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

Table of contents

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[51.] De vaſis quæ ſunt Tubis verticalibus inſtructa. Ad §. 22. & 23.
[52.] De iisdem vaſis, quibus tubi horizontales inſeruntur. Ad §. 24.
[53.] De canalibus recurvis. Ad §. 27.
[54.] HYDRODYNAMICÆ SECTIO QUARTA. De variis temporibus, quæ in effluxu aquarum deſiderari poſſunt. §. 1.
[55.] Experimenta quœ ad Sect. IV. pertinent.
[56.] Ad Theoriam Contractionis Venarum aquearum Experimentum 1.
[57.] Experimentum 2.
[58.] Experimentum 3.
[59.] Experimentum 4.
[60.] Experimentum 5.
[61.] Ad Theoriam aquarum per tubos effluentium. Experimentum 6.
[62.] Experimentum 7.
[63.] Experimentum 8.
[64.] Ad theoriam aquarum, quæ ex vaſis ampliſsi-mis à puncto quietis usque ad datum veloci-tatis gradum effluunt. Experimentum 9.
[65.] Experimentum 10.
[66.] Experimentum 11.
[67.] Experimentum 12.
[68.] HYDRODYNAMICÆ SECTIO QUINTA. De motu aquarum ex vaſis conſtanter plenis. §. 1.
[69.] Problema.
[70.] Solutio.
[71.] Caſus 1.
[72.] Caſus II.
[73.] Scholion 1.
[74.] Scholion 2.
[75.] Scholion 3.
[76.] Scholion 4.
[77.] Corollarium 1.
[78.] Corollarium 3.
[79.] Corollarium 4.
[80.] Problema.
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              <pb o="235" file="0249" n="249" rhead="SECTIO DECIMA."/>
            que ponatur pondus columnæ mercurii (cujus baſis eſt C D & </s>
            <s xml:id="echoid-s6943" xml:space="preserve">cujus altitudo
              <lb/>
            eadem ſit quæ in barometro) = P. </s>
            <s xml:id="echoid-s6944" xml:space="preserve">Utemur autem hypotheſi, ſive globus pro-
              <lb/>
            pellatur ab aëre condenſato ſive à pulveris pyrii aura, potentiam illius fluidi
              <lb/>
            propellentis proportionalem eſſe denſitati.</s>
            <s xml:id="echoid-s6945" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6946" xml:space="preserve">His ad calculum præparatis, globum conſiderabimus in ſitu e, poneu-
              <lb/>
            do A c = x, velocitatemque globi in hoc ſitu = v, ſic erit potentia globum
              <lb/>
            in ſitu e propellens = ({nb/x} - 1) X P, quæ diviſa per maſſam 1 ductaque in ele-
              <lb/>
            mentum ſpatii d x dat incrementum dimidium quadrati velocitatis; </s>
            <s xml:id="echoid-s6947" xml:space="preserve">unde fit v d v
              <lb/>
            = ({nb/x} - 1) X P d x, ſive {1/2} v v = (b - x + nb log. </s>
            <s xml:id="echoid-s6948" xml:space="preserve">{x/b})P. </s>
            <s xml:id="echoid-s6949" xml:space="preserve">Ponatur x = a,
              <lb/>
            habetur altitudo debita velocitati, quacum globus exploditur; </s>
            <s xml:id="echoid-s6950" xml:space="preserve">vocetur iſta
              <lb/>
            altitudo α & </s>
            <s xml:id="echoid-s6951" xml:space="preserve">erit
              <lb/>
            α = (b - a + nb log. </s>
            <s xml:id="echoid-s6952" xml:space="preserve">{a/b}) X P.</s>
            <s xml:id="echoid-s6953" xml:space="preserve"/>
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            <s xml:id="echoid-s6954" xml:space="preserve">(II) Sit v. </s>
            <s xml:id="echoid-s6955" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s6956" xml:space="preserve">in ſclopeto pneumatico longitudo animæ ſeu a = 3 ped.
              <lb/>
            </s>
            <s xml:id="echoid-s6957" xml:space="preserve">Paris. </s>
            <s xml:id="echoid-s6958" xml:space="preserve">longitudo A C = 4 poll. </s>
            <s xml:id="echoid-s6959" xml:space="preserve">fueritque aër captus in A D naturali decies den-
              <lb/>
            ſior ſeu n = 10, diameter animæ ſeu globuli ejiciendi trium linearum ejus-
              <lb/>
            que gravitas ſpecifica ratione mercurii ut 10 ad 17. </s>
            <s xml:id="echoid-s6960" xml:space="preserve">Erit P præterpropter =
              <lb/>
            286; </s>
            <s xml:id="echoid-s6961" xml:space="preserve">indeque invenitur α = 2788, indicio globum ejectum iri velocitate
              <lb/>
            qua in vacuo ad altitudinem 2788 ped. </s>
            <s xml:id="echoid-s6962" xml:space="preserve">aſcendere poſſit. </s>
            <s xml:id="echoid-s6963" xml:space="preserve">Ex præcedente for-
              <lb/>
            mula colligitur jactum globi vehementiſſimum fore pro eadem auræ elaſticæ
              <lb/>
            quantitate, ſi longitudo animæ fiat = n b. </s>
            <s xml:id="echoid-s6964" xml:space="preserve">Si vero animus ad impedimenta
              <lb/>
            alia, quæ globus præter inertiam ſuam & </s>
            <s xml:id="echoid-s6965" xml:space="preserve">reſiſtentiam aëris externi in tranſitu
              <lb/>
            ſuo per Sclopeti animam patitur, advertatur, apparet longitudinem animæ
              <lb/>
            ad jactum vehementiſſimum producendum requiri longe minorem. </s>
            <s xml:id="echoid-s6966" xml:space="preserve">Si longi-
              <lb/>
            tudo n b admodum major ſit longitudine a, quod ita eſt in jactibus fortiori-
              <lb/>
            bus, erit ſine ſenſibili errore α = n b P log. </s>
            <s xml:id="echoid-s6967" xml:space="preserve">{a/b}.</s>
            <s xml:id="echoid-s6968" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6969" xml:space="preserve">Si tormentum ſit verticaliter erectum, fit aliquantum diverſus calculus
              <lb/>
            ſed pro vehementioribus jactibus differentia nequit eſſe ſenſibilis. </s>
            <s xml:id="echoid-s6970" xml:space="preserve">Igitur quia
              <lb/>
            jactus deinceps conſiderabimus tantum vehementiſſimos, brevitatis ergo po-
              <lb/>
            nemus a = nb P X log. </s>
            <s xml:id="echoid-s6971" xml:space="preserve">{a/b}.</s>
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            <s xml:id="echoid-s6973" xml:space="preserve">(III) Prouti in præcedentibus altitudinem determinavimus debitam </s>
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