x INTRODUCTION TO MECHANICS. 



this force is gravity, which counteracts and finally overcomes that of 

 projection. If neither gravity nor any other force (such as the resistance 

 of the air or the friction of the ground) opposed its motion, the cricket- 

 ball, or even a stone thrown by the hand, would proceed onwards in a 

 right line, and with an uniform velocity for ever ! Yet we have no ex- 

 ample of perpetual motion on the surface of the earth ; because the 

 causes referred to ultimately destroy all motion, whether produced by 

 natural or artificial means. 



When we study the celestial bodies, we find that nature abounds with 

 examples of perpetual motion, and that it conduces as much to the 

 harmony of the system of the universe, as the prevalence of it would to 

 the destruction of all stability on the surface of the globe. Providence 

 has therefore ordained insurmountable obstacles to perpetual motion here 

 below 5 and though these obstacles often compel us to contend with 

 great difficulties, yet the generalj result is that order, regularity 'and 

 repose, so essential to the preservation of the various beings of which this 

 world is composed. 



Retarded motion is produced by some force acting on a body in a 

 direction opposed to that which first put it in motion, and thus gradually 

 diminishing its velocity. 



Accelerated motion is produced when the force which put a body in 

 motion continues to act upon it during its motion, so that its velocity 

 is continually increased. Let us suppose, that the instant after a stone 

 is let fall from a high tower the force of gravity were annihilated : the 

 stone would nevertheless descend, for a body, having once received an 

 impulse, will not stop (unless some obstacle impede its course), but move 

 on with a uniform velocity. If, then, the force of gravity be not de- 

 stroyed after having given the first impulse to the stone, but continues to 

 act on it during the whole of its descent, it is easy to understand that its 

 motion will be thereby accelerated. Let us suppose that the impulse 

 given by gravity to the stone during the first instant of its descent be 

 equal to one ; the next instant we shall find that an additional impulse 

 gives the stone an additional velocity equal to one ; so that the accu- 

 mulated velocity is now equal to two ; the following instant another 

 impulse increases the velocity to three, and so on till the stone reaches 

 the ground. The spaces described in a given time follow a law slightly 

 different ; for it has been ascertained, both by experiment and calculations, 

 that heavy bodies descending from a height by the force of gravity, fall 

 sixteen feet in the first second of time, three times that distance in the 

 next, five times in the third second, seven times in the fourth, and so on, 

 regularly increasing both their velocities and the spaces described ac- 

 cording to the number of seconds during which the body has been falling. 

 Thus the height of a building or the depth of a well may be measured 

 by observing the length of time which a stone takes in falling from the 

 top to the bottom. 



If a stone be thrown perpendicularly upwards, it is the same length 

 of time ascending that it is descending. In the first case the velocity 

 is diminished by the force of gravity, in descending it is accelerated by it. 

 The force of projection given to a body in throwing it upwards is equal 

 to the force with which it strikes the ground when it descends again, and 

 this latter force is the effect produced by gravity during the time of its fall. 

 If a stone be thrown upwards gently it will not rise high, and gravity will 

 soon make it descend ; if thrown with violence, it will rise higher, and 

 gravity will be longer in bringing it back to the ground. Suppose that 



