VOL. LXVI.] PHILOSOPHICAL TRANSACTIONS. 83 



has been consumed in producing it, as 4 times tlie mechanical power must be 

 expended in bringing up the fallen body to its first place. 



This then appears to be the foundation, not only of the disputes that have 

 arisen, but of the mistakes that have been made, in the application of the 

 different definitions of quantity of motion, that while those who have adhered 

 to the definition of Sir Isaac Newton, have complained of their adversaries, in 

 not considering the time in which effects are produced, they themselves have not 

 always taken into the account the space that the impelling power is obliged to 

 travel through, in producing the different degrees of velocity. It seems there- 

 fore that, without taking in the collateral circumstances both of time and space, 

 the terms, quantity of motion, momentum, and force of bodies in motion, are 

 absolutely indefinite ; and that they cannot be so easily, distinctly, and fun- 

 damentally compared, as by having recourse to the common measure, viz. 

 mechanic power. 



From the whole of what has been investigated, it therefore appears, that 

 time, properly speaking, has nothing to do with the production of mechanical 

 effects, otherwise than as, by equally flowing, it becomes a common measure ; 

 so that, whatever mechanical eftect is found to be produced in a given time, the 

 uniform continuance of the action of the same mechanical power will, in a 

 double time, produce 2 such effects, or twice that effect. A mechanical power 

 therefore, properly speaking, is measured by the whole of its mechanical effect 

 produced, whether that effect is produced in a greater or a less time ; thus, 

 having treasured up 1000 tuns of water, which I can let out on the overshot 

 wheel of a mill, and descending through a perpendicular of 20 feet, this power 

 applied to proper mechanic instruments, will produce a certain effect, that is, it 

 will grind a certain quantity of corn ; and that, at a certain rate of expending it, 

 it will grind this corn in an hour. But suppose the mill equally adapted to pro- 

 duce a proportionable effect, by the application of a greater impulsive power as 

 with a less, then, if I let out the water twice as fast on the wheel, it will grind 

 the corn twice as fast, and both the water will be expended and the corn ground 

 in half an hour. Here the same mechanical effect is produced ; viz. the grind- 

 ing a given quantity of coin, by the same mechanical power, viz. 1000 tuns of 

 water descending through a given perpendicular of 20 feet, and yet this effect 

 is in one case produced in half the time of the other. What time therefore has 

 to do in the business is this : let the rate of doing the business, or producing 

 the eftect, be what it will, if this rate is uniform, when I have found by experi- 

 ment what is done in a given time, then, proceeding at the same rate, twice the 

 effect will be produced in twice the time, on supposition that I have a supply of 

 mechanic power to go on with. Thus 1000 tuns of water, descending through 

 20 feet of perpendicular, being, as has been shown, a given mechanic power, 



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