The cosmical masses from which comets are derived seem to traverse in great numbers the interstellar spaces. In consequence of the sun's progressive motion, these nebulous bodies are sometimes drawn toward the centre of our system. If, in this approach, they are not disturbed by any of the large planets, they again recede in parabolas or hyperbolas. When, however, as must sometimes be the case, they pass near Jupiter, Saturn, Uranus, or Neptune, their orbits may be transformed into elongated ellipses. The periodicity of many comets may thus be accounted for.

In the present chapter it is proposed to consider the probable consequences of the sun's motion through regions of space in which cometary matter is widely diffused; to compare our theoretical deductions with observed phenomena; and thus refer to their physical cause a variety of facts which have hitherto received no satisfactory explanation.[9]

1. As comets, at least in many instances, owe their periodicity to the disturbing action of the major planets, and as this planetary influence is sometimes sufficient, especially in the case of Jupiter and Saturn, to change the direction of cometary motion, the great majority of periodic comets should move in the same direction with the planets. Now, of the comets known to be elliptical, 70 per cent. have direct motion. In this respect, therefore, theory and observation are in striking harmony.

2. When the relative positions of a comet and the disturbing planet are such as to give the transformed orbit of the former a small perihelion distance, the comet must return to the point at which it received its greatest perturbation; in other words, to the orbit of the planet. The aphelia of the comets of short period ought therefore to be found, for the most part, in the vicinity of the orbits of the major planets. This, as already shown in Chapters II. and III., is strikingly the case. The actual distances of these aphelia, however, as compared with the respective distances of Jupiter, Saturn, Uranus and Neptune, are presented at one view in the following tables:

I. Comets whose Aphelion Distances are nearly Equal to 5.20,
the Radius of Jupiter's Orbit.

Comets.Aph. Dist.
1. Encke's4.09
2. 1819 IV4.81
3. De Vico's5.02
4. Pigott's (1783) 5.28
5. 1867 II5.29
6. 1743 I5.32
7. 1766 II5.47
8. 1819 III5.55
9. Brorsen's5.64
10. D'Arrest's5.75
11. Faye's5.93
12. Bicla's6.19

II. Comets whose Aphelion Distances are nearly Equal to 9.54,
the Radius of Saturn's Orbit.

Comets.Aph. Dist.
1. Peters' (1846 VI.) 9.45
2. Tuttle's (1858 I.)10.42

III. Comets whose Aphelion Distances are nearly Equal to 19.18,
the Radius of Uranus's Orbit.