L 199 J 
and AR=ar, may reprefent the excefs of the atmo- 
fpheres weight above the pillar of water, the refin- 
ance to the pifton-j from the remainder of fleam and 
the effective force, refpeefively, e.g. at the beginning 
of the defeent. Take, then, every-where ak : AK:i 
an : AN, and at all fimilar pofitions the refinance 
be of mn and force kc on its pidon will equal the 
refinance BC of MN and force K , on its pirton ; 
and by what Sir Ifaac Newton has demonnrated 
{.Book 1. Prop. 29.) of the defeent of bodies, we have 
V akTr : \/ 4K£R : : celerity in k : celerity in K. But 
thefe areas being evidently as the correfponding pa- 
rallelograms kq and. and they again as their 
heights, the celerities generated are in the fubdupli- 
cate ratio of a k vAK, as tho’ the refinance had been 
nothing ; and by an obvious enough reafoning from, 
the faid propofition, the times alfo appear to be in 
the above-mention d ratio j which ratio is not any 
way varied, tho’ the refinance prevails from the in- 
terfedting points 0. 
Now, to apply what has been faid to the bufinefs 
in hand ; if TfV be a cylinder of equal content with 
the cylinder MN, the quantity of water delivered by 
both will, as a confequence of the fundamental law 
of mechanics obferved above, be the fame at each 
lift : but the cylinder PJV is no higher than nm, and 
ex hypoth. their rarefactions are equal ; and therefore, 
by what has been proved with regard to the times, 
the time of the phlon's defeent in PfV will be to that 
of the pinon’s defeent in MN: : V ElV \ V AN\ 
whence in any given time the broad cylinder TtV 
will per form more than the longer one MN of equal 
content, and that in the ratio of their, diameters 5 
4 for 
