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

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            <s xml:id="echoid-s487" xml:space="preserve">
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            aqua enim aſcendit ſupra libellam in tubo ſtrictiori, cujus altera extre-
              <lb/>
            mitas aquæ ſubmergitur; </s>
            <s xml:id="echoid-s488" xml:space="preserve">Mercurius vero libellam non attingit. </s>
            <s xml:id="echoid-s489" xml:space="preserve">Hæc vero
              <lb/>
            cum aliquando attente perpenderem, in eandem præter propter incidi cau-
              <lb/>
            ſam, quam olim Patruus meus Jacobus Bernoulli, beate defunctus
              <lb/>
            dederat in tractatu ſuo de gravitate ætheris, nempe aquam in tubo ſtrictiori
              <lb/>
            ideo ultra libellam aſcendere, quod numerus particularum aëreo-ætherea-
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            rum in baſi columnæ, quæ aquæ in tubo ſupereminet, minor ſit nume-
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            ro particularum in ſimili baſi extra tubum; </s>
            <s xml:id="echoid-s490" xml:space="preserve">hoc vero intelligitur ex eo,
              <lb/>
            quod poſitis juxta ſe globulis in tabula horizontali, ſi circino cirulus fiat,
              <lb/>
            globulorum aliquot neceſſario excludantur, quia dividi nequeunt: </s>
            <s xml:id="echoid-s491" xml:space="preserve">Sunt ve-
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            ro preſſiones columnarum aëreo- ætherearum (quarum baſis altera eſt in
              <lb/>
            tubo, altera extra tubum) ut baſes, id eſt, ut numeri globulorum in baſi-
              <lb/>
            bus: </s>
            <s xml:id="echoid-s492" xml:space="preserve">unde ſi numerus globulorum in prima baſi ſit = a, in altera = a + b,
              <lb/>
            preſſio columnæ prioris = g, erit preſſio alterius columnæ = {a + b/a}g, hinc dif-
              <lb/>
            ferentia preſſionum = {b/a}g, cui æquari debet altitudo aquæ ſupra libellam.
              <lb/>
            </s>
            <s xml:id="echoid-s493" xml:space="preserve">Hæc ut rectius intelligantur, conſiderandum erit eſſe g proportionalem qua-
              <lb/>
            drato diametri, quæ reſpondet ſuperficiei fluidi tubo incluſi, & </s>
            <s xml:id="echoid-s494" xml:space="preserve">eidem
              <lb/>
            quadrato ob extremam globulorum parvitatem proportionalem quoque eſſe a,
              <lb/>
            ſic ut ratio g ad a cenſenda ſit conſtans, atque proin altitudo aquæ ſupra li-
              <lb/>
            bellam proportionem ſequi debeat ipſius b; </s>
            <s xml:id="echoid-s495" xml:space="preserve">eſt vero, quod per ſe patet,
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            b ut peripheria ſuperficiei fluidi tubo incluſi, erit igitur altitudo ſupra libel-
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            lam, ut eadem illa peripheria, id quod experientia jam diu confirmavit. </s>
            <s xml:id="echoid-s496" xml:space="preserve">Si
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            porro nunc diverſa conſideremus fluida, videbimus eo tortuoſiorem atque
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            proin majorem eſſe præmemoratam peripheriam, quo majores ſunt fluidi
              <lb/>
            particulæ, & </s>
            <s xml:id="echoid-s497" xml:space="preserve">cum à magnitudine hujus peripheriæ pendeat altitudo fluidi
              <lb/>
            ſupra libellam, percipimus, cur hæc altitudo in eodem tubo non ſequatur
              <lb/>
            rationem gravitatis ſpecificæ inverſam: </s>
            <s xml:id="echoid-s498" xml:space="preserve">ita ſi idem tubulus immergatur ſpi-
              <lb/>
            ritui vini & </s>
            <s xml:id="echoid-s499" xml:space="preserve">aquæ, ille minus aſcendit, quam hæc, cum tamen ob mino-
              <lb/>
            rem ſuam gravitatem ſpiritus aſcendere deberet magis; </s>
            <s xml:id="echoid-s500" xml:space="preserve">hoc vero indicat, ſi
              <lb/>
            recte rem aſſecutus ſum, minores eſſe particulas ſpiritus vini, quam aquæ: </s>
            <s xml:id="echoid-s501" xml:space="preserve">
              <lb/>
            Nunquam tamen meo judicio aſcenſus ſupra libellam in ullo fluido mutari
              <lb/>
            poteſt in deſcenſum, & </s>
            <s xml:id="echoid-s502" xml:space="preserve">omnia fluida ejusdem eſſe hac in re indolis, credi-
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            derim, niſi alia quædam cauſa, nondum hactenus conſiderata, </s>
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