282 FRAGMENTS OF SCIENCE. 



second we impart at starting twice this velocity. To what 

 height will the weight rise? You might be disposed to 

 answer, '* To twice the height; " but this would be quite 

 incorrect. Instead of twice 16, or 32 feet, it would reach 

 a height of four times 16, or 64 feet. So also, if we treble 

 the starting velocity, the weight would reach nine times 

 the height; if we quadruple the speed at starting, we attain 

 sixteen times the height. Thus, with a fourfold velocity 

 of 128 feet a second at starting, the weight would attain an 

 elevation of 256 feet. With a sevenfold velocity at start- 

 ing, the weight would rise to 49 times the height, or to an 

 elevation of 784 feet. 



Now the work done or, as it is sometimes called, the 

 mechanical effect other things being constant, is, as before 

 explained, proportional to the height, and as a double 

 velocity gives four times the height, a treble velocity nine 

 times the height, and so on, it is perfectly plain that the 

 mechanical effect increases as the square of the velocity. 

 If the mass of the body be represented by the letter m, and 

 its velocity by v, the mechanical effect would be propor- 

 tional to or represented by m v 2 . In the case considered, 

 I have supposed the weight to be cast upward, being 

 opposed in its flight by the resistance of gravity; but the 

 same holds true if the projectile be sent into water, mud, 

 earth, timber, or other resisting material. If, for example, 

 we double the velocity of a cannon ball we quadruple its 

 mechanical effect. Hence the importance of augmenting 

 the velocity of a projectile, and hence the philosophy of 

 Sir William Armstrong in using a large charge of powder 

 in his recent striking experiments. 



The measure then of mechanical effect is the mass of the 

 body multiplied by the square of its velocity. 



Now in firing a ball against a target the projectile, after 

 collision, is often found hot. Mr. Fairbairn informs me 

 that in the experiments at Shoeburyness it is a common 

 thing to see a flash, even in broad daylight, when the ball 

 strikes the target. And if our lead weight be examined 

 after it has fallen from a height it is also found heated. 

 Now here experiment and reasoning load us to the remark- 

 able law that, like the mechanical effect, the amount of 

 heat generated is proportional to the product of the mass 

 into the square of the velocity. Double your mass, other 

 things being equal, and you double your amount of heat; 



