Archimedes Texts

71

Book^{*} of the measure of Running Watets;) but yet doth not
run thorowout with the same velocity: Hence it is, that the vul
gar measures of the said River, in divers parts of its Chanel, are
alwaies divers; insomuch, that if a River passing through its cha
nel had such velocity, that it ran 100 Braces in the 1/60 of an hour
and afterwards the said River should be reduced to so much tardi,
ty of motion, as that in the same time it should not run more than
one Brace, it would be necessary that that same River should be
come 100. times bigger in that place where it was retarded; I
mean, 100. times bigger than it was in the place where it was
swifter. And let it be kept well in mind, that this point rightly
understood, will clear the understanding to discover very many
accidents worthy to be known. But for this time let it suffice,
that we have onely declared that which makes for our purpose,
referring apprehensive and studious Wits to the perusal of my
aforenamed Treatise; for therein he shall finde profit and delight
both together.

Now applying all to our principal intent, I say, That by what
hath been declared it is manifest, that if the Brent were 40. Bra
ces broad, and 2 1/2 high, in some one part of its Chanel, that after
wards the same Water of the Brent falling into the Lake, andpas
sing thorow the same to the Sea, it should lose so much of its ve
locity, that it should run but one Brace, in the time wherein
whilst it was in its Chanel at the place aforesaid, it ran 100. Bra
ces. It would be absolutely necessary, that increasing in mea
sure, it should become an hundred times ^{*} thicker; and therefore

if we should suppose that the Lake were 20000. Braces, the
Brent that already hath been supposed in its Chanel 100. Braces,
being brought into the Lake, should be 100. times 100. Brates;
that is, shall be 10000. Braces in thickness, and consequently shall
be in height half a Brace; that is, 100/200 of a Brace, and not 1/2. of a
Brace, as was concluded in the Argument.

Now one may see into what a gross errour of 99. in 100. one
may fall through the not well understanding the true quantity
of Running Water, which being well understood, doth open a
direct way to our judging aright in this most considerable affair.

And therefore admitting that wich hath been demonstrated,
I fay, that I would (if it did concern me) greatly encline to con
sult upon the returning of the Brent again into the Lake: For it
being most evident, that the Brent in the Chanel of its mouth, is
much swifter than the Brent being brought into the Lake, it will
certainly follow thereupon, that the thickness of the Water of
Brent in the Lake, shall be so much greater than that of Brent in
Brent, by how much the Bront in Brent is swifter than thh Brent
in the Lake.