1to adjuſt the Ciſtern ſo, that the exceſs above the ordinary wa
ter, diſcharge into the publick Fountains, that ſo the particular
participants may have alwayes the ſame abundance of
water.
ter, diſcharge into the publick Fountains, that ſo the particular
participants may have alwayes the ſame abundance of
water.
APPENDIX XI.
Much more difficult is the diviſion of the waters which
ſerve to water the fields, it not being poſſible to obſerve
ſo commodiouſly, what quantity of water the whole
Ditch ſends forth in one determinate time, as may be done in
Fountains: Yet nevertheleſs, if the ſecond propoſition by us a
little below demonſtrated, be well underſtood, there may be
thence taken a very ſafe and juſt way to diſtribute ſuch waters.
The Propoſition therefore by us demonſtrated is this: If there
be two Sections, (namely two mouths of Rivers) the quantity of
the water which paſſeth by the firſt, hath a proportion to that
which paſſeth by the ſecond, compounded of the proportions of
the firſt Section to the ſecond, and of the velocity through
the firſt, to the velocity through the ſecond: As I will declare
for example by help of practice, that I may be underſtood by
all, in a matter ſo important. Let the two mouths of the
Rivers be A, and B, and let
2[Figure 2]
the mouth A be in meaſure
and content thirty two feet,
and the mouth B, eight feet.
Here you muſt take notice,
that it is not alwayes true, that
the Water which paſſeth by A,
hath the ſame proportion to that which paſſeth by B, that the
mouth A hath to the mouth B; but onely when the velocityes
by each of thoſe paſſages are equal: But if the velocityes ſhall
be unequal, it may be that the ſaid mouths may emit equal
quantity of Water in equal times, though their meaſure be un
equal; and it may be alſo, that the bigger doth diſcharge a great
er quantity of Water: And laſtly, it may be, that the leſs mouth
diſchargeth more Water than the greater; and all this is mani
feſt by the things noted in the beginning of this diſcourſe, and
by the ſaid ſecond Propoſition. Now to examine the propor
tion of the Water that paſſeth by one Ditch, to that which paſ
ſeth by another, that this being known, the ſame Waters and
mouths of Ditches may be then adjuſted; we are to keep ac
count not onely of the greatneſs of the mouths or paſſages of the
Water, but of the velocity alſo; which we will do, by firſt find
ing two numbers that have the ſame proportion between them
ſerve to water the fields, it not being poſſible to obſerve
ſo commodiouſly, what quantity of water the whole
Ditch ſends forth in one determinate time, as may be done in
Fountains: Yet nevertheleſs, if the ſecond propoſition by us a
little below demonſtrated, be well underſtood, there may be
thence taken a very ſafe and juſt way to diſtribute ſuch waters.
The Propoſition therefore by us demonſtrated is this: If there
be two Sections, (namely two mouths of Rivers) the quantity of
the water which paſſeth by the firſt, hath a proportion to that
which paſſeth by the ſecond, compounded of the proportions of
the firſt Section to the ſecond, and of the velocity through
the firſt, to the velocity through the ſecond: As I will declare
for example by help of practice, that I may be underſtood by
all, in a matter ſo important. Let the two mouths of the
Rivers be A, and B, and let
2[Figure 2]the mouth A be in meaſure
and content thirty two feet,
and the mouth B, eight feet.
Here you muſt take notice,
that it is not alwayes true, that
the Water which paſſeth by A,
hath the ſame proportion to that which paſſeth by B, that the
mouth A hath to the mouth B; but onely when the velocityes
by each of thoſe paſſages are equal: But if the velocityes ſhall
be unequal, it may be that the ſaid mouths may emit equal
quantity of Water in equal times, though their meaſure be un
equal; and it may be alſo, that the bigger doth diſcharge a great
er quantity of Water: And laſtly, it may be, that the leſs mouth
diſchargeth more Water than the greater; and all this is mani
feſt by the things noted in the beginning of this diſcourſe, and
by the ſaid ſecond Propoſition. Now to examine the propor
tion of the Water that paſſeth by one Ditch, to that which paſ
ſeth by another, that this being known, the ſame Waters and
mouths of Ditches may be then adjuſted; we are to keep ac
count not onely of the greatneſs of the mouths or paſſages of the
Water, but of the velocity alſo; which we will do, by firſt find
ing two numbers that have the ſame proportion between them