628 Professcyr Tyndall [June 6, 



in a general way what muscular force means, and each of us would 

 less willingly accept a blow from a pugilist than have his ears boxed 

 by a lady. But these general ideas are not now sufficient for us ; we 

 must learn how to express numerically the exact mechanical value of 

 the two blows ; this is the first point to be cleared up. 



A sphere of lead weighing 1 lb. was suspended at a height of 16 feet 

 above the theatre floor. It was liberated, and fell by gravity. That 

 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 annulled, the weight would proceed through space at 

 the uniform velocity of" 32 feet a second. 



Suppose that instead of being pulled downward 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 im- 

 parted 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 

 has fallen. 



Now the lifting of the weight may be regarded as so much me- 

 chanical work. I might place a ladder against the wait, 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 suddenly 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 concerned, 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 pro- 

 duct of m into h, 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 sixteen 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. 



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

 effect — as before explained, is 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 

 etfect increases as the square of the velocity. If the mass of the body 



