. The Philosophical magazine; a journal of theoretical, experimental and applied physics. ame proportion to one another. Wherefore the equilibriumof one body is a necessary, consequence of the equilibrium ofthe other body. Prop. II.—If a homogeneous mass of fluid revolve about itsaxis, and be in cquilihrio by the attraction of its particles inthe inverse proportion of the square of the distance, all the levelsurfaces will be similar to the outer one; and any stratum ofthe fluid contained between two level surfaces will attract par-ticles in the inside with equal force in opposite directions. S
. The Philosophical magazine; a journal of theoretical, experimental and applied physics. ame proportion to one another. Wherefore the equilibriumof one body is a necessary, consequence of the equilibrium ofthe other body. Prop. II.—If a homogeneous mass of fluid revolve about itsaxis, and be in cquilihrio by the attraction of its particles inthe inverse proportion of the square of the distance, all the levelsurfaces will be similar to the outer one; and any stratum ofthe fluid contained between two level surfaces will attract par-ticles in the inside with equal force in opposite directions. Suppose that the homogeneous fluid body R JS T, revolv-ing about the axis A B, isin cquilihrio by the cen-trifugal force and the at-traction of its particles inthe inverse proportion ofthe square of the distance:— the axis of rotation A Bwill pass through G, thecentre of gravity of the fluidmass. In the interior of therevolving body, trace roundthe point G the surfacesQOP, NLM, KHI,similar and similarly si-tuated to the outer surface, indefinitely near one another, and intercepting. T iQPflE.! Mr! Ivory on the Theory of the Figure of the Earth. 245 intercepting very thin strata of the fluid between them. Thenthe whole fluid body R S T, and the part of it bounded bythe surface O P Q, are similar to one another in their figure;and they revolve about the common axis A B, which cuts themboth similarly; wheiefore, because the first body is in equili-brio, the latter will also be in equilihrio, supposing that it re-volves by itself, the exterior stratum being taken away or an-nihilated *. And, because the body O P Q is in equilibriawhen it revolves by itself, the gravitation at its surface, orthe resultant of the attraction of its particles and the centrifu-gal force, will at every point be perpendicular to that every particle of the fluid contained in the stratumbetween the Surfaces R S T and O P Q will be urged, by thegravitation at the latter surface, perpendi
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