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aplldes is immediately determined, which is one of the moft inte- 

 refting refnlts of this method. For we have not only all that is 

 determined in the laft propofition of the 9th fedion of the Prin- 

 cipia, but alfo the motion of the apfides for excentric orbits. 

 The method in the 9th fedion gives only the limit of the mo- 

 tion of the apfides. It cannot be applied to find the motion in ex- 

 centric orbits ; which muft in fome meafure be confidered as a 

 defed. The limit of the- motion of the apfid is never required, for 

 then the orbit is a circle; but the motion before it has arrived at 

 its limit. The motion indeed approximates indefinitely to 

 the limit, but this is not fo evident from the method of Newton ; 

 we know from that cnly the limit, and nothing of its antecedent 

 ftate. It muft not be underftood, that it is here intended to ob- 

 jed to the truth of the reafoning in the 9th fedion ; the ingenuity 

 there fhewn by the illuflrious author is truly admirable, and is . 

 perhaps in no part of the Principia more ftriking. His pe- 

 netrating mind, doubtlefs, faw at once the full force of that 

 reafoning. It has, however, been a fubjed of difficulty 

 to fome. Walmfly, a very acute mathematician, found from 

 the fame data as in the 2 Cor. 45 Prop, a double motion of the 

 apfides, and therefore confonant to the motion of the lunar apogee. 

 He even has been followed by the ingenious Frifius, who, cor- 

 reding, as he imagined, fome defeds in Walmfly 's folution, found 

 the fame refuit as Walmfly. From which it would follow, that t'cc 

 mean motion of the lunar apogee could be found from the c nf dc- 



latioa 



