10 FRAGMENTS OF SCIENCE. 



upward, it moves in opposition to gravity, which inces- 

 santly retards its motion, and finally brings it to rest at an 

 elevation 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 competent 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 ninefold elevation, a fourfold 

 velocity will give a sixteenfold elevation, and so on. The 

 height attained, then, is not proportional 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 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 

 against a target, it will also do four times the execution. 

 Hence the importance of imparting a high velocity to 

 projectiles in war. Having thus cleared our way to a per- 

 fectly definite conception of the vis viva of moving masses, 

 we are prepared for the announcement that the heat 

 generated by the shock of a falling body against the 

 earth is proportional to the vis viva annihilated. The 

 heat is proportional to the square of the velocity. In the 

 case, therefore, of two cannon-balls of equal weight, if 

 one strike a target with twice the velocity of the other, 

 it will generate four times the heat, if v/ith three times 



