ON THE INTERACTION OF NATURAL FORCES. 141 



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 will 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 foaming brook, the 

 spark-emitting anvil, and the black Cyclops wholly out of sight, 

 and beg a moment's attention for 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 projec- 

 tions, thumbs, which, during the rotation, lift the heavy hammer 

 and permit it to fall again. The falling hammer belabours the 

 mass of metal which is introduced beneath it. The work 

 therefore done by the machine consists, in this case, in the lift- 

 ing of the hammer, to do which the gravity of the latter must 

 be overcome. The expenditure of force will, in the first place, 

 other circumstances being equal, be proportional 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 faHs. If it falls through two feet, it will produce 

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

 however, clear that if the machine, with a certain expenditure 

 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 to see that the 

 work must be measured by the product of the weight into the 

 space through which it ascends. And in this way, indeed, we 

 measure in mechanics. The unit of work is a foot-pound, that 

 is, a pound weight raised to the height of one foot. 



While the work in this case consists in the raising of the 

 heavy hammer-head, the driving force which sets the latter in 

 motion is generated by failing water. It is not necessary that 

 the water should fall vertically, it can also flow in a moderately 

 inclined bed ; but it must always, where it has water-mills to- 



