Astronomical and Nautical Collections. 371 



§. 63. 

 It is manifest that this is a very simple method of correcting 

 the first computation of the elements, and of obtaining the true 

 result of the three observations in question, not very remote from 

 each other. But the orbit of a comet can never be correctly 

 determined from observations very near each other; partly 

 because all observations must, for many reasons, be inaccurate, 

 and partly for a reason not hitherto much considered, that we 

 cannot depend on the sun's place to single seconds, and before 

 the last labours of DELAiMBRE and Von Zach, were liable to 

 still greater errors. An uncertainty or an error of iO" in the 

 sun's longitude may, in certain circumstances, lead to greater 

 inaccuracy than an error of a minute, or even several minutes, in 

 the observed longitude and latitude of the comet : and this fact 

 ought to serve as a warning to computers, and induce them to 

 determine the place of the sun at each observation with great 

 care. But all errors in the longitude or distance of the sun, or 

 in the observed longitude or latitude of the comet, must naturally 

 have so much the more influence on the elements, as the obser- 

 vations are nearer to each other, and the portion of the orbit in 

 question shorter. 



§. 64. 



Various methods have been proposed for applying the re- 

 motest observations to the correction of tne approximate ele- 

 ments of a comet's orbit. They may, however, all be reduced 

 to three; those of Lambert, of Laplace, and of the great 

 Newton. We shall examine them all, and compare them with 

 each other. 



§. 65. 



Lambert proposes to take the distances of the comet from 

 the earth from the construction, or from a rough calculation, to 

 consider their differences from the truth as differential magni- 

 tudes, the higher powers of which maybe omitted in the compu- 

 tation ; and to determine the amount of these differences from 

 the intervals of time observed. Supposing the approximate 



