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

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10793SECTIO QUINTA.
Debet vero iſtud incrementum æquari deſcenſui actuali centri gravitatis;
Atqui iſte deſcenſus, poſita D L = a, eſt per paragraphum ſeptimum ſect. 3.
= {nadx/M}; habetur igitur talis æquatio
{N/M}dv - {n3/mmM}vdx + {n/M}vdx = {nadx/M}, ſeu
dx = Ndv: (na - nv + {n3/mm} v);
Hæc vero ſi ita integretur, ut v & x ſimul evaneſcant, dat
x = {mmN/n3 - nmm} log. {mma - mmv + nnv/mma}
quæ æquatio, poſito c pro numero cujus logarithmus eſt unitas, æquivalet
huic @alteri
v = {mma/mm - nn} X (1 - c{n3 - nmm/mmN} x)
Hæc vero ſolutio quadrat pro caſu primo, ubi aqua ſuperne motu af-
ſunditur communi cum deſcenſu ſuperficiei proximæ.

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