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

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            <s xml:id="echoid-s1340" xml:space="preserve">
              <pb o="52" file="0066" n="66" rhead="HYDRODYNAMICÆ."/>
            titudinem velocitati debitam, quam ſuperficies mn habet, cum pervenit in
              <lb/>
            ſitum fg; </s>
            <s xml:id="echoid-s1341" xml:space="preserve">ſit iſta altitudo = v, erit aſcenſus potent. </s>
            <s xml:id="echoid-s1342" xml:space="preserve">omnis aquæ eo ipſo mo-
              <lb/>
            mento pariter = v: </s>
            <s xml:id="echoid-s1343" xml:space="preserve">Deſcenſus actualis autem eſt per §. </s>
            <s xml:id="echoid-s1344" xml:space="preserve">7. </s>
            <s xml:id="echoid-s1345" xml:space="preserve">= tertiæ propor-
              <lb/>
            tionali ad totam maſſam aquæ, particulam aquæ mngf & </s>
            <s xml:id="echoid-s1346" xml:space="preserve">altitudinem verti-
              <lb/>
            calem HB, id eſt, = {δ/β}a; </s>
            <s xml:id="echoid-s1347" xml:space="preserve">eſt igitur v = {δ/β}a. </s>
            <s xml:id="echoid-s1348" xml:space="preserve">Hæc quidem altitudo dicto
              <lb/>
            citius minuitur ſtatim atque aqua per orificium B fluere cogitur, quod de-
              <lb/>
            monſtravi §. </s>
            <s xml:id="echoid-s1349" xml:space="preserve">18. </s>
            <s xml:id="echoid-s1350" xml:space="preserve">ſed primo tamen temporis puncto aqua ſervabit motum
              <lb/>
            quem acquiſivit, & </s>
            <s xml:id="echoid-s1351" xml:space="preserve">ſic guttula orificio proxima ejicietur velocitate, quæ de-
              <lb/>
            beatur altitudini{mmδ/nnß} a. </s>
            <s xml:id="echoid-s1352" xml:space="preserve">Poteſt autem hæc altitudo non ſolum eſſe tripla
              <lb/>
            aut quadrupla ipſius a, ſed & </s>
            <s xml:id="echoid-s1353" xml:space="preserve">quantumcunque magna: </s>
            <s xml:id="echoid-s1354" xml:space="preserve">ego certe cum tubis
              <lb/>
            vitreis pro lubitu jactus feci decies aut vigeſies altiores ipſius a; </s>
            <s xml:id="echoid-s1355" xml:space="preserve">fuerit v. </s>
            <s xml:id="echoid-s1356" xml:space="preserve">gr.
              <lb/>
            </s>
            <s xml:id="echoid-s1357" xml:space="preserve">δ = 100 pedum, β = uni pollici, diameter autem tubi decupla diametri,
              <lb/>
            quam orificium habet; </s>
            <s xml:id="echoid-s1358" xml:space="preserve">& </s>
            <s xml:id="echoid-s1359" xml:space="preserve">erit {mmδ/nnß} = {10000/1200} a, ita ut in his circumſtan-
              <lb/>
            tiis prima guttula aſſilire demta aëris reſiſtentia debeat ad altitudinem plus-
              <lb/>
            quam octies majorem altitudine ſolita a. </s>
            <s xml:id="echoid-s1360" xml:space="preserve">Sunt cœterum multa impedimenta
              <lb/>
            eaque maximi momenti, quæ jactus enormes cohibeant; </s>
            <s xml:id="echoid-s1361" xml:space="preserve">perditur nempe ali-
              <lb/>
            quid de motu ab impulſu ſuperficiei aqueæ mn in latera fg, dein etiam ab
              <lb/>
            ingenti attritu quem aqua per foraminulum, quod parvulum eſſe debet,
              <lb/>
            tam celeriter lata patitur: </s>
            <s xml:id="echoid-s1362" xml:space="preserve">multum etiam abeſt, quominus aqua C A D m
              <lb/>
            omni ſua celeritate moveatur ob adhæſionem aquæ ad latera tubi, quæ ad-
              <lb/>
            hæſio in tam longo tractu valde notabilis eſt.</s>
            <s xml:id="echoid-s1363" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1364" xml:space="preserve">Interim veram hanc eſſe ſolutionem phænomeni nullum poteſt eſſe
              <lb/>
            dubium, iſtique ſolutioni experimenta quæ feci in omni extenſione ſatisfa-
              <lb/>
            ciunt. </s>
            <s xml:id="echoid-s1365" xml:space="preserve">Dein hâc theoria etiam recte ſolvitur alterum phænomeni momen-
              <lb/>
            tum, quod nempe jactus iſte ſit quaſi momentaneus, poſtque breviſſimum
              <lb/>
            tempusculum ad ſenſus non major ſolito: </s>
            <s xml:id="echoid-s1366" xml:space="preserve">ita in præſenti, quem modo
              <lb/>
            finximus, caſu ſi per regulam §. </s>
            <s xml:id="echoid-s1367" xml:space="preserve">18, paullo mutatam (ibi enim de vaſis
              <lb/>
            verticaliter poſitis tantum dicitur) exploremus, quantum aquæ effluere de-
              <lb/>
            beat ut jactus non amplius milleſimâ parte (quæ utique obſervari in hujus-
              <lb/>
            modi experimentis minimè poteſt) ſuperet jactum ſolitum, cum ab initio
              <lb/>
            fuerit eodem octies major, invenimus tam parvam eſſe illam quantitatem, ut
              <lb/>
            tempus, quo tota ejicitur, nullo modo percipi poſſit.</s>
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