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

Table of Notes

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            ſiderandum eſſe dixi. </s>
            <s xml:id="echoid-s8280" xml:space="preserve">Sit amplitudo iſtius Sectionis = 1, habeantque ibi aquæ
              <lb/>
            velocitatem quæ debeatur altitudini A: </s>
            <s xml:id="echoid-s8281" xml:space="preserve">ponatur, cylindrum aquæ effluxiſſe,
              <lb/>
            qui pro baſe habeat 1 & </s>
            <s xml:id="echoid-s8282" xml:space="preserve">pro longitudine L: </s>
            <s xml:id="echoid-s8283" xml:space="preserve">ſi tempus exprimatur per ſpa-
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            tium diviſum per velocitatem, erit velocitas altitudini A debita exprimenda
              <lb/>
            per √ 2 A, tempuſque fluxus per {L/√2A}. </s>
            <s xml:id="echoid-s8284" xml:space="preserve">His præmiſſis indagabimus in preſ-
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            ſionem motricem, quæ poſſit tempore ({L/√2a}) cylindro L communicare ve-
              <lb/>
            locitatem √ 2 A: </s>
            <s xml:id="echoid-s8285" xml:space="preserve">ſit illa preſſio = p: </s>
            <s xml:id="echoid-s8286" xml:space="preserve">putetur brevioris calculi ergo egiſſe
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            tempore t cylindroque dediſſe velocitatem v; </s>
            <s xml:id="echoid-s8287" xml:space="preserve">erit d v = {pdt/L} & </s>
            <s xml:id="echoid-s8288" xml:space="preserve">v = {pt/L},
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            hinc p = {Lv/t}; </s>
            <s xml:id="echoid-s8289" xml:space="preserve">ponatur jam √ 2 A pro v & </s>
            <s xml:id="echoid-s8290" xml:space="preserve">{L/√2A} pro t atque erit p =
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            (L √2A): </s>
            <s xml:id="echoid-s8291" xml:space="preserve">(L/√2A} = 2 A. </s>
            <s xml:id="echoid-s8292" xml:space="preserve">Eſt igitur preſſio aquam ad effluxum conſtanter
              <lb/>
            ſollicitans æqualis ponderi cylindri aquei, cujus baſis ſit orificium aquas tranſ-
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            mittens ſupra definitum & </s>
            <s xml:id="echoid-s8293" xml:space="preserve">cujus altitudo ſit æqualis duplæ altitudini velocitati
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            aquæ effluentis debitæ: </s>
            <s xml:id="echoid-s8294" xml:space="preserve">& </s>
            <s xml:id="echoid-s8295" xml:space="preserve">tanta quoque eſt reactio, quæ vas repellit. </s>
            <s xml:id="echoid-s8296" xml:space="preserve">Q.</s>
            <s xml:id="echoid-s8297" xml:space="preserve">E.</s>
            <s xml:id="echoid-s8298" xml:space="preserve">D.</s>
            <s xml:id="echoid-s8299" xml:space="preserve"/>
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            <s xml:id="echoid-s8300" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8301" xml:space="preserve">5. </s>
            <s xml:id="echoid-s8302" xml:space="preserve">Eadem eſt demonſtratio ſi aquæ non per orificium ſed per tubum
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            horizontalem cylindricum velocitate uniformi effluant, aut etiam per tubum
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            utcunque inæqualiter amplum: </s>
            <s xml:id="echoid-s8303" xml:space="preserve">poſterius id directe demonſtrari etiam poteſt,
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            ſi bene exprimatur preſſio requiſita in ſingulis guttis, ut hæ debita velocita-
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            tum incrementa aut decrementa ſuſcipiant.</s>
            <s xml:id="echoid-s8304" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8305" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8306" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8307" xml:space="preserve">Altitudo, quam vocavimus A, parum quidem differt in experi-
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            mentis ab altitudine aquæ ſupra orificium effluxus, præſertim ſi aquæ ex vaſe
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            valde amplo per orificium ſimplex, idque non admodum parvum effluant:
              <lb/>
            </s>
            <s xml:id="echoid-s8308" xml:space="preserve">differt autem ſæpius notabiliter orificium effluxus à ſectione minima venæ, quam
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            nos ceu orificium aquas tranſmittens conſideramus; </s>
            <s xml:id="echoid-s8309" xml:space="preserve">id quantitas aquæ dato
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            tempore effluentis cum velocitate ſua comparata in experimentis indicat.</s>
            <s xml:id="echoid-s8310" xml:space="preserve"/>
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            <s xml:id="echoid-s8311" xml:space="preserve">Hinc fit ut propoſitio noſtra §. </s>
            <s xml:id="echoid-s8312" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8313" xml:space="preserve">ad experientiam vocata ordinario
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            non multum diſcrepet ab propoſitione Newtoni §. </s>
            <s xml:id="echoid-s8314" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8315" xml:space="preserve">expoſita; </s>
            <s xml:id="echoid-s8316" xml:space="preserve">ſi vero omnia
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            ſollicite evitentur, quæ contractionem venæ producere & </s>
            <s xml:id="echoid-s8317" xml:space="preserve">quæ velocitatem
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            diminuere poſſunt, vis repellens ſecundum theoriam noſtram fiet tantum non
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            duplo major, quam quæ à Newtono fuit definita & </s>
            <s xml:id="echoid-s8318" xml:space="preserve">tunc talis etiam experi-
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            mentis confirmatur.</s>
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