THE CONSTITUTION OF NATURE. 15 



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 competent 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 can- 

 non pointed to the zenith urge a ball upwards 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 perfectly 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 annihil- 

 ated. 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 with three times the velocity, it will generate 

 nine times the heat, and so on. 



Mr. Joule has shown that a pound weight falling 

 from a height of 772 feet, or 772 pounds falling through 

 one foot, will generate by its collision with the earth 

 an amount of heat sufficient to raise a pound of water 

 one degree Fahrenheit in temperature. 772 " foot- 



