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

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10894HYDRODYNAMICÆ (M X {Nv/M} + ndx X o): (M + ndx) = {Nv/M + ndx}. Poſtquam vero particula
n d x ſuperne jam affuſa eſt, communem acquiſivit motum cum aqua proxi-
me inferiori, ſicque fit aſcenſus potentialis ejusdem aquæ in ſitu c d m l o n p i c
æqualis tertiæ proportionali ad ſpatium C D L O N P I C (M + ndx), ſpa-
tium D t u x y O L D (N + ndx) & altitudinem v + dv, id eſt, =
{(N + ndx) x (v + dv)/M + ndx}, cujus exceſſus ſupra priorem aſcenſum potentialem eſt =
{Ndv + nvdx + ndxdv/M + dx} =, rejectis differentialibus ſecundi ordinis, {Ndv + nvdx/M}.
Habetur igitur talis æquatio {Ndv + nvdx/M} = {nadx/M}, quæ ut prior per tra-
ctata & ad finem deducta dat
x = {N/n} log. {a/a - v}, vel
v = a X (1 - c {-nx/N})
quæ ſolutio valet pro affuſione laterali.

Scholion 1.

§. 4. Sunt hæ æquationes inter ſe admodum diverſæ; diverſitas au-
tem eo major quo minoris eſt amplitudinis vas; & ſi quidem amplitudo va-
ſis ſuprema in cd quaſi infinita ſit præ amplitudine foraminis, evaneſcit n
præ m fitque in priori caſu ſicut in poſteriori.
v = a X (1 - c{-n/N}x)
Eſt igitur hâc in hypotheſi motus utrobique idem quod haud difficulter
quisque prævidere potuerit. Celerior autem ſemper eſt cæteris paribus mo-
tus in priori affuſione, quam in altera.

Conveniet hic rem etiam phyſice explicare, ut eam diſtinctius in omni-
bus phænomenis percipere poſſimus.

Sit loco vaſis cujuſcunque & quamcunque directionem habentis bre-
vioris delineationis gratia cylindrus verticalis cum foramine in fundo, nempe
G H N D (Fig. 29.) ſitque dein vas E F P Q perforatum in R S; fingantur orifi-
11Fig. 29, cia RS & GD perfecte æqualia, & ad minimam diſtantiam ſibi perfecte

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