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: and though the Conclusions are true, yet are the Causes thus assigned deficient, nor is it true, that the Solid in submerging, raiseth and repulseth Masses of Water, equall to the parts of it self submerged; but the Water repulsed, is alwayes less than the parts of the Solid submerged[11]: and so much the more by how much the Vessell in which the Water is contained is narrower: in such manner that it hinders not, but that a Solid may submerge all under Water, without raising so much Water in Mass, as would equall the tenth or twentieth part of its own Bulk: like as on the contrary, a very small quantity of Water, may raise a very great Solid Mass[12], though such Solid should weigh absolutely a hundred times as much, or more, than the said Water, if so be that the Matter of that same Solid be _in specie_ less grave than the Water. And thus a great Beam, as suppose of a 1000 weight, may be raised and born afloat by Water, which weighs not 50: and this happens when the Moment of the Water is compensated by the Velocity of its Motion. [6] How the submersion of Solids in the Water, is effected. [7] What Solids shall float on the Water. [8] What Solids shall sinke to the botome. [9] What Solids shall rest in all places of the Water. [10] The Gravitie of the Water and Solid must be compared in all Problems, of Natation of Bodies. [11] The water repelled is ever less than the parts of the Sollid submerged. [12] _A_ small quantity of water, may float a very great Solid Mass. But because such things, propounded thus in abstract, are somewhat difficult to be comprehended, it would be good to demonstrate them by particular examples; and for facility of demonstration, we will suppose the Vessels in which we are to put the Water, and place the Solids, to be inviron'd and included with sides erected perpendicular to the Plane of the Horizon, and the Solid that is to be put into such vessell to be either a streight Cylinder, or else an upright Prisme. _The which proposed and declared, I proceed to demonstrate the truth of what hath been hinted, forming the ensuing Theoreme._ _THEOREME I._ [Sidenote: The Proportion of the water raised to the Solid submerged.]