the Comet of 1811, 345 



found to agree ; no other correction of the elements 

 would have been requilite, to adapt them to the three 

 obfervations. But this was not to be expefted, on the 

 firft trial. There was a difference of feveral degrees. It 

 was neceffary therefore to make a fecond, and a third 

 hypothefis, in one of which, the perihelion dijiance 

 was changed, and, in the other, the time of perihelion. 

 From the errours of the three, the equations were form- 

 ed, for determining the corrections to be applied to the 

 affumed elements. After two fets of hypothefes, a 

 perihelion diftance, and time of perihelion were obtain- 

 ed, which gave the arc defcribed by the comet, be- 

 tweed the 1 7th of September and the 1 4th of Novem- 

 ber, and meafured by an angle at the fun, within lefs 

 than half a minute of that deduced from the obferv- 

 ed longitudes and latitudes : 



The one being 58<^ 26' 14'' 



The other 58 25 52 



Difference 0^ O 22" 



As this difference is within the limits of the unavoid- 

 able errours of obfervation, I did not attempt to carry 

 the approximation any farther. Some flight variations 

 would probably have been made, by procefTes depend- 

 ing on a comparifon of all the obfervations. But as 

 they would be of little amount ; and 7i^ perfed accura- 

 cy would not be attainable after ail ; I proceeded to cal- 

 culate the remaining elements, from the two already 

 found. The whole together were as follow : 



Perihelion diftance 1 .0329 ; the mean diftance of the 

 fun from the earth being 1 . 



Time of perihelion "Sept. 12th, 1 o'clock, P. M. 

 mean time at Greenwich. s. 



Longitude of the afcending node, 4 20° 22' 



Inclination of the orbit to the ecliptic, 73° 4' 



Longitude of the perihelionf counted 7 ^ .-o |^, 



on the orbit, 3 



Diftance of the perihelion from the node, 2 5° 8' 

 Motion retrograde. 



