Observations on the Comet of Halley. 213 



gitude of the perihelion about two degrees too great ; the perihelion 

 distance about one hundredth part too great ; and the time of pass- 

 ing" the perihelion almost a day too early. This was obviously the 

 result of the parabolic hypothesis. If I had employed observations 

 made after the perihelion passage, the effect on the time of perihe- 

 lion, and the longitude of the perihelion, would have been reversed. 

 Rejecting, therefore, the parabolic hypothesis, I resorted to the el- 

 liptic, adopting the method which is particularly explained by Dr. 

 Bowditch, in the first volume of his translation of the Mecanique Ce- 

 leste, pages 470-3. It so happened, that I had three observations 

 on the comet, in which I had more confidence than in the others, 

 viz. those of Sept. 24th, Oct. 10th and 19th. They were made 

 under favorable circumstances, and I was sure they could not be 

 liable to any great error. I decided, therefore, to correct the ele- 

 ments of the orbit, by these three observations. Taking the mean 

 of each element, according to the calculations of Pontecoulant, Da- 

 moiseau and Lubbock, I assumed these as the approximate elements 

 of the orbit, with the exception of the time of perihelion passage, 

 which I had already determined to be very nearly Nov. 16th. 



With these elements I calculated the comet's places for the three 

 times of observation above mentioned ; I repeated the calculation in 

 five successive operations, varying one of the elements at each ope- 

 ration, while the others remained unaltered. 



The eccentricity I assumed to be constant, (.967392,) as I doubt- 

 ed whether my observations were accurate enough to enable me to 

 correct this element. 



Ithus obtained six equations, containing five unknown quantities, 

 from which the corrections of the elements were to be deduced. 



Applying these corrections to the assumed elements, the result 

 was as follows : 



Perihelion distance, .586016 



Perihelion passage, Nov. 15.947622, Greenwich mean time 



from noon. 

 Place of perihelion on the orbit, 304° 26^ 54'' 

 Longitude of the ascending node, 55 13 5 

 Inclination of the orbit, - 162 15 • 53 



With these elements, I computed the comet's places for the times 

 of all my observations, and found the differences to be no greater 



