THE CONSTITUTION OF NATURE 19 



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 canght 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 compe- 

 tent 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 elevation, a four-fold 

 velocity will give a sixteen-fold elevation, and so on. 

 The height attained, then, is not proportional to the ini- 

 tial 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 mass whatever is com- 

 petent to perform, in virtue of the motion which it at any 

 moment possesses, is jointly proportional to its weight and 

 the square of its velocity. Here, then, we have a second 

 measure of work, in which we simply translate the idea 

 of height into its equivalent idea of motion. 



In mechanics, the product of the mass of a moving 

 body into the square of its velocity, expresses what is 

 called the vis viva^ or living force. It is also sometimes 

 called the ** mechanical effect." If, for example, a cannon 

 pointed to the zenith urge a ball upward with twice the 

 velocity imparted to a second ball, the former will rise to 

 four times the height attained by the latter. If directed 



