HERMANN VON HELMHOLTZ 2-]^ 



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 ham- 

 mer 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 circum- 

 stances 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 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, do we measure in me- 

 chanics. 



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 gen- 

 erated 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 coincided in teaching, 

 that when a hammer of a hundred weight is to be raised one foot, to 

 accomplish this at least a hundred weight of water must fall through 

 the space of one foot ; or what is equivalent to this, two hundred 

 weight must fall full half a foot, or four hundred weight a quarter of a 

 foot, etc. In short, if we multiply the weight of the falling water by 

 the height through which it falls, and regard, as before, the product as 

 the measure of the work, then the work performed by the machine in 

 raising the hammer can, in the most favourable case, be only equal to 

 the number of foot-pounds of water which have fallen in the same 



