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

Table of Notes

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        <div xml:id="echoid-div159" type="section" level="1" n="127">
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              <pb o="144" file="0158" n="158" rhead="HYDRODYNAMICÆ"/>
            tantum ſupra aquam, cui tubus immergitur, quantum infra eandem de-
              <lb/>
            preſſa fuerat, niſi cum tubus totus eſt apertus: </s>
            <s xml:id="echoid-s4157" xml:space="preserve">iſta vero ſuperficies multo
              <lb/>
            minus deprimitur quam antea fuerat elevata. </s>
            <s xml:id="echoid-s4158" xml:space="preserve">Horum rationem dedimus in
              <lb/>
            ſuperiori ſectione: </s>
            <s xml:id="echoid-s4159" xml:space="preserve">Hæc quia ita ſunt, regulas nunc dabo duas pro motu
              <lb/>
            aquarum ubique definiendo, easque porro exemplis illuſtrabo talibus, quæ
              <lb/>
            nulla adhuc theoria explicari potuerunt, cum noſtra autem egregie admo-
              <lb/>
            dum conveniunt.</s>
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          <head xml:id="echoid-head169" xml:space="preserve">Regula 1.</head>
          <p>
            <s xml:id="echoid-s4161" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4162" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4163" xml:space="preserve">Diſpiciendum eſt, aſſumta alicubi in vaſe propoſito velocitate
              <lb/>
            fluidi ceu cognita, quænam reliquis fluidi partibus futura ſit velocitas. </s>
            <s xml:id="echoid-s4164" xml:space="preserve">Ita
              <lb/>
            enim cognoſcetur aſcenſus potentialis totius fluidi ejusque incrementum. </s>
            <s xml:id="echoid-s4165" xml:space="preserve">Ha-
              <lb/>
            ctenus conſideravimus fluida in infinita ſtrata parallela vel potius ad latera
              <lb/>
            vaſis ubique perpendicularia diviſa, ſtatuimusque velocitates hiſce ſtratis re-
              <lb/>
            ciproce proportionales: </s>
            <s xml:id="echoid-s4166" xml:space="preserve">Facile quidem eſt vaſa effingere, ubi aliter moven-
              <lb/>
            tur fluida; </s>
            <s xml:id="echoid-s4167" xml:space="preserve">crediderim autem his in locis motum notabilem nunquam ha-
              <lb/>
            bere fluida ita, ut error ex iſta hypotheſi ſenſibilis naſci fere non poſſit:
              <lb/>
            </s>
            <s xml:id="echoid-s4168" xml:space="preserve">poterit tamen majoris accurationis ergo præfata regula adhiberi. </s>
            <s xml:id="echoid-s4169" xml:space="preserve">Præſertim
              <lb/>
            vero huc pertinet contractio venarum, cum fluida per foramina in tenuibus
              <lb/>
            admodum laminis facta transire coguntur, qua in re magna eſt adhibenda
              <lb/>
            circumſpectio: </s>
            <s xml:id="echoid-s4170" xml:space="preserve">Effectus hujusmodi contractionum haud male, puto, prævi-
              <lb/>
            debuntur, cum recte perpenſa fuerint, quæ in ſectione quarta de illis monui.</s>
            <s xml:id="echoid-s4171" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div161" type="section" level="1" n="129">
          <head xml:id="echoid-head170" xml:space="preserve">Regula 2.</head>
          <p>
            <s xml:id="echoid-s4172" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4173" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4174" xml:space="preserve">Singulis momentis diſpiciendum eſt, quantum vis vivæ, ſeu
              <lb/>
            quodnam productum ex aſcenſu potentiali in maſſam oriatur ad fluxum præ-
              <lb/>
            cipuum, cujus natura quæritur, nihil conferens. </s>
            <s xml:id="echoid-s4175" xml:space="preserve">Id vero rurſus uniuscu-
              <lb/>
            jusque circumſpectæ æſtimationi relinquendum eſt. </s>
            <s xml:id="echoid-s4176" xml:space="preserve">Quod ſic oritur, ad-
              <lb/>
            dendum eſt facto ex aſcenſu potentiali, quem motus præcipuus involvit, in
              <lb/>
            maſſam, aggregatumque productorum demum æquale cenſendum eſt facto
              <lb/>
            ex maſsâ omnis aquæ in ejusdem deſcenſum actualem.</s>
            <s xml:id="echoid-s4177" xml:space="preserve"/>
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            <s xml:id="echoid-s4178" xml:space="preserve">Magni profecto eſt momenti hæc regula, & </s>
            <s xml:id="echoid-s4179" xml:space="preserve">ut puto, fere unica ad mo-
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            tuum menſuras obtinendas, quiin vaſis irregularibus, pluribusque cavitatibus
              <lb/>
            inter ſe communicantibus diviſis fiunt, quod nunc pluribus illuſtrabo exemplis.</s>
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