing its descending so rapidly as it would do were it only to obey the law of gravity, and must therefore render its trajectory more uniform. ~Similar effects on bullet with grooves.~ Let us, however, now come back to the grooves of Mons. Tamisier, and we shall find that they concur in giving to the bullet the two actions of the resistance of the air, which we have demonstrated with respect to the arrow. ~Effect of grooves.~