342 A Short History of Astronomy [CH. xn. 



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 x., 

 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 argu- 

 ment 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, a and /?, rather less than 5" apart. Altogether there 

 are about 50 stars of the same order of brightness as a, and 

 400 like /?. 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 anothi r 

 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 i oo 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 opink n 

 that the odds in favour of a physical relation between il.c 



