Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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rum dato tempore affundendarum ſequi rationem ſeſquiplicatam altitudinum,
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ad quas aquæ à fundo cylindri aſcendunt: </
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">aut viciſſim altitudines ſequi ra-
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tionem ſubtriplicatam quadratorum quantitatum, quibus aquæ dato tempore
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affunduntur.</
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<
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<
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<
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ratum.</
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<
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<
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">Sit idem cylindrus, ſed aquis in foſſa veluti vaſe infinito ſtagnantibus,
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ſubmerſus; </
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<
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">dicaturque altitudo ſubmerſionis = a, quæritur nunc iiſdem po-
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ſitis, ut antea, rurſus æquatio inter altitudinem α ſuperficiei aqueæ internæ ſu-
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pra externam, & </
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<
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">quantitatem q dato tempore affundendam.</
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<
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">Quod ad illam rimæ partem α, quæ aquas ejicit & </
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nam eminet, illam jam vidimus dato tempore erogare quantitatem {2/3} n α √ α:
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</
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<
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">reſidua autem rimæ pars ſubmerſa aquas ubique communi velocitate tranſimit-
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tit, ut ex infra dicendis patebit, & </
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<
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">quidem velocitate √ α, ita, ut multiplica-
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ta hâc velocitate per magnitudinem rimæ ſubmerſæ n a, habeatur quantitas,
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quam dato tempore ejicit = n a √ α. </
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">Si utraque quantitas in ſummam conji-
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ciatur, habebitur ({2/3} α + a)n√α = q.</
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<
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">Ope hujus æquationis cognoſcitur q ex datis altitudinibus a & </
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viciſſim altitudo α ex cognitis quantitatibus a & </
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<
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">Convenire autem hanc æquationem admodum accurate cum experi-
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mentis, ipſe oſtendit celeberrimus eorum auctor, cujus ſolutio ab hâc no-
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ſtra non differt. </
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">Sequitur ex iſta æquatione, elevationes α eo majores eſſe pro
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iiſdem aquarum affuſionibus, quo minor eſt altitudo ſubmerſionis a.</
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<
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">deſcripto cum tubulo vitreo (Fig. </
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<
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obturavi orificium L M, tubumque R N aqua implevi, donec ſuper-
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ficies ejus raderet foraminulum in a: </
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fervavi extremitate attigiſſe punctum f: </
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">poſtea reſerato orificio L M, & </
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fluentibus novas affundebam in vas ſuperius E F P Q adhibita diligentia, ut
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extremitas aquæ in f interea nec aſcenderet nec deſcenderet. </
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