Comets. 255 



elliptic or parabolic motion, to find the situation and dimen- 

 sions of the ellipse or parabola which shall represent the 

 motion of any given comet. In general, three complete ob- 

 servations of its right ascension and declination, with the 

 times at which they were made, suffice for the solution of this 

 problem, (which is, however, by no means an easy one), and for 

 the determination of the elements of the orbit. These consist, 

 mutatis mutandis, of the same data as are required for the 

 computation of the motion of a planet ; (that is to say, the 

 longitude of the perihelion, that of the ascending node, the 

 inclination to the ecliptic, the semi-axis, excentricity, and 

 time of perihelion passage, as also whether the motion is di- 

 rect or retrograde) ; and, once determined, it becomes very 

 easy to compare them with the whole observed course of the 

 comet, by a process exactly similar to that of Art. 502 of 

 tliis work, and thus at once to ascertain their correctness, 

 and to put to the severest trial the truth of those general 

 laws on which all such calculations are founded. 



For the most part, it is found that the motions of comets 

 maybe sufficiently well represented by parabolic orbits, — that 

 is to say, ellipses whose axes are of infinite length, or, at 

 least, so very long that no appreciable error in the calcula- 

 tion of their motions, during all the time they continue visible, 

 would be incurred by supposing them actually infinite. The 

 parabola is that conic section which is the limit between the 

 ellipse on the one hand, which returns into itself, and the 

 hyperbola on the other, which runs out to infinity. A comet, 

 therefore, which should describe an elliptic path, however 

 long its axis, must have visited the sun before, and must 

 again return (unless distui-bed) in some determinate period, — 

 but should its orbit be of the hyperbolic character, when once 

 it had passed its perihelion, it could never more return within 

 the sphere of our observation, but must run off to visit other 

 systems, or be lost in the immensity of space. A very few 

 comets have been ascertained to move in hyperbolas,* but 



* Fop example, that of 1723, calculated by Burckhardt : that of 1771, by both 

 Burckhardt aud linckc ; and the second comet of 1818, by Roseuberg and 

 Schwabn. 



