The Laws of Motion of a Cylinder, &c. 285 
© Sorution. Put 's= 16 +2 feet; f — the variable 
refiftance at the depth p; g— the conftant refiftance 
acting on the furface, perpendicular to the line in 
which the column moves; x = the variable fpace 
penetrated: then the weight of the fyftem —o--_ 
Share 3! oVa4zas. 
m= 6, its initial velocity = —— = c¢, then 
the retarding force at the depth p=g+f—b—=h: 
and, by the hypothefis, asp: f:: p4x:f+ & = 
the variable refiftance at the depth p +x, to which 
adding g — 6, we have h+ fo == the retarding. 
force at the fame point. Put c—v== the velocity 
of the fyftem, when p+ x = the depth penetrated ; 
then the fluxion of time —= , and as 1 fecond : 
c—v 
ae 2 Sie 
= velocity deftroyed by gravity 
tay ee g 
“2 a5% 
in the time : 
c—o° 
m2, ;thereforeas 6:4 + 
age 
v3 hence c—v x = x ieee 
by taking the fluent c—v Sot x ghx +, 
But when c—v ==c", x= nothing, and the fluent 
aaa 25 lft 
corrected is c—vu = cz oa K2hxet _ ; there- 
