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

Table of Notes

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          <pb o="145" file="0159" n="159" rhead="SECTIO OCTAVA."/>
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        <div xml:id="echoid-div162" type="section" level="1" n="130">
          <head xml:id="echoid-head171" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s4181" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4182" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4183" xml:space="preserve">Propoſitum fuerit vas A C R B (Fig. </s>
            <s xml:id="echoid-s4184" xml:space="preserve">37.) </s>
            <s xml:id="echoid-s4185" xml:space="preserve">infinitæ quaſi ratione
              <lb/>
              <note position="right" xlink:label="note-0159-01" xlink:href="note-0159-01a" xml:space="preserve">Fig. 37.</note>
            foraminum mox dicendorum ubique amplitudinis & </s>
            <s xml:id="echoid-s4186" xml:space="preserve">diaphragmate aliquo E F
              <lb/>
            in duas diſtinctum cavitates inter ſe communicantes, mediante foramine G:
              <lb/>
            </s>
            <s xml:id="echoid-s4187" xml:space="preserve">habeat præterea vas iſtud in infima ſui parte aliud foramen D: </s>
            <s xml:id="echoid-s4188" xml:space="preserve">deinde pona-
              <lb/>
            tur vas aquâ plenum uſque in P Q, ſic ut cavitas inferior C E F R tota ſit hu-
              <lb/>
            mido repleta, atque inſuper diaphragmati ſuperjaceat pars altera P Q F E. </s>
            <s xml:id="echoid-s4189" xml:space="preserve">His
              <lb/>
            poſitis, fluidoque jam moveri incipiente, quæritur velocitas aquæ per foramen
              <lb/>
            D in aërem effluentis velaltitudo genitri
              <unsure/>
            x hujus velocitatis.</s>
            <s xml:id="echoid-s4190" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div164" type="section" level="1" n="131">
          <head xml:id="echoid-head172" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s4191" xml:space="preserve">Fuerit altitudo ſuperficiei P Q ſupra foramen D = x, amplitudo fo-
              <lb/>
            raminis D = n, alteriusque G = m. </s>
            <s xml:id="echoid-s4192" xml:space="preserve">Perſpicuum autem eſt aſcenſum potentia-
              <lb/>
            lem cujuſvis guttæ per G transfluentis nihil promovere effluxum per D, totum-
              <lb/>
            que impendi in motum aliquem excitandum inteſtinum, qui mox abſorbetur
              <lb/>
            ſine alio effectu: </s>
            <s xml:id="echoid-s4193" xml:space="preserve">neceſſe igitur eſt ut ſingulis momentis motus generetur no-
              <lb/>
            vus in particulis foramen G tranſeuntibus, non minus atque in particulis per
              <lb/>
            D effiuentibus. </s>
            <s xml:id="echoid-s4194" xml:space="preserve">Sed ſi aſcenſus potentialis guttulæ per D effluentis dicatur v, id
              <lb/>
            eſt, ſi aqua exilire ponatur per D velocitate, cujus altitudo genitrix ſit v, erit
              <lb/>
            ſimilis altitudo ratione guttulæ mole ſua priori æqualis, per G eodem tempo-
              <lb/>
            re transfluentis {nnv/mm}. </s>
            <s xml:id="echoid-s4195" xml:space="preserve">Multiplicatis iſtis aſcenſibus potentialibus per maſſam, quam
              <lb/>
            æqualem habent, quamque vocabo M, erit aggregatum productorum =
              <lb/>
            Mv + {Mnnv/mm}. </s>
            <s xml:id="echoid-s4196" xml:space="preserve">Et cum ob infinitam amplitudinem vaſis alius motus non
              <lb/>
            generetur, erit præfatum aggregatum (per reg. </s>
            <s xml:id="echoid-s4197" xml:space="preserve">2.) </s>
            <s xml:id="echoid-s4198" xml:space="preserve">cenſendum æquale facto ex
              <lb/>
            maſſa omnis aquæ in ejusdem deſcenſum actualem. </s>
            <s xml:id="echoid-s4199" xml:space="preserve">At vero ſi maſſa omnis aquæ
              <lb/>
            dicatur μ, erit (per § 7. </s>
            <s xml:id="echoid-s4200" xml:space="preserve">Sect. </s>
            <s xml:id="echoid-s4201" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s4202" xml:space="preserve">deſcenſus actualis, qui fit dum guttula M ef-
              <lb/>
            fluit = {Mx/μ}, ita ut productum commune ſit = M x. </s>
            <s xml:id="echoid-s4203" xml:space="preserve">Igitur habetur
              <lb/>
            Mv + {Mnnv/mm} = Mx, ſive v = {mmx/nn + mm}. </s>
            <s xml:id="echoid-s4204" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s4205" xml:space="preserve">E. </s>
            <s xml:id="echoid-s4206" xml:space="preserve">F.</s>
            <s xml:id="echoid-s4207" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div165" type="section" level="1" n="132">
          <head xml:id="echoid-head173" xml:space="preserve">Scholium 1.</head>
          <p>
            <s xml:id="echoid-s4208" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4209" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4210" xml:space="preserve">Apparet ex iſto exemplo, motum ſine calculo differentiali </s>
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