322 James Elliot on certain 



what we commonly call the centre of gravity is truly the 

 centre of momentum. The same reasoning applies to the 

 earth in reference to the sun's attraction : its centre of mo- 

 mentum — the centre round which it revolves in its diurnal 

 motion — is the centre of the sphere (or spheroid) ; while the 

 varying centre of gravity is always within the hemisphere 

 nearest the sun. Here, then, is the very desideratum sup- 

 plied, to complete our analogy between the earth's motions 

 and those of the top : here are our two centres, — the one 

 the centre of the mass, the centre of momentum, — the other 

 the proper centre of gravity. 



The next difficulty is this. Sir Isaac Newton, as is well 

 known, has demonstrated that the conical revolution of the 

 axis would not belong to the earth were it a perfect sphere, 

 but that it is indebted for it to its spheroidal form ; whereas 

 the same motion in the top is independent of its form. The 

 reply to that is, that there is no tendency to such a motion 

 in the top while in a vertical position, — that is, when its 

 centre of gravity is directly above or directly below its 

 centre of motion, because then there is no tendency either to 

 fall or to rise, and that the same thing precisely would be 

 the case with the earth if it were a perfect sphere : the 

 centre of gravity would then be directly between the sun 

 and the centre of momentum. But, in the case of a spheroid, 

 the centre of gravity will be a little out of that line, pro- 

 ducing a tendency to fall into it, and this tendency is con- 

 verted into the motion in question. 



Thus, let the point be the centre of the spheroid AB, 

 and consequently its cen- 

 tre of momentum : let the 

 line AB be the transverse 



axis, and S the attracting s 



body ; and let the spheroid 



be divided into two half 



spheroids by a plane, CD, 



coincident with the line OS, and perpendicular to the plane 



BOS. Then, since the half spheroid, CBD, is nearer to S 



than the other half, CAD, the centre of gravity, G, will be 



in the former half, and consequently out of the line OS. 



