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

Table of Notes

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              <pb o="233" file="0247" n="247" rhead="SECTIO DECIMA."/>
            poteſt ejus ope pondus 865 librarum ad altitudinem unius pedis elevari, ſi
              <lb/>
            modo machina adhibeatur perfectiſſima.</s>
            <s xml:id="echoid-s6858" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6859" xml:space="preserve">Ab auctis autem aëris tum denſitate tum calore pendent omnium re-
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            rum hic expoſitarum effectus.</s>
            <s xml:id="echoid-s6860" xml:space="preserve"/>
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            <s xml:id="echoid-s6861" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6862" xml:space="preserve">44. </s>
            <s xml:id="echoid-s6863" xml:space="preserve">Interim non ſolum ab aëre condenſato calefactove vis viva pro
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            machinis movendis impendenda obtineri poteſt, ſed & </s>
            <s xml:id="echoid-s6864" xml:space="preserve">ab aëre rariore aut
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            frigidiore. </s>
            <s xml:id="echoid-s6865" xml:space="preserve">Ubicunque enim æquilibrium ſublatum eſt, vis viva adeſt, quæ
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            impendi poteſt, ſi debita machina excogitetur, ad onera elevanda machina-
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            mentaque circumagenda. </s>
            <s xml:id="echoid-s6866" xml:space="preserve">Methodus autem determinans vim vivam, quæ ab
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            aëre datæ denſitatis datique caloris ſpatium datum occupante elici poteſt,
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            mutatis mutandis eadem eſt cum illa quam §. </s>
            <s xml:id="echoid-s6867" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6868" xml:space="preserve">adhibuimus.</s>
            <s xml:id="echoid-s6869" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6870" xml:space="preserve">45. </s>
            <s xml:id="echoid-s6871" xml:space="preserve">Fuerit nempe rurſus cylindrus verticalis A B C D (Fig. </s>
            <s xml:id="echoid-s6872" xml:space="preserve">63.) </s>
            <s xml:id="echoid-s6873" xml:space="preserve">cum dia-
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              <note position="right" xlink:label="note-0247-01" xlink:href="note-0247-01a" xml:space="preserve">Fig. 63.</note>
            phragmate mobili E F: </s>
            <s xml:id="echoid-s6874" xml:space="preserve">puta aërem E B C F, ut §. </s>
            <s xml:id="echoid-s6875" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6876" xml:space="preserve">naturalem & </s>
            <s xml:id="echoid-s6877" xml:space="preserve">in æquili-
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            brio cum aëre externo: </s>
            <s xml:id="echoid-s6878" xml:space="preserve">preſſio autem aëris cujusvis in E F dicatur p
              <emph style="super">0</emph>
            : </s>
            <s xml:id="echoid-s6879" xml:space="preserve">Finge
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            dein pondus P, quod mediante fune trans duas trochleas M & </s>
            <s xml:id="echoid-s6880" xml:space="preserve">N ducto cum
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            diaphragmate cohæreat, idemque verſus A D trahat, perveneritque ſic dia-
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            phragma ex ſitu E F in G H: </s>
            <s xml:id="echoid-s6881" xml:space="preserve">Denique ponatur rurſus F C = a, F H = x:
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            </s>
            <s xml:id="echoid-s6882" xml:space="preserve">velocitas diaphragmatis in ſitu G H ſeu ponderis in ſitu P = v; </s>
            <s xml:id="echoid-s6883" xml:space="preserve">His poſitis
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            ſi conferantur §. </s>
            <s xml:id="echoid-s6884" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6885" xml:space="preserve">40. </s>
            <s xml:id="echoid-s6886" xml:space="preserve">& </s>
            <s xml:id="echoid-s6887" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6888" xml:space="preserve">patebit fore nunc
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            dv = (P + {ap/a + x} - p) X {dx/v}: </s>
            <s xml:id="echoid-s6889" xml:space="preserve">P vel
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            Pvdv = (P - {px/a + x}) dx, quæ integrata dat
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            {1/2}Pvv = Px - px + ap log.</s>
            <s xml:id="echoid-s6890" xml:space="preserve">{a + x/a}.</s>
            <s xml:id="echoid-s6891" xml:space="preserve"/>
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            <s xml:id="echoid-s6892" xml:space="preserve">At rurſus deſcenſus ponderis P per altitudinem x producta fuit vis viva
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            P x, dum ipſi interim ponderi velocitate v moto ineſt tantum vis viva {1/2} P v v
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            ſeu Px - px + ap log.</s>
            <s xml:id="echoid-s6893" xml:space="preserve">{a + x/a}, Igitur vis viva, quæ reſidua eſt, nempe p x -
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            a p log.</s>
            <s xml:id="echoid-s6894" xml:space="preserve">{a + x/a}, ad aërem tranſiit rurſusque reſtitutione æquilibrii inter aërem
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            internum & </s>
            <s xml:id="echoid-s6895" xml:space="preserve">externum, illa vis viva ad alia corpora pro lubitu transfundi po-
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            terit: </s>
            <s xml:id="echoid-s6896" xml:space="preserve">Igitur ſi habeas ſpatium G B C H aëre plenum cujus denſitas ſit ad
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            denſitatem aëris externi ut C F ad C H, in poteſtate erit vis viva p x -
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            a p log.</s>
            <s xml:id="echoid-s6897" xml:space="preserve">{a + x/a}.</s>
            <s xml:id="echoid-s6898" xml:space="preserve"/>
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