Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO QUARTA.
"/>
quiritur, ut in æquatione ultimâ paragraphi decimi ſexti ponatur {nne/mm} pro
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v, ſic autem erit
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{nne/mm} = {nn(a - z)/mm} - {nna/mm}:</
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xml:space
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preserve
">c{mz/nb}√{g/n}
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hincque deducitur {mz/nb}√{g/n} = log.</
s
>
<
s
xml:id
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xml:space
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">{a/a - e - z}; </
s
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<
s
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xml:space
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">hic vero cum e ponatur defice-
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re notabiliter ab a poteſt rejici littera z ſigno logarithmicali involuta, unde
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obtinetur
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z = {nb/m}√{n/g} X log.</
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<
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xml:space
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<
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">Hæc vero æquatio jam indicat ſpatiolum, quod eſt infinite parvum,
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& </
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<
s
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">per quod deſcendit ſuperficies aquæ, dum à quiete velocitas aquæ effluen-
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tis tanta ſit, quæ debeatur altitudini e; </
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>
<
s
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xml:space
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">ſeque habet hoc ſpatiolum ad illud pa-
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ragrapho decimo ſeptimo indicatum, quo nempe velocitas maxima oritur, ut
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log. </
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<
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xml:space
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">{a/a - e} ad log. </
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<
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xml:space
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">({ma/nb}√{g/n}) ita ut primum ſit infinities minus altero, etſi
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pariter infinite parvo.</
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<
s
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xml:space
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">Si porro definita quantitas z multiplicetur per m, obtinetur quantitas
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aquæ effluentis dum illa velocitas altitudini e debita producitur, quæ proin
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quantitas eſt æqualis
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nb√{n/g} X log.</
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xml:space
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">{a@/a - e}
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atque ſic finitæ magnitudinis, & </
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">quidem eo majoris, quo longior ſumitur tu-
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bus, & </
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">quo major jactus expectatur.</
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<
s
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">Denique tempus, quo idem fit, ſi recte ſeligantur termini rejiciendi,
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reperitur æquale
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2√({nbb/ag} log.</
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<
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atque ſic finitum ſed admodum parvum & </
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">in nullo exemplo ultra minutum ſe-
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cundum facile extendendum.</
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<
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">Hæc omnia accurate examinare ac proſequi volui, tum quod
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multorum phænomenorum, quæ in effluxu aquarum obſervari ſolent, ſolu-
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tio inde pendeat, tum etiam ut illas mutationes, quæ ſenſibus plane ſunt im-
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perceptibiles, animo recte aſſequeremur. </
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