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" mentur, five denique annulus ille rigelcat, & inflexibilis 

 " reddatur, nefcio qui fieri poffit, ut alius fit puncftorum equi- 

 " nodlialium motus a vi folis oriundus, quam calculi Newtoniani 

 " fuadent. Quem tamen longe alium invenere viri permagni 

 " Eulerus & Simpfonus noflras, quos velim leflor confulas. 

 *' Ipfe nil definio." Now from what has been faid it clearly 

 appears, how the motion of the nodes of a folitary moon 

 and rigid annulus may be equal, and yet the quantity of 

 the preceffion afligned by Newton erroneous in the ratio of 

 one to two ; the efficient motive force of an attached annulus 

 being double the efficient motive force of a ring revolving 

 folitarily, with a compound motion round its centre and one 

 of its diameters. • **' 



If then the corredled quantity of lo" 33"', be further cor- 

 redted, by augmenting it in the ratio of two to one, the refult 

 will nearly agree with the quantity invefligated by other emi- 

 nent mathematicians; thus Simpfon makes it 21" 7", Landen 

 27" 7"', D'Alambert 23" nearly; Euler 22"; Frifi 2ii"; Milner 

 21" 6", and Mr. Vince, 21" 6"; fee Phil. Tranf. vol. 77. 



From this review of the folutions of this problem, it appears 

 that Mr. Landen has the honour of having firft detedled the 

 particular fource of Newton's miftake, by difcovering that when 

 a rigid annulus revolves with two motions, one in its own plane 

 and the other round one of its diameters, half the motive force 



G 2 adlmg 



