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

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          <pb o="125" file="0139" n="139" rhead="SECTIO SEPTIMA."/>
          <p>
            <s xml:id="echoid-s3579" xml:space="preserve">Primò autem patet omnem vim vivam quæ particulis effluentibus ineſt
              <lb/>
            tranſire ad aquam externam nec ullo modo promovere ſubſequentem aſcenſum
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            ſeu influxum aquæ externæ in tubum: </s>
            <s xml:id="echoid-s3580" xml:space="preserve">Nimis hæc eſt clara hypotheſis, quam
              <lb/>
            ut majori explicatione opus habeat: </s>
            <s xml:id="echoid-s3581" xml:space="preserve">reſpicit autem aquarum effluxum & </s>
            <s xml:id="echoid-s3582" xml:space="preserve">in hoc
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            unica eſt conſideranda. </s>
            <s xml:id="echoid-s3583" xml:space="preserve">Venit jam altera, quæ pertinet ad aquarum influxum.</s>
            <s xml:id="echoid-s3584" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3585" xml:space="preserve">Secundò igitur non minus perſpicuum mihi quidem eſt, quod ir-
              <lb/>
            ruente aqua per foramen majori velocitate, quam quæ aquæ internæ aſcen-
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            denti ineſt, exceſſus ille rurſus motum quendam inteſtinum in eadem aqua
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            interna cieat, parum aut nihil ad aſcenſum conferentem. </s>
            <s xml:id="echoid-s3586" xml:space="preserve">Hoc ſi ita ſit, pona-
              <lb/>
            turque amplitudo foraminis = 1, amplitudo cylindri = n, aſcenſus potent.
              <lb/>
            </s>
            <s xml:id="echoid-s3587" xml:space="preserve">guttulæ irrumpentis = n n v, ejusque velocitas = n√v, retinebit hæc par-
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            ticula motu ſuo, quem cum reliqua aqua interna communem habet, velocitatem
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            √v, conſervabitque proinde aſcenſum potent. </s>
            <s xml:id="echoid-s3588" xml:space="preserve">v; </s>
            <s xml:id="echoid-s3589" xml:space="preserve">reliquum autem aſcenſus potent. </s>
            <s xml:id="echoid-s3590" xml:space="preserve">
              <lb/>
            nempe n n v - v ad motum particularum inteſtinum transiiſſe cenſendum eſt. </s>
            <s xml:id="echoid-s3591" xml:space="preserve">
              <lb/>
            Hypotheſis iſta, quamvis Phyſica ſit & </s>
            <s xml:id="echoid-s3592" xml:space="preserve">proxime tantum vera, tamen mag-
              <lb/>
            nam habet utilitatem ad motus fluidorum ſine notabili errore determinandos,
              <lb/>
            quoties in vaſe uniformis continuitas, quæ hactenus aſſumta fuit, prærum-
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            pitur, veluti cum aqua per plura foramina tranſire cogitur; </s>
            <s xml:id="echoid-s3593" xml:space="preserve">Imo credide-
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            rim unicam eſſe, cujus ope hujusmodi motus mira phænomena recte expli-
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            cari poſſint. </s>
            <s xml:id="echoid-s3594" xml:space="preserve">Quapropter velim, ut recte animo perpendatur, antequam ad
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            alia divertatur lector.</s>
            <s xml:id="echoid-s3595" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3596" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3597" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3598" xml:space="preserve">Jam igitur quæſtionem ipſam examinabimus, incipiendo ab a-
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            quarum deſcenſu. </s>
            <s xml:id="echoid-s3599" xml:space="preserve">Concipiatur cylindrus A I M B, (Fig. </s>
            <s xml:id="echoid-s3600" xml:space="preserve">36.) </s>
            <s xml:id="echoid-s3601" xml:space="preserve">aqua plenus
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              <note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">Fig. 36.</note>
            usque in X Y & </s>
            <s xml:id="echoid-s3602" xml:space="preserve">aquæ infinitæ R T V S ſubmerſus, ita ut longitudo ejus ſit
              <lb/>
            in ſitu verticali habeat ejus fundum lumen P L, per quod aqua ex vaſe in
              <lb/>
            aquam circumfluam effluere poſſit. </s>
            <s xml:id="echoid-s3603" xml:space="preserve">Quæritur velocitas aquæ internæ, poſt-
              <lb/>
            quam ſuperficies ejus per datum ſpatium X C vel Y D deſcendit, poſita
              <lb/>
            M Y vel I X = a, M V = b, M D = x, amplitudine foraminis = 1, & </s>
            <s xml:id="echoid-s3604" xml:space="preserve">
              <lb/>
            denique amplitudine cylindri = n.</s>
            <s xml:id="echoid-s3605" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3606" xml:space="preserve">Solutio eadem erit, quam pro ſimili quæſtione, ſed ea admodum
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            generali, dedimus in ſectione tertia: </s>
            <s xml:id="echoid-s3607" xml:space="preserve">obſervetur tantum, quod ſumta par-
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            ticula aquæ infinitè parva C D F E æquali guttulæ P L O N eo ipſo tempore
              <lb/>
            ejectæ, deſcenſus actualis ſit nunc æſtimandus ex altitudine D V vel C T,
              <lb/>
            cum in altero caſu definiendus erat ex tota altitudine D M.</s>
            <s xml:id="echoid-s3608" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3609" xml:space="preserve">Sit nempe velocitas ſuperficiei aqueæ C D ea, quæ </s>
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