[ " ] 



of its diameters was lefs than when ic revolved round its centre, 

 though he has differed from Simpfon in the ratio which he has af- 

 figned of their motions in thefe two cafes ; and when the ratio of 

 their motions is admitted to be as one to two, and the other cor- 

 redions propofed by Simpfon are alfo made, the total error on 

 thefe accounts is found to be but 1,5', as has been already • 

 fhewn. 



Mr.Milnsr, in his paper on this fubjcifl in the 69th vol. of 

 the Philofophical Tranfadions, agrees with Frifi in thinking, 

 that the error lies in Newton's afliimption, that the receffion of 

 the nodes of a rigid annulus and a folltary moon, revolving in 

 the perimeter of the annulus, are equal ; whereas in truth, as 

 they affert, (though erroneoufly, as we fliall prefently iliew), tlie 

 receffion of the latter is but one half of that of the former. 



Let us therefore examine particularly whether the receffion 

 of the nodes of a rigid annulus be indeed double the receffion of 

 the nodes of a folitary moon, as has been aflerted. 



Let AE (Fig. i.) reprefent the rigid annulus, indefinitely 



{lender, proje(5led into its own diameter, V p its axis ; let the line of 



the nodes be at right angles to S C, the line joining the centres 



of the fun and earth. From C take the arch C L, and draw 



L M parallel to D B ; let ^ = the gravity of any given quantity 



of matter, as a cubic inch: h = the fpace defcribed in i" by a 



■ it* 



B 2 ■ body 



