■^ 



VI. 



Remarks on the fnethods of correcting the elements of the orbit of 

 a comet in JVewton^s " Principiaf^' and in La Placets " Me- 

 . caniqiie CelesteJ^ 



■-., 



BY NATHANIEL BOWDITCH, LL. D. 



H 



AviNG seen in a late edition of La Motte's translation of 

 Newton's Principia, published in London in 1803, with notes, 

 an attempt of the late Mr. Emerson to prove the accuracy of two 

 equations, given in Book III, Prop. 4S, of that work, for correct- 

 iiig the orbit of a comet by distant observations^ 1 Lave been in- 

 duced to draw up the first section of the following paper, contain- 

 ing the investigation of the correct values of those equations ; be- 

 ins: the substance of a communication I made several 



years ago 



to the late Reverend President Willard, in which I showed that 

 Newton's method would always make the corrections double of 

 what they ought to be. This subject is rendered rather more in- 

 teresting, from the circumstances that several of the commentators 

 on the Principia, besides Emerson, as Gregory,* Le Seur and 



+ 



Jacquier,i have endeavoured to prove the correctness of the equa- 



d 



of 



of it that I have seen, not even in the complete edition of Newton's 

 works, published by Bishop Horsley in 1779 with notes, is any 



* Elements cf Astionomj , Vol. 2, Pag. 790. London, 1715. 

 t Tom. 4, Pag. 6,18, Edit. Pduclp. etc. Geuer. 17.9—1742. 



