SECT, xxxvi.] ORBITS OF COMETS. . 387 



every possible inclination to the plane of the ecliptic, and, 

 unlike the planets, the motion of more than half of those 

 that have appeared has been retrograde, that is, from east to 

 west. They are only visible when near their perihelia ; then 

 their velocity is such, that its square is twice as great as that 

 of a body moving in a circle at the same distance : they con- 

 sequently remain but a very short time within the planetary 

 orbits. And, as all the conic sections of the same focal dis- 

 tance sensibly coincide, through a small arc, on each side of 

 the extremity of their axis, it is difficult to ascertain in which 

 of these curves the comets move, from observations made, as 

 they necessarily must be, at their perihelia (N. 220). Pro- 

 bably 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 hyper- 

 bolas ; 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 cir- 

 cular 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 peri- 

 helion; 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 com- 

 puting the approximate values of these quantities ; but an 

 accurate estimation of them can only be obtained by succes- 



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