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most, even at very long ranges, we infer that this is due to the 
resistance of the air, and are led, not only to consider the causes which 
produce this result, hut the simplest method of obtaining it. It cannot 
be due, as some suppose, to the tendency of the projectile to take that 
position which gives least resistance; for then there would be no neces¬ 
sity to give any rifling at all. The laws which regulate the action of 
impressed forces on a rotating body hafe been pretty well determined; 
and though they do not—owing to the difficulty of determining the re¬ 
sultant action of the resistance of the air—enable us to solve this question 
theoretically, they give great aid in drawing correct conclusions from 
observations derived from experiment. Whatever be the action of the 
resistance of the air, we know that it can be represented by two forces, 
one of which acts through the centre of gravity of the projectile and 
tends to produce a change in its velocity and direction, while the other 
tends to produce rotation round some axis, and thus tends to produce 
a change either in the direction of the axis or in the velocity of rotation, 
or both. 
The latter of these two forces will be considered more particularly. 
It is a law in mechanics that if a rotating body, whose axis and 
velocity of rotation are represented in direction and amount by a straight 
line, be acted on by forces which would produce another rotation whose 
axis and velocity may be similarly represented by another straight line, 
the result is a rotation whose axis and velocity may be similarly repre¬ 
sented by a straight line forming the diagonal of the parallelogram of 
which the two straight lines are the sides. All these lines pass through 
the centre of gravity of the body. If the axis of rotation be a stable 
axis, and the forces be gradually applied, the axis does not change its 
position in the body, but only in space, and the amount of change is 
proportional to the amount of force applied, compared with the force 
which would produce the original rotation. 
This law may be illustrated by the gyroscope. If the gyroscope 
receive a rotation which to the spectator is seen to be in the direction 
of the hands of a clock, it may be represented by a straight line drawn 
in the direction of the axis towards the spectator. If now a weight be 
hung at the extremity of the axis towards the spectator, this tends to 
produce a rotation which may be represented by a straight line drawn 
from the gyroscope to the left; the result is, that the axis takes up a new 
position between the two, and moves to the left. If the weight be hung 
at the extremity of the axis from the spectator, the tendency to produce 
rotation will be represented by a line drawn to the right, and the axis 
will move to the right. So long as the weight is suspended, the de¬ 
flection continues, and it ceases when the weight is removed. It will be 
observed that when the rotation is considerable and the weight not too 
heavy, the deflection is almost exactly to the right or left; but if the 
rotation be low or the weight considerable, there is also a tendency in 
the point of suspension to drop, so that at each gyration it descends 
lower and lower. This fact should be particularly borne in mind, as it 
explains why it is necessary to give a considerable rotation to rifled 
projectiles. 
Another illustration may be given by the spinning of a top. The 
