424 Prof. Forbes on the evidence for a Physical Connexion 



sanctioned and adopted by all succeeding writers on this par- 

 ticular application of the doctrine of chances*. I have pur- 

 posely avoided citing the names of many of these writers, and 

 the passages in their works where Mitchell's results are incor- 

 porated, and his method of research applauded, although I 

 could have made a list both numerous and distinguished. It 

 was necessary for me however to show how far that principle 

 was pushed by living writers of eminence, fhus becoming more 

 widely spread and perpetuated. The necessity of such a de- 

 finite citation has become evident from the misapprehensions 

 to which I have been exposed. If Mitchell's deductions had 

 remained buried in the heavy quartos of the Philosophical 

 Transactions, I should not have thought that the refutation of 

 them was so important. 



Phesdo, Kincardineshire, 

 September 19, 1850. 



Note A. 

 Admitting for the moment that Mitchell is correct in as- 



(13130\ re 

 — — — j for not finding one out of n 



stars within a distance of 1° of a given star, I conceive that he 

 is wrong in raising that quantity again to the ?zth power in order 

 to include all the equal chances which exist in favour of B, 

 C, D being duplicated equally with the given star A. For 

 though the probability of a compound event is measured by the 

 product of the several probabilities of the independent events 

 which must concur to produce it, the several probabilities with 

 reference to the different stars cannot be considered as alto- 

 gether independent. The duplication of A by B, and of B 

 by A, which constitute one event, are counted separately ; 

 and again, the probability of the duplication of the star A by 

 the star B, and that of the star C by the star B (which are 

 two independent events), are not independent of the duplica- 

 tion of C by A. 



* The Edinburgh Reviewer thus explicitly adopts Mitchell's principle of 

 reasoning refuted by our "First Objection." " As probability is the nu- 

 merical measure of our expectation that an event will happen, so it is also 

 that of our belief that it has happened, or that any proposed proposition zstrue. 

 Expectation is merely a belief in the future, and differs in no way so far as 

 the measure ojfits degree is concerned from that in the past.'' — Ed. Rev. 

 July 1850, p. 7- I do not of course mean to say that all writers on Pro- 

 bability have adopted Mitchell's argument, although none that I know of 

 condemn it. I must however cite Mr. Leslie Ellis's paper in the Cambridge 

 Transactions (vol. viii. part 1), as containing a bold and clear exposure of 

 the errors sanctioned by many eminent philosophers on questions of chance, 

 — errors a good deal allied to that which we have here discussed. 



