88 General Method for determining 



node: by adding afterwards to this distance the longitude 

 of this node, we sliall have for the position of the perihe- 

 lion on the orbit, 376' 3' 7", or more simply still 1 6' 3' 'J". 

 By collecting all these elements, therefore, we shall have 

 for the true elements of the orbit of the second comet of 

 1781, 



Perihelion distance .... 0,9609951. 

 29th Nov. 1781. Mean time at Paris of the "I j2h4o' 46" 

 perihelion j " ; . 



Placeof the perihelion of the orbit . . 16^ s' 7". 



Place of the ascending node 77° 22' 55". 



Inclination of the orbit 27° 12' 4". 



The motion of the comet is retrograde. 



The supposition of the parabolic motion of the comets ifj 

 not rio-orous ; it is even infinitely liltle probable, consider- 

 ina; the infinite number of cases which give an elliptic or 

 hyperbolic motion, relative to those which determine the 

 parabolic motion. A comet moved either in a parabolic or 

 hyperbolic orbit will only b'e visible once ; we may sup- 

 pose, therefore, with probability, that comets which de- 

 scribe these curves, if some of them exist, liave long ago 

 disappeared, so that nowadays we only observe those 

 which, being moved in re-entering orbits, are incessantly 

 brought back to intervals more or less large, in the regions 

 dtljoining the sun. If they have been observed with pre- 

 cision, and the visible arc of their orbits be considerable, 

 we may determine wilh tolerable accuracy, by the following 

 method, the time of their revolution. 



For this purpose let us suppose that we have four excel- 

 lent observations which embrace nearly the whole visible 

 part of the orbit; and that we have already determined by 

 the foregoing article, the parabola which nearly satisfies 

 these observations. Let v, v', v", v'", be the anomalies cor- 

 responding to these observations; r, ?', r", r'", the corre- 

 sponding vector radii ; take also 



V'- v = U, *"- V = U', v"- V = U". 

 This being done, we shall calculate by the foregoing ar- 

 ticle, with the parabola which nearly represents these ob>-er- 

 vations, the values of U, U'y U", and those of V, F , F" -, 

 take therefore 



U- F=zm, V -F' = m-, U" - F'' = ra''. 

 We shall afterwards vary by a very small quantity the 

 perihelion distance in this parabola; take then 



U-F=n,U' - F' = n, U" - F" = ?i". 

 We shall afterwards form a third hypothesis, in which, 

 by preserving the same perihelion distance as in the first, 



we 



