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XXXIV, On Olbers's Method of determining the Orbits of 

 Comets, By Professor Encke. 



[Continued from p. 206, and concluded.] 



THE method of Olbers, both in the original form in which 

 the inventor first published it and with the modifications of 

 the formulae introduced by Gauss, is so generally known and 

 spread in Germany, that at present hardly any other is used. 

 This does not appear to be the case abroad. A proof of this 

 is afforded by the excellent work of M. de Pontecoulant, 

 * Theorie Analytique du Systeme du Monde,' the respectable 

 author of which appears to have been entirely unacquainted 

 with it. This is clearly proved not only by the entire omis- 

 sion of it in the chapter containing a detailed account of the 

 calculation of the orbits of comets, but likewise by his stating 

 "that there are indeed some other methods, founded principally 

 on Lambert's theorem, which, however, want the principal re- 

 quisite in a practical point of view, brevity and convenience of 

 calculation" Nobody that has ever made a trial of Olbers's 

 method, or has even only looked at the formulae, will ever seri- 

 ously utter such a reproach against that method. 



Two or three hours are sufficient, even for unpractised com- 

 puters, to determine by it the elements. In favourable cases 

 the desired end may be obtained in one hour ; and all the cal- 

 culations required, together with all the auxiliary trials, do not 

 fill a quarto page. Instead of this one, M. de Pontecoulant 

 gives two other methods : One, peculiar to him, modified after 

 Lagrange's, of which he says " that it deserves to be received 

 by astronomers, as it were, as a final result, in order to avoid loss 

 of time and length of calculation, which other methods but too 

 often cause*-" and the other by Laplace, which, according to the 

 author, is in its simplest form, without contradiction, the most 

 convenient which can be applied for the determination of the 

 orbits of comets f. Now although these precise and unquali- 

 fied opinions are in contradiction to one another, I hope that 

 I shall be justified by the object of this paper and the well- 

 merited good reception which the work of M. de Pontecoulant 

 has met with in our country, if I succinctly explain the rea- 

 sons for which I must dissent from both of them. 



The method of Laplace was, before Olbers's method ap- 

 peared, most frequently, nay almost exclusively, used for the 



• "Elle merite d'etre adoptee definitivement par les astrotwmes, qui doivent 

 desirer d'eviter les longueurs de calcul et la perte de terns, que les autres me» 

 thodes occasionnent trap souvent" — torn. ii. p. 6. 



+ "La methode {de Laplace) ainsi simpltfiee est sans contredit la plus com- 

 mode que Pon puisse employer" — torn. ii. p. 493. 



