Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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echoid-s1968
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72
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86
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HYDRODYNAMICÆ.
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eſſe iſta contractio in tubis longioribus. </
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<
s
xml:id
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echoid-s1969
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xml:space
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preserve
">In tubis divergentibus omnia fiunt
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modo contrario: </
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<
s
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echoid-s1970
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xml:space
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">dilatatur enim vena præ foramine; </
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<
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xml:id
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echoid-s1971
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xml:space
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">aquæ motus retarda-
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tur & </
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<
s
xml:id
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echoid-s1972
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xml:space
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">major aquæ quantitas dato tempore effluit, quam ſine iſta dilatatione
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ſequeretur ex obſervatis amplitudine orificii & </
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<
s
xml:id
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echoid-s1973
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xml:space
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">velocitatibus aquæ per illud
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effluentis. </
s
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<
s
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echoid-s1974
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xml:space
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preserve
">Ex tubis denique cylindricis effluens vena aquea nec contrahitur
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nec dilatatur.</
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<
s
xml:id
="
echoid-s1975
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</
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<
s
xml:id
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echoid-s1976
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xml:space
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">Probe eſt itaque attendendum ad has ſive contractiones ſive dilatatio-
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nes in æſtimandis quantitatibus aquæ dato tempore effluentis, quam quæ-
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ſtionem obiter tractabimus in fine ſectionis.</
s
>
<
s
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="
echoid-s1977
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</
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<
s
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echoid-s1978
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xml:space
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">Nunc autem libet examini ſubjicere mutationes quæ in effluxus aquarum
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lb
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ſuccedunt ab initio motus. </
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<
s
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echoid-s1979
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">In his vero compendii cauſa non attendemus ad
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mutationes venæ; </
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<
s
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echoid-s1980
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">neque enim res ita eſt comparata ut poſſit experimentis ſatis
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accurate confirmari neque magni momenti hic ſunt præfatæ mutationes; </
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<
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echoid-s1981
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">res
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autem ipſa digna eſt, quæ ſollicite perquiratur ut ejus natura animo recte in-
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telligi poſſit.</
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<
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="
echoid-s1982
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</
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<
s
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echoid-s1983
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xml:space
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">De vaſis, quæ tubos hahent annexos, jamjam egimus in ſuperiori ſe-
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ctiones §. </
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<
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echoid-s1984
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">31. </
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echoid-s1985
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echoid-s1986
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">32. </
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echoid-s1987
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<
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echoid-s1988
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">33. </
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<
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echoid-s1989
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xml:space
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">& </
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<
s
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echoid-s1990
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">quidem paragrapho 31. </
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<
s
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echoid-s1991
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xml:space
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">æquationes dedimus ge-
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neraliores, quæcunque fuerit ratio inter amplitudines vaſis & </
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<
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echoid-s1992
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">tubi: </
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<
s
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echoid-s1993
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">ſed ni-
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mis ſunt perplexæ calculumque poſtulant admodum operoſum: </
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<
s
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="
echoid-s1994
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xml:space
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">In paragra-
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pho, qui hunc ſequitur, hypotheſin pertractavi, quæ vas ubique amplitudi-
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nis infinitæ ratione tubi facit, in qua hypotheſi dixi, aquam effluere velocita-
<
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te, qua ad integram altitudinem aquæ ſupra orificium effluxus aſcendere poſ-
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ſit; </
s
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<
s
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="
echoid-s1995
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xml:space
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">ſed tamen in fine paragraphi expreſſe monui, ab initio motus aquam
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tardius deſcendere, quam ſic definitum fuit, nec regulam iſtam prius locum
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habere, quam ſuperficies per ſpatiolum aliquod deſcenderit, quæ res per ſe ſa-
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tis patet, quandoquidem non poſſit in inſtanti velocitas maxima produci à
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ſtatu quietis in tubo, quamvis fiat in vaſe foramine ſimplici perforato.</
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<
s
xml:id
="
echoid-s1996
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<
s
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echoid-s1997
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xml:space
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">Hæc ita perpendens animo concepi mutationes initiales explorare, eas-
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que ad certas menſuras reducere. </
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<
s
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echoid-s1998
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xml:space
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preserve
">Ad hoc autem minime ſufficit præmemorata
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regula, quâ iſtarum mutationum initialium nulla ratio habetur, quamvis cæ-
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terum exacte vera in vaſe infinite amplo; </
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<
s
xml:id
="
echoid-s1999
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xml:space
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">omnes enim mutationes quæ ſta-
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tum maximæ velocitatis præcedunt, fiunt dum ſuperficies per ſpatiolum infi-
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nite parvum deſcendunt; </
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<
s
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echoid-s2000
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xml:space
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">attamen deſcenſus iſte, ſi modo vas fuerit </
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