244 



THE LEVER AND WHEELWORK. 



In expressing the effect of machinery, it is usual to say that the power sus- 

 tains the weight ; but this, in fact, is not the case, and hence arises that ap- 

 pearance of paradox which has already been alluded to. If, for example, it is 

 said that a power of one ounce sustains the weight of one ton, astonishment is 

 not unnaturally excited, because the fact, as thus stated, if the terms be literally 

 interpreted, is physically impossible. No power less than a ton can, in the or- 

 dinary acceptation of the word, support the weight of a ton. It will, however, 

 be asked how it happens that a machine appears to do this ? how it happens 

 that by holding a silken thread, which an ounce weight would snap, many hun- 

 dred weight may be sustained ? To explain this, it will only be necessary 

 to consider the effect of a machine, when the power arid weight are in equi- 

 librium. 



In every machine there are some fixed points or props ; and the arrange- 

 ment of the parts is always such that the pressure, excited by the power or 

 weight, or both, is distributed among these props. If the weight amount to 

 twenty hundred, it is possible so to distribute it that any proportion, however 

 great, of it may be thrown on the fixed points or props of the machine ; the re- 

 maining part only can properly be said to be supported by the power ; and this 

 part can never be greater than the power. Considering the effect in this way, 

 it appears that the power supports just so much of the weight, and no more, as 

 is equal to its own force, and that all the remaining part of the weight is sus- 

 tained by the machine. 



The force of these observations will be more apparent when the nature and 

 properties of the mechanic powers and other machines have been explained. 



When a machine is used dynamically, its effects are explained on different 

 principles. It is true that, in this case, a very small power may elevate a very 

 great weight ; but, nevertheless, in so doing, whatever be the machine used, 

 the total expenditure of power, in raising the weight through any height, is 

 never less than that which would be expended if the power were immediately 

 applied to the weight without the intervention of any machine. This circum- 

 stance arises from a universal property of machines, by which the velocity of 

 the weight is always less than that of the power, in exactly the same propor- 

 tion as the power itself is less than the weight : so that, when a certain power 

 is applied to elevate a weight, the rate at which the elevation is effected is al- 

 ways slow in the same proportion as the weight is great. From a due consid- 

 eration of this remarkable law, it will easily be understood that a machine can 

 never diminish the total expenditure of power necessary to raise any weight or 

 to overcome any resistance. In such cases, all that a machine ever does, or 

 ever can do, is to enable the power to be expended at a slow rate, arid in a 

 more advantageous direction than if it were immediately applied to the weight 

 or the resistance. 



Let us suppose that P is a power amounting to an ounce, and that W is a 

 weight amounting to 50 ounces, and that P elevates W by means of a machine. 

 In virtue of the property already stated, it follows that, while P moves through 

 50 feet, W will be moved through 1 foot ; but in moving P through 50 feet, 50 

 distinct efforts are made, by each of which 1 ounce is movd through 1 foot, 

 and by which collectively 50 distinct ounces might be successively raised 

 through 1 foot. But the weight W is 50 ounces, and has been raised through 

 1 foot ; whence it appears that the expenditure of power is equal to that 

 which would be necessary to raise the weight without the intervention of any 

 machine. 



This important principle may be presented under another aspect, which will 

 perhaps render it more apparent. Suppose the weight W were actually divided 

 into 50 equal parts, or suppose it were a vessel of liquid weighing 50 ounces, 



