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

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            rum dato tempore affundendarum ſequi rationem ſeſquiplicatam altitudinum,
              <lb/>
            ad quas aquæ à fundo cylindri aſcendunt: </s>
            <s xml:id="echoid-s3054" xml:space="preserve">aut viciſſim altitudines ſequi ra-
              <lb/>
            tionem ſubtriplicatam quadratorum quantitatum, quibus aquæ dato tempore
              <lb/>
            affunduntur.</s>
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          <p>
            <s xml:id="echoid-s3056" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3057" xml:space="preserve">19. </s>
            <s xml:id="echoid-s3058" xml:space="preserve">Soluto hoc problemate venio ad alterum Cl. </s>
            <s xml:id="echoid-s3059" xml:space="preserve">Poleno conſide-
              <lb/>
            ratum.</s>
            <s xml:id="echoid-s3060" xml:space="preserve"/>
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            <s xml:id="echoid-s3061" xml:space="preserve">Sit idem cylindrus, ſed aquis in foſſa veluti vaſe infinito ſtagnantibus,
              <lb/>
            ſubmerſus; </s>
            <s xml:id="echoid-s3062" xml:space="preserve">dicaturque altitudo ſubmerſionis = a, quæritur nunc iiſdem po-
              <lb/>
            ſitis, ut antea, rurſus æquatio inter altitudinem α ſuperficiei aqueæ internæ ſu-
              <lb/>
            pra externam, & </s>
            <s xml:id="echoid-s3063" xml:space="preserve">quantitatem q dato tempore affundendam.</s>
            <s xml:id="echoid-s3064" xml:space="preserve"/>
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            <s xml:id="echoid-s3065" xml:space="preserve">Quod ad illam rimæ partem α, quæ aquas ejicit & </s>
            <s xml:id="echoid-s3066" xml:space="preserve">ſupra aquam exter-
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            nam eminet, illam jam vidimus dato tempore erogare quantitatem {2/3} n α √ α:
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            <s xml:id="echoid-s3067" xml:space="preserve">reſidua autem rimæ pars ſubmerſa aquas ubique communi velocitate tranſimit-
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            tit, ut ex infra dicendis patebit, & </s>
            <s xml:id="echoid-s3068" xml:space="preserve">quidem velocitate √ α, ita, ut multiplica-
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            ta hâc velocitate per magnitudinem rimæ ſubmerſæ n a, habeatur quantitas,
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            quam dato tempore ejicit = n a √ α. </s>
            <s xml:id="echoid-s3069" xml:space="preserve">Si utraque quantitas in ſummam conji-
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            ciatur, habebitur ({2/3} α + a)n√α = q.</s>
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            <s xml:id="echoid-s3071" xml:space="preserve">Ope hujus æquationis cognoſcitur q ex datis altitudinibus a & </s>
            <s xml:id="echoid-s3072" xml:space="preserve">α: </s>
            <s xml:id="echoid-s3073" xml:space="preserve">aut
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            viciſſim altitudo α ex cognitis quantitatibus a & </s>
            <s xml:id="echoid-s3074" xml:space="preserve">q.</s>
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            <s xml:id="echoid-s3076" xml:space="preserve">Convenire autem hanc æquationem admodum accurate cum experi-
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            mentis, ipſe oſtendit celeberrimus eorum auctor, cujus ſolutio ab hâc no-
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            ſtra non differt. </s>
            <s xml:id="echoid-s3077" xml:space="preserve">Sequitur ex iſta æquatione, elevationes α eo majores eſſe pro
              <lb/>
            iiſdem aquarum affuſionibus, quo minor eſt altitudo ſubmerſionis a.</s>
            <s xml:id="echoid-s3078" xml:space="preserve"/>
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        <div xml:id="echoid-div115" type="section" level="1" n="88">
          <head xml:id="echoid-head113" style="it" xml:space="preserve">Experimenta quæ ad Sectionem V. pertinent.</head>
          <head xml:id="echoid-head114" xml:space="preserve">Ad §. 5.</head>
          <p>
            <s xml:id="echoid-s3079" xml:space="preserve">VAſe uſus ſum §. </s>
            <s xml:id="echoid-s3080" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3081" xml:space="preserve">deſcripto cum tubulo vitreo (Fig. </s>
            <s xml:id="echoid-s3082" xml:space="preserve">30.) </s>
            <s xml:id="echoid-s3083" xml:space="preserve">Primo autem
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            obturavi orificium L M, tubumque R N aqua implevi, donec ſuper-
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            ficies ejus raderet foraminulum in a: </s>
            <s xml:id="echoid-s3084" xml:space="preserve">aquam tunc tubo ingreſſam ob-
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            fervavi extremitate attigiſſe punctum f: </s>
            <s xml:id="echoid-s3085" xml:space="preserve">poſtea reſerato orificio L M, & </s>
            <s xml:id="echoid-s3086" xml:space="preserve">aquis ef-
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            fluentibus novas affundebam in vas ſuperius E F P Q adhibita diligentia, ut
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            extremitas aquæ in f interea nec aſcenderet nec deſcenderet. </s>
            <s xml:id="echoid-s3087" xml:space="preserve">Hæc dum </s>
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