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

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        <div xml:id="echoid-div249" type="section" level="1" n="193">
          <pb o="230" file="0244" n="244" rhead="HYDRODYNAMICÆ"/>
          <p>
            <s xml:id="echoid-s6751" xml:space="preserve">Sit baſis cylindri unius pedis quadrati, altitudo initialis F C duorum
              <lb/>
            pedum: </s>
            <s xml:id="echoid-s6752" xml:space="preserve">contineaturque in ſpatio B F aër qualis in ſuperficie terræ medius eſſe
              <lb/>
            ſolet, qui ferre poſſit ſuperficie E F 2240 libras: </s>
            <s xml:id="echoid-s6753" xml:space="preserve">ponatur x = 1, ut ſic ha-
              <lb/>
            beatur vis viva, qua duo pedes cubici aëris naturalis in ſpatium unius pedis
              <lb/>
            cubici coërceri poſſunt in vacuo: </s>
            <s xml:id="echoid-s6754" xml:space="preserve">eritque iſta vis viva = 2 X 2240 X log. </s>
            <s xml:id="echoid-s6755" xml:space="preserve">2
              <lb/>
            = 3105, id eſt, talis quæ generatur lipſu libero corporis 3105 librarum
              <lb/>
            per altitudinem unius pedis. </s>
            <s xml:id="echoid-s6756" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s6757" xml:space="preserve">viciſſim, ſi habeatur pes cubicus aëris
              <lb/>
            naturali duplo denſioris, poterit illius ope pondus elevari 3105 librarum ad
              <lb/>
            altitudinem unius pedis in vacuo, dum aëris naturalis denſitatèm aſſumit.</s>
            <s xml:id="echoid-s6758" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6759" xml:space="preserve">Sit porro ſub iisdem reliquis circumſtantiis idem aër in ſpatium duplum,
              <lb/>
            quam antea fuit, expanſum, occupans nunc in cylindro altitudinem quatuor
              <lb/>
            pedum, iſque rurſus condenſetur in ſpatium unius pedis cubici, requiretur
              <lb/>
            ad hanc compreſſionem vis viva, quæ exprimitur per 4 X 1120 log. </s>
            <s xml:id="echoid-s6760" xml:space="preserve">4, quæ
              <lb/>
            priore duplo major eſt. </s>
            <s xml:id="echoid-s6761" xml:space="preserve">Igitur in vacuo ſi habeatur pes cubicus aëris naturali
              <lb/>
            duplo denſioris, poterit illius ope pondus elevari 6210 librarum ad altitud.
              <lb/>
            </s>
            <s xml:id="echoid-s6762" xml:space="preserve">unius pedis, dum aëris naturalis dimidiam denſitatem aſſumit, aut pondus
              <lb/>
            9315 lib. </s>
            <s xml:id="echoid-s6763" xml:space="preserve">dum aëre naturali fit quadruplo rarior.</s>
            <s xml:id="echoid-s6764" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6765" xml:space="preserve">Conſequens inde eſt, ſi aër in ſpatium expandere ſe poſſit infinitum & </s>
            <s xml:id="echoid-s6766" xml:space="preserve">
              <lb/>
            ubique elaſticitatem ſervet denſitati proportionalem, quantitati aëris finitæ
              <lb/>
            vim vivam ineſſe infinitam.</s>
            <s xml:id="echoid-s6767" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6768" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6769" xml:space="preserve">41. </s>
            <s xml:id="echoid-s6770" xml:space="preserve">Hæc autem pertinent ad æſtimationem vis vivæ, quæ aëri in
              <lb/>
            vacuo poſito inſita ſit: </s>
            <s xml:id="echoid-s6771" xml:space="preserve">paullo alius fit computus pro aëre denſiore, qui in at-
              <lb/>
            moſphæra poſitus eſt: </s>
            <s xml:id="echoid-s6772" xml:space="preserve">hic enim maximus expanſionis gradus non ultra æquili-
              <lb/>
            brium cum aëre atmoſphæræ extendi poteſt: </s>
            <s xml:id="echoid-s6773" xml:space="preserve">facile hinc eſt in anteceſſum præ-
              <lb/>
            videre, ſi v. </s>
            <s xml:id="echoid-s6774" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s6775" xml:space="preserve">habeatur pes cubicus aëris naturali duplo denſioris, vim vi-
              <lb/>
            vam quæ in atmoſphæra ab hoc aëre compreſſo elici poſſit, minime eſſe in-
              <lb/>
            finitam. </s>
            <s xml:id="echoid-s6776" xml:space="preserve">Poterunt autem hujuſmodi vires vivæ hunc in modum determinari.</s>
            <s xml:id="echoid-s6777" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6778" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6779" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6780" xml:space="preserve">Sit aër E B C F naturalis & </s>
            <s xml:id="echoid-s6781" xml:space="preserve">in æquilibrio cum aëre externo; </s>
            <s xml:id="echoid-s6782" xml:space="preserve">in-
              <lb/>
            telligatur autem per p preſſio atmoſphæræ, in ſuſtentaculum E F, quæ quidem
              <lb/>
            cum preſſione aëris interni nondum condenſati in æquilibrio eſt. </s>
            <s xml:id="echoid-s6783" xml:space="preserve">Imponatur
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            eidem ſuſtentaculo pondus P; </s>
            <s xml:id="echoid-s6784" xml:space="preserve">fuerit jam aër condenſatus in ſpatium G B C H;
              <lb/>
            </s>
            <s xml:id="echoid-s6785" xml:space="preserve">habeatque ſuſtentaculum pondere P oneratum in ſitu G H velocitatem v, erit
              <lb/>
            retentis reliquis </s>
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