284 The Laws of Motion of a Cylinder, &e. 
fions are true, when all the retarding forces are neg- 
lected in the calculation, excepting the refiflance that 
is given by the Obftacle to the impinging furface, 
that is, to that end of the Cylinder which is per- 
pendicular to the line in which the folid moves, and 
lies contiguous to the refifting matter. If the experi- 
meut were carefully made on an Obftacle confifting 
of homogeneous, yielding matter, the refults of the 
calculation would perhaps be found to coincide 
pretty nearly with, the refults of the mechanical pro- 
cefs; but if earth, fand, or other grofs materials 
are to be penetrated, no fuch coincidence can take 
place. : 
In order to form a theory more confiftent with 
matter of fact, it has been taken for granted, that 
the column is impeded in its defcent after the ftroke 
by a variable force, which increafes in the dire . 
ratio of the depth penetrated: But the conclufions 
that have been drawn from this hypothefis, are not 
mathematically true, becaufe the calculation from 
which they are derived, is improperly conducted ; 
for which reafon, the following method is here 
fubjoined, wherein mechanical principles are more 
ftridtly attended to. 
Prostem lll. If a Block whofe weight = 0, fall 
from a height — a, ona Cylinder whefe we'ght — m, 
and which has already penetrated the Obftacle to a 
depth — p, it is required to determine the fpace pene- 
trated by this ftroke, 
SOLUTION, 
