472 Mr. smeaton on Mechanic Power . 
of the velocity generated at the end of the third minute, 
as 4:36, that is, as 1:9; and lince the fpaces, moved 
through by the man to communicate thefe velocities, are 
alfo as 1:9, it follows, that the fpaces through which 
the man mu if travel, in order to generate thefe velocities 
refpectively (preferving the impelling power perfeftly 
equal), mull be as the fquares of the velocities that are 
communicated to the ball; for, if the man was to be 
brought back again to his original place by a mechanical 
power, equally exerted upon the man equally refilling, 
this would be the meafure of what the man has done in 
order to give motion to the ball. It therefore diredlly 
follows, conformably to what has been deduced from the 
experiments, that the mechanic power that muft of ne- 
ceffity be employed in giving different degrees of velocity 
to the fame body, mult be as the fquare of that velocity ; 
and if the converfe of this propolition did not hold, viz. 
that if a body in motion, in being flopped, would not 
produce a mechanical effe£f equal or proportional to the 
fquare of its velocity, or to the mechanical power em- 
ployed in producing it, the effect would not correfpond 
with its producing caufe. 
Thus the conlequcnces of generating motion upon a 
level plane exadlly correfpond with the generating of 
motion by gravity; viz. that though in two feconds of 
time the equal impulfive power of gravity gives twice the 
velocity to a body that it does in one fecond, yet this col- 
lateral circumftance attends it, that at the end of the 
double time, in confequence of the velocity acquired in 
2 the 
