The science of astronomy, occupied with the simple relations of distance, magnitude, and motion of the heavenly bodies, admits more easily than almost any other science of interesting conclusions founded on the theory of probability. More than a century ago, in 1767, Michell showed the extreme probability of bonds connecting together systems of stars. He was struck by the unexpected number of fixed stars which have companions close to them. Such a conjunction might happen casually by one star, although possibly at a great distance from the other, happening to lie on a straight line passing near the earth. But the probabilities are so greatly against such an optical union happening often in the expanse of the heavens, that Michell asserted the existence of some connection between most of the double stars. It has since been estimated by Struve, that the odds are 9570 to 1 against any two stars of not less than the seventh magnitude falling within the apparent distance of four seconds of each other by chance, and yet ninety-one such cases were known when the estimation was made, and many more cases have since been discovered. There were also four known triple stars, and yet the odds against the appearance of any one such conjunction are 173,524 to 1.[156] The conclusions of Michell have been entirely verified by the discovery that many double stars are connected by gravitation.
Michell also investigated the probability that the six brightest stars in the Pleiades should have come by accidents into such striking proximity. Estimating the number of stars of equal or greater brightness at 1500, be found the odds to be nearly 500,000 to 1 against casual conjunction. Extending the same kind of argument to other clusters, such as that of Præsepe, the nebula in the hilt of Perseus’ sword, he says:[157] “We may with the highest probability conclude, the odds against the contrary opinion being many million millions to one, that the stars are really collected together in clusters in some places, where they form a kind of system, while in others there are either few or none of them, to whatever cause this may be owing, whether to their mutual gravitation, or to some other law or appointment of the Creator.”
The calculations of Michell have been called in question by the late James D. Forbes,[158] and Mr. Todhunter vaguely countenances his objections,[159] otherwise I should not have thought them of much weight. Certainly Laplace accepts Michell’s views,[160] and if Michell be in error it is in the methods of calculation, not in the general validity of his reasoning and conclusions.
Similar calculations might no doubt be applied to the peculiar drifting motions which have been detected by Mr. R A. Proctor in some of the constellations.[161] The odds are very greatly against any numerous group of stars moving together in any one direction by chance. On like grounds, there can be no doubt that the sun has a considerable proper motion because on the average the fixed stars show a tendency to move apparently from one point of the heavens towards that diametrically opposite. The sun’s motion in the contrary direction would explain this tendency, otherwise we must believe that thousands of stars accidentally agree in their direction of motion, or are urged by some common force from which the sun is exempt. It may be said that the rotation of the earth is proved in like manner, because it is immensely more probable that one body would revolve than that the sun, moon, planets, comets, and the whole of the stars of the heavens should be whirled round the earth daily, with a uniform motion superadded to their own peculiar motions. This appears to be mainly the reason which led Gilbert, one of the earliest English Copernicans, and in every way an admirable physicist, to admit the rotation of the earth, while Francis Bacon denied it.
In contemplating the planetary system, we are struck with the similarity in direction of nearly all its movements. Newton remarked upon the regularity and uniformity of these motions, and contrasted them with the eccentricity and irregularity of the cometary orbits.[162] Could we, in fact, look down upon the system from the northern side, we should see all the planets moving round from west to east, the satellites moving round their primaries, and the sun, planets, and satellites rotating in the same direction, with some exceptions on the verge of the system. In the time of Laplace eleven planets were known, and the directions of rotation were known for the sun, six planets, the satellites of Jupiter, Saturn’s ring, and one of his satellites. Thus there were altogether 43 motions all concurring, namely:—
| Orbital motions of eleven planets | 11 |
| Orbital motions of eighteen satellites | 18 |
| Axial rotations | 14 |
| — | |
| 43 |
The probability that 43 motions independent of each other would coincide by chance is the 42nd power of 1/2, so that the odds are about 4,400,000,000,000 to 1 in favour of some common cause for the uniformity of direction. This probability, as Laplace observes,[163] is higher than that of many historical events which we undoubtingly believe. In the present day, the probability is much increased by the discovery of additional planets, and the rotation of other satellites, and it is only slightly weakened by the fact that some of the outlying satellites are exceptional in direction, there being considerable evidence of an accidental disturbance in the more distant parts of the system.
Hardly less remarkable than the uniform direction of motion is the near approximation of the orbits of the planets to a common plane. Daniel Bernoulli roughly estimated the probability of such an agreement arising from accident as 1 ÷ (12)6 the greatest inclination of any orbit to the sun’s equator being 1-12th part of a quadrant. Laplace devoted to this subject some of his most ingenious investigations. He found the probability that the sum of the inclinations of the planetary orbits would not exceed by accident the actual amount (·914187 of a right angle for the ten planets known in 1801) to be 1/10! (·914187)10 or about ·00000011235. This probability may be combined with that derived from the direction of motion, and it then becomes immensely probable that the constitution of the planetary system arose out of uniform conditions, or, as we say, from some common cause.[164]
If the same kind of calculation be applied to the orbits of comets, the result is very different.[165] Of the orbits which have been determined 48·9 per cent. only are direct or in the same direction as the planetary motions.[166] Hence it becomes apparent that comets do not properly belong to the solar system, and it is probable that they are stray portions of nebulous matter which have accidentally become attached to the system by the attractive powers of the sun or Jupiter.