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

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            <s xml:id="echoid-s1745" xml:space="preserve">
              <pb o="65" file="0079" n="79" rhead="SECTIO QUARTA."/>
            quidem impedimenta nunc majora nunc minora nunquam omnem aquæ ve-
              <lb/>
            locitatem permittant, quam vi theoriæ, qua horum impedimentorum ra-
              <lb/>
            tio nulla habetur, acqui
              <unsure/>
            ere deberet.</s>
            <s xml:id="echoid-s1746" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1747" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1748" xml:space="preserve">6. </s>
            <s xml:id="echoid-s1749" xml:space="preserve">Ex præmiſſis nunc ſatis patere puto perfectum conſenſum fore
              <lb/>
            inter quantitatem aquæ effluentis ejuſque velocitatem, ſi modo foramini, quod
              <lb/>
            eſt in vaſe, ſubſtituatur aliud foramen eo uſque diminutum, donec ſectionem
              <lb/>
            venæ maxime contractæ non ſuperet: </s>
            <s xml:id="echoid-s1750" xml:space="preserve">atque perinde erit, in quonam venæ
              <lb/>
            loco, aut in quânam profunditate à ſuperficie aquæ foramen hoc eſſe conſti-
              <lb/>
            tuatur, ſive in a c ſive in d e, quandoquidem velocitates ſemper proxime re-
              <lb/>
            ſpondebunt toti altitudini aquæ ſupra eum locum, quo foramen fingitur: </s>
            <s xml:id="echoid-s1751" xml:space="preserve">am-
              <lb/>
            plitudinem hujus foraminis mente concipiendi vocabo deinceps Sectionem ve-
              <lb/>
            næ aqueæ contractæ.</s>
            <s xml:id="echoid-s1752" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1753" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1754" xml:space="preserve">7. </s>
            <s xml:id="echoid-s1755" xml:space="preserve">Quod ſi jam Sectio iſta, de quâ modo diximus, conſtantem
              <lb/>
            haberet rationem ad orificium, in eadem ratione diminuendum cogitatione
              <lb/>
            foret foramen effluxus, poſtmodumque calculus de quantitate aquæ dato tem-
              <lb/>
            pore effluentis inſtituendus. </s>
            <s xml:id="echoid-s1756" xml:space="preserve">Ita nempe poſita iſta ratione = {1/α} nominatâque
              <lb/>
            amplitudine orificii n, cenſenda eſſet Sectio venæ ſolidæ = {n/α}.</s>
            <s xml:id="echoid-s1757" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1758" xml:space="preserve">At variabilis cum ſit ſub diverſis circumſtantiis, regulas in hanc'
              <unsure/>
            rem à
              <lb/>
            priori dare non licet: </s>
            <s xml:id="echoid-s1759" xml:space="preserve">mutatur autem maxime à craſſitie laminæ, in quâ
              <unsure/>
            fora-
              <lb/>
            men eſt, aucta vel diminuta: </s>
            <s xml:id="echoid-s1760" xml:space="preserve">aliquid etiam, quamvis id parum, conferre po-
              <lb/>
            teſt magnitudo foraminis, amplitudines vaſis, hæque tam abſolutæ, quam rela-
              <lb/>
            tivæ, ut & </s>
            <s xml:id="echoid-s1761" xml:space="preserve">fortaſſe altitudo aquæ ſupra foramen. </s>
            <s xml:id="echoid-s1762" xml:space="preserve">Interim aſſumtis lamina te-
              <lb/>
            nui, vaſe ampliſſimo, foramine ad 4. </s>
            <s xml:id="echoid-s1763" xml:space="preserve">vel 6. </s>
            <s xml:id="echoid-s1764" xml:space="preserve">lineas in diametro aſſurgente; </s>
            <s xml:id="echoid-s1765" xml:space="preserve">ſolet
              <lb/>
            ratio inter foramen & </s>
            <s xml:id="echoid-s1766" xml:space="preserve">Sectionem venæ contractæ non multum recedere ab illâ,
              <lb/>
            quam Newtonus ſtatuit, nempe ut √ 2 ad 1. </s>
            <s xml:id="echoid-s1767" xml:space="preserve">Sæpe autem ab aliis major ob-
              <lb/>
            ſervata fuit, atque ab aliis etiam minor.</s>
            <s xml:id="echoid-s1768" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1769" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1770" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1771" xml:space="preserve">Quæcunque vero ſit, in quolibet caſu illam indicabimus, ut an-
              <lb/>
            te, per {α/1.</s>
            <s xml:id="echoid-s1772" xml:space="preserve">} Huicque poſitioni nunc calculum pro temporibus ſuperinſtruemus;
              <lb/>
            </s>
            <s xml:id="echoid-s1773" xml:space="preserve">brevitatis autem gratia conſiderabimus tantum vaſa cylindrica, atque in his
              <lb/>
            duo potiſſimum examinabimus temporum genera; </s>
            <s xml:id="echoid-s1774" xml:space="preserve">primum quod punctum
              <lb/>
            maximæ velocitatis definit, alterum, quod depletioni reſpondet. </s>
            <s xml:id="echoid-s1775" xml:space="preserve">In utroque
              <lb/>
            vero caſu motum à quiete incipere ponemus.</s>
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