1ſelves, as have the mouths, which are the numbers 32 and 8
in our example: Then this
3[Figure 3]
being done, let the velocity
of the Water by the paſſa
ges A and B, be examined
(which may be done keeping
account what ſpace a piece
of Wood, or other body that
ſwimmeth, is carried by the ſtream in one determinate time; as
for inſtance in 50 pulſes) and then work by the golden Rule, as
the velocity by A, is to the velocity by B, ſo is the number 8, to
another number, which is 4. It is clear by what is demonſtra
ted in the ſaid ſecond Propoſition, that the quantity of water,
which paſſeth by the mouth A, ſhall have the ſame proportion of
that which paſſeth by the mouth B, that 8 hath to 1. Such pro
portion being compoſed of the proportions of 32 to 8, and of 8 to
4; namely, tothe greatneſs of the mouth A, to the greatneſs of the
mouth B, and of the velocity in A, to the velocity in B. This being
done, we muſt then contract the mouth which diſchargeth more
then its juſt quantity of water, or enlarge the other which diſchar
geth leſs, as ſhal be moſt commodious in practice, which to him that
hath underſtood this little that hath been delivered, will be very
afie.
in our example: Then this
3[Figure 3]being done, let the velocity
of the Water by the paſſa
ges A and B, be examined
(which may be done keeping
account what ſpace a piece
of Wood, or other body that
ſwimmeth, is carried by the ſtream in one determinate time; as
for inſtance in 50 pulſes) and then work by the golden Rule, as
the velocity by A, is to the velocity by B, ſo is the number 8, to
another number, which is 4. It is clear by what is demonſtra
ted in the ſaid ſecond Propoſition, that the quantity of water,
which paſſeth by the mouth A, ſhall have the ſame proportion of
that which paſſeth by the mouth B, that 8 hath to 1. Such pro
portion being compoſed of the proportions of 32 to 8, and of 8 to
4; namely, tothe greatneſs of the mouth A, to the greatneſs of the
mouth B, and of the velocity in A, to the velocity in B. This being
done, we muſt then contract the mouth which diſchargeth more
then its juſt quantity of water, or enlarge the other which diſchar
geth leſs, as ſhal be moſt commodious in practice, which to him that
hath underſtood this little that hath been delivered, will be very
afie.
APPENDIX XII.
Theſe opperations about Water, as I have hitherto on ſun
dry occaſions obſerved, are involved in ſo many difficul
ties, and ſuch a multiplicity of moſt extravagant accidents,
that it is no marvel if continually many, and very important er
rours be therein committed by many, and even by Ingeneers
themſelves, and Learned-men; and becauſe many times they
concern not onely the publique, but private intereſts: Hence it
is, that it not onely belongeth to Artiſts to treat thereof, but very
oft even the vulgar themſelves pretend to give their judgement
therein: And I have been troubled many times with a neceſſity
of treating, not onely with thoſe, which either by practice, or
particular ſtudy, underſtood ſomewhat in theſe matters; but alſo
with people wholly void of thoſe notions, which are neceſſary for
one that would on good grounds diſcourſe about this particular;
and thus many times have met with more difficulty in the thick
skulls of men, than in precipitous Torrents, and vaſt Fennes.
And in particular, I had occafion ſome years paſt to go ſee the
Gave or Emiſſary of the Lake of Perugia, made many years agon
by Braccio Fortobraccio, but for that it was with great ruines by
Time decayed, and rendred unuſeful, it was repaired with in
dry occaſions obſerved, are involved in ſo many difficul
ties, and ſuch a multiplicity of moſt extravagant accidents,
that it is no marvel if continually many, and very important er
rours be therein committed by many, and even by Ingeneers
themſelves, and Learned-men; and becauſe many times they
concern not onely the publique, but private intereſts: Hence it
is, that it not onely belongeth to Artiſts to treat thereof, but very
oft even the vulgar themſelves pretend to give their judgement
therein: And I have been troubled many times with a neceſſity
of treating, not onely with thoſe, which either by practice, or
particular ſtudy, underſtood ſomewhat in theſe matters; but alſo
with people wholly void of thoſe notions, which are neceſſary for
one that would on good grounds diſcourſe about this particular;
and thus many times have met with more difficulty in the thick
skulls of men, than in precipitous Torrents, and vaſt Fennes.
And in particular, I had occafion ſome years paſt to go ſee the
Gave or Emiſſary of the Lake of Perugia, made many years agon
by Braccio Fortobraccio, but for that it was with great ruines by
Time decayed, and rendred unuſeful, it was repaired with in