96 Prof. Boole on the Theory of Probabilities. 



to uiaxiy classes of salts, to sulphurets and other compounds. 

 Attempts to apply it to the chlorides have hitherto proved un- 

 successful, chiefly owing to the want of a conducting substance 

 perfectly iuditierent to chlorine, which even plumbago can 

 scaixjely be supposed to be. 



The galvanometer may perhaps, by this method, shortly be- 

 come a useful instnmient in qualitative analyses. 



Jl'.MliiU : MjtJ Uiil ' ''(i ■ i 'I! iM' I , ■ .■■i;i j I I :^, I I > i--'ii>.' > I ■ • > -I I .... .. 



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m-3^(II. \iFur titer Observations on the Theory ofProbabiliiies. 



j;T ■> ' >;• By George Boole. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



SOME commimications which 1 have received since the pub- 

 lication of my letter on the Theory of Probabilities in the 

 last Number of your Journal, have led me to think that a little 

 further explanation of certain points involved in it may be desi- 

 rable. This explanation I the more readily offer, because it 

 appears to me that upon one of the points in question, viz. the 

 prevalent doctrine among mathematicians concerning the inves- 

 tigation of the probabilities of causes, I have made a statement 

 which a more careful survey of authorities does not fully warrant. 

 As the question lies at the foundation of some of the most in- 

 teresting applications of the theory of probabilities, I am desirous 

 of stating how it has really been viewed by eminent writers ; and 

 I shall subsequently notice certain other points suggested to me 

 in the correspondence above referred to. .,^1 -a jjwi 



The problem under discussion was the following :— Given the 

 probability p of the truth of the proposition. If the condition 

 A has been satisfied, the event B has not happened. Required 

 the probability P of the truth of the proposition. If the event 

 B has happened, the condition A has not been satisfied. And 

 its correct solution, as given in my letter, is 



c[\'-a)-^a[l-pY • • • • ii-i 



c and a being arbitrary constants whose interpretation is assigned. 

 I have remarked that it has generally been erroneously held, 

 that the solution of the above question is P=jt?. It is to this 

 point that I desire first to refer. 



i^i^The doctrine that P=/? is expressly taught in the Edinburgh 

 Review (Quetelet on Probabilities). Speaking of a certain com- 

 bination of phaenomena observed in rock-crystal, the Reviewer 

 says, " The chances against such a coincidence happening thir- 

 teen times in succession by mere accident are more than 8000 



