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

Table of Notes

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            <s xml:id="echoid-s2477" xml:space="preserve">Fuit igitur quantitas aquæ experimento inventa ad quantitatem, quam
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            theoria ſepoſita impedimentorum conſideratione indicat, ut 11922 ad 26830;
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            </s>
            <s xml:id="echoid-s2478" xml:space="preserve">qui numeri, quamvis non parum differant, tamen egregie theoriam confir-
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            mant, quod ipſum nunc clare ob oculos ponam.</s>
            <s xml:id="echoid-s2479" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2480" xml:space="preserve">In formula nb√{n/g} X log. </s>
            <s xml:id="echoid-s2481" xml:space="preserve">{a/a - e}, poſuimus pro a altitudinem velo-
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            citati maximæ aquæ effluentis debitam, qualis revera fuit in experimento,
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            non qualis remotis obſtaculis futura fuiſſet; </s>
            <s xml:id="echoid-s2482" xml:space="preserve">fecimus nempe a = 141: </s>
            <s xml:id="echoid-s2483" xml:space="preserve">in theo-
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            ria vero eſt a = 433. </s>
            <s xml:id="echoid-s2484" xml:space="preserve">Quod ſi autem valor iſte poſterior aſſumatur, retinen-
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            do valorem altitudinis e = 73, fit nb√{n/g} log. </s>
            <s xml:id="echoid-s2485" xml:space="preserve">{a/a - e} proxime = 6700, qui
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            numerus nunc multo minor eſt numero per experimentum eruto, cum antea
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            fuerit admodum major. </s>
            <s xml:id="echoid-s2486" xml:space="preserve">Talis autem fit cum altitudo e ſervare valorem ponitur:
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            </s>
            <s xml:id="echoid-s2487" xml:space="preserve">Verum prouti altitudo a aucta fuit ab 141 uſque ad 433, ita certe etiam altitu-
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            do e eſt augenda, foretque utraque altitudo in eadem ratione augenda, ſi im-
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            pedimenta primis guttulis æqualiter reſiſterent & </s>
            <s xml:id="echoid-s2488" xml:space="preserve">ſequentibus: </s>
            <s xml:id="echoid-s2489" xml:space="preserve">ſed minorem
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            reſiſtentiam offendunt cæteris paribus particulæ, quo tardius moventur, atque
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            proin etiam guttulæ quæ cadunt cis terminum R minus retardantur, quam quæ
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            terminum iſtum tranſgrediuntur: </s>
            <s xml:id="echoid-s2490" xml:space="preserve">Facile eſt exinde colligere in minori ratione
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            augendam eſſe altitudinem e quam alteram a, ipſam vero rationem dicere non
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            poſſumus, niſi à poſteriori, faciendo ſcilicet, ut theoria conveniat cum ex-
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            perimento; </s>
            <s xml:id="echoid-s2491" xml:space="preserve">ita reperitur ponendum eſſe e = 120, qui numerus animo ad om-
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            nes circumſtantias bene attento plane ſatisfacit.</s>
            <s xml:id="echoid-s2492" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2493" xml:space="preserve">Sic igitur manifeſtum mihi videtur, experimenti ſucceſſum talem
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            fuiſſe, ut plane cum theoria conveniat. </s>
            <s xml:id="echoid-s2494" xml:space="preserve">Hujusmodi autem exempla omni-
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            no demonſtrant, veras motuum leges in fluidis nos tradidiſſe, eaque inter
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            infinita alia ſelegi, quod nullam habent nexum neque affinitatem cum regu-
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            la communi, quæ fluida ubique velocitate effluere ſtatuit, toti altitudini
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            aquæ ſupra foramen debita, neque poſſint principiis conſuetis ſolvi. </s>
            <s xml:id="echoid-s2495" xml:space="preserve">Cæte-
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            rum quoniam in hoc experimento motus aquæ retardatus fuit, aliud inſtitue-
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            re volui, quo omnia impedimenta admodum diminuerentur, ut ſic appare-
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            ret eo magis ad ſe invicem accedere numeros experimenti & </s>
            <s xml:id="echoid-s2496" xml:space="preserve">regulæ, quo
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            minora eſſent impedimenta.</s>
            <s xml:id="echoid-s2497" xml:space="preserve"/>
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Impressum