Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ.
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<
s
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xml:space
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">Denique punctum E maximo reſpondens deſcenſui obtinetur ope hu-
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jus æquationis,
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ξ - αlog.</
s
>
<
s
xml:id
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echoid-s1288
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xml:space
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">ξ = β - αlog.</
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>
<
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xml:space
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">β</
s
>
</
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<
s
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xml:space
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preserve
">Alter caſus ſeorſim ſubducendus calculo eſt, cum mm = 2nn, ubi
<
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oritur
<
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v = {αξ - αβ - ξβlog.</
s
>
<
s
xml:id
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echoid-s1291
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xml:space
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">ξ + ξβlog.</
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>
<
s
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xml:space
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">β/gβ}
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atque ſi capiatur, poſito c pro numero, cujus logarithmus eſt unitas,
<
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ξ = c
<
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">{α - β/β}</
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>
β determinabitur ſic locus maximæ velocitatis, cujus altitudo
<
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generatrix eſt = c
<
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style
="
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">{α - β/β}</
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>
β - α, dum maximus deſcenſus, qui proportiona-
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lis eſt toti aquæ effluenti, definitur faciendo
<
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αξ - αβ - ξβlog.</
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>
<
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xml:id
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echoid-s1293
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xml:space
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">ξ + ξβlog.</
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>
<
s
xml:id
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xml:space
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">β = o</
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>
</
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<
s
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xml:space
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">Non dubito, quin hæc ad amuſſim experientiæ eſſent reſponſura, ſi
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modo adhæſio aquæ ad latera tubi motum non retardaret; </
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<
s
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xml:space
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">puto tamen, even-
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tum experimentorum talem eſſe poſſe, ut intelligenti, qui horum impedi-
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mentorum rationem habeat, ſatis @ſtendant propoſitionum veritatem.</
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<
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xml:space
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">Ultimo loco communicabo veram ſolutionem phænomeni ali-
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cujus, quod primo aſpectu valde videtur paradoxon. </
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<
s
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xml:space
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">Poſtquam enim ex
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omnibus hactenus dictis luculenter apparet fieri non poſſe, ut aquæ multo
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majori velocitate effluant quam qualis altitudini aquæ ſupra foramen debetur,
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(poſſunt tamen aliquanto majori, præſertim ſi foramina ſunt magna, con-
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fer ea quæ dixi de velocitatibus maximis §. </
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<
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">16.) </
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<
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xml:space
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">multis mirum fortaſſe videbitur,
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contingere aliquando in fontibus ſalientibus, ut aqua ad temporis momen-
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ium jactum faciat longe altiorem, quam ſecundum regulas noſtras fieri poſſe
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videtur. </
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<
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xml:space
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">Verum tantum abeſt, ut hæ inde aliquid roboris perdant, quin
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potius egregie confirmentur. </
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<
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xml:space
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">Solutio autem paradoxi in eo conſiſtit, quod
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nos hactenus aquas conſideraverimus continuas, & </
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tas: </
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<
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>
. </
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<
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xml:space
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">De la Hire non fieri hujusmodi ſaltus irrregu-
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lares, niſi aër una cum aqua tubum prope ſcaturiginem fuerit ingreſſus,
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quod ſæpe fieri indicavi §. </
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<
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<
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xml:space
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">Iſte vero aër ſimul cum aqua fertur usque ad
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orificium effluxus, per quod mox erumpit: </
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<
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xml:space
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">id dum fit, maſſa aquea </
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