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

Table of figures

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            communi menſura idemque ponemus = θ, & </s>
            <s xml:id="echoid-s2848" xml:space="preserve">mutabitur pro vaſis ſeu ca-
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            nalibus cylindricis æquatio (α) in hanc
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            t = {nθ/2√(mm - nn)} X log. </s>
            <s xml:id="echoid-s2849" xml:space="preserve">{m√a + √(mmv - nnv)/m√a - √(mmv - nnv)}
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            altera vera ſignata (β) talis fit
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            t = {nθ/2m} X log. </s>
            <s xml:id="echoid-s2850" xml:space="preserve">{√a + √v/√a - √v},
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            ex quarum utraque apparet, non poſſe non breviſſimo tempore aquas om-
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            nem fere velocitatem acquirere, idque eo citius quo amplior eſt tubus,
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            quo brevior, & </s>
            <s xml:id="echoid-s2851" xml:space="preserve">quo magis verticalis: </s>
            <s xml:id="echoid-s2852" xml:space="preserve">Neque accelerationes ullo modo eſſe
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            perceptibiles, niſi prælongi ſtatuantur aquæ ductus & </s>
            <s xml:id="echoid-s2853" xml:space="preserve">tunc quoque brevi
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            tempore omnes fere accelerationum gradus percurri, quod utrumque nunc
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            exemplo illuſtrabo.</s>
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            <s xml:id="echoid-s2855" xml:space="preserve">(I) Quæritur tempus quo fluidum ex cylindro conſtanter pleno verticali,
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            ſedecim pedes anglicos longo & </s>
            <s xml:id="echoid-s2856" xml:space="preserve">cujus diameter quintupla ſit diametri fo-
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            raminis, velocitatem acquirit quæ debeatur altitudini {99/100}a, idque in hypo-
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            theſi, ad quam æquatio ſecunda pertinet; </s>
            <s xml:id="echoid-s2857" xml:space="preserve">ſic eſt {n/m} = {1/25}, v = {99/100}a,
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            b = a, unde tempus quod corpus inſumit cadendo libere per ſpatium {bb/a},
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            ſeu θ = uni minuto ſecundo; </s>
            <s xml:id="echoid-s2858" xml:space="preserve">hinc fit t = {1/50} log. </s>
            <s xml:id="echoid-s2859" xml:space="preserve">399. </s>
            <s xml:id="echoid-s2860" xml:space="preserve">id eſt, proxime no-
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            næ parti unius minuti ſecundi, quod tempusculum utique imperceptibile
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            eſt; </s>
            <s xml:id="echoid-s2861" xml:space="preserve">Cum vero tempus notabile aſſumitur, fiunt mutationes altitudinum v,
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            inſenſibiles. </s>
            <s xml:id="echoid-s2862" xml:space="preserve">Si tempus ſimile (quo nempe velocitas pariter nonaginta no-
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            vem centeſimis partibus altitudinis, quanta poſt tempus infinitum fit, debi-
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            ta generetur) in prima hypotheſi quæratur, nempe tempus quo obtinetur
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            v = {99/100} X ({mma/mm - nn}) reperitur illud præcedente paullulum majus,
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            ſed exceſſu inſenſibili: </s>
            <s xml:id="echoid-s2863" xml:space="preserve">unde patet in hujusmodi vaſis non poſſe fere aquas
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            ſat celeriter affundi in vas ſuperius, ut hypotheſi ſatisfiat, nec adeoque ratio-
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            ne ejusdem hypotheſeos experimenta alia ſumi poſſe, quam ut exploretur,
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            num revera tanta ſit altitudo B P in figura trigeſima, quanta vi paragraphi
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            quinti eſſe debet, ut punctum e aut f, durante fluxu ſitum ſervet, quem
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            ante fluxum obturato orificio L M, nullaque exiſtente aqua in vaſe ſuperiore
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            habuit.</s>
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