Prof. Helmholtz on the Interaction of Natural Forces. 493 



in this way, indeed, do 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. Experi- 

 ment and theory coincide in teaching, that when a hammer of a 

 hundredweight is to be raised one foot, to accomplish this at least a 

 hundredweight of water must fall through the space of one foot ; 

 or what is equivalent to this, two hundredweight must fall half 

 a foot, or four hundredweight a quarter of a foot, &c. 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 time. In practice, indeed, this ratio is by no means 

 attained : a great portion of the work of the falling water escapes 

 unused, inasmuch as part of the force is willingly sacrificed for 

 the sake of obtaining greater speed. 



I will further remark, that this relation remains unchanged 

 whether the hammer is driven immediately by the axle of the 

 wheel, or whether — by the intervention of whcelwork, endless 

 screws, pulleys, ropes, — the motion is transferred to the hammer. 

 We may, indeed, by such arrangements succeed in raising a 

 hammer of ten hundredweight, when by the first simple arrange- 

 ment the elevation of a hammer one hundredweight might alone 

 be possible ; but either this heavier hammer is raised to only 

 one-tenth of the height, or tenfold the time is required to raise 

 it to the same height ; so that, however we may alter, by the in- 

 terposition of machinery, the intensity of the acting force, still 

 in a certain time, during which the mill-stream furnishes us with 

 a definite quantity of water, a certain definite quantity of woi-k, 

 and no more, can be performed. 



Our machinei-y, therefore, has in the first place done nothing 

 more than make use of the gravity of the falling water in order 

 to overpower the gravity of the hammer, and to raise the latter. 

 When it has lifted the hammer to the necessary height, it again 

 liberates it, and the hammer falls upon the metal mass which 

 is pushed beneath it. But why docs the falling hammer here 

 exercise a greater force than when it is permitted simply to 

 press with its own weight on the mass of metal ? Why is its 

 power greater as the height from which it falls is increased ? 



