The observed orbits of these five comets present some slight discordances among themselves, but if we suppose each comet to move in the average of the observed paths it is a simple matter to fix their several positions at the present time. They have all receded from the sun nearly on line toward the bright star Sirius, and were all of them, at the beginning of the year 1900, standing nearly motionless inside of a space not bigger than the sun and distant from the sun about 150 radii of the earth's orbit. The great rapidity with which they swept through that part of their orbit near the sun (see § 162) is being compensated by the present extreme slowness of their motions, so that the comets of 1668 and 1882, whose passages through the solar system were separated by an interval of more than two centuries, now stand together near the aphelion of their orbits, separated by a distance only 50 per cent greater than the diameter of the moon's orbit, and they will continue substantially in this position for some two or three centuries to come. The slowness with which these bodies move when far from the sun is strikingly illustrated by an equation of celestial mechanics which for parabolic orbits takes the place of Kepler's Third Law--viz.: r^3 / T^2 = 178, where _T_ is the time, in years, required for the comet to move from its perihelion to any remote part of the orbit, whose distance from the sun is represented, in radii of the earth's orbit, by _r_. If the comet of 1668 had moved in a parabola instead of the ellipse supposed above, how many years would have been required to reach its present distance from the sun? 178. RELATION OF COMETS TO THE SOLAR SYSTEM.--The orbits of these comets illustrate a tendency which is becoming ever more strongly marked. Because comet orbits are nearly parabolas, it used to be assumed that they were exactly parabolic, and this carried with it the conclusion that comets have their origin outside the solar system. It may be so, and this view is in some degree supported by the fact that these nearly parabolic orbits of both comets and meteors are tipped at all possible angles to the plane of the ecliptic instead of lying near it as do the orbits of the planets; and by the further fact that, unlike the planets, the comets show no marked tendency to move around their orbits in the direction in which the sun rotates upon his axis. There is, in fact, the utmost confusion among them in this respect, some going one way and some another. The law of the solar system (gravitation) is impressed upon their movements, but its order is not.