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

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6753SECTIO TERTIA.

Experimenta quæ ad Sect. 3. pertinent.

Prænotanda.

PLurima quidem ſunt in hâc Sectione eaque fere præcipua, quæ vix
ad experimenta revocari immediate poſſunt; Etenim cum Auctores ha-
ctenus motum in fluidis effluentibus alium non conſideraverint,
quam qui fiunt per foramina valde parva, cumque proin nova ſit theoria
quam dedimus pro amplitudinibus foraminum qualibuscunque, hæc ipſa
eſt, cujus confirmatio maxime juvaret. At non video, quomodo in Cy-
lindris verticalibus, de quibus potiſſimum egimus, velocitas aquæ effluen-
tis obſervari poſſit, præſertim cum foramen eſt valde amplum (ſecus enim
ex tempore depletionis aliquod de velocitatibus judicium ferri poteſt.) Hæc
ita perpendens cogitavi demum ſcopo noſtro inſervire poſſe paragraphos 16.
& 20. in quorum priore determinata fuit velocitas maxima aquæ effluentis
ex cylindris verticaliter poſitis, in altero autem demonſtratum eſt, eundem
eſſe motum ex cylindris oblique poſitis & verticalibus, ſi utrobique altitudi-
nes verticales ſimiles aſſumantur: Commode igitur utemur cylindris oblique
poſitis, ut ex maxima amplitudine jactus aquei poſſit velocitas maxima aquæ
ſeu altitudo eidem debita experimento haberi: & hâc quidem ratione accu-
rate velocitas illa maxima, qualis revera eſt, explorari poteſt, etiamſi ſo-
ramina ſint quantumlibet magna, quæ proin ſi convenire obſervetur cum re-
gulis noſtris, de integra theoria dubium ſupereſſe nullum poterit.

Priusquam vero rem ipſam aggrediar, præmittendum erit theorema
mechanicum, quod ſequitur.

Lemma.

Sit A B (Fig. 21.) linea verticalis, B D horizontalis; linea autem A D
11Fig. 21. directionem habeat qualemcunque, ſub cujus directione corpus in A proje-
ctum intelligatur, arcum deſcribens parabolium A C, cujus nempe tangens
in A eſt recta A D, erit altitudo debita velocitati, qua corpus in A proje-
ctum fuit, = {BC2 X AD2/4AB. BD. CD} atque ſi AD fuerit horizontalis ſive angulus B A D
rectus, erit eadem illa altitudo = {BC2/4AB}.

Jam vero quæ mihi obſervata fuerint exponam.

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Scan	Original
91	77
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93	79
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95	81
96	82
97	83
98	84
99	85
100	86
101	87
102	88
103	89
104
105	91
106	92
107	93
108	94
109	95
110	96
111	97
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119	105
120	106