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

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11298HYDRODYNAMICÆ ctum in motum aquarum exerere debeat, quiſque videt ex eo, quod in utro-
que modo omnis aquæ tubum ingredientis inertia ſit ab aqua inferiore ſupe-
randa. Sed idem etiam à priori demonſtrari poterit inquirendo in motum, qui
inde oriri debeat, ſecundum æquationem paragraphi octavi Sect. III. quæ hæc eſt:
Ndv - {mmvydx/nn} + {mmvdx/y} = - yxdx;
accommodabitur autem ad præſentem caſum, ſi pro m, x & - d x ſubſtituas re-
ſpective n, a, & {ndx/y}, (cujus rei ratio patebit, ſi hæc cum illis contuleris) ſi-
mulque y infinitum ponas; tunc enim evaneſcit tertius æquationis terminus,
fitque omnino, ut pro præſenti negotio ſupra invenimus,
Ndv + nvdx = nadx.

Poſtquam in his ſcholiis motus utriuſque indolem, quantum ſimplexrei
conſideratio phyſica permittit, eorumque differentiam oſtendimus, ſimulque
modum illos producendi ad legem hypotheſeos mechanicum tradidimus, ſu-
pereſt, ut reliqua phænomena notabiliora etiam indicentur, quod nunc faciam.

Corollarium 1.

§. 8. Si in vaſe R S N H omnè fundum abſit, erit orificium L M =
orificio R S; poteſt etiam hoc ab illo ſuperari, ſi nempe vaſis divergant late-
ra. In his autem caſibus nullum habet terminum altitudo v in æquatione
v = {mma/mm - nn} X (1 - c{n3 - nmm/mmN} x)
& fit infinita, ſi quantitas aquæ ejectæ indicata per n x eſt infinita.

Id quidem per ſe patet ex æquatione, cum n eſt major quam m; at
cum amplitudines orificiorum ſunt æquales, recurrendum eſt ad æquationem
differentialem paragraphi tertii, ex qua iſta æquatio proxima deducta fuit, nempe
{N/M}dv - {n3/mmM}vdx + {n/M}vdx = {n/M}adx,
quæ poſito n = m dat N d v = n a d x, id eſt, v = {nax/N}, ubi v fit manifeſte in-
finita ſi x eſt infinita.

§. 9. Sin autem vaſi propoſito fundum ſit, atque in eo foramen,

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