374 Astroiiofiiical ami ^iautica/ Collections. 



found, we may obtain by interpolation a hypothesis in which 

 both will be correct ; and this must again be examined by a new 

 calculation.] 



§.68. 



Notwithstanding the convenience and utility of this method 

 am disposed to believe that the same conciseness and facility 

 may be attained by taking, with Newton, for the foundation of 

 the three hypotheses, the longitude of the node, and the inclina- 

 tion of the orbit, instead of the time and distance of the peri- 

 helium, and that this method will then possess essential ad- 

 vantages over that of Laplace. I call this the Newtonian 

 method, since it could only be by want of recollection that the 

 great Euler, who had certainly read Newton's works, and 

 who had no manner of occasion to adorn himself with borrowed 

 plumes, could have mentioned it as his own invention ; " Se- 

 quentem methodum su7n asscciUus." Theor. met. Plan, et Com. 

 p. 140. It was, however, first suggested by Newton, and 

 illustrated in detail by Grfgory, Princip. III. 42; although 

 ascribed by many late writers to Euler, without any mention of 

 Newton's name. 



§. 69. 



It has commonly been supposed that this method was only 

 to be used with advantage, when an attempt was to be made to 

 find the elements of an elliptic orbit; an experiment which sel- 

 dom affords any satifactory result ; although, if any person 

 chooses to undertake so thankless a labour, he cannot employ a 

 more convenient method. But it may be employed in a much 

 shorter form for the correction of the parabolic elements : as in- 

 deed Struyk has already employed it, although with unne- 

 cessary prolixity, and with many superfluous calculations, not 

 being at the time acquainted with the elegant theorem of La.m- 

 bert. Beschr. der Staartst. Amst. 1753. I adopted it in a 

 shorter form 17 years ago, in determining the elements of the 

 comet of 1779, from observations which I had made almost 

 without anv instruments. Astr. Ja/irb. Berl. 1782. 



