ON THE INTERACTION OF NATURAL FORCES. 159 



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

 hundredweight must fall half a foot, or four hundred- 

 weight 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 un- 

 changed whether the hammer is driven immediately by 

 the axle of the wheel, or whether — by the intervention 

 of wheelwork, endless screws, pulleys, ropes — the motion 

 is transferred to the hammer. We may, indeed, by such 

 arrangements succeed in raising a hammer of ten hun- 

 dredweight, when by the first simple arrangement 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 



