274. The Laws of Motion of a Cylinder, &es 
Data, from what point above the top of the pillat 
a falling Body fhall repeatedly defcend, fo as to be 
juft able to drive it intirely into the obftacle by a 
given number of ftrokes. Dara. Weight of the 
block — a, height of the Cylinder = ¢, its fpecific 
gravity ==, area of its bafe e; laftly, let it be 
known from. experiment, that if a column of the 
fame matter, whofe height is f, and bafe g, be 
projected againft the fame obftacle, with the velocity 
n per fecond, it will penetrate it to a depth r. 
_ So.ution. Let q = the weight of a cubic foot 
of water, s== 1635 fect; y==the given number 
of ftrokés; and r—=the required diftance; then 
the weights of the two Cylinders are = dqce and 
dqfg. Now, if a body in motion be refifted by a 
conftant force, the fpace defcribed by it, till its 
motion is deftroyed, is .as its quantity of matter 
and the fqiare of its initial velocity direftly, and 
as the refifting force inverfely; therefore, when the 
quantity of matter and velocity are given, the force 
is asthe fpace defcribed inverfely ; hence the retard- 
ing force, which acts on the Cylinder mentioned in 
the data, is éafily compared with gravity, fuppofing 
the refiftance of the obftacle to be exerted folely on 
the impinging furface of this folid; which fuppo- 
fition is evidently true, when the effects of fridtion 
and of the condenfation of the materials in the 
obftacle are’ taken equal nothing, which affumption 
is demanded by the conditions of the Problem, for 
without it the retarding fort cannot’ be uniform. 
In 
