The perihelia of the asteroidal orbits are very unequally distributed; one hundred and thirty-six—a majority of the whole number determined—being within the 120° from longitude 290° 50´ to 59° 50´. The maximum occurs between 30° and 60°, where thirty-five perihelia are found in 30° of longitude.
9. Distribution of the Ascending Nodes.
An inspection of the column containing the longitudes of the ascending nodes, in Table II., indicates two well-marked maxima, each extending about sixty degrees, in opposite parts of the heavens.
| I. | From | 310° to | 10°, | containing | 61 | ascending | nodes. |
| II. | " | 120° to | 180°, | " | 59 | " | " |
| Making in 120° | 120 | " | " | ||||
A uniform distribution would give 89. An arc of 84°—from 46° to 130°—contains the ascending nodes of all the old planets. This arc, it will be noticed, is not coincident with either of the maxima found for the asteroids.
10. The Periods.
Since, according to Kepler's third law, the periods of planets depend upon their mean distances, the clustering tendency found in the latter must obtain also in the former. This marked irregularity in the order of periods is seen below.
| Between | 1100 | and | 1200 | days | 6 | periods. |
| " | 1200 | " | 1300 | " | 7 | " |
| " | 1300 | " | 1400 | " | 43 | " |
| " | 1400 | " | 1500 | " | 13 | " |
| " | 1500 | " | 1600 | " | 46 | " |
| " | 1600 | " | 1700 | " | 54 | " |
| " | 1700 | " | 1800 | " | 20 | " |
| " | 1800 | " | 1900 | " | 13 | " |
| " | 1900 | " | 2000 | " | 19 | " |
| " | 2000 | " | 2100 | " | 33 | " |
| " | 2100 | " | 2200 | " | 2 | " |
| " | 2200 | " | 2300 | " | 2 | " |
| " | 2300 | " | 2400 | " | 8 | " |
| " | 2400 | " | 2800 | " | 0 | " |
| " | 2800 | " | 2900 | " | 2 | " |
The period of Hilda (153) is more than two and a half times that of Medusa (149). This is greater than the ratio of Saturn's period to that of Jupiter. The maximum observed between 2000 and 2100 days corresponds to the space immediately interior to chasm I. on a previous page, that between 1300 and 1400 to the space interior to the second, and that between 1500 and 1700 to the part of the zone within the fourth gap. The table presents quite numerous instances of approximate equality; in forty-three cases the periods differing less than twenty-four hours. It is impossible to say, however, whether any two of these periods are exactly equal. In cases of a very close approach two asteroids, notwithstanding their small mass, may exert upon each other quite sensible perturbations.