Castelli, Benedetto
,
Of the mensuration of running waters
,
1661
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
Table of figures
<
1 - 18
[out of range]
>
<
1 - 18
[out of range]
>
page
|<
<
of 137
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
068/01/040.jpg
"
pagenum
="
26
"/>
I ſay that the proportion of the ſuperficies of the Veſſel A D is
<
lb
/>
in proportion to the meaſure of the ſection of the Emiſſary
<
lb
/>
H L, as the velocity of the Emiſſary or Cock to the line A F;
<
lb
/>
which is manifeſt, for that the Water in the Veſsel moving by
<
lb
/>
the line A F; as far as F, and the whole maſs of Water A G
<
lb
/>
diſcharging it ſelf, and in the ſame time the ſame quantity of
<
lb
/>
Water being diſcharged by the ſection of the Emiſſary H L; it
<
lb
/>
is neceſſary by what I have demonſtrated in the third Propoſition,
<
lb
/>
and alſo explained in the beginning of this Treatiſe, that the ve
<
lb
/>
locity by the Emiſſary or Cock be in proportion to the velocity
<
lb
/>
of the abatement, as the ſuperficies of the Veſſel to the mea
<
lb
/>
ſure of the ſection of the Emiſſary, which was to be demon
<
lb
/>
ſtrated.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>That which hath been demonſtrated in the Veſſel, falls out ex
<
lb
/>
actly alſo in our Lake of
<
emph
type
="
italics
"/>
Perugia,
<
emph.end
type
="
italics
"/>
and its Emiſsary; and becauſe
<
lb
/>
the immenſity of the ſuperficies of the Lake is in proportion to
<
lb
/>
the ſuperficies of the Emiſsary or Sluice, as many millions to
<
lb
/>
one, as may be eaſily calculated; it is manifeſt, that ſuch abate
<
lb
/>
ment ſhall be imperceptible, and almoſt nothing, in two dayes
<
lb
/>
ſpace, nay in four or ſix: and all this will be true, when we
<
lb
/>
ſuppoſe that for that time there entreth no other Water into the
<
lb
/>
Lake from Ditches or Rivolets, which falling into the Lake would
<
lb
/>
render ſuch abatement yet leſs.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Now we ſee, that it's neceſsary to examine ſuch abatements
<
lb
/>
and riſings, with excellent reaſons, or at leaſt, with accurate ex
<
lb
/>
periments, before we reſolve and conclude any thing; and how
<
lb
/>
farre the vulgar are diſtant from a right judgment in ſuch
<
lb
/>
matters.</
s
>
</
p
>
<
p
type
="
head
">
<
s
>APPENDIX XIII.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>For greater confirmation of all this which I have ſaid, I
<
lb
/>
will inſtance in another like caſe, which alſo I met with here
<
lb
/>
tofore, wherein, for that the buſineſs was not rightly un
<
lb
/>
derſtood, many diſorders, vaſt expences, and conſiderable miſ
<
lb
/>
chiefs have followed. </
s
>
<
s
>There was heretofore an Emiſsary or
<
lb
/>
Sluice made to drain the Waters, which from Rains, Springs, and
<
lb
/>
Rivolets fall into a Lake; to the end, the ſhores adjoyning on
<
lb
/>
the Lake, ſhould be free from the overflowing of the Waters;
<
lb
/>
but becauſe perhaps the enterprize was not well managed and
<
lb
/>
carried on, it fell out, that the Fields adjacent to the ſaid Chanel
<
lb
/>
could not drain, but continued under water; to which diſorders
<
lb
/>
a preſent remedy hath been uſed, namely, in a time convenient
<
lb
/>
to ſtop up the Sluice, by meanes of certain Floodgates kept on
<
lb
/>
purpoſe for that end; and thus abating the Level of the Water </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>