20 FRAGMENTS OF SCIENCE 



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

 Hence the importance of imparting a high velocity to pro- 

 jectiles 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 gen- 

 erated by the shock of a falling body against the earth is 

 proportional to the vis viva annihilated. The heat is pro- 

 portional to the square of the velocity. In the case, there- 

 fore, of two cannon-balls of equal weight, if one strike 

 a target with twice the velocity of the other, it will gen- 

 erate 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 means, the quan- 

 tity of heat generated by the stoppage of its motion would 

 be that stated above. Six times that velocity, or 1,338 

 feet, would not be an inordinate one for a cannon-ball as 

 it quits the gun. Hence, a cannon-ball moving with a 

 velocity of 1,338 feet a second, would, by collision, gen- 

 erate an amount of heat competent to raise its own weight 

 of water 36 degrees Fahrenheit in temperature. If com- 

 posed of iron, and. if all the heat generated were concen- 

 trated in the ball itself, its temperature would be raised 

 about 360 degrees Fahrenheit; because one degree in the 

 case of water is equivalent to about ten degrees in the 



