THE CONSTITUTION OF NATURE. 15 



mass whatever is competent to perform, in virtue of the 

 motion which it at any moment possesses, is jointly pro- 

 portional to its weight and the square of its velocity. 

 Here, then, we have a second measure of work, in whicli 

 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 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 velo- 

 city 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-pounds " 

 constitute the mechanical equivalent of heat. Now, a 

 body falling from a height of 772 feet, has, upon 

 striking the earth, a velocity of 223 feet a second ; and 

 if this velocity were imparted to the body, by any other 





