242 Professor TyndaVs Lecture on Force, 



[A sphere of lead weighing one pound was suspended at a height 

 16 feet above the theatre floor. It was liberated, and fell by- 

 gravity. The weight required exactly a second to fall to the 

 earth from that elevation ; and the instant before it touched the 

 earth, it had a velocity of 32 feet a second. That is to say, if at 

 that instant the earth were annihilated, and its attraction an- 

 nulled, the weight would proceed through space at the uniform 

 velocity of 32 feet a second.] 



Suppose that instead of being pulled down by gravity, the 

 weight is cast upward in opposition to the force of gravity, with 

 what velocity must it start from the earth's surface in order to 

 reach a height of 16 feet ? "With a velocity of 32 feet a second. 

 This velocity imparted to the weight by the human arm, or by 

 any other mechanical means, would carry the weight up to the 

 precise height from which it had fallen. 



Now, the lifting of the weight may be regarded as so much 

 mechanical wort. I might place a ladder against a wall, and 

 carry the weight up a height of 16 feet; or I might draw it up 

 to this height by means of a string and pulley, or I might sud- 

 denly jerk it up to a height of 16 feet. The amount of work 

 done in all these cases, as far as the raising of the weight is con- 

 cerned, would be absolutely the same. The absolute amount of 

 work done depends solely upon two things : first of all, on the 

 quantity of matter that is lifted ; and secondly, on the height to 

 which it is lifted. If you call the quantity or mass of matter m, 

 and the height through which it is lifted A, then the product of m 

 into ^, or mh, expresses the amount of work done. 



Supposing, now, that instead of imparting a velocity of 32 feet 

 a second to the weight, we impart twice this speed, or 64 feet a 

 second. To what height will the weight rise ! You might be- 

 disposed to answer, "To twice the height:" but this would be 

 quite incorrect. Both theory and experiment inform us that the 

 weight would rise to four times the height ; instead of twice 16^ 

 or 32 feet, it would reach 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 six- 

 teen times the height. Thus, with a velocity of 128 feet a second 

 at starting, the weight would attain an elevation of 256 feet. 

 Supposing we augment the velocity of starting seven times, we 

 should raise the weight to 49 times the height, or to an elevation 

 of 784 feet. 



