1I ſay that the proportion of the ſuperficies of the Veſſel A D is
in proportion to the meaſure of the ſection of the Emiſſary
H L, as the velocity of the Emiſſary or Cock to the line A F;
which is manifeſt, for that the Water in the Veſsel moving by
the line A F; as far as F, and the whole maſs of Water A G
diſcharging it ſelf, and in the ſame time the ſame quantity of
Water being diſcharged by the ſection of the Emiſſary H L; it
is neceſſary by what I have demonſtrated in the third Propoſition,
and alſo explained in the beginning of this Treatiſe, that the ve
locity by the Emiſſary or Cock be in proportion to the velocity
of the abatement, as the ſuperficies of the Veſſel to the mea
ſure of the ſection of the Emiſſary, which was to be demon
ſtrated.
in proportion to the meaſure of the ſection of the Emiſſary
H L, as the velocity of the Emiſſary or Cock to the line A F;
which is manifeſt, for that the Water in the Veſsel moving by
the line A F; as far as F, and the whole maſs of Water A G
diſcharging it ſelf, and in the ſame time the ſame quantity of
Water being diſcharged by the ſection of the Emiſſary H L; it
is neceſſary by what I have demonſtrated in the third Propoſition,
and alſo explained in the beginning of this Treatiſe, that the ve
locity by the Emiſſary or Cock be in proportion to the velocity
of the abatement, as the ſuperficies of the Veſſel to the mea
ſure of the ſection of the Emiſſary, which was to be demon
ſtrated.
That which hath been demonſtrated in the Veſſel, falls out ex
actly alſo in our Lake of Perugia, and its Emiſsary; and becauſe
the immenſity of the ſuperficies of the Lake is in proportion to
the ſuperficies of the Emiſsary or Sluice, as many millions to
one, as may be eaſily calculated; it is manifeſt, that ſuch abate
ment ſhall be imperceptible, and almoſt nothing, in two dayes
ſpace, nay in four or ſix: and all this will be true, when we
ſuppoſe that for that time there entreth no other Water into the
Lake from Ditches or Rivolets, which falling into the Lake would
render ſuch abatement yet leſs.
actly alſo in our Lake of Perugia, and its Emiſsary; and becauſe
the immenſity of the ſuperficies of the Lake is in proportion to
the ſuperficies of the Emiſsary or Sluice, as many millions to
one, as may be eaſily calculated; it is manifeſt, that ſuch abate
ment ſhall be imperceptible, and almoſt nothing, in two dayes
ſpace, nay in four or ſix: and all this will be true, when we
ſuppoſe that for that time there entreth no other Water into the
Lake from Ditches or Rivolets, which falling into the Lake would
render ſuch abatement yet leſs.
Now we ſee, that it's neceſsary to examine ſuch abatements
and riſings, with excellent reaſons, or at leaſt, with accurate ex
periments, before we reſolve and conclude any thing; and how
farre the vulgar are diſtant from a right judgment in ſuch
matters.
and riſings, with excellent reaſons, or at leaſt, with accurate ex
periments, before we reſolve and conclude any thing; and how
farre the vulgar are diſtant from a right judgment in ſuch
matters.
APPENDIX XIII.
For greater confirmation of all this which I have ſaid, I
will inſtance in another like caſe, which alſo I met with here
tofore, wherein, for that the buſineſs was not rightly un
derſtood, many diſorders, vaſt expences, and conſiderable miſ
chiefs have followed. There was heretofore an Emiſsary or
Sluice made to drain the Waters, which from Rains, Springs, and
Rivolets fall into a Lake; to the end, the ſhores adjoyning on
the Lake, ſhould be free from the overflowing of the Waters;
but becauſe perhaps the enterprize was not well managed and
carried on, it fell out, that the Fields adjacent to the ſaid Chanel
could not drain, but continued under water; to which diſorders
a preſent remedy hath been uſed, namely, in a time convenient
to ſtop up the Sluice, by meanes of certain Floodgates kept on
purpoſe for that end; and thus abating the Level of the Water
will inſtance in another like caſe, which alſo I met with here
tofore, wherein, for that the buſineſs was not rightly un
derſtood, many diſorders, vaſt expences, and conſiderable miſ
chiefs have followed. There was heretofore an Emiſsary or
Sluice made to drain the Waters, which from Rains, Springs, and
Rivolets fall into a Lake; to the end, the ſhores adjoyning on
the Lake, ſhould be free from the overflowing of the Waters;
but becauſe perhaps the enterprize was not well managed and
carried on, it fell out, that the Fields adjacent to the ſaid Chanel
could not drain, but continued under water; to which diſorders
a preſent remedy hath been uſed, namely, in a time convenient
to ſtop up the Sluice, by meanes of certain Floodgates kept on
purpoſe for that end; and thus abating the Level of the Water