20 FRAGMENTS OF SCIENCE. 



height ; in like manner, a threefold velocity will give a 

 ninefold elevation, a fourfold velocity will give a sixteen- 

 fold elevation, and so on. The height attained, then, or the 

 work done, is not proportional to the velocity, but to the 

 square of the velocit} r . As before, the work is also pro- 

 portional to the weight elevated. Hence the work which 

 any moving masses whatever are competent to perform, by 

 the motion which they at any moment possess, is jointly 

 proportional to the weight and the square of the 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, Ave point a cannon 

 upward, and start a ball with twice the velocity imparted 

 by a second cannon, the ball will rise to four times the 

 height. The speedier ball, if directed against a target, 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 perfectly clear conception of the 

 vis viva of moving masses, we are prepared for the an- 

 nouncement that the heat generated by the collision of a 

 falling body against the earth is proportional to the vis 

 viva annihilated. In point of fact it is not an annihilation 

 at all, but a transference of vis viva from the mass, to its 

 ultimate particles. This, as we now learn, 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 with three times the velocity, it will generate 

 nine times the heat, and so on. 



Mr. Joule has shown that in falling from a height of 772 

 feet, a body will generate an amount of heat sufficient to 



