55 



The poiut C is the centre of gravity of the Hne M'M 

 when the attraction of the sun is disregarded ; but G is 

 the centre of gravity of the same line M'M when the 

 •attraction of the sun is considered. 



Let the extremity M of the Hne M'M receive an impulse 

 in the direction MN, at right angles to SM. In obedience 

 to this impulse M will begin to move about the centre of 

 gravity G. Let the point M move through an indefinitely 

 small arc Mm. Then Gm is not greater than GM. But 

 SG, Gftn, are together greater than Sm ; therefore SM is 

 greater than Sm; therefore the particle at M has ap- 

 proached S in moving from M to m. 



But if the line M'M move in an orbit about the centre 

 S, the centrifugal force generated by the orbitual motion 

 acting on the particle at M, will tend to make it move in 

 the arc ]\1N, and therefore resist the approach of the par- 

 ticle to S, and therefore resist the motion of the line M'M 

 about the centre of gravity G. The same may be said 

 of every particle between G and M ; but the centre of 

 gravity C of the Avhole line M'M always lies between G 

 and M ; therefore the orbitual motion of the line M'M 

 about the centre S, resists the rotatory motion of the Same 

 line M'M about the centre of gravity G. But the line M'M 

 is made up of the centres of gravity of the laminae which 

 compose the whole sphere ; hence the rotation of the 

 sphere about the centre of gravity G is resisted by the 

 orbitual motion of the sphere about the centre S. 



If it be objected that M'M will not move about the 

 centre G, but about the centre C, then let the circle 

 GKL (Fig. 8), be the locus of the point G ; and because CM 

 is equal to Cm, therefore SM is equal to SC, Cm. But SC, 

 Cm are greater than Sm : the rest of the argument fol- 

 lows as before. 



If a sphere (Fig. 9), having no independent axial rota- 

 tion, moves in an orbit about a centre of attraction S, 



