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dirf(5lion. But by Cor 2 Prop 30. lib. 3, Prlncipla, in any 

 given portion of the nodes, the mean horary motion of the 

 nodes of a folitary rev Iving moon, is juft half the horary 

 motion of the nodes of a moon continually in fyzige. And 

 Mr. Landen, in his memoir , has (hewn, that when a rigid 

 annulus revolves with two motions, one in its own plane, and 

 the other about one of its diameters, half the whole motive 

 force adting upon the ring is confumcd in counterading the 

 centrifugal force of the ring, by whii h it endeavours to revolve 

 round a momentary axis, in confequence of its two motions ; 

 and the other half only is cffi acious in producing the angular 

 motion of the ling about its diameter; fo that the motion of 

 the nodes of a detached ri , id anntdus, being produced by half 

 the mean folar force, is exacflly equal to that of the orbit of 

 a folitary moon. For in the cafe of a folitary moon no cen- 

 trifu^ial force to produce a revolution round a momentary axis 

 can take place, there being nothing for the body to aift upon ; 

 but in a rigid ring, its two motions compounded will give the 

 ring a tendency to revolve about an axis neither perpendicular 

 to nor in the plane of the ring, and therefore this axis cannot 

 be permanent ; fince each particle of the ring will adl by its 

 centrifugal force to imprefs on it a new motion about an axis 

 perpendicular to the former. But if the rigid annulus, fo 

 revolving, be attached to the equator of a fphcre, the ca'e will 

 be widely difftrent; for the whole motive force is here em- 

 ployed in giving motion to the annulus and fphere together 



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