Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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to ad finitum aut viciſſim à finito ad infinitum in aquis fluentibus non recte aſ-
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ſecuti à plurimis difficultatibus ſe extricare non potuerunt, quæ aliâs facilè ad-
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mittunt ſolutionem, ſi autem loco vaſis fere infiniti, cujuſmodi nulla ſunt, ſu-
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matur vas valde amplum, aut etiam quod in multis caſibus ſufficit, medio-
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criter amplum, erunt formulæ proxime veræ, & </
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ad verum accedent pro indole quæſtionis: </
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">de his quædam monebo in ſequen-
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tibus experimentis. </
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">Interim ſic ſatis jam apparet ex theoria, quod potiſſimum
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explicare conſtitueram, cur aqua ex vaſe ampliſſimo ſimplici omni ſtatim ve-
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locitate effluat, & </
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vero præcilæ de his quæſtionibus ex æquationibus ipſis erunt deducendæ.</
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<
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">Tandem quod pertinet ad tempus depletionis, patet cum am-
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plitudo vaſis vel mediocriter ſuperat amplitudinem tubi annexi, poſſe ſine
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ſenſibili errore cenſeri illud = {mα/n} θ intelligendo per θ tempus, quo corpus à
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quiete libere cadendo abſolvit altitudinem, quam aqua ab initio fluxus habuit
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ſupra orificium tubi extremum, atque ſumendo pro {mα/n} rationem quæ eſt
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inter amplitudinem vaſis & </
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dimenta vero, quæ in his caſibus fortuito ſuperveniunt, tempus iſtud admo-
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dum augent. </
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">Si vero tempus deſideretur, quo ſuperficies aquæ per datam de-
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ſcendat altitudinem erit illud ſumendum = {mα/n} (θ - Τ) ſumto pro Τ tem-
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pore quod corpus inſumit libere cadendo per altitudinem, quam aqua in fine
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fluxus ſupra foramen habet.</
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">QUum magna pars hujus ſectionis poſita ſit in contractione venæ aqueæ
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per foramen in lamina tenui factum fluentis, animo concepi de iſta
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contractione experimenta inſtituere accurata, non quidem menſuras
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accipiendo diametrorum, quam methodum non ſuſſicienti accuratione fieri
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poſſe expertus ſum, ſed obſervando velocitates actuales ex amplitudine jactus,
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& </
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ſum, quod tempore unius minuti primi 144. </
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quentia ſumſi.</
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