Mr, smeaton on Mechanic Power, 473 
the firft half, the body has fallen from where it fet for- 
ward through four times the perpendicular; and, there- 
fore, though the velocity is only doubled, yet four times 
the mechanical power has been confumed in producing 
it, as four times the mechanical power muft be expended 
in bringing up the fallen body to its firft place. 
This then appears to be the foundation, not only of 
the difputes that have arifen, but of the miifakcs that 
have been made, in the application of the different defi- 
nitions of quantity of motion; that while thole, that 
have adhered to the definition of Sir Isaac newton, 
have complained of their adverfaries, in not conndering 
the time in which effedts are produced, they themfelves 
have not always taken into the account the fpace that 
the impelling power is obliged to travel through, in pro- 
ducing the different degrees of velocity. It feems, there- 
fore, that, without taking in the collateral circumft ances 
both of time and fpace, the terms, quantity of motion, 
momentum, and force of bodies in motion, are abfolutely 
indefinite; and that they cannot be fo eafily, diftindtlv, 
and fundamentally compared, as by having recourfe to 
the common meafure, viz. mechanic power. 
From the whole of what has been inveftigated, it there- 
fore appears, that time, properly fpeaking, has nothing 
to do with the production of mechanical effedts, other- 
wife than as, by equally flowing, it becomes a common 
meafure; fo that, whatever mechanical effedt is found to 
be produced in a given time, the uniform continuance of 
the adtion of the fame mechanical power will, in a double 
time, 
