14 FRAGMENTS OF SCIENCE. 



tion in opposition to the force of gravity, without being 

 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 un- 

 opposed 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 gra- 

 vity, which incessantly retards its motion, and finally 

 brings it to rest at an elevation of sixteen feet. If not 

 here caught by the bricklayer, 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 velocity 

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

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

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

 and so on. The height attained, then, is not propor- 

 tional to the initial velocity, but to the square of the 

 velocity. As before, the work is also proportional to 

 the weight elevated. Hence the work which any moving 



