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[Footnote 15: It is true that since this essay was written reasons have been given for concluding that comets consist of swarms of meteors enveloped in aeriform matter. Very possibly this is the constitution of the periodic comets which, approximating their orbits to the plane of the Solar System, form established parts of the System, and which, as will be hereafter indicated, have probably a quite different origin.]

[Footnote 16: Though this rule fails at the periphery of the Solar System, yet it fails only where the axis of rotation, instead of being almost perpendicular to the orbit-plane, is very little inclined to it; and where, therefore, the forces tending to produce the congruity of motions were but little operative.]

[Footnote 17: It is true that, as expressed by him, these propositions of Laplace are not all beyond dispute. An astronomer of the highest authority, who has favoured me with some criticisms on this essay, alleges that instead of a nebulous ring rupturing at one point, and collapsing into a single mass, “all probability would be in favour of its breaking up into many masses.” This alternative result certainly seems the more likely. But granting that a nebulous ring would break up into many masses, it may still be contended that, since the chances are infinity to one against these being of equal sizes and equidistant, they could not remain evenly distributed round their orbit. This annular chain of gaseous masses would break up into groups of masses; these groups would eventually aggregate into larger groups; and the final result would be the formation of a single mass. I have put the question to an astronomer scarcely second in authority to the one above referred to, and he agrees that this would probably be the process.]

[Footnote 18: The comparative statement here given differs, slightly in most cases and in one case largely, from the statement included in this essay as originally published in 1858. As then given the table ran thus:–

Mercury. 1/362

Venus.  1/282

Earth.  1/289  1 Satellite.

Mars.  1/326

Jupiter. 1/14  4 Satellites.

Saturn. 1/6.2  8 Satellites, and three rings.

Uranus. 1/9   4 (or 6 according to Herschel).
 

The calculations ending with these figures were made while the Sun’s distance was still estimated at 95 millions of miles. Of course the reduction afterwards established in the estimated distance, entailing, as it did, changes in the factors which entered into the calculations, affected the results; and, though it was unlikely that the relations stated would be materially changed, it was needful to have the calculations made afresh. Mr. Lynn has been good enough to undertake this task, and the figures given in the text are his. In the case of Mars a large error in my calculation had arisen from accepting Arago’s statement of his density (0.95), which proves to be something like double what it should be. Here a curious incident may be named. When, in 1877, it was discovered that Mars has two satellites, though, according to my hypothesis, it seemed that he should have none, my faith in it received a shock; and since that time I have occasionally considered whether the fact is in any way reconcilable with the hypothesis. But now the proof afforded by Mr. Lynn that my calculation contained a wrong factor, disposes of the difficulty–nay, changes the objection to a verification. It turns out that, according to the hypothesis, Mars ought to have satellites; and, further, that he ought to have a number intermediate between 1 and 4.]