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. [156] Herschel, *Outlines of Astronomy*, 1849, p. 565; but Todhunter, in his *History of the Theory of Probability*, p. 335, states that the calculations do not agree with those published by Struve. 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.” [157] *Philosophical Transactions*, 1767, vol. lvii. p. 431. 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. [158] *Philosophical Magazine*, 3rd Series, vol. xxxvii. p. 401, December 1850; also August 1849.