Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO DECIMA.
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di viribus motricibus, quarum fortaſſe plures novæ non ſine inſigni mechani-
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cæ practicæ incremento & </
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<
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">perfectione excogitari poterunt, movendis.</
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<
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xml:space
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">Ut incipiamus ab aëre in vacuo, conſiderabimus cylindrum ver-
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ticaliter poſitum A B C D (Fig. </
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<
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xml:space
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">62.) </
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<
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xml:space
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">cum ſuſtentaculo E F, quod omni pon-
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">Fig. 62.</
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dere deſtitutum liberrime ſurſum dèorſumque moveri poſſit. </
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<
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xml:space
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">Sit ſpatio E B C F
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aër incluſus, totus autem cylindrus in vacuo poſitus fingatur: </
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<
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">Sit preſſio aëris
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E B C F tanta qua ſuſtinere poſſit pondus p, quod æquale erit preſſioni colum-
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næ atmoſphæræ, ſi aër iſte ſit naturalis. </
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<
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xml:space
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">Superveniat jam aliud pondus P: </
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<
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">ita
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fiet ut operculum deſcendat in G H motibuſque reciprocis ad puncta H & </
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<
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">F
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agitetur. </
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<
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">Ut motum definiamus, utemur hypotheſi ordinaria, quod preſſio-
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nes aëris cæteris paribus ſint denſitatibus proportionales.</
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<
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xml:space
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">Fuerit itaque F C = a, F H = x; </
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<
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xml:space
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">velocitas ſuſtentaculi in ſitu G H = v,
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erit preſſio, qua ſuſtentaculum G H ad ulteriorem deſcenſum urgetur = P + p
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- {a/a - x} p, huicque preſſioni æqualis cenſenda eſt vis, quæ pondus ſuſtenta-
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culo incumbens animat; </
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<
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">igitur ſi hanc vim dividas per maſſam habebis vim
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accelerantem, quæ multiplicata per tempuſculum ſeu per {dx/v}, dabit incre-
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mentum velocitatis dv, eſt itaque
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dv = (P + p - {ap/a - x}) X {dx/v}: </
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xml:space
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">(P + p), vel
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{1/2} (P + p) vv = (P + p) x - ap log. </
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xml:space
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<
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xml:space
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">Sed ex deſcenſu ponderis (P + p) per altitudinem x generatur vis viva
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potentialis (P + p) x, & </
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<
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xml:space
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">cum ſuſtentaculum eſt in ſitu G H, ineſt corpori (P + p)
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vis viva actualis {1/2} (P + p) vv, id eſt, (P + p) x - ap log. </
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<
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xml:space
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">{a/a - x}, quæ à prio-
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ri deficit quantitate ap log. </
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<
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xml:space
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">{a/a - x}, hæcque in compreſſionem aëris tranſiit.</
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<
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xml:space
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">Dico itaque non poſſe aërem occupantem ſpatium a condenſari in ſpa-
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tium a - x, quin vis viva impendatur, quæ generatur ex deſcenſu ponderis
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p per altitudinem a log. </
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<
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xml:space
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">{a/a - x} quocunque modo illa compreſsio facta fuerit; </
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t
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eſt autem modis fieri infinitis. </
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<
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xml:space
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plo illuſtrabo.</
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