Galilei, Galileo - Discourse concerning the natation of bodies

Galilei, Galileo, Discourse concerning the natation of bodies, 1663

That is to ſay, that by how much the one is leſs grave than the other,
by ſo much is it in a conſtitution of moving more ſwiftly than that.

Having prefatically explicated theſe things, we may begin to en
quire, what Bodyes thoſe are which totally ſubmerge in Water, and
go to the Bottom, and which thoſe that by conſtraint float on the
top, ſo that being thruſt by violence under Water, they return to
ſwim, with one part of their Maſs viſible above the Surface of the
Water: and this we will do by conſidering the reſpective operati
on of the ſaid Solids, and of Water: Which operation followes
the Submerſion and ſinking; and this it is, That in the Submerſion

that the Solid maketh, being depreſſed downwards by its proper
Gravity, it comes to drive away the water from the place where it
ſucceſſively ſubenters, and the water repulſed riſeth and aſcends
above its firſt levell, to which Aſcent on the other ſide it, as being a
grave Body of its own nature, reſiſts: And becauſe the deſcending
Solid more and more immerging, greater and greater quantity of
Water aſcends, till the whole Sollid be ſubmerged; its neceſſary to
compare the Moments of the Reſiſtance of the water to Aſcenſion,
with the Moments of the preſſive Gravity of the Solid: And if the
Moments of the Reſiſtance of the water, ſhall equalize the Moments

of the Solid, before its totall Immerſion; in this caſe doubtleſs there
ſhall be made an Equilibrium, nor ſhall the Body ſink any farther.
But if the Moment of the Solid, ſhall alwayes exceed the Moments

wherewith the repulſed water ſucceſſively makes Reſiſtance, that
Solid ſhall not only wholly ſubmerge under water, but ſhall deſcend
to the Bottom. But if, laſtly, in the inſtant of totall Submerſion,

the equality ſhall be made between the Moments of the prement
Solid, and the reſiſting Water; then ſhall reſt enſue, and the ſaid
Solid ſhall be able to reſt indifferently, in whatſoever part of the
water. By this time is manifeſt the neceſſity of comparing the

Gravity of the water, and of the Solid; and this compariſon might
at firſt ſight ſeem ſufficient to conclude and determine which are the
Solids that float a-top, and which thoſe that ſink to the Bottom in the
water, aſſerting that thoſe ſhall float which are leſſe grave in ſpecie
than the water, and thoſe ſubmerge, which are in ſpecie more grave.
For it ſeems in appearance, that the Sollid in ſinking continually,
raiſeth ſo much Water in Maſs, as anſwers to the parts of its own
Bulk ſubmerged: whereupon it is impoſſible, that a Solid leſs grave
in ſpecie, than water, ſhould wholly ſink, as being unable to raiſe a
weight greater than its own, and ſuch would a Maſs of water equall
to its own Maſs be. And likewiſe it ſeems neceſſary, that the graver
Solids do go to the Bottom, as being of a Force more than ſufficient
for the raiſing a Maſſe of water, equall to its own, though inferiour
in weight. Nevertheleſs the buſineſs ſucceeds otherwiſe: and

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