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

Table of Notes

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            dus P operculum detinens in ſitu E F non differt à preſſione Atmoſphæræ ſuper-
              <lb/>
            incumbentis, quam proinde per P in ſequentibus deſignabimus.</s>
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          </p>
          <p>
            <s xml:id="echoid-s5806" xml:space="preserve">Notetur autem hanc preſſionem minime æqualem eſſe ponderi abſo-
              <lb/>
            luto cylindri verticalis aërei operculo E F in atmoſphæra ſuperincumbentis,
              <lb/>
            quod hactenus inconſiderate affirmarunt auctores: </s>
            <s xml:id="echoid-s5807" xml:space="preserve">ſed eſt preſſio iſta æqualis
              <lb/>
            quartæ proportionali ad ſuperficiem terræ, magnitudinem operculi E F & </s>
            <s xml:id="echoid-s5808" xml:space="preserve">pon-
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            deri totius atmoſphæræ in ſuperficiem terræ.</s>
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            <s xml:id="echoid-s5810" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5811" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5812" xml:space="preserve">Quæratur jam pondus π, quod aërem E C D F in ſpatium e C
              <lb/>
            D f condenſare valeat, poſitis velocitatibus particularum in utroque aëre,
              <lb/>
            naturali ſcilicet & </s>
            <s xml:id="echoid-s5813" xml:space="preserve">condenſato, iisdem: </s>
            <s xml:id="echoid-s5814" xml:space="preserve">ſit autem E C = 1 & </s>
            <s xml:id="echoid-s5815" xml:space="preserve">e C = s: </s>
            <s xml:id="echoid-s5816" xml:space="preserve">Cum
              <lb/>
            vero operculum E F transponitur in e f, majorem à fluido patitur niſum duplici
              <lb/>
            modo: </s>
            <s xml:id="echoid-s5817" xml:space="preserve">primo quod numerus particularum ratione ſpatii, cui includuntur,
              <lb/>
            major nunc eſt, & </s>
            <s xml:id="echoid-s5818" xml:space="preserve">ſecundo quod quævis particula ſæpius impulſum repetit:
              <lb/>
            </s>
            <s xml:id="echoid-s5819" xml:space="preserve">ut recte calculum ponamus incrementi, quod à prima pendet cauſa, parti-
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            culas conſiderabimus ceu quieſcentes, atque numerum earum, quæ opercu-
              <lb/>
            lo in ſitu E F ſunt contiguæ, faciemus = n, & </s>
            <s xml:id="echoid-s5820" xml:space="preserve">erit numerus ſimilis pro ſi-
              <lb/>
            tu operculi in e f = n: </s>
            <s xml:id="echoid-s5821" xml:space="preserve">({eC/EC})
              <emph style="super">{2/3}</emph>
            , ſeu = n: </s>
            <s xml:id="echoid-s5822" xml:space="preserve">s
              <emph style="super">{2/3}</emph>
            :</s>
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            <s xml:id="echoid-s5824" xml:space="preserve">Notetur autem fluid
              <unsure/>
            um à nobis conſiderari non magis condenſatum
              <lb/>
            in parte inferiori, quam in ſuperiori, quale eſt, cum pondus P veluti infi-
              <lb/>
            nitè majus eſt pondere proprio fluidi: </s>
            <s xml:id="echoid-s5825" xml:space="preserve">Perſpicuum hinc eſt, hoc nomine
              <lb/>
            vim fluidi eſſe, ut ſunt numeri n & </s>
            <s xml:id="echoid-s5826" xml:space="preserve">n: </s>
            <s xml:id="echoid-s5827" xml:space="preserve">s
              <emph style="super">{2/3}</emph>
            , id eſt, ut s
              <emph style="super">{2/3}</emph>
            ad 1. </s>
            <s xml:id="echoid-s5828" xml:space="preserve">Quod vero
              <lb/>
            attinet ad alterum incrementum à ſecunda proveniens cauſa, invenitur id re-
              <lb/>
            ſpiciendo motum particularum; </s>
            <s xml:id="echoid-s5829" xml:space="preserve">atque ſic apparet impulſus eo ſæpius fieri,
              <lb/>
            quo propius ad ſe invicem ſitæ ſunt particulæ: </s>
            <s xml:id="echoid-s5830" xml:space="preserve">Erunt ſcilicet impulſuum nu-
              <lb/>
            meri reciproce ut diſtantiæ mediæ inter ſuperficies particularum: </s>
            <s xml:id="echoid-s5831" xml:space="preserve">Iſtæque di-
              <lb/>
            ſtantiæ mediæ ita determinabuntur.</s>
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          <p>
            <s xml:id="echoid-s5833" xml:space="preserve">Particulas ponemus eſſe ſphæricas, diſtantiamque mediam inter cen-
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            tra globulorum pro ſitu operculi E F vocabimus D; </s>
            <s xml:id="echoid-s5834" xml:space="preserve">diametrumque globuli
              <lb/>
            deſignabimus per d: </s>
            <s xml:id="echoid-s5835" xml:space="preserve">ita erit diſtantia media inter ſuperficies globulorum =
              <lb/>
            D - d: </s>
            <s xml:id="echoid-s5836" xml:space="preserve">patet vero in ſitu operculi e f fore diſtantiam mediam inter centra
              <lb/>
            globulorum = D ∛ s, atque proinde diſtantiam mediam inter ſuperficies
              <lb/>
            globulorum = D ∛ s - d. </s>
            <s xml:id="echoid-s5837" xml:space="preserve">Igitur reſpectu ſecundæ cauſæ erit vis aëris </s>
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