Galilei, Galileo - Discourse concerning the natation of bodies

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

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A Rule to equi
librate Solids in
the water.

It followes, moreover, that a Solid leſs grave than the water, being put
into a Veſſell of any imaginable greatneſs, and water being circumfuſed
about it to ſuch a height, that as much water in Maſs, as is the part of
the Solid ſubmerged, doth/> weigh abſolutely as much as the whole Solid;
it ſhall by that water be juſtly ſuſtained, be the circumfuſed Water in
quantity greater or leſſer.

For, if the Cylinder or Priſme M, leſs grave than the water, v.
gra. in Subſequiteriall proportion, ſhall be put into the capaci
ous Veſſell A B C D, and the water raiſed about it, to three
quarters of its height, namely, to its Levell A D: it ſhall be ſuſtained
and exactly poyſed in Equi
librium. The ſame will hap
pen, if the Veſſell E N S F

[Figure 6]

were very ſmall, ſo, that be
tween the Veſſell and the So
lid M, there were but a very
narrow ſpace, and only capable of ſo much water, as the hundredth
part of the Maſs M, by which it ſhould be likewiſe raiſed and erected,
as before it had been elevated to three fourths of the height of the
Solid: which to many at the firſt ſight, may ſeem a notable Paradox,
and beget a conceit, that the Demonſtration of theſe effects, were
ſophiſticall and fallacious: but, for thoſe who ſo repute it, the Ex
periment is a means that may fully ſatisfie them. But he that ſhall
but comprehend of what Importance Velocity of Motion is, and how
it exactly compenſates the defectus and want of Gravity, will ceaſe to
wonder, in conſidering that at the elevation of the Solid M, the great
Maſs of water A B C D abateth very little, but the little Maſs of
water E N S F decreaſeth very much, and in an inſtant, as the Solid
M before did liſe, howbeit for a very ſhort ſpace: Whereupon the
Moment, compounded of the ſmall Abſolute Gravity of the water
E N S F, and of its great Velocity in ebbing, equalizeth the Force and
and Moment, that reſults from the compoſicion of the immenſe Gra
vity of the water A B C D, with its great ſlowneſſe of ebbing;
ſince that in the Elevation of the Sollid M, the abaſement of the leſ

ſer water E S, is performed juſt ſo much more ſwiftly than the great
Maſs of water A C, as this is more in Maſs than that which we thus
demonſtrate.

T he proportion
according to
which water ri
ſeth and falls in
different Veſſels
at the Immerſi
on and Elevati
on of solids.

In the riſing of the Solid M, its elevation hath the ſame proportion
to the circumfuſed water E N S F, that the Surface of the ſaid water,
hath to the Superficies or Baſe of the ſaid Solid M; which Baſe hath
the ſame proportion to the Surface of the water A D, that the abaſe

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