58 Royal Institution : — 



We all have ideas more or less distinct regarding force ; we know 

 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 one pound was suspended at a height of 

 1 6 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 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 has fallen. 



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

 nical work. I might place a ladder against the wall, and carry the 

 weight up a height of 1 6 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 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 quan- 

 tity or mass of matter m, and the height through which it is lifted 

 A, then the product 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 1 6, or 64 feet. So also, if we treble the starting 

 velocity, the weight would reach nine times the height ; if we qua- 

 druple the speed at starting, it would 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 mecha- 

 nical effect increases as the square of the velocity. If the mass of 



