Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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catum fuit, in æquatione paragraphi decimi ponendum x = o, ſint
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unsure
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ulque
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ſolus primus ſeriei terminus adhibendus rurſusque ponendum m α pro
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√(mmαα - 2nn); </
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<
s
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echoid-s1907
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xml:space
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">atque ſic fit
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t = {2mα/n}√a.</
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<
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<
s
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echoid-s1909
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xml:space
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">Tum denique tempus, quod impenditur in deſcenſum ſuperficiei per
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altitudinem a - c exprimetur in ſimili hypotheſi hac æquatione
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t = {2ma/n} (√a - √c).</
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<
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echoid-s1910
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">}</
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<
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echoid-s1911
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xml:space
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">§. </
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">14. </
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">Præmiſſæ æquationes non accurate quidem, proxime tamen
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ſatisfacient, cum vas non infinitæ, permagnæ tamen amplitudinis eſt: </
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<
s
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echoid-s1914
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xml:space
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">imo
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non multum admodum defie
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ient, cum numerus m vel mediocriter ſuperat
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numerum n. </
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<
s
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echoid-s1915
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xml:space
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">Liceat quædam hic verba adjicere circa experimentum quod in
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fine paragraphi undecimi indicavi, deturque hæc venia inſtituto noſtro,
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quod in phænomenis motuum experientia cognitis potiſſimum verſatur il-
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luſtrandis examinandisque. </
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<
s
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echoid-s1916
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xml:space
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preserve
">Dixi autem in citato paragrapho cum aqua ho-
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rizontaliter effluit, primam guttulam totam ſtatim obtinere amplitudinem
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jactus; </
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<
s
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echoid-s1917
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xml:space
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">atque idem hoc quidem indicat theoria pro vaſis ampliſſimis; </
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<
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echoid-s1918
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xml:space
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">at ve-
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ro in vaſis mediocriter amplis, quædam guttulæ minori impetu effluere de-
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berent, priusquam punctum maximæ velocitatis adſit, hæque guttulæ in-
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cidere deberent in locum aliquem medium inter maximum jactum & </
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<
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echoid-s1919
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xml:space
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">pun-
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ctum, quod foramini verticaliter reſpondet; </
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<
s
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echoid-s1920
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xml:space
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preserve
">atque hoc etiam ita fieri ob-
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ſervavi, ex vaſis amplitudinis veluti decies foramine majoris. </
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<
s
xml:id
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echoid-s1921
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xml:space
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preserve
">Verum cum
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experimentum aliquando ſumerem de vaſe pedem dimidium alto, quod am-
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plitudinem præter propter centuplam haberet foraminis, ne minima quidem
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particula aquæ, quantum videre potui, notabiliter à jactu aquæ pleno de-
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fecit. </
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<
s
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echoid-s1922
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xml:space
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">Videamus itaque quænam aquæ quantitas in hoc caſu effluere deberet
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ante punctum maximæ velocitatis; </
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<
s
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echoid-s1923
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xml:space
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">erit autem tanta, quantam continet cy-
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lindrus ejusdem amplitudinis in altitudine
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a - a: </
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<
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">({mmαα - nn/nn})
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(vid. </
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<
s
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echoid-s1930
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xml:space
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">nec differt fere hæc minima altitudo ab hac multo com-
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pendioſiori, nempe {2nna/mmαα} log. </
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<
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echoid-s1931
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">{mα/n} (vid. </
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<
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">11.) </
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<
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