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

Table of Notes

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            (1 - {mm/nn})vdξ + ξdv = - xdξ
              <lb/>
            cujus integralis, quod patet multiplicatis terminis per ξ - {mm/nn} hæc eſt
              <lb/>
            v = ξ
              <emph style="super">{mm/nn} - 1</emph>
            ſ - xξ
              <emph style="super">- {mm/nn}</emph>
            dξ.
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            <s xml:id="echoid-s1131" xml:space="preserve">Fuerit v. </s>
            <s xml:id="echoid-s1132" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1133" xml:space="preserve">canalis rectus & </s>
            <s xml:id="echoid-s1134" xml:space="preserve">ita inclinatus verſus horizontem, ut ſinus anguli
              <lb/>
            intercepti inter utrumque ſit ad ſinum totum ut 1 ad g, erit ξ = gx; </s>
            <s xml:id="echoid-s1135" xml:space="preserve">unde
              <lb/>
            v = {nna/2nn - mm} (({a/x})
              <emph style="super">{nn - mm/nn}</emph>
            - {x/a})
              <lb/>
            quæ æquatio cum non differat ab æquatione §. </s>
            <s xml:id="echoid-s1136" xml:space="preserve">13. </s>
            <s xml:id="echoid-s1137" xml:space="preserve">pro Cylindris verticalibus
              <lb/>
            data, ſequitur in utroque caſu velocitates aquæ easdem eſſe, poſtquam deſ-
              <lb/>
            cenſus verticales ſuperficiei aquæ iidem ſunt: </s>
            <s xml:id="echoid-s1138" xml:space="preserve">Igitur accelerationes in locis
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            homologis utrobique ſimiles ſunt ratione altitudinum verticalium, & </s>
            <s xml:id="echoid-s1139" xml:space="preserve">hoc tan-
              <lb/>
            tum diſcriminis intercedit, quod in canali inclinato lentius fiant, idque in
              <lb/>
            ratione ut 1 ad g: </s>
            <s xml:id="echoid-s1140" xml:space="preserve">facile igitur ſenſibus percipi poterunt hæ accelerationes in
              <lb/>
            canalibus valde inclinatis, quæ in verticalibus ob nimiam mutationum celeri-
              <lb/>
            tatem non poſſunt. </s>
            <s xml:id="echoid-s1141" xml:space="preserve">Cœterum patet per ſe ex eo, quod frictiones à longitu-
              <lb/>
            dine tubi augeantur, non poſſe non velocitates inde diminui, ad quod ani-
              <lb/>
            mum advertent ii, quibus experimenta hâc de re inſtituere animus erit.</s>
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