522 Prof. G. Boole on the Theory of Probabilities, 



fess (by implication) that there is some essential want of har- 

 mony among the intellectual powers. Upon either of these 

 grounds, and more especially vipon the latter, this whole question 

 appears to me to deserve the most careful examination. It would 

 be no rash assertion to say, that it is of far less importance to 

 know whether an a priori argument for the physical connexion 

 of the double stars is valid, than it is to know whether the human 

 mind is so constituted as to become of necessity the sport of its 

 own inconsistencies. 



Let us consider, first, what is the proper statement of the 

 problem considered by Mr. Mitchell; secondly, whether that 

 problem admits of solution on the principles of the theory of 

 probabilities. 



Mr. IVIitchell assumes it as a fit expression of the idea of a 

 distribution of the stars over the sky "by mere chance," that 

 any star is as likely to be found in any one spot of the heavens 

 as in any other. Supposing then that there are 230 stars equal 

 in brightness to /3 Capricorni, he estimates the probability, that 

 upon the above principle of distribution no such double star 

 would appear in the heavens as 13 Capricorni to be about 80 to 1 . 

 From this, and from similar calculations relating to the Pleiades, 

 and from the extension of "the same argument to the smaller 

 stars as well as those which are collected together in clusters, 

 such as the Prjesepe Cancri, the nebula in the hilt of Perseus's 

 Sword,&c.,as to those stars which appear double, treble, &c. when 

 seen through telescopes," he thinks it may be concluded with 

 "the highest probability (the odds against the conti-aiy opinion 

 being many million millions to one) that the stars are really col- 

 lected 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 gra- 

 vitation, or to some other law or appointment of the Creator." 



It is impossible to reason vipon chance. With reference to the 

 phfenomena of material nature, the idea of universal causation 

 seems to be interwoven in the very texture of our minds. Dis- 

 missing the idea of chance, let us then consider the meaning of 

 the assumption that it is as likely that a particular star will be 

 found in one spot of the sky as in another. Such a principle 

 vpould, as implied by Prof. Forbes, be a legitimate expression of 

 the hypothesis, that the distribution of the stars has been effected 

 according to a law or manner, of the consequences of which we 

 should be unable to form any opinion. The proper statement 

 of Mr. Mitchell's problem, as relates to /8 Capricorni, would 

 therefore be the following : — 



1 . Upon the hypothesis that a given number of stars have been 

 distributed over the heavens according to a law or manner whose 

 consequences we should be altogether unable to foretell, what is 



