Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO SEXTA.
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v = {(b - β + f - φ) gx - ({bg/2a} + {bgg/2αγ)} xx/ga - gx + {αgg/γ} + {g
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/γ} {x/γ} + MN} Q.</
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<
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<
s
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xml:space
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">Quia linea mn = mg - nh + gh = h - β + f - m, ponemus
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mn = c, ſimulque multiplicabimus denominatorem & </
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2γγαα: </
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v = {2gγγaαcx - (gγγαb + ggγaß)xx/2gγγaaα - 2gγγaαx + 2ggγaαα + 2g
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aαx + 2γγaαMN}</
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<
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<
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">Si fiat v =o, patet tunc valorem x denotare totam fluidi ſuper-
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ficiei excurſionem in tubo ac, quæ ſic invenitur æqualis {2γaαc/γαb + gαβ}, in altero
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vero tubo fit = {2gaαc/γαb + gαβ}.</
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">Igitur poterit aqua in tubo ſtrictiori ad quamcunque elevari altitudi-
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nem, ſi modo ratio amplitudinum g & </
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">Pars illa vaſis c A d, quam neutra ſuperficierum unquam attin-
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gi ponimus, nihil pertinet ad iſtas fluidi excurſiones ſive augendas ſive dimi-
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nuendas: </
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">facere tamen poteſt, ut inferius oſtendetur, ad accelerandas retar-
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dandaſque oſcillationes.</
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<
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">Ponatur uterque tubus communis amplitudinis, erit, poſito
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nempe g = γ,
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v = 2gaαcx - (gαb + gaβ)xx/2gaaα + 2gaαα + 2aαMN}.</
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<
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">In hoc caſu maxima ſuperficiei utriuſque velocitas eſt, cum in medio
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totius excurſionis poſitæ ſunt, ſecus ac fit, cum tubi ſunt inæqualis amplitu-
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dinis.</
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