Page:Discourse Concerning the Natation of Bodies.djvu/18

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, 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 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 abase-ment