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Natation Of Bodies

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mit a Board of Ebony into the Water, you do not put therein a Solid more grave in specie than the Water, but one lighter, for besides the Ebony, there is in the Water a Mass of Air, united with the Ebony, and such, and so light, that of both there results a Composition less grave than the Water: See, therefore, that you remove the Air, and put the Ebony alone into the Water, for so you shall immerge a Solid more grave then the Water, and if this shall not go to the Bottom, you have well Philosophized, and I ill.

Now, since we have found the true Cause of the Natation of those Bodies, which otherwise as being graver than the Water, would descend to the bottom, I think, that for the perfect and distinct knowledge of this business, it would be good to proceed in a way of discovering demonstratively those particular Accidents that do attend these effects, and,

PROBL. I.

To finde the proportion Figures ought to have to the waters Gravity, that by help of the contiguous Air, they may swim.

To finde what proportion severall Figures of different Matters ought to have, unto the Gravity of the Water, that so they may be able by vertue of the Contiguous Air to stay afloat.

Let, therefore, for better illustration, D F N E be a Vessell, wherein the water is contained, and suppose a Plate or Board, whose thickness is comprehended between the Lines I C and O S, and let it be of Matter exceeding the water in Gravity, so that being put upon the water, it dimergeth and abaseth below the Levell of the said water, leaving the little Banks A I and B C, which are at the greatest height they can be, so that if the Plate I S should but descend any little space farther, the little Banks or Ramparts would no longer consist, but expulsing the Air A I C B, they would diffuse themselves over the Superficies I C, and would submerge the Plate. The height AIBC is therefore the greatest profundity that the

little Banks of water admit of. Now I say, that from this, and from the proportion in Gravity, that the Matter of the Plate hath to the water, we may easily finde of what thickness, at most, we may make the said Plates, to the end, they may be able to bear up above water: for if the Matter of the Plate or Board I S were, for Example, as heavy again as the water, a Board of that Matter shall be, at the most of a thickness equall to the greatest height of the Banks, that is, as thick as A I is high: which we will thus demonstrate. Let the Solid I S be double in Gravity to the water, and let it be a regular

Prisme