Full text: Bernoulli, Daniel: Hydrodynamica s. de viribus et motibus fluidorum commentarii

SECTIO DECIMA. que ponatur pondus columnæ mercurii (cujus baſis eſt C D & cujus altitudo
eadem ſit quæ in barometro) = P. Utemur autem hypotheſi, ſive globus pro-
pellatur ab aëre condenſato ſive à pulveris pyrii aura, potentiam illius fluidi
propellentis proportionalem eſſe denſitati.

194.1.

Fig. 64.

His ad calculum præparatis, globum conſiderabimus in ſitu e, poneu-
do A c = x, velocitatemque globi in hoc ſitu = v, ſic erit potentia globum
in ſitu e propellens = ({nb/x} - 1) X P, quæ diviſa per maſſam 1 ductaque in ele-
mentum ſpatii d x dat incrementum dimidium quadrati velocitatis; unde fit v d v
= ({nb/x} - 1) X P d x, ſive {1/2} v v = (b - x + nb log. {x/b})P. Ponatur x = a,
habetur altitudo debita velocitati, quacum globus exploditur; vocetur iſta
altitudo α & erit
α = (b - a + nb log. {a/b}) X P.

(II) Sit v. gr. in ſclopeto pneumatico longitudo animæ ſeu a = 3 ped. Paris. longitudo A C = 4 poll. fueritque aër captus in A D naturali decies den-
ſior ſeu n = 10, diameter animæ ſeu globuli ejiciendi trium linearum ejus-
que gravitas ſpecifica ratione mercurii ut 10 ad 17. Erit P præterpropter =
286; indeque invenitur α = 2788, indicio globum ejectum iri velocitate
qua in vacuo ad altitudinem 2788 ped. aſcendere poſſit. Ex præcedente for-
mula colligitur jactum globi vehementiſſimum fore pro eadem auræ elaſticæ
quantitate, ſi longitudo animæ fiat = n b. Si vero animus ad impedimenta
alia, quæ globus præter inertiam ſuam & reſiſtentiam aëris externi in tranſitu
ſuo per Sclopeti animam patitur, advertatur, apparet longitudinem animæ
ad jactum vehementiſſimum producendum requiri longe minorem. Si longi-
tudo n b admodum major ſit longitudine a, quod ita eſt in jactibus fortiori-
bus, erit ſine ſenſibili errore α = n b P log. {a/b}.

Si tormentum ſit verticaliter erectum, fit aliquantum diverſus calculus
ſed pro vehementioribus jactibus differentia nequit eſſe ſenſibilis. Igitur quia
jactus deinceps conſiderabimus tantum vehementiſſimos, brevitatis ergo po-
nemus a = nb P X log. {a/b}.

(III) Prouti in præcedentibus altitudinem determinavimus debitam ve-

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer