[Sidenote: _A_ Rule to equilibrate 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, do 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._
[Illustration]
For, if the Cylinder or Prisme M, less grave than the water, _v. gra._
in Subsequiteriall proportion, shall be put into the capacious 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 _Equilibrium_. The same will happen; if the Vessell E N S F
were very small, so, that between the Vessell and the Solid 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 Experiment 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 defect 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 rise, 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 composition of the immense Gravity 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 lesser 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.
[Sidenote: _T_he proportion according to which water riseth and
falls in different Vessels at the Immersion and Elevation 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
abasement or ebbing of the water A C, hath to the rise or elevation of
the said Solid M. Therefore, by Perturbation of proportion, in the
ascent of the said Solid M, the abasement of the water A B C D, to the
abasement of the water E N S F, hath the same proportion, that the
Surface of the water E F, hath to the Surface of the water A D; that
is, that the whole Mass of the water E N S F, hath to the whole Mass A
B C D, being equally high: It is manifest, therefore, that in the
expulsion and elevation of the Solid M, the water E N S F shall exceed
in Velocity of _M_otion the water A B C D, asmuch as it on the other
side is exceeded by that in quantity: whereupon their Moments in such
operations, are mutually equall.
[Illustration]
_And, for ampler confirmation, and clearer explication of this, let
us consider the present Figure, (which if I be not deceived, may
serve to detect the errors of some Practick Mechanitians who upon a
false foundation some times attempt impossible enterprizes,) in
which, unto the large Vessell E I D F, the narrow Funnell or Pipe I
C A B is continued, and suppose water infused into them, unto the
Levell L G H, which water shall rest in this position, not without
admiration in some, who cannot conceive how it can be, that the
heavie charge of the great Mass of water G D, pressing downwards,
should not elevate and repulse the little quantity of the other,
contained in the Funnell or Pipe C L, by which the descent of it is
resisted and hindered: But such wonder shall cease, if we begin to
suppose the water G D to be abased only to Q D, and shall
afterwards consider, what the water C L hath done, which to give
place to the other, which is descended from the Levell G H, to the
Levell Q O, shall of necessity have ascended in the same time, from
the Levell L unto A B. And the ascent L B, shall be so much greater
than the descent G Q, by how much the breadth of the Vessell G D,
is greater than that of the Funnell I C; which, in summe, is as
much as the water G D, is more than the water L C: but in regard
that the Moment of the Velocity of the Motion, in one Moveable,
compensates that of the Gravity of another what wonder is it, if
the swift ascent of the lesser Water C L, shall resist the slow
descent of the greater G D?_
The same, therefore, happens in this operation, as in rhe Stilliard,
in which a weight of two pounds counterpoyseth an other of 200,
asoften as that shall move in the same time, a space 100 times greater
than this: which falleth out when one Arme of the Beam is an hundred
times as long as the other. Let the erroneous opinion of those
therefore cease, who hold that a Ship is better, and easier born up in
a great abundance of water, then in a lesser quantity[13], (_this was
believed by_ Aristotle _in his Problems, Sect. 23, Probl. 2._) it being
on the contrary true, that its possible, that a Ship may as well float
in ten Tun of water, as in an Ocean.
[13] A ship flotes as well in ten Tun of Water as in an Ocean.
[Sidenote: A Solid specifiaclly graver than the water, cannot be
born up by any quantity of it.]
But following our matter, I say, that by what hath been hitherto
demonstrated, we may understand how, that