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

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            <s xml:id="echoid-s2128" xml:space="preserve">
              <pb o="78" file="0092" n="92" rhead="HYDRODYNAMICÆ"/>
            to ad finitum aut viciſſim à finito ad infinitum in aquis fluentibus non recte aſ-
              <lb/>
            ſecuti à plurimis difficultatibus ſe extricare non potuerunt, quæ aliâs facilè ad-
              <lb/>
            mittunt ſolutionem, ſi autem loco vaſis fere infiniti, cujuſmodi nulla ſunt, ſu-
              <lb/>
            matur vas valde amplum, aut etiam quod in multis caſibus ſufficit, medio-
              <lb/>
            criter amplum, erunt formulæ proxime veræ, & </s>
            <s xml:id="echoid-s2129" xml:space="preserve">modo magis modo minus
              <lb/>
            ad verum accedent pro indole quæſtionis: </s>
            <s xml:id="echoid-s2130" xml:space="preserve">de his quædam monebo in ſequen-
              <lb/>
            tibus experimentis. </s>
            <s xml:id="echoid-s2131" xml:space="preserve">Interim ſic ſatis jam apparet ex theoria, quod potiſſimum
              <lb/>
            explicare conſtitueram, cur aqua ex vaſe ampliſſimo ſimplici omni ſtatim ve-
              <lb/>
            locitate effluat, & </s>
            <s xml:id="echoid-s2132" xml:space="preserve">cur ſecus ſit de aquis ex vaſe per tubum ejectis: </s>
            <s xml:id="echoid-s2133" xml:space="preserve">Menſuræ
              <lb/>
            vero præcilæ de his quæſtionibus ex æquationibus ipſis erunt deducendæ.</s>
            <s xml:id="echoid-s2134" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2135" xml:space="preserve">§. </s>
            <s xml:id="echoid-s2136" xml:space="preserve">22. </s>
            <s xml:id="echoid-s2137" xml:space="preserve">Tandem quod pertinet ad tempus depletionis, patet cum am-
              <lb/>
            plitudo vaſis vel mediocriter ſuperat amplitudinem tubi annexi, poſſe ſine
              <lb/>
            ſenſibili errore cenſeri illud = {mα/n} θ intelligendo per θ tempus, quo corpus à
              <lb/>
            quiete libere cadendo abſolvit altitudinem, quam aqua ab initio fluxus habuit
              <lb/>
            ſupra orificium tubi extremum, atque ſumendo pro {mα/n} rationem quæ eſt
              <lb/>
            inter amplitudinem vaſis & </s>
            <s xml:id="echoid-s2138" xml:space="preserve">ſectionem venæ, ſive contractam ſive dilatatam. </s>
            <s xml:id="echoid-s2139" xml:space="preserve">Impe-
              <lb/>
            dimenta vero, quæ in his caſibus fortuito ſuperveniunt, tempus iſtud admo-
              <lb/>
            dum augent. </s>
            <s xml:id="echoid-s2140" xml:space="preserve">Si vero tempus deſideretur, quo ſuperficies aquæ per datam de-
              <lb/>
            ſcendat altitudinem erit illud ſumendum = {mα/n} (θ - Τ) ſumto pro Τ tem-
              <lb/>
            pore quod corpus inſumit libere cadendo per altitudinem, quam aqua in fine
              <lb/>
            fluxus ſupra foramen habet.</s>
            <s xml:id="echoid-s2141" xml:space="preserve"/>
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        <div xml:id="echoid-div79" type="section" level="1" n="55">
          <head xml:id="echoid-head75" style="it" xml:space="preserve">Experimenta quœ ad Sect. IV. pertinent.</head>
          <p>
            <s xml:id="echoid-s2142" xml:space="preserve">QUum magna pars hujus ſectionis poſita ſit in contractione venæ aqueæ
              <lb/>
            per foramen in lamina tenui factum fluentis, animo concepi de iſta
              <lb/>
            contractione experimenta inſtituere accurata, non quidem menſuras
              <lb/>
            accipiendo diametrorum, quam methodum non ſuſſicienti accuratione fieri
              <lb/>
            poſſe expertus ſum, ſed obſervando velocitates actuales ex amplitudine jactus,
              <lb/>
            & </s>
            <s xml:id="echoid-s2143" xml:space="preserve">quantitates datis temporibus effluentes; </s>
            <s xml:id="echoid-s2144" xml:space="preserve">In experimentis automato uſus
              <lb/>
            ſum, quod tempore unius minuti primi 144. </s>
            <s xml:id="echoid-s2145" xml:space="preserve">vicibus pulſabat, atque ſic ſe-
              <lb/>
            quentia ſumſi.</s>
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