Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ
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<
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<
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">elevatio indicata per c unius pollicis, immerſio cylindri b
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80. </
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<
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<
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<
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<
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xml:space
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">dein ponatur diameter tubi tripla diametri forami-
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nis, id eſt, nn = 81, erit v = {2 - z - 2α
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/nn}, atque ſi porro ponatur
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z = c = 1, ut habeatur altitudo velocitatis, cum utraque ſuperficies eſt ad
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libellam poſita, erit v = {α - 2/nnα}, id eſt, proxime v = {1/307} poll. </
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<
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xml:space
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">cum ſecundum
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paragraphum decimum debuiſſet oriri v = {1/162} poll. </
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<
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">& </
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<
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">ſecundum paragraphum
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quartum v = o. </
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">In eodem exemplo fit ſpatium integrum, quod ſuperficies
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percurrit non omnino octo quintarum partium unius pollicis, locusque
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maximæ velocitatis eſt præterpropter ſexaginta novem centeſimarum partium
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ejusdem menſuræ infra altitudinem initialem.</
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<
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">Non difficilius eſſet ad omnes vaſorum figuras extendere, quæ
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hactenus dicta ſunt, imo etiam ad ſpatia finita, quibus aqua externa deter-
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minetur: </
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<
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">fiunt autem formulæ plerumque adeo prolixæ, ut conſultius du-
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xerim easdem ſilentio præterire, & </
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<
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">ſpecimine ſaltem aliquo particularem oſten-
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dere modum, quo theoria ad quoslibet caſus alios eruendos applicanda ſit.</
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<
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">Attentionem particulariorem merentur, quæ de motu aquarum in tu-
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bis inferius largiter apertis, & </
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<
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">profundiſſime ſubmerſis indicavi, quia in his
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motus oſcillatorius, ut in pendulis, conſtantis durationis eſt, & </
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">undarum
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in mari fluxus illuſtratur ab illis. </
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">Exiſtimavi autem prius de refluxu aquarum
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in cylindris ſubmerſis generaliter tractandum eſſe, atque oſtendendum in iſta
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hypotheſi refluxum non differre à præcedente fluxu, quam motus totus
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oſcillatorius examinetur. </
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<
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">Jam igitur de iſto refluxu commentabimur, dein-
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ceps utrumque motum in diverſis caſibus combinaturi, ne aliquid in argu-
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mento deſiderari poſſit.</
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<
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">Poſtquam aquæ deſcenderunt in vaſe ſubmerſo, quantum id
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ipſis natura rei permittit, duo potiſſimum conſideranda ſe offerunt; </
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<
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exceſſus altitudinis ſuperficiei externæ ſupra internam & </
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<
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">ſecundo vis viva ſeu
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productum ex aſcenſu potentiali in maſſam illius aquæ, quæ ex cylindro in </
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