Mr. smeaton on Mechanic Power . 47 1 
quence have actually been obliged to go through in the 
fecond minute, will be according to the mean of the ex- 
tremes of velocity at the beginning and end thereof, 
that is, three yards in the fecond minute ; fo that being- 
one yard from his original place at the beginning of the 
fecond minute, at the end of it he will have moved the 
fum of the journies of the firft and fecond minute, that 
is, in the whole four yards from his original place. As, 
he has now generated a velocity in the ball of four, yards, 
per minute, in the third minute be mult travel four yards 
to keep up with the ball, and one more in generating the 
equal increment of velocity ; fo that in the third minute, 
he muft travel five yards to keep up the fame impelling 
jx)wer upon the ball that he did in the firft minute in 
travelling one, fo that thefe five yards in the third mi- 
nute, added to the four yards that he had travelled in the 
two preceding minutes, fets him at the end of the third, 
minute nine yards from whence he fet out, having then 
given the ball a velocity capable of carrying it uniformly 
forward at the rate of fix yards per minute, as before 
fated. We may now leave the further purfuit of thefe 
proportions, and fee how the account hands. He gene- 
rated a velocity of two yards per minute in the firfi minute, 
the fquare of which is four, when he had moved but one 
yard from his place;, and he had generated a velocity of fix 
yards per minute, the fquare of which is thirty-fix, at the 
end of the third minute, when he had travelled nine 
yards from his place. Now, fince the fquare of the ve- 
locity, generated at the end of the firfi minute, is to that 
oi 
