INTRODUCTION TO MECHANICS. xvii 



circumference to the centre of the circle C. This force would, there- 

 fore, with more propriety be called the tangential than the centrifugal 

 force, or rather, the inertia of the body which inclines it to move in 

 the direction of the tangent is the tangential force. But motion in 

 the direction of the tangent would remove the body farther from the 

 centre ; a tendency, therefore, to such motion is a tendency to leave 

 the centre, and that part of its force which tends to produce motion thus 

 away from the centre is called the centrifugal force. 



If a ball be thrown in an horizontal direction, it is acted upon by no 

 less than three forces: the force of projection first given to it; the 

 resistance of the air through which it passes; and the force of gravity, 

 which finally brings it to the ground. Gravity and the resistance of the 

 air act continually ; and as the whole effect produced by them is always 

 so great as to overpower any force of projection we can communicate 

 to a body, the latter is gradually overcome, and the body brought to the 

 ground ; but the stronger the projectile force, the longer will these powers 

 be in subduing it. A shot fired from a cannon, for instance, will go 

 much further than a ball thrown by the hand. Bodies thus projected 

 describe a curve line in their descent. If the forces of projection and of 

 gravity both produced uniform motion, the ball would move in the 

 diagonal of a parallelogram, but the motion produced by the force of pro~ 

 jection alone is uniform, that produced by gravity is accelerated; and it is 

 this acceleration which brings the ball sooner to the ground, and makes it 

 fall in a curve instead of a straight line (see fig. 13). If a ball at 

 A be projected, in a horizontal direction, with a force capable of carrying 

 it to F (which we will suppose to be 100 feet) in a second, then, if it were 

 not acted upon by gravity, it would proceed from F to G, another 100 

 feet, in the next second, and the same distance G H in a third, and H I 

 in a fourth second. Now, if the ball, when at A, be allowed to fall, by 

 the force of gravity alone, from A towards E, it will fall 16 feet to B 

 during the first second* ; then three times as much, or 48 feet the next 

 second ; and five times as much, or 80 

 feet, in the third second ; and seven 

 times as much, or 1 12 feet, in the fourth 

 second. Then, in order to find the line 

 in which the ball will move, by the united 

 forces of projection and gravity, we must 

 draw a line B K parallel to the horizontal 

 line A F, and 16 feet below it ; then 

 another line C L, also parallel, at the dis- 

 tance of 48 feet more; then another line, 

 D M, 80 feet further; then another, EN, 112 feet further. Then, at the 

 end of the first second the ball will be at K, at the same distance from 

 B as F is from A ; at the end of the next second it will be at L, the 

 same distance from C that G is from A ; at the end of the third second 

 it will be at M ; and at the end of the fourth second at N ; and thus you 

 see the curve line A K L M N is described in its fall, instead of a straight 

 line, which would be the case if A B, B C, C D, D E, were all equal. 



We have not taken notice of the resistance of the air, which much 

 complicates these results in practice. The principles of its operation 

 may easily be understood from the mode in which the other forces act ; 

 but the degree and manner in which it modifies their effects cannot be 

 shown without much difficulty and intricacy of explanation. It is, how- 



* Sec page x. 



C 



