H, Helmholtz on the Interaction of Natural Forces. 193 



w 



the height through whicli it falls, and regard, as before, the pro- 

 duct as tlie measure of the work, then tlie work performed by 

 the machine in raising the hammer, can, in the most favorable 

 case, be onlj^ equal to the number of foot-pounds of water Avhich 

 have fallen in the same time. In practice, indeed, this ratio is 

 by no means attained: a great portion of the work of tlic 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 

 Avheel, or whether — by the intervention of wheelwork, cndleas 

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

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

 hammer of ten hundred weight, when by the first simple ar- 

 rangement the elevation of a hammer one hundred weight 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 interposition 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 

 work, and no more, can be performed. 



• Our machinery, therefpre, has in the first place done nothing 

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

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

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

 liberates it, and the hammer fiills upon the metal mass wliich is 

 pushed beneath it. But why does the falling hammer here ex- 

 ercise 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 ? AVe find, 

 hi fact, that the work performed by the hammer is determined 

 by its velocity. In other cases, also, the velocity of moving 

 masses is a means of producing great eifects. I only remind you 

 of tl)e destructive eifocts of musket-bullets, which in a state of 

 rest are the most harmless things in the world. I remind you 

 of the windmill, which derives its force from the moving air. 

 It may appear surprising that motion, which Ave are accustomed 

 to regard as a non-essential and transitory endowment of bodies, 

 can produce such great effects. But the fact is, that motion 

 appears to us under ordinary circumstances transitory, because 

 the movement of all terrestrial bodies is resisted perpetually by 



other forces, friction, resistance of the air, &c., so that the motion 

 is incessantly weakened and finally neutralized. A body, how- 

 ever, which is opposed by no resisting force, when once set m 

 lotion, moves onward eternally with undiminished velocity. 

 Thus we know that the planetary bodies have moved w^ithout 



SECONn SERIES, VOL. XXIV, NO. 71. SEPT., 1807. 



