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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Scan	Original
101	87
102	88
103	89
104
105	91
106	92
107	93
108	94
109	95
110	96
111	97
112	98
113	99
114	100
115	101
116	102
117	103
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119	105
120	106
121	107
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