Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii

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        <div xml:id="echoid-div77" type="section" level="1" n="54">
          <p>
            <s xml:id="echoid-s1968" xml:space="preserve">
              <pb o="72" file="0086" n="86" rhead="HYDRODYNAMICÆ."/>
            eſſe iſta contractio in tubis longioribus. </s>
            <s xml:id="echoid-s1969" xml:space="preserve">In tubis divergentibus omnia fiunt
              <lb/>
            modo contrario: </s>
            <s xml:id="echoid-s1970" xml:space="preserve">dilatatur enim vena præ foramine; </s>
            <s xml:id="echoid-s1971" xml:space="preserve">aquæ motus retarda-
              <lb/>
            tur & </s>
            <s xml:id="echoid-s1972" xml:space="preserve">major aquæ quantitas dato tempore effluit, quam ſine iſta dilatatione
              <lb/>
            ſequeretur ex obſervatis amplitudine orificii & </s>
            <s xml:id="echoid-s1973" xml:space="preserve">velocitatibus aquæ per illud
              <lb/>
            effluentis. </s>
            <s xml:id="echoid-s1974" xml:space="preserve">Ex tubis denique cylindricis effluens vena aquea nec contrahitur
              <lb/>
            nec dilatatur.</s>
            <s xml:id="echoid-s1975" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1976" xml:space="preserve">Probe eſt itaque attendendum ad has ſive contractiones ſive dilatatio-
              <lb/>
            nes in æſtimandis quantitatibus aquæ dato tempore effluentis, quam quæ-
              <lb/>
            ſtionem obiter tractabimus in fine ſectionis.</s>
            <s xml:id="echoid-s1977" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1978" xml:space="preserve">Nunc autem libet examini ſubjicere mutationes quæ in effluxus aquarum
              <lb/>
            ſuccedunt ab initio motus. </s>
            <s xml:id="echoid-s1979" xml:space="preserve">In his vero compendii cauſa non attendemus ad
              <lb/>
            mutationes venæ; </s>
            <s xml:id="echoid-s1980" xml:space="preserve">neque enim res ita eſt comparata ut poſſit experimentis ſatis
              <lb/>
            accurate confirmari neque magni momenti hic ſunt præfatæ mutationes; </s>
            <s xml:id="echoid-s1981" xml:space="preserve">res
              <lb/>
            autem ipſa digna eſt, quæ ſollicite perquiratur ut ejus natura animo recte in-
              <lb/>
            telligi poſſit.</s>
            <s xml:id="echoid-s1982" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1983" xml:space="preserve">De vaſis, quæ tubos hahent annexos, jamjam egimus in ſuperiori ſe-
              <lb/>
            ctiones §. </s>
            <s xml:id="echoid-s1984" xml:space="preserve">31. </s>
            <s xml:id="echoid-s1985" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1986" xml:space="preserve">32. </s>
            <s xml:id="echoid-s1987" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1988" xml:space="preserve">33. </s>
            <s xml:id="echoid-s1989" xml:space="preserve">& </s>
            <s xml:id="echoid-s1990" xml:space="preserve">quidem paragrapho 31. </s>
            <s xml:id="echoid-s1991" xml:space="preserve">æquationes dedimus ge-
              <lb/>
            neraliores, quæcunque fuerit ratio inter amplitudines vaſis & </s>
            <s xml:id="echoid-s1992" xml:space="preserve">tubi: </s>
            <s xml:id="echoid-s1993" xml:space="preserve">ſed ni-
              <lb/>
            mis ſunt perplexæ calculumque poſtulant admodum operoſum: </s>
            <s xml:id="echoid-s1994" xml:space="preserve">In paragra-
              <lb/>
            pho, qui hunc ſequitur, hypotheſin pertractavi, quæ vas ubique amplitudi-
              <lb/>
            nis infinitæ ratione tubi facit, in qua hypotheſi dixi, aquam effluere velocita-
              <lb/>
            te, qua ad integram altitudinem aquæ ſupra orificium effluxus aſcendere poſ-
              <lb/>
            ſit; </s>
            <s xml:id="echoid-s1995" xml:space="preserve">ſed tamen in fine paragraphi expreſſe monui, ab initio motus aquam
              <lb/>
            tardius deſcendere, quam ſic definitum fuit, nec regulam iſtam prius locum
              <lb/>
            habere, quam ſuperficies per ſpatiolum aliquod deſcenderit, quæ res per ſe ſa-
              <lb/>
            tis patet, quandoquidem non poſſit in inſtanti velocitas maxima produci à
              <lb/>
            ſtatu quietis in tubo, quamvis fiat in vaſe foramine ſimplici perforato.</s>
            <s xml:id="echoid-s1996" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1997" xml:space="preserve">Hæc ita perpendens animo concepi mutationes initiales explorare, eas-
              <lb/>
            que ad certas menſuras reducere. </s>
            <s xml:id="echoid-s1998" xml:space="preserve">Ad hoc autem minime ſufficit præmemorata
              <lb/>
            regula, quâ iſtarum mutationum initialium nulla ratio habetur, quamvis cæ-
              <lb/>
            terum exacte vera in vaſe infinite amplo; </s>
            <s xml:id="echoid-s1999" xml:space="preserve">omnes enim mutationes quæ ſta-
              <lb/>
            tum maximæ velocitatis præcedunt, fiunt dum ſuperficies per ſpatiolum infi-
              <lb/>
            nite parvum deſcendunt; </s>
            <s xml:id="echoid-s2000" xml:space="preserve">attamen deſcenſus iſte, ſi modo vas fuerit </s>
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