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

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146132HYDRODYNAMICÆ

Fuerit v. gr. elevatio indicata per c unius pollicis, immerſio cylindri b
80. poll. ipſaque a 81. poll. dein ponatur diameter tubi tripla diametri forami-
nis, id eſt, nn = 81, erit v = {2 - z - 2α- z/nn}, atque ſi porro ponatur
z = c = 1, ut habeatur altitudo velocitatis, cum utraque ſuperficies eſt ad
libellam poſita, erit v = {α - 2/nnα}, id eſt, proxime v = {1/307} poll. cum ſecundum
paragraphum decimum debuiſſet oriri v = {1/162} poll. & ſecundum paragraphum
quartum v = o. In eodem exemplo fit ſpatium integrum, quod ſuperficies
percurrit non omnino octo quintarum partium unius pollicis, locusque
maximæ velocitatis eſt præterpropter ſexaginta novem centeſimarum partium
ejusdem menſuræ infra altitudinem initialem.

§. 12. Non difficilius eſſet ad omnes vaſorum figuras extendere, quæ
hactenus dicta ſunt, imo etiam ad ſpatia finita, quibus aqua externa deter-
minetur: fiunt autem formulæ plerumque adeo prolixæ, ut conſultius du-
xerim easdem ſilentio præterire, & ſpecimine ſaltem aliquo particularem oſten-
dere modum, quo theoria ad quoslibet caſus alios eruendos applicanda ſit.

Attentionem particulariorem merentur, quæ de motu aquarum in tu-
bis inferius largiter apertis, & profundiſſime ſubmerſis indicavi, quia in his
motus oſcillatorius, ut in pendulis, conſtantis durationis eſt, & undarum
in mari fluxus illuſtratur ab illis. Exiſtimavi autem prius de refluxu aquarum
in cylindris ſubmerſis generaliter tractandum eſſe, atque oſtendendum in iſta
hypotheſi refluxum non differre à præcedente fluxu, quam motus totus
oſcillatorius examinetur. Jam igitur de iſto refluxu commentabimur, dein-
ceps utrumque motum in diverſis caſibus combinaturi, ne aliquid in argu-
mento deſiderari poſſit.

PARS SECUNDA.

De aſcenſu aquarum.

§. 13. Poſtquam aquæ deſcenderunt in vaſe ſubmerſo, quantum id
ipſis natura rei permittit, duo potiſſimum conſideranda ſe offerunt; primo
exceſſus altitudinis ſuperficiei externæ ſupra internam & ſecundo vis viva ſeu
productum ex aſcenſu potentiali in maſſam illius aquæ, quæ ex cylindro in

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