24)4: Mr. Ivory on the Theory of the Figure of the Earth. 



spective bodies, the attractive forces will be simply propor- 

 tional to any two such lines. The lines y and f, in the di- 

 rections of which the forces act, are likewise similarly situated 

 within the two bodies. And as what has just been })roved is 

 true of the attractions of any two molecules similarly situated 

 in the two bodies, it follows that the resultants of all the at- 

 tractive forces acting upon the two points will be to one an- 

 other in the proportion of any homologous lines of the re- 

 spective bodies, and that they will act in similar directions. 

 Again : since the velocity of rotation is the same in both bodies, 

 the centrifugal forces urging the particles placed in the two 

 assumed points, will be proportional to the respective distances 

 from the axes of revolution ; that is, to r and /, or to any ho- 

 mologous lines of the respective bodies ; and, as the same 

 forces act in the prolongations of r and ;', they will have si- 

 milar directions. Wherefore, since any two particles similarly 

 placed on the surfaces, or within the respective bodies, are 

 urged in like directions and with proportional intensities by 

 the attractive and centrifugal forces that act upon them, it is 

 easy to prove that the pressures propagated by these forces in 

 the two bodies will be entirely similar, and will always have the 

 same proportion to one another. Wherefore the equilibrium 

 of one body is a necessary consequence of the equilibrium of 

 the other body. 



Prop. II. — If a homogeneous mass of fluid revolve about its 

 axis, and be in equilibrio by the attraction of its particles in 

 the inverse proportion of the square of the distance, all the level 

 surfaces will be similar to the outer one ; and any stratum of 

 the 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 S T, revolv- 

 ing about the axis A B, is 

 /;/. equilibrio by the cen- 

 trifugal force and the at- 

 traction of its particles in 

 the inveise proportion of 

 the square of the distance: 

 — the axis of rotation A B 

 will pass through G, the 

 centre of gravity of the fluid 

 mass. In the interior of the 

 revolving body, trace round 

 the point G the surfaces 

 QOP, NLM, KHI, 

 similar and similarly si- 

 tuated to the outer surface, indefinitely near one another, and 



intercepting 



