.Astronomical and Nautical Collections. 385 



observations before the perihelium may have been the more erro- 

 neous, as the comet, though without a tail, had still a very con- 

 siderable apparent diameter, and it is not easy to distinguish the 

 centre of gravity of this mass of vapours as the proper point of 

 observation : and secondly, that the method of Newton or of 

 EuLEK, by which Lexell determined the ellipsis and the period 

 of this comet, was particularly ill adapted to the occasion, as 

 the orbit was so little inclined to the ecliptic. I do not, how- 

 ever, deny that this paradoxical comet described an ellipsis con- 

 siderably different from a parabola, since observations so rough 

 as those of Lambert, {Beytrage III. 318,)are sufficientto show 

 the inadequacy of a parabolic orbit, and even the observations 

 after the perihelium, taken separately, cannot be represented by 

 any one parabola. It is remarkable, that so great a mathema- 

 tician as Duse'jour should have fancied, tha the had discovered 

 more than one parabola which was capable of giving the obi- 

 served places at three different times with perfect accuracy. 

 {Traite 11. xv). 



§. 82. 



For the determination of elliptic elements the greatest care 

 and accuracy is required in the choice and management of the 

 observations : and we must pay proper regard to parallax, aber- 

 ration, and nutation. It might, perhaps, be eligible to compute 

 all the observations with the greatest accuracy for a parabola 

 approaching very near to the orbit : the diflerences of the obser- 

 vations from the computation, so far as they depend on the 

 elliptic form of the orbit, must then exhibit a uniform and regular 

 increase and decrease. Abrupt changes and irregularities 

 imply errors either in the observation or in the computation ; 

 and we must not omit to pay attention to single seconds. With 

 these precautious we may be able to form some estimate of the 

 probable errors of the observations, and to make allowance for 

 them ; we may then proceed to the investigation of an elliptic 

 orbit, especially when the comet has been seen in both branches 

 of the curve, both before and after its passage through the 

 perihelium. 



[T1)C Tiiblc of Coniclb in a future Number.] 



