Observations on the Comet of Halley. 213 



i 



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. 



t 



I thus 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 

 w r as 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 



