NATURAL PHILOSOPHY. 121 



expenditure of force will, in the first place, other circumstances being equal, 

 be proportional to the weight of the hammer ; it will, for example, be double 

 when the weight of the hammer is doubled. But the action of the hammer 

 depends not upon its weight alone, but also upon the height from which it 

 falls. If it falls through two feet, it will produce a greater effect than if it 

 falls through only one foot. It is, however, clear that if the machine, with 

 a certain expenditure of force, lifts the hammer a foot in height, the same 

 amount of force must be expended to raise it a second foot in height. The 

 work is therefore not only doubled when the weight of the hammer is in- 

 creased twofold, but also when the space through which it falls is doubled. 

 From this it is easy 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 fall- 

 ing 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 



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

 periment 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 half a foot, or four hundred 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 favorable 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 Avheel, 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, suc- 

 ceed in raising a hammer of ten hundred weight, when by the first simple 

 arrangement, 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, therefore, has, in the first place, done nothing more than 

 ninke 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 



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