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

Table of figures

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            <s xml:id="echoid-s3919" xml:space="preserve">Cum vero amplitudo foraminis rationem habet finitam ad amplitudi-
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            nem tubi, aſcenſus fit ultra ſuperficiem R S veluti usque in s t: </s>
            <s xml:id="echoid-s3920" xml:space="preserve">minor au-
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            tem ſemper erit Vt quam Vy, niſi cum omne fundum abeſt, tunc enim
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            erit V t = V y. </s>
            <s xml:id="echoid-s3921" xml:space="preserve">Prouti monuimus §. </s>
            <s xml:id="echoid-s3922" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3923" xml:space="preserve">in deſcenſu differentiam inter V Y & </s>
            <s xml:id="echoid-s3924" xml:space="preserve">
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            V y, proportionalem eſſe & </s>
            <s xml:id="echoid-s3925" xml:space="preserve">originem debere aſcenſui potentiali aquæ durante
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            deſcenſu ejectæ, ita nunc obſervari poteſt in aſcenſu differentiam inter V y
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            & </s>
            <s xml:id="echoid-s3926" xml:space="preserve">V t originem habere ab illiſione guttularum L o n P in maſſam aquæ ſu-
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            perjacentis, quæ quidem illiſio non promovet aſcenſum, ſed in inutilem mo-
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            tum inteſtinum impenditur, prouti indicatum fuit §. </s>
            <s xml:id="echoid-s3927" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3928" xml:space="preserve">Ergo cum omne
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            fundum I M abeſt, aqua tubum eadem velocitate ingreditur, qua jam gau-
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            det aqua tubum antea ingreſſa & </s>
            <s xml:id="echoid-s3929" xml:space="preserve">nulla fit colliſio, quæ cauſa eſt cur in iſto
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            caſu tantum aſcendat aqua ultra ſuperficiem R S, quantum fuerat infra il-
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            lam depreſſa, quod æquatio, uti mox videbimus, indicat.</s>
            <s xml:id="echoid-s3930" xml:space="preserve"/>
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            <s xml:id="echoid-s3931" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3932" xml:space="preserve">16. </s>
            <s xml:id="echoid-s3933" xml:space="preserve">Determinabitur maximus aſcenſus s t, faciendo v = o. </s>
            <s xml:id="echoid-s3934" xml:space="preserve">Igitur
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            ut motus omnis recte definiatur, alternatim adhibendæ erunt formulæ §. </s>
            <s xml:id="echoid-s3935" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3936" xml:space="preserve">3.
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            </s>
            <s xml:id="echoid-s3937" xml:space="preserve">& </s>
            <s xml:id="echoid-s3938" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3939" xml:space="preserve">erutæ, quod nunc hoc unico illuſtrabo exemplo, quo nn = 1.</s>
            <s xml:id="echoid-s3940" xml:space="preserve"/>
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            <s xml:id="echoid-s3941" xml:space="preserve">Si proinde nn = 1, fit v = b (1 - {α/ξ} - {1/2} (ξ - {αα/ξ}): </s>
            <s xml:id="echoid-s3942" xml:space="preserve">eritque
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            v = o, cum ſumitur ξ = 2b - α, id eſt, cum ſumitur V t = V y. </s>
            <s xml:id="echoid-s3943" xml:space="preserve">Igi-
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            tur ſi verbi gratia tubus A B M I aqua plenus, omnique fundo deſtitutus fue-
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            rit ad medietatem usque immerſus aquæ exteriori, atque tota ipſius longi-
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            tudo dicatur a, aqua ſic agitabitur ut primo infra T V deſcendat, ſpatio
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            o, 297a, deinde ſimili ſpatio ſuper eandem T V elevetur, rurſusque infra eam
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            deprimatur ſpatio o, 240a, eodemque lineam illam iterum tranſcendat, & </s>
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            ſic porro.</s>
            <s xml:id="echoid-s3945" xml:space="preserve"/>
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            <s xml:id="echoid-s3946" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3947" xml:space="preserve">17. </s>
            <s xml:id="echoid-s3948" xml:space="preserve">Patet etiam cum α eſt = o, tubo ſcilicet ab omni aqua va-
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            cuo, fore generaliter v = {b/nn} - {ξ/nn + 1}: </s>
            <s xml:id="echoid-s3949" xml:space="preserve">aſcenſumquè integrum conſequen-
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            ter fore {nn + 1/nn}b vel aſcenſum ſupra ſuperficiem exteriorem aquæ = {b/nn}.</s>
            <s xml:id="echoid-s3950" xml:space="preserve"/>
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            <s xml:id="echoid-s3951" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3952" xml:space="preserve">18. </s>
            <s xml:id="echoid-s3953" xml:space="preserve">Venio nunc ad tubos infinite ſubmerſos, in quibus deſcenſum
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            cum ſuis affectionibus determinavimus §. </s>
            <s xml:id="echoid-s3954" xml:space="preserve">10. </s>
            <s xml:id="echoid-s3955" xml:space="preserve">Utemur autem eadem plane
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            methodo ad hunc caſum definiendum quâ ibi uſi ſumus: </s>
            <s xml:id="echoid-s3956" xml:space="preserve">erit nobis igitur
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            depreſſio initialis V y(= b - α) = c, aſcenſus inde factus y d (= ξ - α) = z.</s>
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