SCT. XXXVI. ORBITS OF COMETS. 339 



have every possible inclination to the plane of the eclip- 

 tic, 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 consequently remain 

 but a very short time within the planetary orbits. And 

 as all the conic sections of the same focal distance sen- 

 sibly 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). Probably they all move in extremely eccen- 

 tric 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 forever, to wander through 

 boundless space, to the remote systems of the universe. 

 If a planet be supposed to revolve in a circular orbit, the 

 radius of which 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 connection be- 

 tween the motion of comets and planets, that by Kep- 

 ler'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 dis- 

 tance, 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 ap- 

 proximate 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, 



