_^b CLEMENT OF MECHANICAL POWER. 215 



effects, the powers of men and animals. Hence, in a mechani- 

 cal sense, the idea of work is become identical with that of 

 the expenditure of force, and in this way I will apply it. 



How, then, can we measure this expenditure, and compare 

 it in the case of different machines ? 



I must here conduct you a portion of the way as short a 

 portion as possible over the uninviting field of mathematico- 

 mechanical ideas, in order to bring you to a point of view from 

 which a more rewarding prospect will open. And though the 

 example which I shall here choose, namely, that of a water- 

 mill with iron hammer, appears to be tolerably romantic, still, 

 alas, I must leave the dark forest valley, the spark-emitting 

 anvil, and the black Cyclops wholly out of sight, and beg a 

 moment's attention to the less poetic side of the question, 

 namely, the machinery. This is driven by a water-wheel which 

 in its turn is set in motion by the falling water. The axle of the 

 water-wheel has at certain places small projections, thumbs, 

 which, during the rotation, lift the heavy hammer and permit 

 it to fall again. The falling hammer belabors the mass of 

 metal, which is introduced beneath it. The work therefore 

 done by the machine consists, in this case, in the lifting of the 

 hammer, to do which the gravity of the latter must be over- 

 come. The expenditure of force will, in the first place, other 

 circumstances being equal, be proportioned to the weight of 

 the hammer ; it will, for example, be double when the weight 

 of the hammer is doubled. But the action of the hammer 

 depends not upon its weight alone, but also upon the height 

 from which it falls. If it falls through two feet, it will pro- 

 duce a greater effect than if it falls through only one foot. It 

 is, however, clear that if the machine, with a certain expendi- 

 ture of force, lifts the hammer a foot in height, the same 

 amount of force must be expended to raise it a second foot in 

 height. The work is therefore not only doubled when the 

 weight of the hammer is increased twofold, but also when the 

 space through which it falls is doubled. From this it is easy 



