Hydrostatics.

2 73

Surface of a Fluid A B, float thereon 'withoutany Part immersed ; for being devoid of

Gra-

to which let A and B be two Bodies of equal Bulk, butdifferent Quantities of Matter ; and let B and C be twoother Bodies with equal Quantities of Matter, but ofdifferent Bulks.

f D rcDensity 1

And let j B —Bulk ? in the Body A.

l M—Quantity of Matter )f D — Density 1

Also "j B —Bulk J- in the Body B.

(- M— M ! .ter JC d —Denhty 1

And ‘j b —Bulk in the Body C.t m — Matter J

8. Then, because the Density of any Body is pro-portional to the Quantity of Matter under equal Bulks,we shall have D : D :: M: M : and, because whenthe Quantities of Matter are equal, the Bulks must bereciprocally as the Densities, therefore we have D : d ::

b : B. Whence D _ - —— ; consequently T)MB

— db M. But B — B, and M=m ; therefore DBm

— db M. Whence we have D : d :: b M : m B ; andB : b :: d M : D m ; and M : m :: D B : db.

9. The Specific Gravity of Bodies being as theWeights, that is, as the Quantities of Matter, in equalBulks, will be as the Density : Therefore D : d :: S :s ; and by Substitution of Ratios we have the generalTheorem above become SB ?n~sb M. And since theAbsolute Weights (A, a, ) of any two Bodies are asthe Quantities of Matter, we have S B a — Ash.Wherefore S : /•:: Ab : a B ; that is, the Specific Gra-vities will be as the Absolute Weights directly, andthe Bulks inversely, or as the Absolute Weights dividedby the Bulks.

10. Also A : a :: S B : s b ; that is, the AbsoluteWeights of Bodies are in the compound Ratio of theirSpecific Gravities and Bulks. Or the Absolute Weightof any Body is had by multiplying its Bulk and SpecificGravity together.

Vol. I.

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