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

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A Rule to equi­
librate Solids in
the water.
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: /permanent/archimedes/galil_natat_074_en_1663/figures not scanned
[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
The proportion
according to
which water ri­
ſeth and falls in
different Veſſels
at the Immerſi­
on and Elevati­
on of solids.

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