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342 observed. There were also not a few cases in which not merely two, but three, four, or more stars were found close enough to one another to be reckoned as forming a multiple star.

Herschel had begun with the idea that a double star was due to a merely accidental coincidence in the direction of two stars which had no connection with one another and one of which might be many times as remote as the other. It had, however, been pointed out by Michell (chapter, § 219), as early as 1767, that even the few double stars then known afforded examples of coincidences which were very improbable as the result of mere random distribution of stars. A special case may be taken to make the argument clearer, though Michell's actual reasoning was not put into a numerical form. The bright star Castor (in the Twins) had for some time been known to consist of two stars, α and β, rather less than 5" apart. Altogether there are about 50 stars of the same order of brightness as α, and 400 like β. Neither set of stars shews any particular tendency to be distributed in any special way over the celestial sphere. So that the question of probabilities becomes: if there are 50 stars of one sort and 400 of another distributed at random over the whole celestial sphere, the two distributions having no connection with one another, what is the chance that one of the first set of stars should be within 5" of one of the second set? The chance is about the same as that, if 50 grains of wheat and 400 of barley are scattered at random in a field of 100 acres, one grain of wheat should be found within half an inch of a grain of barley. The odds against such a possibility are clearly very great and can be shewn to be more than 300,000 to one. These are the odds against the existence—without some real connection between the members—of a single double star like Castor; but when Herschel began to discover double stars by the hundred the improbability was enormously increased. In his first paper Herschel gave as his opinion that "it is much too soon to form any theories of small stars revolving round large ones," a remark shewing that the idea had been considered; and in 1784 Michell returned to the subject, and expressed the opinion that the odds in favour of a physical relation between the