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

Table of Notes

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            - dz = {f + φ/F} X {z/x} X √ ({P/p} b) xdt;
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            <s xml:id="echoid-s7087" xml:space="preserve">Ex comparatione harum duarum æquationum oritur
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            - dz = {f + φ/F - f} X {g/b} X {√b/√Pp} X dv,
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            quæ cum debitæ conſtantis additione integrata dat
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            z = g - {f + φ/F - f} X {g/b} X {√b/√Pp} X v. </s>
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            Si jam in æquatione prima ſubſtituatur valor iſte inventus pro z, ſimulque
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            ponatur {dx/v} pro dt, fiet
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            vdv = {F - f/F} X {b/x} X P X dx - {f + φ/F} X {√(bP)/x√p} X vdx, ſive
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            {Fvdv√p/(F - f) X bP√p - (f + φ) X v√ (bP)} = {dx/x},
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            quæ æquatio poſt debitam ſui integrationem, facta x = a, abit in hanc
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            log. </s>
            <s xml:id="echoid-s7089" xml:space="preserve">{a/b} = [-F(f + φ) v√ p - F (F - f) p√ (Pb) X log.</s>
            <s xml:id="echoid-s7090" xml:space="preserve">(1 - {(f + φ)v/(F - f) √ (bPp)})]: </s>
            <s xml:id="echoid-s7091" xml:space="preserve">
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            (f + φ)
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            X √Pb.</s>
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            <s xml:id="echoid-s7093" xml:space="preserve">(VIII) Si jam per experimentum innotuerit valor ipſius v, poterit in-
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            de deduci valor ipſius P, qui denotat elaſticitatem auræ pulveris pyrii non-
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            dum expanſæ: </s>
            <s xml:id="echoid-s7094" xml:space="preserve">Quod ut exemplo illuſtremus, eodem utemur experimento,
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            quod jam articulo IV. </s>
            <s xml:id="echoid-s7095" xml:space="preserve">expoſuimus, ut appareat inde, quodnam ab avolatione
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            auræ elaſticitatis augmentum arguat. </s>
            <s xml:id="echoid-s7096" xml:space="preserve">Sic igitur ponetur calculus.</s>
            <s xml:id="echoid-s7097" xml:space="preserve"/>
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            <s xml:id="echoid-s7098" xml:space="preserve">Quia pondus globi, quod erat trium librarum, indicavimus per uni-
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            tatem, erunt quatuor unicæ pulveris adhibitæ exprimendæ per {1/12}: </s>
            <s xml:id="echoid-s7099" xml:space="preserve">igitur
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            p = {1/12}. </s>
            <s xml:id="echoid-s7100" xml:space="preserve">Menſuras aperturarum, quas conſideramus, non accepi: </s>
            <s xml:id="echoid-s7101" xml:space="preserve">ſolet autem
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            hiatus à globo r
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            elictus conſtituere in ſimili tormento præterpropter partem
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            decimam quintam amplitudinis animæ; </s>
            <s xml:id="echoid-s7102" xml:space="preserve">amplitudinem luminis accenſoriihic
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            fere negligi poſſe puto; </s>
            <s xml:id="echoid-s7103" xml:space="preserve">itaque ſtatuam F = 15; </s>
            <s xml:id="echoid-s7104" xml:space="preserve">f = 1; </s>
            <s xml:id="echoid-s7105" xml:space="preserve">φ = 0: </s>
            <s xml:id="echoid-s7106" xml:space="preserve">Deinde
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            habetur rurſus a = 7, 7; </s>
            <s xml:id="echoid-s7107" xml:space="preserve">b = 0, 08; </s>
            <s xml:id="echoid-s7108" xml:space="preserve">altitudo ad quam globus in vacuo
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            aſcendere poſſit ſeu {1/2} vv = 58750, ſeuv = 343: </s>
            <s xml:id="echoid-s7109" xml:space="preserve">Igitur æquatio ultima
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            ſuperioris articuli hæc erit
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            log.</s>
            <s xml:id="echoid-s7110" xml:space="preserve">96 = { - 5251/√P} + 17, 5 log. </s>
            <s xml:id="echoid-s7111" xml:space="preserve">{√P/√P-300},
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            cui proxime ſatisfit cum ſumitur √ P = 534 & </s>
            <s xml:id="echoid-s7112" xml:space="preserve">proinde P = 285156,
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            quod efficit pondus columnæ mercurialis ejusdem cum anima tormenti </s>
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