158 ox THE IXTERACTION OF NATURAL FORCES. 



places small projections, thumbs, wliich, during the rota- 

 tion, 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 lifting 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 falls. 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 falling 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 set in motion, move from a 

 higher to a lower position. Experiment and theory 

 concur in teaching, that when a hammer of a hundred- 

 weight is to be raised one foot, to accomplish this at 

 least a hundredweight of water must fall through the 



