CHAPTER V.

THE POSITION AND ARRANGEMENT OF COMETARY ORBITS.

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]

[9] This chapter is the substance of a paper read before the American Philosophical Society, November 19, 1869.

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's 4.09 2. 1819 IV 4.81 3. De Vico's 5.02 4. Pigott's (1783) 5.28 5. 1867 II 5.29 6. 1743 I 5.32 7. 1766 II 5.47 8. 1819 III 5.55 9. Brorsen's 5.64 10. D'Arrest's 5.75 11. Faye's 5.93 12. Bicla's 6.19

=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.

Comets. Aph. Dist.

1. 1867 I 19.28 2. November meteors 19.65 3. 1866 I 19.92

=IV.= COMETS WHOSE APHELION DISTANCES ARE NEARLY EQUAL TO 30.04, THE RADIUS OF NEPTUNE'S ORBIT.

Comets. Aph. Dist.

1. Westphal's (1852 IV.) 31.97 2. Pons' (1812) 33.41 3. Olbers' (1815) 34.05 4. De Vico's (1846 IV.) 34.35 5. Brorsen's (1847 V.) 35.07 6. Halley's[10] 35.37

[10] Halley's comet _in aphelio_ is too remote from the plane of the ecliptic to be much disturbed by Neptune. Has the original position of the orbit been changed by Jupiter's influence?

The coincidences here pointed out (some of which have been noticed by others) appear, then, to be necessary consequences of the motion of the solar system through spaces occupied by meteoric nebulæ. Hence the observed facts receive an obvious explanation.

In regard to comets of long period we have only to remark that, for anything we know to the contrary, there may be causes of perturbation far exterior to the orbit of Neptune.

3. From what we observe in regard to the _larger_ bodies of the universe--a clustering tendency being everywhere apparent,--it seems highly improbable that cometic matter should be uniformly distributed in the sidereal spaces. We would expect, on the contrary, to find it collected in groups or clusters. This view is also in remarkable harmony with the facts of observation. In 150 years, from 1600 to 1750, 16 comets were visible to the naked eye; of which 8 appeared in the 25 years from 1664 to 1689. Again, during 60 years, from 1750 to 1810, only 5 comets were visible to the naked eye, while in the next 50 years there were double that number. The probable cause of such variations is sufficiently obvious. As the sun in its progressive motion approaches a cometary group, the latter is drawn toward the centre of our system; the nearer members with greater velocity than the more remote. Those of the same cluster would enter the solar domain at periods not very distant from each other; the forms of their orbits depending upon their original relative positions with reference to the sun's course, and also on planetary perturbations. It is evident also that the passage of the solar system through a region of space comparatively destitute of cometic clusters would be indicated by a corresponding paucity of comets.

4. The line of apsides of a large proportion of comets will be approximately coincident with the solar orbit. The point towards which the sun is moving is in longitude about 260°. The quadrants bisected by this point and that directly opposite extend from 215° to 305°, and from 35° to 125°. The number of cometary perihelia found in these quadrants up to July, 1868 (periodic comets being counted but once) was 159, or 62 per cent.; in the other two quadrants, 98, or 38 per cent.

This tendency of the perihelia to crowd together in two opposite regions has been noticed by different writers.

5. Comets whose positions before entering our system were very remote from the solar orbit must have _overtaken_ the sun in its progressive motion; hence their perihelia must fall, for the most part, in the vicinity of the point towards which the sun is moving; and they must in general have very small perihelion distances. Now, what are the observed facts in regard to the longitudes of the perihelia of the comets which have approached within the least distance of the sun's surface? But three have had a perihelion distance less than 0.01. _All_ these, it will be seen by the following table, have their perihelia in close proximity to the point referred to:

=I.= COMETS WHOSE PERIHELION DISTANCES ARE LESS THAN 0.01.

Perihelion Passage. Per. Dist. Long. of Per.

1. 1668, Feb. 28_d._ 13_h._ 0.0047 277° 2´ 2. 1680, Dec. 17 23 0.0062 262 49 3. 1843, Feb. 27 9 0.0055 278 39

In Table II. all but the last have their perihelia in the same quadrant.

=II.= COMETS WHOSE PERIHELION DISTANCES ARE GREATER THAN 0.01 AND LESS THAN 0.05.

Perihelion Passage. Per. Dist. Long. of Per.

1. 1689, Nov 29_d._ 4_h._ 0.0189 269° 41´ 2. 1816, March 1 8 0.0485 267 35 3. 1826, Nov 18 9 0.0268 315 31 4. 1847, March 30 6 0.0425 276 2 5. 1865, Jan 14 7 0.0260. 141 15

The perihelion of the first comet in Table III. is remote from the direction of the sun's motion; that of the second is distant but 14°, and of the third 21°.

=III.= COMETS WHOSE PERIHELION DISTANCES ARE GREATER THAN 0.05 AND LESS THAN 0.1.

Perihelion Passage. Per. Dist. Long. of Per.

1. 1593, July 18_d._ 13_h._ 0.0891 176° 19´ 2. 1780, Sept. 30 22 0.0963 246 35 3. 1821, March 21 12 0.0918 239 29

With greater perihelion distances the tendency of the perihelia to crowd together round the point indicated is less distinctly marked.

6. Few comets of small perihelion distance should have their perihelia in the vicinity of longitude 80°, the point opposite that towards which the sun is moving. Accordingly we find, by examining a table of cometary elements, that with a perihelion distance less than 0.1 there is not a single perihelion between 35° and 125°; between 0.1 and 0.2 but 3; and between 0.2 and 0.3 only 1.