Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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            turalis E C D F ad vim aëris compreſſi e C D f ut {1/D - d} ad {1/D∛s - d}, ſeu ut
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            D∛s - d ad D - d: </s>
            <s xml:id="echoid-s5838" xml:space="preserve">Conjunctis vero ambabus cauſis erunt prædictæ vires,
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            ut s
              <emph style="super">{2/3}</emph>
            X (D ∛s - d) ad D - d.</s>
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            <s xml:id="echoid-s5840" xml:space="preserve">Rationi D ad d aliam ſubſtituere poſſumus magis intelligibilem:
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            <s xml:id="echoid-s5841" xml:space="preserve">nempe ſi putemus operculum E F pondere infinito depreſſum deſcendere
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            usque in ſitum mn, in quo particulæ omnes ſe tangunt, atque lineam mC
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            vocemus m, erit D ad d ut 1 ad ∛ m, quâ ratione ſubſtituta, erunt tandem
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            viresaëris naturalis E C D F & </s>
            <s xml:id="echoid-s5842" xml:space="preserve">compreſſi e C D fut s
              <emph style="super">{2/3}</emph>
            X (∛s - ∛m) ad 1 - ∛m,
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            ſeu ut s - ∛mss ad 1 - ∛m. </s>
            <s xml:id="echoid-s5843" xml:space="preserve">Eſt igitur π = {1 - ∛m/s - ∛mss} X P.</s>
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            <s xml:id="echoid-s5845" xml:space="preserve">§ 5. </s>
            <s xml:id="echoid-s5846" xml:space="preserve">Ex omnibus phænomenis judicare poſſumus aërem naturalem
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            admodum condenſari poſſe, & </s>
            <s xml:id="echoid-s5847" xml:space="preserve">fere in ſpatiolum infinite parvum comprimi;
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            </s>
            <s xml:id="echoid-s5848" xml:space="preserve">facta igitur m = o, fit π = {P/s}, ita ut pondera comprimentia ſint fere
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            in ratione inverſa ſpatiorum, quæ aër diverſimode compreſſus occupat; </s>
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            quod multiplex experientia confirmavit. </s>
            <s xml:id="echoid-s5850" xml:space="preserve">Et poteſt certe hæc regula tuto
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            accipi in aëre rariore quam eſt naturalis; </s>
            <s xml:id="echoid-s5851" xml:space="preserve">an vero etiam poſſit in aëre ad-
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            modum denſiori, non ſatis exploratum habeo: </s>
            <s xml:id="echoid-s5852" xml:space="preserve">nec dum enim fuerunt ex-
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            perimenta ea accuratione, quæ hic requiritur, inſtituta: </s>
            <s xml:id="echoid-s5853" xml:space="preserve">unico opus eſt ad
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            definiendum valorem litteræ m, ſed eo accuratiſſime inſtituendo & </s>
            <s xml:id="echoid-s5854" xml:space="preserve">quidem
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            cum aëre vehementer compreſſo; </s>
            <s xml:id="echoid-s5855" xml:space="preserve">gradus autem caloris in aëre, dum com-
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            primitur, ſollicitè invariatus conſervetur.</s>
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            <s xml:id="echoid-s5857" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5858" xml:space="preserve">6. </s>
            <s xml:id="echoid-s5859" xml:space="preserve">Elaſticitas interim aëris nonſolum à condenſatione augetur, ſed
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            & </s>
            <s xml:id="echoid-s5860" xml:space="preserve">ab aucto calore, & </s>
            <s xml:id="echoid-s5861" xml:space="preserve">quia conſtat calorem intendi ubique creſcente motu par-
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            ticularum inteſtino, ſequitur, elaſticitatem aëris ſpatium non mutantis auctam,
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            intenſiorem arguere motum in particulis aëris, quod cum hypotheſi noſtra re-
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            cte convenit: </s>
            <s xml:id="echoid-s5862" xml:space="preserve">perſpicuum enim eſt, eo majus requiri pondus P ad continen-
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            dum aërem in ſitu E C D F, quo majori velocitate particulæ aëreæ agitantur:
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            </s>
            <s xml:id="echoid-s5863" xml:space="preserve">lmo non difficile eſt videre pondus P ſecuturum rationem duplicatam iſtius ve-
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            locitatis, ideo quod ab aucta velocitate tum numerus impetuum tum intenſitas
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            corundem æqualiter creſcat, utrumq; </s>
            <s xml:id="echoid-s5864" xml:space="preserve">veroſeorſim proportionale ſit ponderi P.</s>
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