14 FEAGMENTS OF SCIENCE. 



the height to which it is raised. It is expressed by the 

 product of these two factors. 



But a body may be caused to reach a certain ele-- 

 vation in opposition to the force of gravity, without be- 

 ing actually carried up. If a hodman, for example, 

 wished to land a brick at an elevation of sixteen feet 

 above the place where he stood, he would probably 

 pitch it up to the bricklayer. He would thus impart, 

 by a sudden effort, a velocity to the brick sufficient to 

 raise it to the required height; the work accomplished 

 by that effort being precisely the same as if he had 

 slowly carried up the brick. The initial velocity to be 

 imparted, in this case, is well known. To reach a 

 height of sixteen feet, the brick must quit the man's 

 hand with a velocity of thirty-two feet a second. It is 

 needless to say, that a body starting with any velocity, 

 would, if wholly unopposed or unaided, continue to 

 move for ever with the same velocity. But when, as 

 in the case before us, the body is thrown upwards, it 

 moves in opposition to gravity, which incessantly re- 

 tards its motion, and finally brings it to rest at an ele- 

 vation of sixteen feet. If not here caught by the brick- 

 layer, it would return to the hodman with an accelerated 

 motion, and reach his hand with the precise velocity it 

 possessed on quitting it. 



An important relation between velocity and work is 

 here to be pointed out. Supposing the hodman com- 

 petent to impart to the brick, at starting, a velocity of 

 sixty-four feet a second, or twice its former velocity, 

 would the amount of work performed be twice what it 

 was in the first instance? No; it would be four times 

 that quantity; for a body starting with twice the velo- 

 city of another, will rise to four times the height. In 

 like manner, a three-fold velocity will give a nine-fold 

 elevation, a four-fold velocity will give a sixteen-fold 



