between Stars forming Binary or Multiple Groups. 417 



argument; since a hypothetical probability or expectation, 

 based on ignorance, and failing the moment that it is con- 

 fronted with a fact, can hardly be seriously claimed as a source 

 of Knowledge. Let us see, then, to what this definition of 

 "scattering by mere chance as it may happen" must neces- 

 sarily lead. 



SO. It appears from the reasoning already cited from Mit- 

 chell's paper, that, however numerous may be the stars in- 

 cluded by the terms of the problem, the approximation of any 

 two of them within a certain distance of one another, affords 

 a presumption which increases in force without limit as the di- 

 stance diminishes*, that such an approximation has been the 

 result of a specific cause, and is not casual, a result surely inad- 

 missible. The argument therefore for the physical duplicity of 

 two stars, because their apparent distance is less than a given 

 number of degrees or minutes, shows that there must be a limit 

 to the argument, or a certain distance at which no such conclu- 

 sion would be deducible. If no one star deviated from the ave- 

 rage distance which each star in the heavens may have from its 

 neighbours, no argument could be drawn one way or other for 

 the physical connexion of two stars, since there is nothing in re- 

 spect of juxtaposition to distinguish these two stars from the en- 

 tire mass of stars which we suppose to be spaced in a perfectly 

 uniform manner. Let us conceive the stars to be in tact quite 

 symmetrically distributed over the sky. Mitchell's argument 

 for duplicity is derived from comparative smallness of angular 

 distance; but if the angular distance of each star from its 

 neighbours be throughout the same, no argument can be 

 applied to one star which will not be equally applicable to 

 every other, and consequently the numerical argument for 

 physical connexion or prevailing cause will cease the moment 

 that a distribution perfectly symmetrical is supposed^ a result 

 too absurd to require refutation. 



[31.] It is in reality explicitly assumed as the basis of the 

 argument, that by the law of mere chance, scattering as it 

 might happen, the chance of finding one star in a given space 

 is proportional exactly to the space included in the imaginary 

 limit. When there are many stars in question, the chance of 

 finding each one in a given space is still stated to be as the 

 space considered, and it is stated as an improbability that two 

 stars should be found crowded into one space, or three stars 

 into two spaces, or four stars into three spaces, and so forth. 

 Thus our random law appears to indicate a preference for 



* For, as the area which includes the two stars diminishes, the fraction 

 in § 8, which expresses the improbability of their both beimg contained in 

 it, approaches indefinitely nearer to unity. 



Phil. Mag. S. 3. Vol. 37. No. 252. Dec. 1 850. 2 E 



