Olbers's Exsai/ on Comets. 145 



§ 48. 

 The elements thus found are these : 



Longitude of the g, 5'.25°.18'.7" 

 Indination of the orbit 41°.21'.30" 

 Longitude of the perihelium 4'.25°.ir.H" 

 Distance at the perihelium .11782 

 Time of the perihelium 1769 October 7 10h.22ra. 

 Jf now we compare these elements with those which are 

 already known, they will approach very near to them, and they 

 agree almost exactly with those which Lambert has deduced, 

 from observations, like these, before the perihelium, but coiq- 

 puted with much greater labour and by frequent repetitions. 

 The inclination is somewhat too great in both cases, probably 

 from some irregularity of the observations. Pingre' has com- 

 puted the orbit by Laplace's method from the same observatious 

 which I have employed : but the distance and time of the 

 perihelium, which are the only elements that he has determined, 

 differ much more from the truth than mine : and a very super- 

 ficial comparison is sufficient to shew the superior conciseness 



of this method. 



§49. 



The errors of the method and those of the observations being 

 combined in this example, I shall add a second, from which 

 the latter are excluded. The following longitudes and latitudes 

 of the comet of 1681 are not derived from observation, but 

 computed by Halley, according to his parabolic theory of 

 this comet; so that it will appear from this instance, how 

 accurately we may determine again, by the method h^re ex- 

 plained, the distances from the earth and sun. 



Times <t A Log R 



Jan. 5. 6 1| °8 49 49 §C 15 15 9 26 22 18 9.99282 



9. 7 18 44 36 24 12 54 10 29 2 9.99303 



13. 7 9 26 21 22 17 30 10 4 33 20 9.99325 



Consequently r— 4.0411, f "=4.0055, and T=8.0466. Hence 

 we find Log M=. 137562, and the three quadratic equation^ 

 r'=V(.967 54-. 59292 §' + 1.24328 ?'=) 

 ^'=^(.96941 - .40185 ^' + 2.20087 {') 

 *"=V(.019726-, 122756 e'H. 265982 y»; 

 Vol. Xn. ' L 



