360 PATHS OF COMETS. SECT. XXXV. 



very short time within the planetary orbits. And, as all the 

 conic sections of the same focal distance sensibly coincide, through 

 a small arc, on each side of the extremity of their axis, it is diffi- 

 cult to ascertain in which of these curves the comets move, from 

 observations made, as they necessarily must be, near their peri- 

 helia (N. 227). Probably they all move in extremely excentric 

 ellipses ; although, in most cases, the parabolic curve coincides 

 most nearly with their observed motions. Some few seem to 

 describe hyperbolas ; such, being once visible to us, would vanish 

 for ever, to wander through boundless space, to the remote 

 systems of the universe. If a planet be supposed to revolve in a 

 circular orbit, whose radius is equal to the perihelion distance of 

 a comet moving in a parabola, the areas described by these two 

 bodies in the same time will be as unity to the square root of 

 two, which forms such a connexion between the motion of comets 

 and planets, that, by Kepler's law, the ratio of the areas described 

 during the same time by the comet and the earth may be found ; 

 so that the place of a comet may be computed at any time in its 

 parabolic orbit, estimated from the instant of its passage at the 

 perihelion. It is a problem of very great difficulty to determine 

 all the other elements of parabolic motion namely, the comet's 

 perihelion distance, or shortest distance from the sun, estimated 

 in parts of the mean distance of the earth from the sun ; the 

 longitude of the perihelion ; the inclination of the orbit on the 

 plane of the ecliptic ; and the longitude of the ascending node. 

 Three observed longitudes and latitudes of a comet are sufficient 

 for computing the approximate values of these quantities ; but 

 an accurate estimation of them can only be obtained by successive 

 corrections, from a number of observations, distant from one 

 another. When the motion of a comet is retrograde, the place of 

 the ascending node is exactly opposite to what it is when the 

 motion is direct. Hence the place of the ascending node, together 

 with the direction of the comet's motion, show whether the 

 inclination of the orbit is on the north or south side of the plane 

 of the ecliptic. If the motion be direct, the inclination is on the 

 north side ; if retrograde, it is on the south side. 



The identity of the elements is the only proof of the return of 

 a comet to our system. Should the elements of a new comet be 

 the same, or nearly the same, with those of any one previously 

 known, the probability of the identity of the two bodies is very 



