142 ON THE INTERACTION OF NATURAL FORCES. 



set in motion, move from a higher to a lower position. Ex- 

 periment and theory concur 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 favour- 

 able 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 wheel work, 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 of 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 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, 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 does the falling hammer here exer- 

 cise 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 



