That is to say, that by how much the one is less grave than the other, by so much is it in a constitution of moving more swiftly than that.
Having prefatically explicated these things, we may begin to enquire, what Bodyes those are which totally submerge in Water, and go to the Bottom, and which those that by constraint float on the top, so that being thrust by violence under Water, they return to swim, with one part of their Mass visible above the Surface of the Water: and this we will do by considering the respective operation of the said Solids, and of Water: Which operation followes the Submersion and sinking; and this it is, How the submersion of Solids in the water is effected.That in the Submersion that the Solid maketh, being depressed downwards by its proper Gravity, it comes to drive away the water from the place where it successively subenters, and the water repulsed riseth and ascends above its first levell, to which Ascent on the other side it, as being a grave Body of its own nature, resists: And because the descending Solid more and more immerging, greater and greater quantity of Water ascends, till the whole Sollid be submerged; its necessary to compare the Moments of the Resistance of the water to Ascension, with the Moments of the pressive Gravity of the Solid: What Solids shall float on the Water.And if the Moments of the Resistance of the water, shall equalize the Moments of the Solid, before its totall Immersion; in this case doubtless there shall be made an Equilibrium, nor shall the Body sink any farther. What Solids shall sinke to the botome.But if the Moment of the Solid, shall alwayes exceed the Moments wherewith the repulsed water successively makes Resistance, that Solid shall not only wholly submerge under water, but shall descend to the Bottom. What Solids shall rest in all places of the Water.But if, lastly, in the instant of totall Submersion, the equality shall be made between the Moments of the prement Solid, and the resisting Water; then shall rest, ensue, and the said Solid shall be able to rest indifferently, in whatsoever part of the water. The Gravitie of the Water and Solid must be compared in all Problems of Natation of BodiesBy this time is manifest the necessity of comparing the Gravity of the water, and of the Solid; and this comparison might at first sight seem sufficient to conclude and determine which are the Solids that float a-top, and which those that sink to the Bottom in the water, asserting that those shall float which are lesse grave in specie than the water, and those submerge, which are in specie more grave. For it seems in appearance, that the Sollid in sinking continually, raiseth so much Water in Mass, as answers to the parts of its own Bulk submerged: whereupon it is impossible, that a Solid less grave in specie than water, should wholly sink, as being unable to raise a weight greater than its own, and such would a Mass of water equall to its own Mass be. And likewise it seems necessary, that the graver solids do go to the Bottom, as being of a Force more than sufficient for the raising a Masse of water, equall to its own, though inferiour in weight. Nevertheless the business succeeds otherwise: andthough
