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II. On Olbers's Method of determining the Orbits of Comets, 

 By Professor Encke.* 



P|R. OLBERS had the kindness to transmit to me last 

 ^r. year the preceding paper, and to permit me to insert it 

 in this volume. It completes his excellent method of deter- 

 mining the orbits of comets in a point in which greater facility 

 and a quicker approximation to the truth by trials more me- 

 thodically conducted had been desired by many of those who 

 employed this method, and it finishes in some measure the 

 structure, the foundation of which Olbers laid in the year 

 1797. 



Dr. Olbers supposes in this addition that his readers are ac- 

 quainted with his former formulae. Although this method was 

 already carried to such a degree of perfection in the first me- 

 moirf, that even the master-hand of the author of the The o- 

 ria motus,Scc, 9 made no essential alterations in it, but only some 

 abbreviations, and although consequently the subject might 

 be considered as exhausted, yet I hope I shall not incur cen- 

 sure if I once more completely explain this method of Dr. 

 Olbers. The development of the necessary formulas will give 

 rise to some remarks, partly regarding the accuracy of the me- 

 thod in general, partly referring to the above important ad- 

 dition lately made to it by Olbers himself. Those remarks 

 are indeed not new, but their being placed together in this 

 publication will, I trust, by no means be deemed improper. 



Lambert's theorem is a main part of Olbers's method. The 

 manner of solving it given by Olbers admitting of some abbre- 

 viations, I shall begin with explaining this little improvement. 



Denoting two radii vectores of a parabola, the minimum focal 

 distance of which is q 9 by r, r, the corresponding true anoma- 

 lies by v, t/, and the interval of time between them by t, the 

 double area described will be by Kepler's laws, 



F = K t */ 2 q, 

 where K is the constant of the Theoria motus : 

 K = 00172021. 

 On the other hand we have 



F SB /r 2 d v 9 from v = v, to v = */. 



Substituting for r, its value, r = — %—% 



° cos \ V 2 



* Encke's Jahrbuch for 1833, page 264. 



t Memoir on the most easy and most convenient Method of Calcu- 

 lating the Orbit of a Comet, by William Olbers. Weimar 1797. 



