COROLLARY II.
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.
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.
The 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 Motion 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.
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 ship flotes as well in ten Tun of Water as in an Ocean. a great abundance of water, then in a lesser quantity, (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.
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