216 INTERACTION OFNATURAL FORCES. 



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 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. Experiment and theory coincide 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 hun- 

 dred 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 

 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, end- 

 less 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 arrangement, the elevation of a hammer of one hundred 

 weight might alone be possible ; but either this heavier ham- 

 mer is raised to only one tenth of the height, or tenfold tho 



