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force, acting on a detached rigid ring, revolving with a two-fold 



motion, one round its centre, the other round a diameter, is 



equal to the efficient force by which the plane of the ring is 



moved round its diameter ; whereas the former is to the latter 



as two to one ; half the whole motive force being counteraded and 



rendered inefficient by the centrifugal force, adly, He fuppofes, 



that the whole efficient motive force, adling on a detached rigid 



annulus, revolving in the fame manner as before, is equal tcJ 



the whole efficient motive force ading on an annulus, attached 



to and conneded with a fphere, which is alfo falfe in the ratio 



of one to two ; the centrifugal force in the cafe of an attached 



annulus vanifhing; and therefore no part of the whole force is 



rendered ineffedual ; and confequently half the motive force in 



the latter cafe will produce an equal effed as the whole in 



the former, half of the force in the former cafe not contributing 



in any degree to the motion of the annulus round its diameter, 



but being totally employed in counterading the tendency of the . 



ring to revolve round a momentary axis. 



Mr. Milner's and Frifi's calculations become likewife corred 

 in the refult, in the fame manner as Simpfon's, by the mutual 

 counteradion of equal and contrary errors. Thus they both 

 hold, that the preceffion of a rigid annulus is double that of a 

 folitary moon, whereas they are equal, as we have already de- 

 monftrated, by which the preceffion- would come out twice greater 

 than the truth ; but they likewife are of opinion, that the pre- • 



ceffion 



