THE CONSTITUTION OF NATURE. 19 



times the work, and so on. If, moreover, he carries up two 

 pounds instead of one, other things being equal, he does 

 twice the work ; if three, four, or five pounds, he does three, 

 four, or five times the work. In fact, it is plain that the 

 work performed depends on two factors, the weight raised 

 and 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 elevation 

 in opposition to the force of gravity, without being actually 

 carried up to the elevation. If a hodman, for example, 

 wished to land a brick at an elevation of sixteen feet above 

 the place where he stands, 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 pre- 

 cisely the same as if he had slowly carried up the brick. 

 The initial velocity which must be imparted in the case here 

 assumed, 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 forever with the same velocity. 

 But when, in the case before us, the body is thrown upward, 

 it moves in opposition to gravity, 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. 



Supposing the man competent to impart to the brick, at 

 starting, a speed of sixty-four feet a second, or twice its 

 former speed, would the amount of work performed in this 

 effort be only twice what it was in the first instance ? No ; 

 it would be four times that quantity. A body starting with 

 twice the velocity of another, will rise to four times the 



