44 THE LEVER AND WHEELWORK. 



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

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

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

 aid that a power of one ounce sustains the weight of one ton. astonishment is 

 ot unnaturally excited, because the fact, as thus stated, if the terms be literally 

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

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

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

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

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

 o consider the effect of a machine, when the power and weight are in equi- 

 ibrium. 



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 

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

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

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

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

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

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

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

 ained by the machine. 



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

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



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

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

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

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

 ever less than that which would be expended if the power were immediately 

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

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

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

 on as the power itself is less than the weight ; so that, when a certain power 

 s 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- 

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

 ever diminish the total expenditure of power necessary to raise any weight or 

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

 ver can do, is to enable the power to be expended at a slow rate, and in a 

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

 r the resistance. 



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

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

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

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

 istinct efforts are made, by each of which 1 ounce is moved through 1 foot, 

 nd by which collectively 50 distinct ounces might be successively raised 

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



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

 -hich would be necessary to raise the weight without the intervention of any 

 nachine. 



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

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

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



